Plug in the value of $$x$$ and $$y$$ and use order of operations rule. $$x=2$$ and $$y=-3$$
$$5(4x-3y)-7y^2=5(4(2)-3(-3))-7(-3)^2=5(8+9)-7(9)=5(17)-63=85-63=22$$
For one hour he earns $18, then for t hours he earns$18t. If he wants to earn at least $78, therefore, the number of working hours multiplied by 18 must be equal to 78 or more than 78. $$18t≥78$$ 3- Choice B is correct $$(108-(3×9))÷9=9^3÷81=9$$ 4- Choice B is correct The ratio of boys to girls is $$3∶ 5$$. Therefore, there are 3 boys out of 8 students. To find the answer, first, divide the total number of students by 8, then multiply the result by 3. $$240÷8=30 ⇒ 30×3=90$$ 5- Choice A is correct Probability$$=\frac{number \space of \space desired \space outcomes}{number \space of \space total \space outcomes}=\frac{9}{9+15+14+16}=\frac{9}{54}\frac{1}{6}=0.16$$ 6- Choice D is correct Let’s compare each fraction: $$\frac{2}{3}<\frac{3}{4}<\frac{7}{9}<\frac{4}{5}$$ Only choice D provides the right order. 7- Choice B is correct Let $$y$$ be the width of the rectangle. Then; $$14×y=84→y=\frac{84}{16}=6$$ 8- Choice B is correct $$4×\frac{5}{16}=\frac{20}{16}=1.25$$ A. $$1.25>2$$ B. $$1<1.25<2$$ This is the answer! C. $$\frac{3}{8}=1.25$$ D. $$1.25=2^2$$ 9- Choice B is correct In any rectangle, The measure of the sum of all the angles equals $$180^\circ$$. 10- Choice C is correct $$\frac{824}{17}=48.5$$ ## The Absolute Best Book to Ace the 6th Grade ACT AspireMathTest Original price was:$21.99.Current price is: $14.99. Satisfied 272 Students 11- Choice B is correct The area of the trapezoid is: Area $$=\frac{base \space 1+base \space 2}{2}×height=\frac{12+10}{2}x=A→ 11x=A→x=\frac{A}{11}$$ 12- Choice B is correct $$\frac{72}{8}=9, \frac{648}{72}=9, \frac{5,832}{648}=9$$, Therefore, the factor is 9. 13- Choice C is correct Simplify each option provided. A. $$13-(3×6)+(7×(-6))=13-18+(-42)=-5-42=-47$$ B. $$(\frac{25}{400})+(\frac{7}{50})=\frac{25}{400}+\frac{56}{400}=\frac{81}{400}$$ C. $$((22×\frac{30}{6})-(7×\frac{144}{12}))×\frac{18}{2}=(110-84)×9=26×9=234$$ (this is the answer) D. $$(\frac{6}{24}+\frac{12}{33})-50=(\frac{1}{4}+\frac{1}{3})-50=(\frac{3}{12}+\frac{4}{12})-50=\frac{7}{12}-50=\frac{-593}{15}$$ 14- Choice D is correct To find the discount, multiply the number ($$100\%$$- rate of discount) Therefore; $$450(100\%-16\%)=450(1-0.16)=450-(450×0.16)$$ 15- Choice A is correct 1,400 out of 11,900 equals to $$\frac{1,400}{11,900}=\frac{200}{1,700}=\frac{2}{17}$$ 16- Choice C is correct The opposite of Nicolas’s integer is $$25$$. So, the integer is $$-25$$. The absolute value of $$25$$ is also $$25$$. 17- Choice C is correct 1 yard = 3 feet, Therefore, $$33,759 ft×\frac{1 \space yd}{3 \space ft}=11,253$$ yd 18- Choice B is correct $$16\%$$ of the volume of the solution is alcohol. Let $$x$$ be the volume of the solution. Then: $$16\%$$ of $$x=38$$ ml ⇒ $$0.16x=38 ⇒ x=38÷0.16=237.5$$ 19- Choice C is correct $$(-2)(9x-8)=(-2)(9x)+(-2)(-8)=-18x+16$$ 20- Choice D is correct 1 pt = 16 fluid ounces. $$576÷16=36$$ Then: 576 fluid ounces = 36 pt 21- Choice D is correct 1 kg = 1000 g and 1 g = 1000 mg, 120 kg = 120 × 1000 g = 120 × 1000 × 1000 = 120,000,000 mg 22- Choice C is correct The diameter of a circle is twice the radius. Radius of the circle is $$\frac{14}{2}=7$$. Area of a circle $$= πr^2=π(7)^2=49π=49×3.14=153.86≅153.9$$ 23- Choice B is correct Average (mean) $$=\frac{sum \space of \space terms}{number \space of \space terms}=\frac{15+17+12+16+21+23}{6}=\frac{104}{6}=17.33$$ 24- Choice C is correct Prime factorizing of $$18=2×3×3$$, Prime factorizing of $$24=2×2×2×3$$ LCM $$= 2×2×2×3×3=72$$ 25- Choice B is correct The coordinate plane has two axes. The vertical line is called the $$y$$-axis and the horizontal is called the $$x$$-axis. The points on the coordinate plane are addressed using the form $$(x,y)$$. Point A is one unit on the left side of the $$x$$-axis, therefore its $$x$$ value is 4 and it is two units up, therefore its $$y$$ axis is 2. The coordinate of the point is: (4, 2) ## Best 6th Grade ACT Aspire Math Prep Resource for 2022 Original price was:$18.99.Current price is: $13.99. Satisfied 222 Students 26- Choice B is correct $$α$$ and $$β$$ are supplementary angles. The sum of supplementary angles is 180 degrees. $$α+β=180^\circ→α=180^\circ-β=180^\circ-125^\circ=55^\circ,$$ Then, $$\frac{α}{β}=\frac{55}{125}=\frac{11}{25}$$ 27- Choice C is correct Opposite number of any number $$x$$ is a number that if added to $$x$$, the result is 0. Then: $$7+(-7)=0$$ and $$4+(-4)=0$$ 28- Choice D is correct $$-5<2x+7≤3$$→ (add ($$-7$$)all sides) $$(-7)+(-5)<2x+7+(-7)≤3+(-7)$$ →$$-12<2x≤-4$$→(divide all sides by 2),$$-6<x≤-2$$ In inequality $$-6<x≤-2$$, $$x$$ is fewer or equal to $$-2$$ and more than $$-6$$. Only choice D represents the same inequality on the number line. 29- Choice B is correct A. Number of books sold in April is: $$690$$ Number of books sold in July is: $$1,150→ \frac{690}{1,150}≠2$$ B. Number of books sold in July is: $$1,150$$ Half the number of books sold in May is: $$\frac{1,150}{2}=575→690>575$$ (it’s correct) C. Number of books sold in June is: $$375$$ Half the number of books sold in April is: $$\frac{690}{3}=230→240<375$$ D. $$690+375=1,065>1,150$$ 30- Choice B is correct $$51∶18=17∶6, 17×3=51$$ and $$8×3=18$$ 31- The answer is 175. $$-60=115-x$$; First, subtract 115 from both sides of the equation. Then: $$-60-115=115-115-x→-175=-x$$, Multiply both sides by ($$-1$$): →$$x=175$$ 32- The answer is 340. The ratio of boys to girls is $$4: 5$$. Therefore, there are 4 boys out of 9 students. To find the answer, first, divide the total number of students by 9, then multiply the result by 4. $$765 ÷ 9 = 85 ⇒ 85 × 4 = 340$$ 33- The answer is 43. Plug in the value of $$x$$ and $$y$$ and use order of operations rule. $$x=2$$ and $$y=-1$$ $$6(2x-3y)+(3-2x)^2=6(2(2)-3(-1))+(3-2(2))^2=6(4+3)+(-1)^2 = 42+1=43$$ 34- The answer is 30.7. $$\frac{215}{7}≅30.71≅30.7$$ 35- The answer is 378. Volume of a box $$= ength×width×height=6×7×9=378$$ 36- The answer is 6. Let y be the width of the rectangle. Then; $$15×y=90→y=\frac{90}{15}=6$$ 37- The answer is 7. $$420=2^2×3^1×5^1×7^1$$ 38- The answer is 13. $$\frac{104}{8}=13, \frac{1,352}{104}=13, \frac{17,576}{1,352}=13$$ Therefore, the factor is 13 39- The answer is 1,256. 1 yard = 3 feet Therefore, $$3,768 ft.×\frac{1 \space yd}{3 \space ft}=1,256 \space yd$$ 40- The answer is 60. Prime factorizing of $$20=2×2×5$$ Prime factorizing of $$12=2×2×3$$ LCM $$=2×2×3×5=60$$ 41- The answer is 491. The diameter of a circle is twice the radius. Radius of the circle is $$\frac{25}{2}$$. Area of a circle $$= πr^2=π(\frac{25}{2})^2=156.25π=156.25×3.14=490.625≅491$$ 42- The answer is 13.5. Average (mean) $$= \frac{sum \space of \space terms}{number \space of \space terms}=\frac{10+11+15+14+15+17+12.5}{7}=13.5$$ 43- The answer is 70. Since E is the midpoint of AB, then the area of all triangles DAE, DEF, CFE, and CBE are equal. Let x be the area of one of the triangles, then: $$4x=140→x=35$$ The area of DEC $$=2x=2(35)=70$$ 44- The answer is 8. The perimeter of a rectangle is: $$2×(4+7)=2×11=22$$ The perimeter of circle is: $$2πr=2×3×\frac{10}{2}=30$$ The difference in the perimeter is: $$30-22=8$$ 45- The answer is 30. Find the difference of each pair of numbers: 2, 3, 5, 8, 12, 17, 23, _, 38 The difference of 2 and 3 is 1, 3 and 5 is 2, 5 and 8 is 3, 8 and 12 is 4, 12 and 17 is 5, 17 and 23 is 6, 23 and next number should be 7. The number is 23 + 7 = 30 46- The answer is $$-122$$. Use PEMDAS (order of operation): $$[6 × (–24) + 8] – (–4) + [4 × 5] ÷ 2 = [–144 + 8] – (–4) + [20] ÷ 2 = [–144 + 8] – (–4) + 10 = [–136] – (–4) + 10 = [–136] + 4 + 10 = –122$$ ## The Best Books to Ace the 6th Grade ACT Aspire Math Test Original price was:$15.99.Current price is: $10.99. Satisfied 81 Students Original price was:$18.99.Current price is: $13.99. Satisfied 222 Students Original price was:$16.99.Current price is: $11.99. Satisfied 79 Students Original price was:$17.99.Current price is: $12.99. Satisfied 144 Students ## Related to This Article ### More math articles ### What people say about "Full-Length 6th Grade ACT Aspire Math Practice Test-Answers and Explanations - Effortless Math: We Help Students Learn to LOVE Mathematics"? No one replied yet. X 32% OFF Limited time only! Save Over 32% SAVE$7
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