Test practice 4 Flashcards
A certain apprentice has enrolled in 85 hours of training courses. The equation 10x + 15y = 85
represents this situation, where x is the number of on-site training courses and y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?
10x + 15y = 85
15 - 10 = 5
Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?
A.6
B.10
C.14
D.24
Choice D is correct.
-square x
p = 4s
p = 4(12)
p = 48
-square y
p = 2(48)
p = 96
-the lenght of one side of square y
p = 4s
96 = 4s
s = 24
y > 14
4x + y < 18
The point (x, 53) is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of x?
A. -9
B. -5
C. 5
D. 9
Choice A is correct
4x + y < 18
4x + 53 < 18
x < -8.75
x must be less than -8.75. Therefore, the correct answer is -9
The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If w represents the nth term of the sequence, which equation gives w in terms of n?
A. w = 4(9^n)
B. w = 4(9^n-1)
C. w = 9(4^n)
D. w = 9(4^n-1)
Choice D is correct.
When w is 9, n is 1
Since each term after the first is 4 times the preceding term, w is 9 * 4
The value of w is 9 * 4 * 4, or 9 * 4^2, when n is 3
The value of w is 9 * 4^n - 1
RS = 20 / ST = 48 / TR = 52
The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W. What is the value of tanW?
A. 5/13
B. 5/12
C. 12/13
D. 12/5
Choice B is correct.
Hypotenuse = 52
Adjacent side = ST
Opposite side = RS
T = 20/48
T = 5/12
The graph of 9x - 10y = 19 is translated down 4 units in the xy-plane. What is the x-coordinate of the x-intercept of the resulting graph?
The correct answer is 59/9
9x - 10y = 19
9x - 10y + 4 = 19
9x - 10y - 40 = 19
9x - 10y = 59 (y=0)
9x = 59
x = 59/9
Line p is defined by 2y + 18x = 9. Line r is perpendicular to line p in the xy-plane. What is the slope of line r?
A. -9
B. -1/9
C. 1/9
D. 9
The correct answer is c.
2y + 18x = 9
2y = -18x + 9
y = -9x + 9
-slope = -9
-perpendicular formula = -1 / m
Therefore, -1/ -9 = 1 / 9
A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?
A. 588
B. 726
C. 897
D. 1107
Choice A is correct.
-The volume of the sample is 0.90^3 = 0.729
-Density = 0.729 (807 kg / 1 cubic meter)
= 588
