Which expression is equivalent to 600−−−√

?(1 point)
Responses

610−−√
6 square root of 10

106–√
10 square root of 6

2425−−√
24 square root of 25

2524−−√
A function is shown.

g(x)=6(2x+7)

What is the value of g(20)
?
A function is shown.

f(x)=−3x2+5

What is f(−2)
?
Which expressions are equivalent to 12x2−48x+48
?



Select TWO correct answers.

(2 points)
Responses

12(x−2)2
12 times open paren x minus 2 close paren squared

−12(x2+4x+4)
negative 12 times open paren x squared plus 4 x plus 4 close paren

12(x−4)(x−1)
12 open paren x minus 4 close paren open paren x minus 1 close paren

−12(x+2)2
negative 12 times open paren x plus 2 close paren squared

12(x2−4x+4)

1 answer

Let's break down each part of your question step by step.

  1. Equivalent expression for 600

    To simplify 600: 600=100×6=100×6=106 So the expression equivalent to 600 is 10 square root of 6.

  2. Value of g(20) where g(x)=6(2x+7)

    Substitute x=20 into the function: g(20)=6(2(20)+7)=6(40+7)=6(47)=282

  3. Value of f(2) where f(x)=3x2+5

    Substitute x=2 into the function: f(2)=3(2)2+5=3(4)+5=12+5=7

  4. Expressions equivalent to 12x248x+48

    Let's factor 12x248x+48: 12(x24x+4)=12(x2)2 So one correct answer is 12(x − 2)².

    Now let's examine the other options for correctness:

    • −12(x² + 4x + 4): This is equivalent to 12(x+2)2, which is not equivalent.
    • 12(x − 4)(x − 1): This is not equivalent, as this expands to 12(x25x+4).
    • −12(x + 2)²: This is not equivalent, as it represents a reflection and different dimensions.
    • 12(x² − 4x + 4): This expression is the same as what we factored, thus is also equivalent.

So, the two correct responses are:

  1. 12(x − 2)²
  2. 12(x² − 4x + 4)

In summary:

  • Equivalent to 600: 10 square root of 6
  • Value of g(20): 282
  • Value of f(2): -7
  • Equivalent expressions: 12(x − 2)² and 12(x² − 4x + 4).