Answer: 7
Step-by-step explanation:
The greatest common factor is 2
This is because we start by taking the largest factor that goes into both coefficients. Since the first coefficient is 2, we have to try 2 and 1. Since 2 is larger and goes into 36 evenly, we use that.
Then we use the smallest number of each variable. There are 4 r's in both equations. So, that is the number that we take. There are 2 s's in the first term, so we take that number.
The area of the new rug is
x² + 2x - 15
Since
A = l x w
The new rug is 3 in shorter than her old rug, so we divide the area by (x - 3)
(x² + 2x - 15) / (x - 3)
By factoring
(x - 3)(x + 5) / (x - 3)
Cancelling out terms
x + 5
The width is 5 inches wider
Answer:
Step-by-step explanation:
Draw an auxiliary line in the trapezoid forming a triangle and a rectangle. The dimensions of the rectangle are 3 x 4, so the length of the auxiliary line must be 4.
The auxiliary line also creates a 45-45-90 triangle. The auxiliary line itself makes up one leg of the triangle, and since we know it is 4, we can use the Pythagorean Theorem to find y:
The length of x can be found by adding the bottom leg of the 45-45-90 triangle and the bottom dimension of the rectangle: