Unit Test — Unit test Answers

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An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters, and the length of the path is 5 meters more than the width.

0.5(x)(x + 5) = 29

0.5(x)(x + 5) = 841

x2 + (x + 5)2 = 29

x2 + (x + 5)2 = 841

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A rectangle’s length is 5 inches more than twice its width. Its area is 50 square inches. Which equation can be used to find its width, w?

2w(2w + 5) = 50

2w(w + 5) = 50

w(2w + 5) = 50

w(w + 5) = 50

Which equation is an example of the commutative property of multiplication?

(4 + 2i) = (2i + 4)

(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)

(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)

(4 + 2i) = (4 + 2i + 0)

What is the sum of 12 – 5i and –3 + 4i?

–16 + 63i

9 – i

9 – 9i

15 – 9i

If 5 + 6i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

–5 – 6i

5 – 6i

6 – 5i

6 + 5i

Which of the following is the complete list of roots for the polynomial function ?

–5, 3

–5, 3, –4 + i, –4 – i

–5, 3, –4 + i, 4 + i

–4 + i, –4 – i

Which expression is equivalent to (4 + 6i)2?

–20 + 48i

8 + 12i

16 – 36i

20 + 48i

Solve for in the equation .

x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction

x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction

x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

When graphed, which parabola opens downward?

y = –3x2

y = (x – 3)2

y = one-third x squared

y = x2 – 3

Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.

(m – 5)(m + 5) = 99

(m – 10)(m + 10) = 99

m2 – 25 = –99

m2 – 100 = –99

What is the value of i 20+1?

–1

–i

Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Select two options.

y = x2 + 5x + 10

y + 5x = x2 + 10 + 4x – 10

0 = x2 – 9x

0 = x2 – 9x + 20

One x-value of a solution to the system is 4.

Which pair of complex numbers has a real-number product?

(1 + 3i)(6i)

(1 + 3i)(2 – 3i)

(1 + 3i)(1 – 3i)

(1 + 3i)(3i)

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction

y = 2 (x minus 1) squared minus 11

y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction

y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction

Which graph shows a system of equations with a solution at (2, –1)?

Option

Which is a solution to the equation?(x − 3)(x − 5) = 35

x = −8

x = −5

x = 2

x = 10

The first three steps in determining the solution set of the system of equations algebraically are shown in the table.y = −x2 +2x − 9 y = −6x + 6

(5, −24) and (3, −12)

(5, 36) and (3, 24)

(−5, −24) and (−3, 12)

(−5, 36) and (−3, 24)

What is the value of i 97 – i?

–i

–2i

i Superscript 96

What is the greatest possible integer value of x for which is an imaginary number?

Which statement describes the graph of this polynomial function?

The graph crosses the x-axis at x = 2 and x = –1 and touches the x-axis at x = 0.

The graph touches the x-axis at x = 2 and x = –1 and crosses the x-axis at x = 0.

The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.

The graph touches the x-axis at x = –2 and x = 1 and crosses the x-axis at x = 0.

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