Test practice 3 Flashcards
Which expression is equivalent to
(m^4 q^4 z^-1) (m q^5 z^3) where m, q, and z are positive?
A. m^4 q ^20 z^-3
B. m^5 ^9 z^2
C. m^6 q^8 z^-1
D. m^20 q^12 z^-2
B. m^5 ^9 z^2
y = 76
y = x^2 - 5
What is the value of x?
A. -76/5
B. -9
C. 5
D. 76
B. -9
If X/Y = 4 and 24X / NY = 4, what is the value of N?
The correct answer is 24
The equation 24X / NY = 4 can be rewritten as 24 / N X / Y
It’s given that X / Y = 4. Substituting 4 for
X / Y in the equation, yields 24 / N 4 = 4
Multiplying both sides of this equation by n yields
24 4 = 4n
Dividing both sides of this equation by 4 yields 24 = n
Therefore, the value of n is 24
Square A has side lengths that are 166 times the side lengths of square B. The area of square A is K times the area of square B. What is the value of K?
The correct answer is 27,556
The area of a square is S^2, where S is the side length of the square.
S^2 = X^2
Area of square A = 166x^2 or 27556x^2
It’s given that the area of square A is K times the area of square B. Therefore:
27556x^2 = kx^2
Therefore, the value of K is 27,556
A scientist initially measures 12000 bacteria in a growth medium. 4 hours later, the scientist measures 24000 bacteria.
Assuming exponential growth, the formula P = C (2)^rt gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r?
A. 1/12000
B. 1/4
C. 4
D. 12000
Choice B is correct.
P = C (2)^rt
24000 = 12000 (2)^4r
2 = 2^4r
2^1 = 2^4r
1 = 4r
1/4 = r
x - 29 = (x - a) (x - 29)
Which of the following are solutions to the given equation, where a is a constant and a > 30?
I. a
I. a + 1
III. 29
A. I and II only
B. I and III only
C. II and III only
D. I, II, and III
Choice C is correct.
x - 29 = (x - a) (x - 29)
~ Subtracting the expression x - 29 from both sides of the given equation yields
0 = x - ax - 29 - x - 29
~ which can be rewritten as
0 = x - ax - 29 + -1x - 29
~ Since the two terms on the right-hand side of this equation have a common factor of x - 29, it can be rewritten as
0 = x - 29x - a + - 1
~ Since x - a - 1 is equivalent to x - a + 1, the equation 0 = x - 29x - a - 1 can be rewritten as
0 = x - 29x - a + 1
~ By the zero product property, it follows that
x - 29 = 0 or x - a + 1 = 0
~ Adding 2 to both sides of the equation x - 29 = 0 yields x = 29
~ Adding a + 1 to both sides of the equation x - a + 1 = 0 yields x = a + 1
~ Therefore, the two solutions to the given equation are
29 and a + 1. Thus, a is not a solution.
The function f is defined by f(x) = 270(0.1)^x. What is the value of f(0)?
A. 0
B. 1
C. 27
D. 270
Choice D is correct.
f(x) = 270(0.1)^x
f0 = 270 * 1
f0 = 270
In right triangle RST, the sum of the measures of angle R and angle S is 90 degrees. The value of sin(R) is √15 / 4. What is the value of cos(S)?
A. √15 / 15
B. √15 / 4
C. 4 * √15 / 15
D. √15
Choice B is correct.
The sine of any acute angle is equal to the cosine of its complement. It’s given that in right triangle RST, the sum of the measures of angle R and angle S is 90 degrees.
Therefore, angle R and angle S are complementary and the value of sinR is equal to the value of cosS
The function f is defined by f(x) = (x - 6)(x - 2)(x + 6). In the xy-plane, the graph of y = g(x) is the result of translating the graph of y = f(x) up 4 units. What is the value of g(0)?
The correct answer is 76.
f(x) = (x - 6)(x - 2)(x + 6) + 4
g(0) = (0 - 6)(0 - 2)(0 + 6) + 4
g(0) = 72 + 4
g(0) = 76
A cube has a volume of 474552 cubic units. What is the surface area, in square units, of the cube?
The correct answer is 36,504.
V = s^3
474552 = s^3
78 = s
Since each face of a cube is a square, it follows that each face has an edge length of 78 units. The area of a square can be found using the formula
A = s^2
A = 78^2
A = 6084
Since a cube has 6 faces, the surface area, in square units, of this cube is 66084 or 36504
For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0) = 14, which equation defines q?
A. q(x) = 0.55(14)^x
B. q(x) = 1.45(14)^x
C. q(x) = 14(0.55)^x
D. q(x) = 14(1.45)^x
Choice C is correct.
q(x) = 14(0.55)^x
q(0) = 14(0.55)^0
q(0) = 14 * 1
q(0) = 14
Which of the following expressions is(are) a factor of 3X^2 + 20X - 63
I. X - 9
II. 3X - 7
A. I only
B. II only
C. I and II
D. Neither I nor II
Choice B is correct.
3X^2 + 20X - 63
3X^2 + 27X - 7x - 63
3X(x + 9) - 7(x + 9)
(3x - 7)(x + 9)
4x - 9y = 9y + 5
hy = 2 + 4x
In the given system of equations, h is a constant. If the system has no solution, what is the value of h?
A. -9
B. 0
C. 9
D. 18
Choice D is correct.
A small business owner budgets $2200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?
The correct answer is 182.
s = small / L = large
4.90s + 11.60L =< 2200
s + L => 200
s => 200 - L
4.90s => 4.90(200 - L)
4.90s => 980 - 4.90L
4.90s + 11.60L => 980 - 4.90L + 11.60L
4.90s + 11.60L => 980 + 6.70L
980 + 6.70L =< 4.90s + 11.60L =< 2200
6.70L =< 1220
L =< 182.09
Since the number of large candles the owner purchases must be a whole number, the maximum number of large candles the owner can purchase is the largest whole number less than 182.09, which is 182
f(x) = 5470(0.64)^x/12
The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by
p% of its value the preceding year, what is the value of p?
A. 4
B. 5
C. 36
D. 64
Choice C is correct
f(x) = a(r)^x/h
r < 1
100(1 - r)% or 36%
