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3,201 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.611 x + 4.829 at x = 3.061 | The linear relation y = m x + b with slope m = 4.611 and intercept b = 4.829 evaluated at x = 3.061 yields y = 18.94. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,202 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.326 x + -17.59 at x = 8.436 | The linear relation y = m x + b with slope m = -3.326 and intercept b = -17.59 evaluated at x = 8.436 yields y = -45.65. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,203 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.267 x + -9.964 at x = 3.6 | The linear relation y = m x + b with slope m = -2.267 and intercept b = -9.964 evaluated at x = 3.6 yields y = -18.13. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,204 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.992 x + 13.7 at x = -5.745 | The linear relation y = m x + b with slope m = 4.992 and intercept b = 13.7 evaluated at x = -5.745 yields y = -14.98. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,205 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.407 x + -8.748 at x = -6.772 | The linear relation y = m x + b with slope m = 3.407 and intercept b = -8.748 evaluated at x = -6.772 yields y = -31.82. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,206 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.3409 x + -17.2 at x = -8.206 | The linear relation y = m x + b with slope m = 0.3409 and intercept b = -17.2 evaluated at x = -8.206 yields y = -20. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,207 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.984 x + 13.22 at x = 4.501 | The linear relation y = m x + b with slope m = 1.984 and intercept b = 13.22 evaluated at x = 4.501 yields y = 22.15. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,208 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.988 x + 15.13 at x = -5.783 | The linear relation y = m x + b with slope m = 4.988 and intercept b = 15.13 evaluated at x = -5.783 yields y = -13.72. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,209 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.0482 x + 12.08 at x = 7.679 | The linear relation y = m x + b with slope m = 0.0482 and intercept b = 12.08 evaluated at x = 7.679 yields y = 12.45. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,210 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.454 x + 5.407 at x = 9.593 | The linear relation y = m x + b with slope m = 4.454 and intercept b = 5.407 evaluated at x = 9.593 yields y = 48.13. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,211 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.078 x + -9.079 at x = 3.246 | The linear relation y = m x + b with slope m = 2.078 and intercept b = -9.079 evaluated at x = 3.246 yields y = -2.337. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,212 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.784 x + -11.58 at x = 9.18 | The linear relation y = m x + b with slope m = -1.784 and intercept b = -11.58 evaluated at x = 9.18 yields y = -27.95. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,213 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.715 x + 16.56 at x = -7.325 | The linear relation y = m x + b with slope m = -1.715 and intercept b = 16.56 evaluated at x = -7.325 yields y = 29.13. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,214 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.223 x + 4.351 at x = -9.914 | The linear relation y = m x + b with slope m = 4.223 and intercept b = 4.351 evaluated at x = -9.914 yields y = -37.51. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,215 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.904 x + -13.06 at x = 1.116 | The linear relation y = m x + b with slope m = -4.904 and intercept b = -13.06 evaluated at x = 1.116 yields y = -18.53. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,216 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.965 x + -0.4409 at x = -2.144 | The linear relation y = m x + b with slope m = 1.965 and intercept b = -0.4409 evaluated at x = -2.144 yields y = -4.654. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,217 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.189 x + 15.07 at x = 3.025 | The linear relation y = m x + b with slope m = -4.189 and intercept b = 15.07 evaluated at x = 3.025 yields y = 2.397. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,218 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.3865 x + 15.7 at x = 6.321 | The linear relation y = m x + b with slope m = 0.3865 and intercept b = 15.7 evaluated at x = 6.321 yields y = 18.15. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,219 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.5482 x + -15.06 at x = 9.441 | The linear relation y = m x + b with slope m = -0.5482 and intercept b = -15.06 evaluated at x = 9.441 yields y = -20.24. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,220 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.236 x + 4.052 at x = -2.265 | The linear relation y = m x + b with slope m = -1.236 and intercept b = 4.052 evaluated at x = -2.265 yields y = 6.852. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,221 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.391 x + 12.47 at x = 9.676 | The linear relation y = m x + b with slope m = 3.391 and intercept b = 12.47 evaluated at x = 9.676 yields y = 45.29. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,222 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.752 x + -5.181 at x = -6.14 | The linear relation y = m x + b with slope m = -3.752 and intercept b = -5.181 evaluated at x = -6.14 yields y = 17.86. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,223 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.906 x + 9.726 at x = 5.168 | The linear relation y = m x + b with slope m = -4.906 and intercept b = 9.726 evaluated at x = 5.168 yields y = -15.63. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,224 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.806 x + 8.368 at x = -6.17 | The linear relation y = m x + b with slope m = 1.806 and intercept b = 8.368 evaluated at x = -6.17 yields y = -2.772. