QuestionThe length of a rectangle is 7 yd more than twice the width $x$ . The area is $490 \mathrm{yd}^{2}$ .
Part: 0 / 3 $\square$
Part 1 of 3 (a) Write an equation in terms of $x$ that represents the given relationship.
The equation is $\square$ . $\square$

Studdy Solution

STEP 1

1. Let $x$ be the width of the rectangle in yards.
2. The length of the rectangle is $7$ yards more than twice the width.
3. The area of the rectangle is $490 \text{ yd}^2$ .
4. We need to write an equation that represents the relationship between the width and the length of the rectangle given the area.

STEP 2

1. Express the length of the rectangle in terms of the width $x$ .
2. Write the area equation using the width and the length.
3. Simplify the equation to obtain a quadratic equation in terms of $x$ .

STEP 3

Express the length of the rectangle in terms of the width $x$ .
Given that the length $L$ is $7$ yards more than twice the width $x$ , we can write: $L = 2x + 7$

STEP 4

Write the area equation using the width $x$ and the length $L$ .
The area $A$ of the rectangle is given by: $A = \text{width} \times \text{length}$ Substitute the given area and the expression for the length: $490 = x \times (2x + 7)$

STEP 5

Simplify the equation to obtain a quadratic equation in terms of $x$ .
Distribute $x$ on the right-hand side: $490 = x(2x + 7)$ $490 = 2x^2 + 7x$ Rearrange to form a standard quadratic equation: $2x^2 + 7x - 490 = 0$
The equation representing the given relationship is: $2x^2 + 7x - 490 = 0$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms