AnswersAlgebra IIExpressions and Equations

Expressions and Equations — Test Answers

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1
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What is the vertex of the absolute value function?

A
open paren 4 comma 1 close paren
B
open paren 1 comma negative 4 close paren
C
open paren 1 comma 4 close paren
D
open paren 4 comma negative 1 close paren
2
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The area of a rhombus can be evaluated using the formula 1 half d sub 1 d sub 2 , where d sub 1 represents the measure of one of its diagonals and d sub 2 represents the measure of its other diagonal. When d sub 1 is a terminating decimal and d sub 2 is a repeating decimal, what can be concluded about the area of the rhombus?

A
The area is irrational because both diagonals are irrational.
B
The area is rational because the formula will multiply both rational diagonals and the fraction 1 half .
C
The area is irrational because the formula will multiply two decimals by a fraction.
D
The area is rational because the product of an irrational diagonal and rational diagonal will be multiplied by the rational fraction 1 half .
3

The standard diameter of a golf ball is 42 point 6 7 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0 point 0 0 2 mm. Which function could represent this situation?

A
f of x is equal to x minus absolute value of 42 point 6 7
B
f of x is equal to 42 point 6 7 minus absolute value of x
C
f of x is equal to start absolute value 42 point 6 7 minus x end absolute value
D
f of x is equal to absolute value of x minus 42 point 6 7
4

Which is the graph of f of x is equal to absolute value of x reflected across the x -axis, translated 3 units left, 4 units up, and dilated by a factor of 4 ?

A
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening downward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 7 comma 0) and (1 comma 0).
B
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening downward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 4 comma 0) and (negative 2 comma 0).
C
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening upward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 4 comma 8) and (negative 2 comma 8).
D
Image with description On a coordinate plane, the scale on the x axis ranges from negative 8 to 2 in increments of 1, and the scale on the y axis ranges from negative 2 to 8 in increments of 1. The V-shaped graph opening upward has a vertex at (negative 3 comma 4) and the graph passes through the points (negative 6 comma 7) and (0 comma 7).
6

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse by the formula A squared plus b squared is equal to c squared If A is a rational number and b is a rational number, why could c be an irrational number?

A
The left side of the equation will result in a rational number, which could be a non-perfect square.
B
The square of rational numbers is irrational, and sum of two irrational numbers is irrational.
C
The product of two rational numbers is rational, and the sum of two rational numbers is irrational.
D
The left side of the equation will result in a rational number, which is a perfect square.
7

Given the function f of x is equal to 2 start absolute value x plus 6 end absolute value minus 4 , for what values of x is f of x is equal to 6 ?

A
x is equal to 26 , x is equal to negative 14
B
x is equal to negative 1 , x is equal to negative 11
C
x is equal to negative 1 , x is equal to 11
D
x is equal to 14 , x is equal to negative 26
8

To find the area of a trapezoid, Dylan uses the formula cap A is equal to 1 half open paren b sub 1 plus b sub 2 close paren h The bases have lengths of 3 point 6 cm and 12 and 1 third cm. The height of the trapezoid is square root of 5 cm. The area of the trapezoid is irrational because

A
the height is irrational, and it is multiplied by the other rational dimensions.
B
the entire answer is being multiplied by a fraction.
C
the bases have an irrational sum that will be multiplied by the rational height.
D
the values of the variables are all irrational numbers.
10

Why is the product of a rational number and an irrational number irrational?

A
because the product is always a repeating or a terminating decimal
B
because the product is always a fraction
C
because the product is always a negative number
D
because the product is always a non-terminating, non-repeating decimal
11

Which of the following formulas, when evaluated using rational values for the variables, will result in an irrational number?

A
the formula for the area of a rectangle
B
the formula for the area of a circle
C
the formula for the area of a triangle
D
the formula for the area of a trapezoid
12

Given the function f of x is equal to 0 point 5 start absolute value x minus 4 end absolute value minus 3 , for what values of x is f of x is equal to 7 ?

A
x is equal to negative 1 , x is equal to 9
B
x is equal to negative 24 , x is equal to 16
C
x is equal to 1 , x is equal to negative 9
D
x is equal to negative 16 , x is equal to 24
15

Which of the following is always irrational?

A
the sum of two fractions
B
the product of a repeating decimal and the square root of a non-perfect square
C
the product of a fraction and a repeating decimal
D
the sum of a terminating decimal and the square root of a perfect square
16

Sam is determining the area of a triangle. In this triangle, the value for the height is a terminating decimal, and the value for the base is a repeating decimal. What can be concluded about the area of this triangle?

A
The area is irrational because the numbers in the formula are irrational and the numbers substituted into the formula are rational.
B
The area will be rational because both the height and the base are irrational.
C
The area is rational because the numbers in the formula are rational and the numbers substituted into the formula are rational.
D
The area will be irrational because the height is irrational.
17

Which of the following is the parent function of all absolute value functions?

A
f of x is equal to 2 absolute value of x
B
f of x is equal to 3 x
C
f of x is equal to absolute value of x
D
f of x is equal to x squared
18

Which number expresses 6 point 7 2 as a fraction in simplest form?

A
6 and 3 fifths
B
6 and 7 tenths
C
6 and 3 fourths
D
6 and 18 over 25
21

2 point 3 5 times 2 thirds is equal to

A
27 over 30
B
7 over 30
C
47 over 30
D
7 over 15

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