A photographer needs a frame for an 5 x 7 inch picture, such that the total area is 80 in? Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
4x^2 + 24x = 45
4x^2 + 12x = 45
2x^2 + 24 = 45
2x^2 + 12x = 45

4·x² + 24·x = 45

Step-by-step explanation:

The total area of the frame and picture needed by the photographer = 80 in²

The size of the picture that will be in the frame = 5 × 7 inch

The length of the picture = 7 inches

The width of the picture = 5 inches

Let x represent the width of the frame, we get;

The width of the total area = The width of the picture + 2 × The width of the frame

Therefore, the width of the total area = 5 + 2·x

The length of the total area = The length of the picture + 2 × The width of the frame

Therefore, the length of the total area = 7 + 2·x

We get;

The total area = Total length × Total width

∴ The total area = (5 + 2·x) × (7 + 2·x)

We are given that the total area = 80, therefore, by transitive property of equality, we have;

(5 + 2·x) × (7 + 2·x) = 80

35 + 10·x + 14·x + 4·x² = 80

4·x² + 24·x = 80 - 35 = 45

∴ 4·x² + 24·x = 45

Therefore, the quadratic equation that can be used in solving for the width is 4·x² + 24·x = 45.

452,489 to the nearest thousand is 452,000

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.