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,225 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.163 x + 5.009 at x = 6.168 | The linear relation y = m x + b with slope m = 3.163 and intercept b = 5.009 evaluated at x = 6.168 yields y = 24.52. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,226 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.789 x + 19.2 at x = 9.346 | The linear relation y = m x + b with slope m = -2.789 and intercept b = 19.2 evaluated at x = 9.346 yields y = -6.857. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,227 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.632 x + -0.2865 at x = 4.081 | The linear relation y = m x + b with slope m = -4.632 and intercept b = -0.2865 evaluated at x = 4.081 yields y = -19.19. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,228 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.06 x + -19.71 at x = 9.685 | The linear relation y = m x + b with slope m = 1.06 and intercept b = -19.71 evaluated at x = 9.685 yields y = -9.446. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,229 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.384 x + -15.56 at x = -4.453 | The linear relation y = m x + b with slope m = 1.384 and intercept b = -15.56 evaluated at x = -4.453 yields y = -21.73. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,230 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.003256 x + -13.18 at x = -6.125 | The linear relation y = m x + b with slope m = 0.003256 and intercept b = -13.18 evaluated at x = -6.125 yields y = -13.2. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,231 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.388 x + 6.887 at x = 2.059 | The linear relation y = m x + b with slope m = 2.388 and intercept b = 6.887 evaluated at x = 2.059 yields y = 11.81. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,232 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.245 x + 3.527 at x = 4.919 | The linear relation y = m x + b with slope m = -3.245 and intercept b = 3.527 evaluated at x = 4.919 yields y = -12.44. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,233 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.726 x + 17.34 at x = 7.11 | The linear relation y = m x + b with slope m = -3.726 and intercept b = 17.34 evaluated at x = 7.11 yields y = -9.146. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,234 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.81 x + 9.156 at x = -4.513 | The linear relation y = m x + b with slope m = 3.81 and intercept b = 9.156 evaluated at x = -4.513 yields y = -8.04. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,235 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.477 x + -19.08 at x = 9.396 | The linear relation y = m x + b with slope m = 3.477 and intercept b = -19.08 evaluated at x = 9.396 yields y = 13.59. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,236 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.777 x + 4.578 at x = 3.614 | The linear relation y = m x + b with slope m = 1.777 and intercept b = 4.578 evaluated at x = 3.614 yields y = 11. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,237 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.831 x + -19.92 at x = -1.458 | The linear relation y = m x + b with slope m = 3.831 and intercept b = -19.92 evaluated at x = -1.458 yields y = -25.51. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,238 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.731 x + 6.001 at x = 7.077 | The linear relation y = m x + b with slope m = 1.731 and intercept b = 6.001 evaluated at x = 7.077 yields y = 18.25. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,239 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.77 x + 13.77 at x = -1.862 | The linear relation y = m x + b with slope m = -1.77 and intercept b = 13.77 evaluated at x = -1.862 yields y = 17.07. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,240 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.783 x + 0.7318 at x = -0.08851 | The linear relation y = m x + b with slope m = -3.783 and intercept b = 0.7318 evaluated at x = -0.08851 yields y = 1.067. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,241 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.1726 x + -18.26 at x = 4.424 | The linear relation y = m x + b with slope m = 0.1726 and intercept b = -18.26 evaluated at x = 4.424 yields y = -17.5. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,242 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.53 x + 16.74 at x = 0.6482 | The linear relation y = m x + b with slope m = -4.53 and intercept b = 16.74 evaluated at x = 0.6482 yields y = 13.8. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,243 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.838 x + -4.326 at x = -3.306 | The linear relation y = m x + b with slope m = -1.838 and intercept b = -4.326 evaluated at x = -3.306 yields y = 1.749. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,244 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.801 x + 12.31 at x = 9.805 | The linear relation y = m x + b with slope m = 3.801 and intercept b = 12.31 evaluated at x = 9.805 yields y = 49.58. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,245 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.744 x + 7.582 at x = 9.156 | The linear relation y = m x + b with slope m = -2.744 and intercept b = 7.582 evaluated at x = 9.156 yields y = -17.54. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,246 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.17 x + -12.12 at x = -3.416 | The linear relation y = m x + b with slope m = 4.17 and intercept b = -12.12 evaluated at x = -3.416 yields y = -26.37. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,247 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.372 x + 5.012 at x = -9.443 | The linear relation y = m x + b with slope m = -4.372 and intercept b = 5.012 evaluated at x = -9.443 yields y = 46.29. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,248 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.6805 x + -19.04 at x = 5.944 | The linear relation y = m x + b with slope m = -0.6805 and intercept b = -19.04 evaluated at x = 5.944 yields y = -23.08. