ACT Form 72F Math Answer Explanation


Choice E

$$\frac{4}{y}=0.4$$ $$\Rightarrow \frac{4}{y}\times y=0.4\times y$$ $$\Rightarrow 4=0.4y$$ $$\Rightarrow y=10$$

2019 June(72F) Math Question 2

Word Problems Practice

- Cost

2. A motel manager's costs are 24% higher this year than they had been when the room rate was s60.00. If the room rate had increased by the same percent as the manager's costs, what would the room rate be this year?

Choice J

$$60\times1.24=74.4$$

Choice C

$$$10\times40+$10\times(1\frac{1}{2})\times7$$ $$=$400+$105$$ $$=$505$$

Choice J

$$3x^{9}\cdot 5x^{9}$$ $$=3\times5\times x^{9+9}$$ $$=15x^{18}$$

Choice B

$$T=\pi r^{2}+\pi rs$$ $$T=\pi 3^{2}+\pi \times3\times5$$ $$=9\pi+15\pi$$ $$=24\pi$$

2019 June(72F) Math Question 6

Angles Practice

- Parallel Lines

6. In the figure below, C lies on both AE and BD, AB and DE are parallel and congruent, and 2 angle measures are given. What is the measure of ∠ACB

Choice K

$$180°-45°-65°=70°$$

Choice B

$$35=5\cdot7$$ $$28=2\cdot2\cdot7$$ $$8=2\cdot2\cdot2$$ $$2\cdot2\cdot2\cdot5\cdot7=280$$

2019 June(72F) Math Question 8

Quadratic Equations Practice

- Factoring

8. Which of the following polynomial equations has solutions -2 and 5

$$x=-2,5$$ $$f(x)=(x-5)(x+2)^{2}$$ $$f(-2)=0$$ $$f(5)=0$$

Choice F

$$60\div(3+5+7)=60\div15=4$$ $$4\times7=28$$

Choice F

$$f(9)=6$$ $$f(12)=8$$ $$F.\ f(x)=\frac{2}{3}n$$ $$f(9)=\frac{2}{3}\times9=6$$ $$f(12)=\frac{2}{3}\times12=8$$

Choice C

$$(\frac{2+8}{2},\frac{5+11}{2})=(5,8)$$

Choice F

$$1\times1\times\frac{1}{9}=\frac{1}{9}$$

Choice C

$$=3x^{2}+x^{2}-4x-6x-5-7$$ $$=4x^{2}-10x-12$$

2019 June(72F) Math Question 14

Logarithms Practice

- Logarithm Expressions

14. For all positive integers a, let E represent the sentence a is even" and let P represent the sentence"a is prime. When a= 22,  which of the following statements is true?

Choice H

22 is even.

22 is not prime.

Choice C

$$=\mid-42+32\mid=\mid-10\mid=10$$

Choice G

$$11x+6y=3$$ $$y=\frac{-11}{6}x+3$$

Choice A

$$g(2,4,3)$$ $$=4\times2\times4-3\times2\times (-3)^{2}$$ $$=32-54=-22$$

2019 June(72F) Math Question 18

Angles Practice

- Circles

Use the following information to answer questions 18-21
A family plans to remodel their kitchen. They have a total budget of $45,000 to cover expenses in 6 categories. Not all the budget has been assigned. the budget amounts that have been assigned are shown in the table below.
Expense category    Budget amount 
Appliances                 $4,000
Cabinets                     $9,000
Flooring                      $5,000
Lighting                      $3,000
Labor                               ?
Other                               ?
Total budget             $45,000
18. In a circle graph illustrating the 6 budget amounts in the table, what should be the measure of the central angle of the Flooring sector?

Choice H

$$x°:360°=5000:45000$$ $$\Rightarrow x=40°$$

2019 June(72F) Math Question 19

Statistics Practice

- Mean, Median

19. The amount budgeted for Appliances is the sum of the prices of 5 appliances -- 1 refrigerator, 1 dishwasher, 1 built-in cooktop, and 2 ovens(1 conventional and 1 microwave). What is the average price per appliance?

Choice A

$$4000\div5=800$$

$$3000:9000=1:3=\frac{1}{3}$$

Choice E

$$4000+9000+5000+3000=21000$$ $$45000-21000=24000$$ $$\frac{24000}{45000}=\frac{8}{15}=0.53333...$$

2019 June(72F) Math Question 22

Angles Practice

- Other Shapes

22. In the figure below. 5 angle measures are given. The angle marked with a measure of y° is an exterior angle What is the value of y?

$$(2x-10)+y=180 \Rightarrow 2x+y=190$$ $$(x+25)+(2x+10)+(3x-25)+(2x-10)=360$$ $$\Rightarrow …

Choice D

$$7-2=5$$ $$9-4=5$$ $$8-0=8$$ $$5\times8=40$$

Choice G

$$\tan C=\frac{8}{15}$$

Choice B

$$3a-5b=22---(1)$$ $$a+3b=-2---(2)$$ $$(2)\times3-(1)$$ $$\Rightarrow (3a+9b)-(3a-5b)=(-2)\times3-22$$ …

Choice F

$$3r+4p+50=545$$ $$\Rightarrow 3r+4p=495$$

Choice C

$$1st\ rectangle:\ 1\times2+4\times2=10$$ $$2nd\ rectangle:\ …

2019 June(72F) Math Question 28

Quadratic Equations Practice

- Factoring

28. Which of the expressions below is a factor of the polynomial 2x+x-6x?
I. x
II. 2x+3
III. x-2

Choice F

$$2x^{3}+x^{2}-6x$$ $$=x(2x^{2}+x-6)$$ $$=x(2x-3)(x+2)$$

2019 June(72F) Math Question 29

Probability Practice

- One Event

29. Shown below. a circular dartboard has 4 sectors(red, white, blue, and green) whose areas are in the ratio of 1:2:3:4. respectively. Brad will throw 1 dart at the dartboard. and it will hit the dartboard at a random point contained in I of the sectors. What is the probability that the sector the dart hits is Not the blue sector?

