Question
page 12 of 12
Question 1
A)Which expression is equivalent to 600−−−√
600
?(1 point)
Responses
610−−√
6
10
6 square root of 10
106–√
10
6
10 square root of 6
2425−−√
24
25
24 square root of 25
2524−−√
25
24
25 square root of 24
Question 2
A)
A function is shown.
g(x)=6(2x+7)
g
(
x
)
=
6
(
2
x
+
7
)
What is the value of g(20)
g
(
20
)
?
(1 point)
$$
Question 3
A)
A function is shown.
f(x)=−3x2+5
f
(
x
)
=
−
3
x
2
+
5
What is f(−2)
f
(
−
2
)
?
(1 point)
$$
Question 4
A)
Which expressions are equivalent to 12x2−48x+48
12
x
2
−
48
x
+
48
?
Select TWO correct answers.
(2 points)
Responses
12(x−2)2
12
(
x
−
2
)
2
12 times open paren x minus 2 close paren squared
−12(x2+4x+4)
−
12
(
x
2
+
4
x
+
4
)
negative 12 times open paren x squared plus 4 x plus 4 close paren
12(x−4)(x−1)
12
(
x
−
4
)
(
x
−
1
)
12 open paren x minus 4 close paren open paren x minus 1 close paren
−12(x+2)2
−
12
(
x
+
2
)
2
negative 12 times open paren x plus 2 close paren squared
12(x2−4x+4)
12
(
x
2
−
4
x
+
4
)
12 times open paren x squared minus 4 x plus 4 close paren
Question 1
A)Which expression is equivalent to 600−−−√
600
?(1 point)
Responses
610−−√
6
10
6 square root of 10
106–√
10
6
10 square root of 6
2425−−√
24
25
24 square root of 25
2524−−√
25
24
25 square root of 24
Question 2
A)
A function is shown.
g(x)=6(2x+7)
g
(
x
)
=
6
(
2
x
+
7
)
What is the value of g(20)
g
(
20
)
?
(1 point)
$$
Question 3
A)
A function is shown.
f(x)=−3x2+5
f
(
x
)
=
−
3
x
2
+
5
What is f(−2)
f
(
−
2
)
?
(1 point)
$$
Question 4
A)
Which expressions are equivalent to 12x2−48x+48
12
x
2
−
48
x
+
48
?
Select TWO correct answers.
(2 points)
Responses
12(x−2)2
12
(
x
−
2
)
2
12 times open paren x minus 2 close paren squared
−12(x2+4x+4)
−
12
(
x
2
+
4
x
+
4
)
negative 12 times open paren x squared plus 4 x plus 4 close paren
12(x−4)(x−1)
12
(
x
−
4
)
(
x
−
1
)
12 open paren x minus 4 close paren open paren x minus 1 close paren
−12(x+2)2
−
12
(
x
+
2
)
2
negative 12 times open paren x plus 2 close paren squared
12(x2−4x+4)
12
(
x
2
−
4
x
+
4
)
12 times open paren x squared minus 4 x plus 4 close paren
Answers
GPT-4o mini
Let's tackle each question one by one:
### Question 1
You need to simplify the square root of 600:
- We can factor 600 as \( 600 = 100 \times 6 = 10^2 \times 6 \).
- Therefore, \( \sqrt{600} = \sqrt{100 \times 6} = \sqrt{100} \times \sqrt{6} = 10\sqrt{6} \).
Thus, the correct expression equivalent to \( \sqrt{600} \) is:
**10 square root of 6**.
### Question 2
You are given the function \( g(x) = 6(2x + 7) \) and need to find \( g(20) \):
- Substitute \( x = 20 \):
\[
g(20) = 6(2(20) + 7) = 6(40 + 7) = 6(47) = 282.
\]
Thus, \( g(20) = 282 \).
### Question 3
For the function \( f(x) = -3x^2 + 5 \), find \( f(-2) \):
- Substitute \( x = -2 \):
\[
f(-2) = -3(-2)^2 + 5 = -3(4) + 5 = -12 + 5 = -7.
\]
So \( f(-2) = -7 \).
### Question 4
You need to determine which expressions are equivalent to \( 12x^2 - 48x + 48 \). Let's analyze each option.
1. **Option 1: \( 12(x-2)^2 \)**
- Expanding: \( 12((x)^2 - 4x + 4) = 12x^2 - 48x + 48 \) **(Correct)**
2. **Option 2: \( -12(x^2 + 4x + 4) \)**
- Expanding: \( -12(x^2 + 4x + 4) = -12x^2 - 48x - 48 \) **(Incorrect)**
3. **Option 3: \( 12(x-4)(x-1) \)**
- Expanding: \( 12(x^2 - 5x + 4) = 12x^2 - 60x + 48 \) **(Incorrect)**
4. **Option 4: \( -12(x + 2)^2 \)**
- Expanding: \( -12(x^2 + 4x + 4) = -12x^2 - 48x - 48 \) **(Incorrect)**
5. **Option 5: \( 12(x^2 - 4x + 4) \)**
- Expanding: \( 12(x^2 - 4x + 4) = 12x^2 - 48x + 48 \) **(Correct)**
The two correct answers are:
1. **12(x−2)²**
2. **12(x²−4x+4)**
### Summary of Answers
1. **10 square root of 6**
2. **282**
3. **−7**
4. **12(x−2)²** and **12(x²−4x+4)**
### Question 1
You need to simplify the square root of 600:
- We can factor 600 as \( 600 = 100 \times 6 = 10^2 \times 6 \).
- Therefore, \( \sqrt{600} = \sqrt{100 \times 6} = \sqrt{100} \times \sqrt{6} = 10\sqrt{6} \).
Thus, the correct expression equivalent to \( \sqrt{600} \) is:
**10 square root of 6**.
### Question 2
You are given the function \( g(x) = 6(2x + 7) \) and need to find \( g(20) \):
- Substitute \( x = 20 \):
\[
g(20) = 6(2(20) + 7) = 6(40 + 7) = 6(47) = 282.
\]
Thus, \( g(20) = 282 \).
### Question 3
For the function \( f(x) = -3x^2 + 5 \), find \( f(-2) \):
- Substitute \( x = -2 \):
\[
f(-2) = -3(-2)^2 + 5 = -3(4) + 5 = -12 + 5 = -7.
\]
So \( f(-2) = -7 \).
### Question 4
You need to determine which expressions are equivalent to \( 12x^2 - 48x + 48 \). Let's analyze each option.
1. **Option 1: \( 12(x-2)^2 \)**
- Expanding: \( 12((x)^2 - 4x + 4) = 12x^2 - 48x + 48 \) **(Correct)**
2. **Option 2: \( -12(x^2 + 4x + 4) \)**
- Expanding: \( -12(x^2 + 4x + 4) = -12x^2 - 48x - 48 \) **(Incorrect)**
3. **Option 3: \( 12(x-4)(x-1) \)**
- Expanding: \( 12(x^2 - 5x + 4) = 12x^2 - 60x + 48 \) **(Incorrect)**
4. **Option 4: \( -12(x + 2)^2 \)**
- Expanding: \( -12(x^2 + 4x + 4) = -12x^2 - 48x - 48 \) **(Incorrect)**
5. **Option 5: \( 12(x^2 - 4x + 4) \)**
- Expanding: \( 12(x^2 - 4x + 4) = 12x^2 - 48x + 48 \) **(Correct)**
The two correct answers are:
1. **12(x−2)²**
2. **12(x²−4x+4)**
### Summary of Answers
1. **10 square root of 6**
2. **282**
3. **−7**
4. **12(x−2)²** and **12(x²−4x+4)**