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,249 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.351 x + 13.62 at x = -5.057 | The linear relation y = m x + b with slope m = 4.351 and intercept b = 13.62 evaluated at x = -5.057 yields y = -8.38. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,250 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.2642 x + 18.35 at x = 6.65 | The linear relation y = m x + b with slope m = -0.2642 and intercept b = 18.35 evaluated at x = 6.65 yields y = 16.59. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,251 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.216 x + 0.787 at x = -5.265 | The linear relation y = m x + b with slope m = 3.216 and intercept b = 0.787 evaluated at x = -5.265 yields y = -16.15. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,252 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.271 x + 3.999 at x = -1.229 | The linear relation y = m x + b with slope m = -4.271 and intercept b = 3.999 evaluated at x = -1.229 yields y = 9.249. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,253 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.043 x + -2.142 at x = -7.503 | The linear relation y = m x + b with slope m = -4.043 and intercept b = -2.142 evaluated at x = -7.503 yields y = 28.2. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,254 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.745 x + 16.67 at x = -2.452 | The linear relation y = m x + b with slope m = 4.745 and intercept b = 16.67 evaluated at x = -2.452 yields y = 5.033. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,255 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.901 x + 7.735 at x = 5.653 | The linear relation y = m x + b with slope m = 3.901 and intercept b = 7.735 evaluated at x = 5.653 yields y = 29.79. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,256 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.38 x + 12.1 at x = -8.904 | The linear relation y = m x + b with slope m = -4.38 and intercept b = 12.1 evaluated at x = -8.904 yields y = 51.1. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,257 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.107 x + -2.726 at x = -7.963 | The linear relation y = m x + b with slope m = 1.107 and intercept b = -2.726 evaluated at x = -7.963 yields y = -11.55. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,258 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.442 x + -17.91 at x = 6.999 | The linear relation y = m x + b with slope m = -4.442 and intercept b = -17.91 evaluated at x = 6.999 yields y = -49. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,259 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.9832 x + 4.692 at x = -1.778 | The linear relation y = m x + b with slope m = -0.9832 and intercept b = 4.692 evaluated at x = -1.778 yields y = 6.44. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,260 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.646 x + 11.5 at x = 2.48 | The linear relation y = m x + b with slope m = 3.646 and intercept b = 11.5 evaluated at x = 2.48 yields y = 20.54. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,261 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.4659 x + -1.432 at x = -1.438 | The linear relation y = m x + b with slope m = -0.4659 and intercept b = -1.432 evaluated at x = -1.438 yields y = -0.7617. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,262 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.202 x + -15.95 at x = 3.018 | The linear relation y = m x + b with slope m = 1.202 and intercept b = -15.95 evaluated at x = 3.018 yields y = -12.32. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,263 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.758 x + -18.96 at x = 0.3443 | The linear relation y = m x + b with slope m = 1.758 and intercept b = -18.96 evaluated at x = 0.3443 yields y = -18.36. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,264 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.8781 x + -15.68 at x = -9.754 | The linear relation y = m x + b with slope m = 0.8781 and intercept b = -15.68 evaluated at x = -9.754 yields y = -24.25. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,265 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 2.133 x + 3.715 at x = 6.816 | The linear relation y = m x + b with slope m = 2.133 and intercept b = 3.715 evaluated at x = 6.816 yields y = 18.25. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,266 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.044 x + -14.96 at x = 0.178 | The linear relation y = m x + b with slope m = 4.044 and intercept b = -14.96 evaluated at x = 0.178 yields y = -14.24. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,267 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.446 x + -0.744 at x = 2.417 | The linear relation y = m x + b with slope m = -1.446 and intercept b = -0.744 evaluated at x = 2.417 yields y = -4.239. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,268 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.141 x + -14.49 at x = -9.119 | The linear relation y = m x + b with slope m = -3.141 and intercept b = -14.49 evaluated at x = -9.119 yields y = 14.15. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,269 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.723 x + 3.381 at x = 0.2625 | The linear relation y = m x + b with slope m = -3.723 and intercept b = 3.381 evaluated at x = 0.2625 yields y = 2.403. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,270 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.517 x + -5.69 at x = 1.673 | The linear relation y = m x + b with slope m = 1.517 and intercept b = -5.69 evaluated at x = 1.673 yields y = -3.152. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,271 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.4114 x + -14.18 at x = -0.6095 | The linear relation y = m x + b with slope m = 0.4114 and intercept b = -14.18 evaluated at x = -0.6095 yields y = -14.43. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,272 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.033 x + -8.357 at x = 9.405 | The linear relation y = m x + b with slope m = 1.033 and intercept b = -8.357 evaluated at x = 9.405 yields y = 1.361. