1. First, let us define the width of the rectangle as w and the length as l.
2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:
l = w + 6
3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:
24 = 2w + 2l
4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:
24 = 2w + 2l
if l = w + 6, then: 24 = 2w + 2(w + 6)
24 = 2w + 2w + 12 (Expand 2(w + 6) )
24 = 4w + 12
12 = 4w (Subtract 12 from each side)
w = 12/4 (Divide each side by 4)
w = 3 in.
5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :
l = w + 6
l = 3 + 6
l = 9 in.
6. Therefor the rectangle has a width of 3 in. and a length of 9 in.
First step is to factor. With a polynomial function in the form ax² + bx + c = f(x), we have to find what factors of term C have a sum of term B.
So with this, we need factors of -90 add up to become -1. Your factors are - 10 and 9.
f(x) = x² + 9x - 10x - 90
Now we group together and pull out GCFs.
f(x) = (x² + 9x) + (10x - 90)
f(x) = x(x² + 9) - 10(x + 9)
f(x) = (x - 10)(x + 9)
Now, set each factor equal to zero.
x - 10 = 0, x + 9 = 0
For the first equation you are going to add 10 to both sides to get x by itself. Subtract 9 from both sides in the second equation for the same reason.
x = 10, x = -9
Your zeros are at x = -9, 10 or at the ordered pairs (-9, 0) and (10, 0).
Answer:
Step-by-step explanation:
<h3>Given</h3>
<u>Function </u>
<h3>To find </h3>
<h3>Solution</h3>
We can see all 3 graphs have y-intercept of -2
Since the slope is negative, it is decreasing function, therefore possible options are A or C
<u>Checking x-intercept and comparing with same of A and C</u>
- y = 0
- -3/2x - 2 = 0
- -3/2x = 2
- x = -4/3 = -1.33
As we see it matches Option C, which is the answer
Answer:
D
Step-by-step explanation: i believe it is D
Answer:
y=-1/4x-6
Step-by-step explanation:
The equation of a line is:
y=mx+b (slope-intercept form) where m is the slope and b is the y-intercept. x and y are the x and y coordinates for a point on the line.
Now that we know the equation, we plug in the given numbers into the equation:
y=mx+b
-8=-1/4(8)+b
-8=-2+b
b=-6
Now we know the y-intercept so the equation is:
y=-1/4x-6
