AnswersGeometry - Semester 1 PathwaysUsing Triangle Congruence Theorems

Using Triangle Congruence Theorems — Cumulative exam Answers

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The equation |p| = 2 represents the total number of points that can be earned or lost during one turn of a game. Which best describes how many points can be earned or lost during one turn?

A
–2
B
2
C
0 or 2
D
–2 or 2
2
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Mr. Valenzuela’s new bottle of shampoo contains 60 ounces of shampoo. He uses ounce of shampoo each time he washes his hair. Which equation can be used to find x, the number of washes after which 24 ounces will remain in the bottle?

Question illustration
A
One-fourth x minus 60 equals 24
Option A
B
60 minus one-fourth x equals 24
Option B
C
One-fourth x minus 24 equals 60
Option C
D
24 minus one-fourth x equals 60
Option D
3

According to the Rational Root Theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20., –2, 1, Which is an actual root of f(x)?

Question illustration
A
Negative five-halves
Option A
B
–2
C
1
D
Ten-thirds
Option D
4

Which function has the same maximum value as f(x) = – |x + 3| – 2?

A
Option
Option A
B
f(x) = (x + 3)2 – 2
C
Option
Option C
D
f(x) = –(x – 6)2 – 3
5

Angles 1 and 2 are supplementary.

Question illustration
A
m1 + m2 = 90°
Option A
B
m1 + m2 = 100°
Option B
C
m1 + m2 = 180°
Option C
D
m1 + m2 = 200°
Option D
6

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?

A
2w(2w + 5) = 50
B
2w(w + 5) = 50
C
w(2w + 5) = 50
D
w(w + 5) = 50
7

The step function g(x) is defined as shown.g(x) = What is the range of g(x)?

Question illustration
A
–3 ≤ g(x) ≤ 5
B
0 ≤ g(x) ≤ 10
C
{–3, 2, 5}
D
{0, 4, 10}
8

Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
9

Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

A
0
B
4
C
25
D
100
10

Over which interval does the exponential show a more rapid rate of change?

Question illustration
A
mc025-2.jpg
Option A
B
mc025-3.jpg
Option B
C
mc025-4.jpg
Option C
D
mc025-5.jpg
Option D
11

Omar grouped the terms and factored the GCF out of the groups of the polynomial 3x3 – 15x2 – 4x + 20. His work is shown.Step 1: (3x3 – 15x2) + (–4x + 20)Step 2: 3x2(x – 5) + 4(–x + 5)

A
Omar should realize that his work shows that the polynomial is prime.
B
Omar should go back and regroup the terms in Step 1 as (3x3 – 15x2) – (4x + 20).
C
In Step 2, Omar should factor only out of the first expression.
D
Omar should factor out a negative from one of the groups so the binomials will be the same.
12

Clara writes the equation (x – 13)(x + 8) = 196 to solve for the missing side length of a rectangle represented by the factor x + 8. What is the missing side length represented by x + 8 units of the rectangle?

A
7
B
15
C
20
D
28
13

Marisol grouped the terms and factored the GCF out of the groups of the polynomial 6x3 – 22x2 – 9x + 33. Her work is shown.Step 1: (6x3 – 22x2) – (9x + 33)Step 2: 2x2(3x – 11) – 3(3x + 11)

A
Marisol should realize that her work shows that the polynomial is prime.
B
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) – (9x – 33).
C
Marisol should go back and group the terms in Step 1 as (6x3 – 22x2) + (9x – 33).
D
Marisol should refactor the expression in Step 2 as 2x2(3x + 11) – 3(3x + 11).
14

When graphed, which parabola opens downward?

Question illustration
y
y = –3x2
y
y = (x – 3)2
C
Option
Option C
y
y = x2 – 3
15

What is a solution to (x + 6)(x + 2) = 60?

A
x = −6
B
x = −4
C
x = 4
D
x = 12
16

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

A
(4 + 2i) = (2i + 4)
B
(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)
C
(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)
D
(4 + 2i) = (4 + 2i + 0)
17

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
18

Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?

A
The difference has 3 terms and a degree of 6.
B
The difference has 4 terms and a degree of 6.
C
The difference has 3 terms and a degree of 7.
D
The difference has 4 terms and a degree of 7.
19

Question text not available

Question illustration
B
Both the domain and range of the transformed function are the same as those of the parent function.
N
Neither the domain nor the range of the transformed function are the same as those of the parent function.
T
The range of the transformed function is the same as the parent function, but the domains of the functions are different.
T
The domain of the transformed function is the same as the parent function, but the ranges of the functions are different.
20

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

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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