Which algebraic equation represents the words:

Twenty percent of your grade is 80 points. What was your grade?

(1 point)
Responses

20x = 80
20x = 80

.20x = 80
.20x = 80

.20 = 80x
.20 = 80x

20/80 = x

7 answers

The phrase "Twenty percent of your grade is 80 points" can be translated into an algebraic equation as follows:

Twenty percent can be represented as 0.20, and if we let \( x \) represent your grade, we have:

\[ 0.20x = 80 \]

Thus, the correct equation from the options given is:

.20x = 80

Solve the equation using the inverse operation: x/4 = 12(1 point)
Responses

Inverse operation is subtraction; x = 8
Inverse operation is subtraction; x = 8

Inverse operation is addition; x = 16
Inverse operation is addition; x = 16

Inverse operation is multiplication; x = 48
Inverse operation is multiplication; x = 48

Inverse operation is division; x = 48

To solve the equation \( \frac{x}{4} = 12 \) using the inverse operation, we need to isolate \( x \).

The inverse operation of division (which is what the equation is currently doing by dividing \( x \) by 4) is multiplication. Thus, we can multiply both sides of the equation by 4:

\[ x = 12 \times 4 \]

Calculating that gives:

\[ x = 48 \]

Therefore, the correct response is:

Inverse operation is multiplication; x = 48

Bill goes to the market to buy some apples. The cost of the apples that he likes is $1.25 per pound. If he has $5 to spend on apples, how many pounds (x) can he buy?

Set up an equation to solve the problem.

(1 point)
Responses

1.25x = 5
1.25x = 5

5x = 1.25
5x = 1.25

1.25 + x = 5
1.25 + x = 5

1.25/5 = x

To set up an equation based on the information given, we know that the cost of apples is $1.25 per pound and Bill has $5 to spend.

Let \( x \) represent the number of pounds of apples he can buy. The total cost of the apples will be equal to the price per pound multiplied by the number of pounds, which must equal the amount of money Bill has.

This can be expressed in the equation:

\[ 1.25x = 5 \]

Thus, the correct response is:

1.25x = 5

in the expression: 4x 2−2x+1
(2 points)
How many terms are there?Response area

What is the leading coefficient of the first term? Response area .

responses
0
1
2
3
4

In the expression \( 4x^2 - 2x + 1 \):

  1. How many terms are there?

    The expression consists of three distinct parts: \( 4x^2 \), \( -2x \), and \( +1 \). Therefore, there are 3 terms.

  2. What is the leading coefficient of the first term?

    The first term of the expression is \( 4x^2 \). The leading coefficient is the numerical factor in this term, which is 4.

So to summarize:

  • Number of terms: 3
  • Leading coefficient of the first term: 4