Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

4x^2 + 22x - 1 = 0

Step-by-step explanation:

Given that

The area is 31 square feet

And, the painting is 5 feet wide by 6 feet long

We need to find out which quadratic equation can be used

So,

(5 + 2x)(6 + 2x) = 31

30 + 10x + 12x + 4x^2 = 31

30 + 22x + 4x^2 = 31

4x^2 + 22x - 1 = 0

The above equation can be used for measuring out the thickness of the frame x

correct answer:

b.(19,-2)

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is