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<image>Find the equation of the figure in point-slope form .
|
$y-3=\frac{2}{3}(x-8)$
|
mathverse_vi_3003
|
|
<image>Let $f$ be the function given by the following graph. What is the domain of $f$?
|
$[-5,-3) \cup(-3,5]$
|
mathverse_vi_3008
|
|
<image>The graph shows the progress of two competitors in a cycling race.
Who is traveling faster?
Choices:
A:Justin
B:Oliver
|
B
|
mathverse_vi_3013
|
|
<image>The graph shows the progress of two competitors in a cycling race.
How much faster is Oliver traveling?
|
$10km / h$
|
mathverse_vi_3018
|
|
<image>The side profile of a bridge is overlapped with the coordinate axes such that $(x, y)$ represents a point on the arc that is $x$ meters horizontally from one end of the bridge and $y$ meters vertically above the road.
Pedestrians are able to climb the full arch of the bridge. Find the average steepness of the climb over the interval $[0,20]$.
|
1.6
|
mathverse_vi_3023
|
|
<image>What is the average rate of change in the graph?
|
$\frac{9}{10}$
|
mathverse_vi_3028
|
|
<image>What does the graph tell you?
Choices:
A:The cost of a call increases by $\$ 0.90$ for each additional minute
B:Each additional dollar will buy an additional 0.9 minutes of call time
C:The cost of a call decreases by $\$ 0.90$ for each additional minute
D:Each additional dollar will buy 0.9 minutes less of call time than the previous dollar
|
A
|
mathverse_vi_3033
|
|
<image>What is the average rate of change in the graph?
|
$\frac{1}{2000}$
|
mathverse_vi_3038
|
|
<image>What does the average rate of change in the graph tell you?
Choices:
A:An increase in demand of 500 units will decrease the price of each toy by $\$ 1$
B:An increase in demand of 500 units will increase the price of each toy by $\$ 1$
C:The price of each toy increases by $\$ 0.50$ for each additional 1000 units demanded
D:The price of each toy decreases by $\$ 0.50$ for each additional 1000 units demanded
|
C
|
mathverse_vi_3043
|
|
<image>What is the average rate of change in the graph?
|
0
|
mathverse_vi_3048
|
|
<image>What does the average rate of change in the graph tell you?
Choices:
A:The number of earthquakes per year increased by 6 each year.
B:The number of earthquakes per year did not change.
C:There were a total of 6 earthquakes over the 4 years.
D:The number of earthquakes per year decreased by 6 each year.
|
B
|
mathverse_vi_3053
|
|
<image>Does the graphed function have an even or odd power?
Choices:
A:Odd
B:Even
|
B
|
mathverse_vi_3058
|
|
<image>The graph shows Charlie's speed while he is competing in a bike race. Which situation corresponds to the graph?
Choices:
A:Charlie starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed steadily until the end of the race
B:Charlie starts off at a constant speed and then increases his speed at a steady rate
C:Charlie hits his maximum speed about halfway through the race
D:Charlie increases his speed at a constant rate throughout
|
D
|
mathverse_vi_3063
|
|
<image>The graph shows John's speed while he is competing in a walking race. Which situation corresponds to the graph?
Choices:
A:John increases his speed for the first half of the race and then decreases his speed in the second half
B:John increases his speed at a constant rate throughout the entire race
C:John starts off by increasing his pace gradually and then stops as he trips over a stick, but then recovers and is able to increase his speed steadily until the end of the race
D:John starts off by increasing his pace gradually and then continues to steadily increase his pace at a faster rate
|
D
|
mathverse_vi_3068
|
|
<image>The graph shows Jimmy's speed while he is competing in a bike race. Which situation corresponds to the graph?
Choices:
A:Jimmy starts off by increasing his pace gradually and then stops as he trips over a stick,but then recovers and is able to increase his speed until the end of the race
B:Jimmy starts off at a constant speed and then increases his speed at a steady rate
C:Jimmy starts off by increasing his pace gradually and then maintains a constant speed
D:Jimmy hits his maximum speed about halfway through the race
|
A
|
mathverse_vi_3073
|
|
<image>The graph shows Bart's speed while he is competing in a walking race. Which situation corresponds to the graph?
Choices:
A:Bart increases his speed for the first half of the race and then slows in the second half
B:Bart starts off by increasing his pace gradually and then maintains a constant speed
C:Bart starts off at a constant speed and then increases his speed at a steady rate
D:Bart increases his speed at a constant rate throughout the entire race
|
A
|
mathverse_vi_3078
|
|
<image>The graph shows Frank's speed while he is competing in a walking race. Which situation corresponds to the graph?