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,273 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.1768 x + 6.307 at x = -7.108 | The linear relation y = m x + b with slope m = 0.1768 and intercept b = 6.307 evaluated at x = -7.108 yields y = 5.05. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,274 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.626 x + 12.77 at x = 1.189 | The linear relation y = m x + b with slope m = -2.626 and intercept b = 12.77 evaluated at x = 1.189 yields y = 9.645. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,275 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -4.454 x + -6.247 at x = 9.53 | The linear relation y = m x + b with slope m = -4.454 and intercept b = -6.247 evaluated at x = 9.53 yields y = -48.69. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,276 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.406 x + -11.95 at x = -8.632 | The linear relation y = m x + b with slope m = 1.406 and intercept b = -11.95 evaluated at x = -8.632 yields y = -24.08. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,277 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -3.106 x + -0.971 at x = 3.837 | The linear relation y = m x + b with slope m = -3.106 and intercept b = -0.971 evaluated at x = 3.837 yields y = -12.89. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,278 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -0.326 x + 7.697 at x = 7.04 | The linear relation y = m x + b with slope m = -0.326 and intercept b = 7.697 evaluated at x = 7.04 yields y = 5.402. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,279 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 0.661 x + -6.574 at x = -4.007 | The linear relation y = m x + b with slope m = 0.661 and intercept b = -6.574 evaluated at x = -4.007 yields y = -9.222. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,280 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -1.714 x + -15.81 at x = 7.522 | The linear relation y = m x + b with slope m = -1.714 and intercept b = -15.81 evaluated at x = 7.522 yields y = -28.7. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,281 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 4.105 x + -0.1628 at x = 8.399 | The linear relation y = m x + b with slope m = 4.105 and intercept b = -0.1628 evaluated at x = 8.399 yields y = 34.32. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,282 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 1.388 x + 7.729 at x = -0.6693 | The linear relation y = m x + b with slope m = 1.388 and intercept b = 7.729 evaluated at x = -0.6693 yields y = 6.8. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,283 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = -2.869 x + -0.7702 at x = 5.367 | The linear relation y = m x + b with slope m = -2.869 and intercept b = -0.7702 evaluated at x = 5.367 yields y = -16.17. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,284 | mathematics | algebra | linear_relation | 2 | worked_example | Evaluate linear function y = 3.147 x + 12.29 at x = -2.482 | The linear relation y = m x + b with slope m = 3.147 and intercept b = 12.29 evaluated at x = -2.482 yields y = 4.482. Linear models appear throughout science whenever a rate of change is approximately constant. | y = m x + b | basic arithmetic | Evaluate and interpret a linear function in a scientific context. |
3,285 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.06364 | The common logarithm log₁₀(0.06364) = -1.196. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,286 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 8185 | The common logarithm log₁₀(8185) = 3.913. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,287 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 1.2042e-06 | The common logarithm log₁₀(1.2042e-06) = -5.919. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,288 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 1.3143e-06 | The common logarithm log₁₀(1.3143e-06) = -5.881. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,289 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.01971 | The common logarithm log₁₀(0.01971) = -1.705. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,290 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 4.532 | The common logarithm log₁₀(4.532) = 0.6563. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,291 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 5.1147e-05 | The common logarithm log₁₀(5.1147e-05) = -4.291. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,292 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.1927 | The common logarithm log₁₀(0.1927) = -0.7151. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,293 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 37.67 | The common logarithm log₁₀(37.67) = 1.576. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,294 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 8.9641e+04 | The common logarithm log₁₀(8.9641e+04) = 4.953. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,295 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.02084 | The common logarithm log₁₀(0.02084) = -1.681. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,296 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 5.0549e+05 | The common logarithm log₁₀(5.0549e+05) = 5.704. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,297 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 2.4517e-04 | The common logarithm log₁₀(2.4517e-04) = -3.611. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,298 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.002566 | The common logarithm log₁₀(0.002566) = -2.591. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,299 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 4.2398e-04 | The common logarithm log₁₀(4.2398e-04) = -3.373. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
3,300 | mathematics | logarithms | common_logarithm | 3 | worked_example | Common logarithm of 0.001393 | The common logarithm log₁₀(0.001393) = -2.856. Logarithms convert multiplicative relationships into additive ones and are indispensable for expressing quantities that span many orders of magnitude (pH, sound intensity, stellar magnitudes, earthquake energy). | log10(x) | exponents | Compute and interpret common logarithms of scientific quantities. |
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