Choice E

$$P(Not\ blue)$$ $$=1-P(Blue)$$ $$=1-\frac{3}{1+2+3+4}$$ $$=1-\frac{3}{10}$$ …

Choice J

$$3x+1=5x-9$$ $$\Rightarrow 2x=10$$ $$\Rightarrow x=5$$ …

Choice C

72f

$$\cos L=\frac{a}{c}=\frac{7}{16}$$ $$\sin N=\frac{a}{c}=\frac{7}{16}$$

Choice K

$$(3.5+0.25n)(2500-100n)$$

Choice B

$$2\pi r=20$$ $$r=\frac{20}{2\pi}=\frac{10}{\pi}$$

Choice K

$$30°:60°:90°$$ $$\Rightarrow 1:\sqrt{3}:2$$ $$?=500\times\sqrt{3}=500\sqrt{3}$$

Choice C

$$45°:45°:90°$$ $$\Rightarrow 1:1:\sqrt{2}$$ $$\overline{AC}=5\times\sqrt{2}=5\sqrt{2}$$

Choice G

$$1\times4=4$$

Choice D

72f

$$450°=90°\times5$$

Choice J

72f

Choice C

$$\sqrt[3]{3x-9}+10=13$$ $$\Rightarrow \sqrt[3]{3x-9}=3$$ $$\Rightarrow (\sqrt[3]{3x-9})^{3}=3^{3}$$ …

2019 June(72F) Math Question 40

Word Problems Practice

- % Interest

40. Ten years ago, Tara invested $2, 000 at 6% interest compounded monthly. Which of the following expressions represents todays value of the investment?

Choice J

$$=$2000(1+\frac{0.06}{12})^{120}$$

Choice A

$$2\div7$$ $$=0.285714285714...$$ $$=0.\overline{285714}$$

Choice K

$$\frac{60+65+70+75+80\times2+85\times3+90\times2+95\times4+100\times5}{20}$$ $$=\frac{60+65+70+75+160+255+180+380+500}{20}$$ $$=\frac{1475}{20}$$ $$=87.25$$

$$P=\frac{64G}{S}$$ $$\Rightarrow G=\frac{P\times S}{64}$$ $$\Rightarrow …

Choice K

x quarters,

x+5 dimes,

x+1 …

$$(3,9)\rightarrow(1,3)$$ $$(3k,9k)=(1,3)$$ $$k=\frac{1}{3}$$ $$(9,24)\Rightarrow(9\times\frac{1}{3},24\frac{1}{3})=(3,8)$$

Choice F

72f

$$5^{2}+8^{2}=x^{2}=89$$ $$\Rightarrow x=\sqrt{89}\approx 9.43$$ $$9.43\times2=18.86$$

2019 June(72F) Math Question 47

Word Problems Practice

- 1 Variable Equations

47. Robert writes a check for $20. When he records the check in his check register, he accidentally adds $20 to his balance instead of subtracting $20. which causes a discrepancy between what Roberts check register shows and what it should show. Because of his mistake. Roberts check register shows.

Choice E

$$x-20 \Rightarrow x+20$$ $$(x+20)-(x-20)=+40$$ $$$40\ …

2019 June(72F) Math Question 48

Word Problems Practice

- Temperature

48. For a certain location in Grand Canyon National Park the highest temperature on record is 120° F and the lowest temperature on record is -18°F. Which of the statements below is necessarily true about the temperatures on record for this location?
I. The range of temperatures is 138.
II. The range of temperatures is 102F.
III. The median temperature is 69F

Choice F

The range of temperatures is …

Choice A

$$x+3=0$$ $$\Rightarrow x=-3$$

Choice G

$$Circle\ area=\pi r^{2}$$ $$\pi \times …

Choice D

$$\frac{3^{x}3^{4}}{(3^{4})^{5}}=\frac{1}{9}$$ $$\Rightarrow \frac{3^{x+4}}{3^{4\times5}}=\frac{1}{9}$$ $$\Rightarrow \frac{3^{x+4}}{3^{20}}=\frac{1}{9}=3^{-2}$$ …

Choice J

All real numbers except 7.

Choice D

72f

By the Law of Sines, …

Choice G

$$F.\ f(x) > 0 \Rightarrow |f(x)| …

Choice D

To minimize 2/(y-x),

we simply …

Choice F

72f

$$\Rightarrow (-r,s)$$

2019 June(72F) Math Question 57

Matrices Practice

- Multiplication

57. Which of the following matrices is equal to the matrix product

Choice E

$$=\begin{bmatrix}2 & -5 \\-3 & …

Choice G

72f

$$\overline{AE}=\overline{BE}$$ $$\overline{AG}=\overline{GE}$$ $$\Rightarrow \overline{EF'}:\overline{GH'}$$ $$=\overline{BE}:\overline{BG}$$ …

2019 June(72F) Math Question 59

Probability Practice

- More than One Event

59. Suppose that a will be randomly selected from the set
{-3,-2,-1, 0, 1} and that b will be randomly selected from the set {-2,-1, 0, 1} . What is the probability that ab>0?

Choice D

$$ab\gt 0,$$ $$(-)(-)\gt 0,$$ $$(+)(+)\gt …

Choice G

72f

B is between D and …