Choices:
A:Frank starts off at a constant speed and then increases his speed at a steady rate
B:Frank starts off by increasing his pace gradually and then maintains a constant speed
C:Frank starts off by increasing his pace gradually, then increases his pace at a faster rate as he sees his arch rival beside him and finally increases his pace at a more gradual pace
D:Frank increases his speed at a constant rate throughout the entire race
|
B
|
mathverse_vi_3083
|
|
<image>Consider the graph shown.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of people $(y)$ attending a parent/teacher conference when there are $x$ parents, each bringing 2 children.
B:The number of layers $(y)$ resulting from a rectangular piece of paper being folded in half $x$ times.
C:The number of handshakes $(y)$ made by $x$ people in a room if every person shakes hands with every other person.
|
B
|
mathverse_vi_3088
|
|
<image>State the diameter.
|
8
|
mathverse_vi_3093
|
|
<image>The equation could be described as \frac{240}{\text{Resistance}}=\text{Current}
What happens to the current as the resistance increases?
Choices:
A:The current increases.
B:The current decreases.
|
B
|
mathverse_vi_3098
|
|
<image>Consider the graph shown.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.
B:The number of layers, y, resulting from a rectangular piece of paper being folded in half x times.
C:The number of people, y, attending a parent/teacher conference when there are x parents who each bring 2 children.
|
B
|
mathverse_vi_3103
|
|
<image>A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.
The amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \cdot \ln \left(\frac{1}{x}\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.
Which statements represent the meaning of the intersection point of the graphs?
Choose all answers that apply:
Choices:
A:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \mathrm{mg}$.
B:
C:It gives the solution to the equation $-1.25 \cdot \ln \left(\frac{1}{x}\right)=4$.
D:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.
E:
F:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.
|
C
|
mathverse_vi_3108
|
|
<image>Functions f and g can model the heights (in meters) of two airplanes. Here are the graphs of f and g, where t is the number of minutes that have passed since noon at a local airport.
The airplanes have the same height about 9 minutes after noon.
What is the other time the airplanes have the same height?
Round your answer to the nearest ten minutes.
About _ minutes after noon
|
90
|
mathverse_vi_3113
|
|
<image>For the following exercises, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.
Find the linear function y, where y depends on t, the number of years since 1980.
|
y=-2 t+180
|
mathverse_vi_3118
|
|
<image>A cake maker has rectangular boxes. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.
State the coordinates of the center of the cake in the form $(a, b)$.
|
Center $=(20,10)$
|
mathverse_vi_3123
|
|
<image>Consider the graph of $y=4-x$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
|
$=(4,0)$
|
mathverse_vi_3128
|
|
<image>Consider the graph of $y=x-4$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
|
$(4,0)$
|
mathverse_vi_3133
|
|
<image>Consider the graph of $y=4-x$.
If the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?
State the coordinates in the form $(a, b)$.
|
$(0,14)$
|
mathverse_vi_3138
|
|
<image>Archimedes drained the water in his tub.
The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.
How much water was initially in the tub?
|
Bugs Bunny
|
mathverse_vi_3143
|
|
<image>Consider the graph of y=\sin x.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=5\sin x
|
y=\sin x=\left(90^\circ ,5\right)
|
mathverse_vi_3148
|
|
<image>Consider the graph of y=\sin x.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=-5\sin x
|
\left(x,y\right)=\left(270^\circ ,5\right)
|
mathverse_vi_3153
|
|
<image>By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=\cos \left(x+45^\circ \right)
|
\left(315^\circ ,1\right)
|
mathverse_vi_3158
|
|
<image>By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=5 \sin x$
|
$(x, y)=\left(90^{\circ}, 5\right)$
|
mathverse_vi_3163
|
|
<image>By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=\cos \left(x+45^{\circ}\right)$
|
$(x, y)=\left(315^{\circ}, 1\right)$
|
mathverse_vi_3168
|
|
<image>The perpendicular height of the solid figure is 12m.
Hence, find the length of the diameter of the solid figure's base.
|
diameter $=10 \mathrm{~m}$
|
mathverse_vi_3173
|
|
<image>The diagram shows a solid figure with a slant height of 13 m. The radius of the base of the solid figure is denoted by $r$.
Find the value of $r$.
|
$r=5$
|
mathverse_vi_3178
|
|
<image>A solid figure has a side $GF$ of length 15cm as shown.
Now, we want to find $y$, the length of the diagonal $DF$.
Calculate $y$ to two decimal places.
|
$y=21.61$
|
mathverse_vi_3183
|
|
<image>The length of CD side is 12cm.
Calculate the area of the triangular divider correct to two decimal places.
|
Area $=124.85 \mathrm{~cm}^{2}$
|
mathverse_vi_3188
|
|
<image>Find the volume of a concrete pipe with length 13 metres. Write your answer correct to two decimal places.
|
Volume $=1633.63 \mathrm{~m}^{3}$
|
mathverse_vi_3193
|
|
<image>The length is 13 centimeters.
The pipe is made of a particularly strong metal.
Calculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place.
|
Weight $=63.3 \mathrm{~g}$
|
mathverse_vi_3198
|
|
<image>The figure shows a solid figure with radius of 6 centimeters.
Find the volume of the solid figure, rounding your answer to two decimal places.
|
Volume $=904.78 \mathrm{~cm}^{3}$
|
mathverse_vi_3203
|
|
<image>The radius of solid figure in figure is 5 centimeters. Find the volume of the figure shown, correct to two decimal places.
|
Volume $=883.57 \mathrm{~cm}^{3}$
|
mathverse_vi_3208
|
|
<image>Find the volume of the solid figure shown. The perpendicular height is 6 centimeters.
Round your answer to two decimal places.
|
Volume $=25.13 \mathrm{~cm}^{3}$
|
mathverse_vi_3213
|
|
<image>Find the volume of the solid figure shown. The slant height is 8 centimeters.
Round your answer to two decimal places.
|
Volume $=32.45 \mathrm{~cm}^{3}$
|
mathverse_vi_3218
|
|
<image>The diameter is 3 centimeters.
Find the volume of the solid, correct to two decimal places.
|
Volume $=10.45 \mathrm{~cm}^{3}$
|
mathverse_vi_3223
|
|
<image>Find the volume of the solid figure pictured here. The radius is 4.1 centimeters.
(Give your answer correct to 1 decimal place.)
|
220.0 \mathrm{~cm}^{3}
|
mathverse_vi_3228
|
|
<image>Find the volume of the solid figure pictured. The perpendicular height is 6.
(Give your answer correct to 2 decimal places.)
|
56.55 units $^{3}$
|
mathverse_vi_3233
|
|
<image>Find the volume of the solid figure shown.
Round your answer to two decimal places.
|
Volume $=113.10 \mathrm{~cm}^{3}$
|
mathverse_vi_3238
|
|
<image>Find the volume of the solid figure shown.
Round your answer to two decimal places.
|
Volume $=33.51 \mathrm{~cm}^{3}$
|
mathverse_vi_3243
|
|
<image>The diameter of large solid figure is 12 centimeters. Find the volume of the solid.
Round your answer to two decimal places.
|
Volume $=508.94 \mathrm{~cm}^{3}$
|
mathverse_vi_3248
|
|
<image>Find the volume of the solid shown, giving your answer correct to two decimal places.
|
Volume $=2854.54 \mathrm{~cm}^{3}$
|
mathverse_vi_3253
|
|
<image>Find the volume of the solid shown, giving your answer correct to two decimal places.
|
Volume $=46827.83 \mathrm{~mm}^{3}$
|
mathverse_vi_3258
|
|
<image>Find the volume of the following solid figure.
Round your answer to three decimal places.
|
Volume $=452.389$ cubic units
|
mathverse_vi_3263
|
|
<image>Find the volume of the following solid figure.
Round your answer to three decimal places.
|
Volume $=34159.095 \mathrm{~cm}^{3}$
|
mathverse_vi_3268
|
|
<image>Consider the following solid figure with a height of 35 cm. Find the surface area of the solid figure.
Round your answer to two decimal places.
|
Surface Area $=2827.43 \mathrm{~cm}^{2}$
|
mathverse_vi_3273
|
|
<image>The following solid figure has a base radius of 21 m.
Find the surface area.
Give your answer to the nearest two decimal places.
|
Surface Area $=9236.28 \mathrm{~m}^{2}$
|
mathverse_vi_3278
|
|
<image>Find the surface area of the given solid figure. The radius is 98. All measurements in the diagram are in mm.
Round your answer to two decimal places.
|
Surface Area $=109603.88 \mathrm{~mm}^{2}$
|
mathverse_vi_3283
|
|
<image>The diagram shows a water trough. The height is 2.49 m.
Find the surface area of the outside of this water trough.
Round your answer to two decimal places.
|
Surface Area $=9.86 \mathrm{~m}^{2}$
|
mathverse_vi_3288
|
|
<image>Find the height $h$ mm of this closed solid figure if its surface area (S) is 27288(mm)^2.
Round your answer to the nearest whole number.
|
$h=58$
|
mathverse_vi_3293
|
|
<image>A solid figure has a surface area of 54105(mm)^2.
What must the height $h$ mm of the solid figure be?
Round your answer to the nearest whole number.
|
$h=30$
|
mathverse_vi_3298
|
|
<image>Find the surface area of the solid figure shown. The radius is 6 cm.
Give your answer to the nearest two decimal places.
|
Surface Area $=603.19 \mathrm{~cm}^{2}$
|
mathverse_vi_3303
|
|
<image>Consider the solid pictured and answer the following:
Hence what is the total surface area? The length is 24 cm.
Give your answer to the nearest two decimal places.
|
$\mathrm{SA}=3298.67 \mathrm{~cm}^{2}$
|
mathverse_vi_3308
|
|
<image>Write an equation for the surface area of the above solid figure if the length is $L$. You must factorise this expression fully.
|
Surface area $=2 \pi(R+r)(L+R-r)$ square units
|
mathverse_vi_3313
|
|
<image>Find the surface area of the solid figure shown.
Round your answer to two decimal places.
|
Surface Area $=1520.53 \mathrm{~cm}^{2}$
|
mathverse_vi_3318
|
|
<image>Find the surface area of the solid figure shown.
Round your answer to two decimal places.
|
Surface Area $=254.47 \mathrm{~cm}^{2}$
|
mathverse_vi_3323
|
|
<image>Find the surface area of the following solid figure.
Round your answer to two decimal places.
|
Surface Area $=39647.77 \mathrm{~mm}^{2}$
|
mathverse_vi_3328
|
|
<image>What is the area of the circular base of the solid figure?
Round your answer to three decimal places.
|
Area $=113.097$ units $^{2}$
|
mathverse_vi_3333
|
|
<image>Find the total surface area.
Round your answer to three decimal places.
|
Surface Area $=603.186$ units $^{2}$
|
mathverse_vi_3338
|
|
<image>Find the surface area of the following solid figure.
Round your answer to two decimal places.
|
Surface Area $=52647.45$ units $^{2}$
|
mathverse_vi_3343
|
|
<image>The top one has a radius of 5mm. We wish to find the surface area of the entire solid. Note that an area is called 'exposed' if it is not covered by the other object.
What is the exposed surface area of the bottom solid figure? Give your answer correct to two decimal places.
|
S.A. of rectangular prism $=4371.46 \mathrm{~mm}^{2}$
|
mathverse_vi_3348
|
|
<image>One side of the left solid figure is 33. The height of middle solid figure is 11.
Find the surface area of the solid.
Round your answer to two decimal places.
|
Surface Area $=8128.50$ units $^{2}$
|
mathverse_vi_3353
|
|
<image>Find the surface area of the composite figure shown. The radius is 4 cm.
Round your answer to two decimal places.
|
Surface Area $=235.87 \mathrm{~cm}^{2}$
|
mathverse_vi_3358
|
|
<image>The height of the bottom solid figure is 33.1 mm.
Hence find the total surface area of the shape, correct to two decimal places.
|
Total S.A. $=3222.80 \mathrm{~mm}^{2}$
|
mathverse_vi_3363
|
|
<image>A solid with a radius of 2.5cm and a height of 10cm contains balls. What is the surface area of each ball? Give your answer correct to one decimal place.
|
Surface area $=78.5 \mathrm{~cm}^{2}$
|
mathverse_vi_3368
|
|
<image>The height of solid figure is 22 cm.
Hence, find the total surface area of the shape.
Give our answer to two decimal places.
|
Total surface area $=4194.03 \mathrm{~cm}^{2}$
|
mathverse_vi_3373
|
|
<image>Find the solid surface area if the side length is 14.2 and the radius is half that.
|
S.A. $=1209.84$
|
mathverse_vi_3378
|
|
<image>A solid figure has one side of length 14cm as shown.
If the size of \angle DFH is \theta °, find theta to two decimal places.
|
11.83
|
mathverse_vi_3383
|
|
<image>The following is a solid figure with bottom side length 12cm.
