Answer: The length of the rectangle is 15 inches
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The perimeter of a rectangle is expressed as 2 length + 2 width
Perimeter = 2(L + W)
The rectangle has a perimeter of 52 inches. It means that
2(L + W) = 52
L + W = 52/2 = 26 - - - - - - - 1
The length of the rectangle is 4 inches more than its width. It means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W + 4 + W = 26
2W = 26 - 4 = 22
W = 22/2 = 11
L = W + 4 = 11 + 4 = 15
Answer: 75 feet²
Step-by-step explanation:
The scale means that for every one unit in the scale drawing, it is 30 units in the actual room. We will convert the dimensions using proportions.
x = 90
-
x = 120
The area of a rectangle can be found by multiplying the length by the width:
A = L * W
A = 90 * 120
A = 10,800 inches²
To get this into square feet, we will divide by 144. Why? There are 12 inches in a foot. 12 times 12 is 144.
10,800 inches² / 144 = 75 feet²
The area of the room, in square feet, is 75 feet².
Answer:
x = 2 and x = -3
Step-by-step explanation:
We need to find the value of x in the below expression.
Adding 1 to both sides,
Squaring both sides,
Hence, this is the required solution.
Answer:
(-5,1)
(-2,4)
Step-by-step explanation:
y = x + 6
y = x^2 + 8x + 16
Since both equations are equal to y, we can set them equal to each other
x + 6 = x^2 + 8x + 16
Subtract x from each side
x -x + 6
= x^2 + 8x-x + 16
6 = x^2 +7x +16
Subtract 6 from each side
6-6 = x^2 +7x +16-6
0 = x^2 +7x +10
Factor
What 2 numbers multiply together to give us 10 and add together to give us 7?
5*2 = 10
5+2 =7
0 = (x+5) (x+2)
Using the zero product property
x+5 = 0 x+2 = 0
x = -5 x=-2
Now we need to find the y's that go with the x's
x=-5
y= x+6
y =-5+6
y=-1
(-5,1)
x=-2
y = -2+6
y=4
(-2,4)
