Practice Test 7 - 8th Grade Math

19 of the 20 questions below are in this test; the other one can't be scored yet. Answer them in any order, then submit to see your score and every explanation.

Classify the system. Does it have one solution, no solution, or infinitely many solutions? $\begin{cases} 2x + y = 5 \\ 2x + y = 8 \end{cases}$
Which statement correctly describes the equation $\frac{2x + 6}{3} = \frac{2x}{3} + 2$ ?
A system of equations has the solution $(2, 5)$ . If both equations are multiplied by 3, what is the solution to the new system?
The formula for the surface area of a cylinder is $SA = 2\pi r^2 + 2\pi rh$ . If a cylindrical tank has a surface area of $198\pi$ square feet and a radius of $\frac{9}{2}$ feet, what is the height of the tank?
In a right triangle, which side must be labeled $c$ when using $a^2+b^2=c^2$ ?
When using elimination to solve $\begin{cases} 3x + 4y = 10 \\ 2x - 4y = 5 \end{cases}$ , what happens when you add the two equations?
A chemistry student needs to prepare a solution that is $\frac{2}{5}$ acid and $\frac{3}{5}$ water. If she has $4\frac{1}{2}$ liters of pure acid available, how many liters of water should she add to create the desired mixture?
The population of the United States is about $3\times10^8$ people, and the world population is about $7\times10^9$ people. About how many times larger is the world population than the U.S. population?
Two horizontal lines are $l_1: y=3$ and $l_2: y=7$ . They are reflected over the $x$ -axis to form $l_1'$ and $l_2'$ . Which statement is true?
Elena simulates drawing colored balls from a bag by using a random number generator. She assigns 1-4 for blue balls, 5-7 for red balls, and 8-10 for green balls. After 60 trials, she records 18 blue outcomes, 25 red outcomes, and 17 green outcomes. What can Elena conclude about her simulation?
Lines $\ell_1: y=-\tfrac{1}{2}x+4$ and $\ell_2: y=-\tfrac{1}{2}x-1$ are parallel. Both lines are rotated $90^\circ$ counterclockwise about the origin. Which statement is true about $\ell_1'$ and $\ell_2'$ ?
A right triangle has a hypotenuse of 17 units and one leg of 8 units. What is the length of the other leg?
Triangle $ABC$ has vertices $A(2,3)$ , $B(6,3)$ , and $C(4,6)$ . Triangle $DEF$ has vertices $D(-2,-3)$ , $E(-6,-3)$ , and $F(-4,-6)$ . Which transformation maps triangle $ABC$ onto triangle $DEF$ ?
The table presents statistical summaries for daily step counts recorded by fitness trackers in two different cities. What comparison of the cities' walking activity is most appropriate?
Two points are $R(6,8)$ and $S(2,3)$ . What is the distance between them? (Round to the nearest tenth.)
A relationship is described by the equation $3y - 9x = 0$ . A student solves for $y$ and gets $y = 3x$ , then concludes it's proportional. Another student rearranges to get $3y = 9x$ and concludes it's non-proportional because "it doesn't look like $y = kx$ ." Who is correct?
Maria knows that $\sqrt{50}$ is between 7 and 8. She wants to find a better approximation by determining which tenth $\sqrt{50}$ is closest to. She calculates that $7.1^2 = 50.41$ and $7.0^2 = 49$ . What should Maria conclude about the location of $\sqrt{50}$ ?
A student solving $5x - 3 = 2x + 9$ writes their final answer as " $x = 4$ ". To demonstrate complete mathematical precision, what should be included?
The cylindrical grain silo depicted below has a diameter of 12 feet. If 432π cubic feet of grain fills the silo to exactly 2/3 of its total height, what is the total height of the silo?
Triangle $RST$ has vertices $R(-2,1)$ , $S(-5,1)$ , and $T(-3,4)$ . Triangle $R'S'T'$ has vertices $R'(2,1)$ , $S'(5,1)$ , and $T'(3,4)$ . Which transformation maps $RST$ onto $R'S'T'$ ?

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