Now, if the size of \angle VAW is \theta °, find \theta to two decimal places.
|
68.34
|
mathverse_vi_3388
|
|
<image>All edges of the following solid are 7 cm long.Find z, the size of \angle AGH, correct to 2 decimal places.
|
54.74
|
mathverse_vi_3393
|
|
<image>A solid figure has CF edge with length of 15. Find z, the size of \angle BXC, correct to 2 decimal places.
|
10.74
|
mathverse_vi_3398
|
|
<image>The length of BC side is 10 cm.
Calculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.
|
75.15 \mathrm{m}^2
|
mathverse_vi_3403
|
|
<image>All the sloping edges of the solid figure are 12 cm long.
Find Y, the size of \angle PNM, correct to two decimal places.
|
69.30
|
mathverse_vi_3408
|
|
<image>Find the length of AF in terms of AB, BD and DF.
|
\sqrt{AB^2+BD^2+DF^2}
|
mathverse_vi_3413
|
|
<image>The length of AB side is 19cm.
Calculate the area of the divider correct to two decimal places, using your rounded answer from the previous part.
|
94.59 \mathrm{m}^2
|
mathverse_vi_3418
|
|
<image>The radius is 3 cm. Find L.
Give your answer rounded down to the nearest cm.
|
14
|
mathverse_vi_3423
|
|
<image>Find the volume of the solid figure shown. The height is 13 cm.
Round your answer to two decimal places.
|
Volume $=367.57 \mathrm{~cm}^{3}$
|
mathverse_vi_3428
|
|
<image>Calculate the volume of the solid. Correct to one decimal place.
|
Volume $=70.7 \mathrm{~cm}^{3}$
|
mathverse_vi_3433
|
|
<image>Calculate the volume of the solid figure. Correct to one decimal place. The height is 9 cm.
|
Volume $=127.2 \mathrm{~cm}^{3}$
|
mathverse_vi_3438
|
|
<image>Calculate the volume of the solid with a diameter of 6 cm. Correct to one decimal place.
|
Volume $=169.6 \mathrm{~cm}^{3}$
|
mathverse_vi_3443
|
|
<image>Find the volume of the solid with a diameter of 8 cm.
Rounding to two decimal places.
|
Volume $=502.65 \mathrm{~cm}^{3}$
|
mathverse_vi_3448
|
|
<image>Calculate the volume of the solid. The height is 15 cm.
Round your answer to one decimal place.
|
Volume $=577.3 \mathrm{~cm}^{3}$
|
mathverse_vi_3453
|
|
<image>The inner radius is 4 cm. Find the volume of concrete required to make the pipe, correct to two decimal places.
|
Volume $=816.81 \mathrm{~cm}^{3}$
|
mathverse_vi_3458
|
|
<image>The weight of an empty glass jar is 250g. The height (h) is 26 cm.
Calculate its total weight when it is filled with water, correct to 2 decimal places.
|
Weight $=18.63 \mathrm{~kg}$
|
mathverse_vi_3463
|
|
<image>The cylindrical glass has radius of 4 cm.
If Xavier drinks 4 glasses for 7 days, , how many litres of water would he drink altogether?
Round your answer to one decimal place.
|
Weekly water intake $=15.5$ Litres
|
mathverse_vi_3468
|
|
<image>The solid is 3 cm thick. Calculate the volume of the solid, correct to one decimal places.
|
Volume $=89.1 \mathrm{~cm}^{3}$
|
mathverse_vi_3473
|
|
<image>Find the volume of the figure shown, correct to two decimal places. The height of both solid figures is 2 cm.
|
Volume $=609.47 \mathrm{~cm}^{3}$
|
mathverse_vi_3478
|
|
<image>Find the volume of the figure shown. The middle solid figure has a diameter of 3 cm and height of 10 cm.
Round your answer to two decimal places.
|
Volume $=874.93 \mathrm{~cm}^{3}$
|
mathverse_vi_3483
|
|
<image>The radius of hole is 2cm. Find the volume of the solid, correct to two decimal places.
|
Volume $=944.07 \mathrm{~cm}^{3}$
|
mathverse_vi_3488
|
|
<image>Find the total surface area of the solid with a side length equal to 6 cm.
|
216.\mathrm{cm}^2
|
mathverse_vi_3493
|
|
<image>Find the surface area of the solid figure with length equal to 12 m.
|
288 \mathrm{m}^2
|
mathverse_vi_3498
|
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