Answer:
(4x-7)(4x+7)
Step-by-step explanation:
This is called the Difference of Two Squares (DOTS).
These are the conditions that must be met for DOTS to work:
•There must be 2 terms.
•They must be separated by a negative sign.
•Each term must be a perfect square.
First, you have to find 2 square numbers that times together to make 16.
4×4=16
As we want 16x², you just need to make the 4 become 4x:
4x times 4x equals 16x²
Then, find 2 squares that times together to make 49.
7×7=49
You can put the two squares into a bracket with the x variable first, then the number:
(4x-7)(4x+7)
In the brackets, you always put the negative sign in the first one and then the plus sign in the second one.
You can double check your answer by expanding it back out again using FOIL:
F-First
O-Outer
I-Inner
L-Last
Times the First two in the two brackets:
4x times 4x equals 16x²
Times the Outer two:
4x times 7 equals 28x
Times the Inner two:
-7 times 4x equals -28x
Times the Last two:
-7 times 7 equals -49
Form an equation:
16x²+28x-28x-49
The 28x cancel out to leave:
16x²-49
Hope this helps :)
Answer:
Vertically opposite angles
You can make some algebraic equations and solve it.
The first would be:

The second would be

You can then rearrange the second into

And subsitute it into the first like so:

After that, distribute the y into the parantheses.

Subtract the 21 on both sides and multiply by -1 on both sides:

You then can factor it into:

With Zero Product Property, we can determine y to be either -3 and 7. Since the variables are interchangable, you can say the same about x, just that whatever x is, y must be the other value.
Thus, the answer is 7 and -3.
We need to convert this equation to slope-intercept form first.
We can do that by solving for y.
x - 5y = 15
<em><u>Add 5y to both sides.</u></em>
x = 5y + 15
<em><u>Subtract 15 from both sides.</u></em>
x - 15 = 5y
<em><u>Divide both sides by 5.</u></em>
y = 1/5x - 3
We now know the slope is 1/5.
The slope of the line perpendicular to the line with a slope of 1/5 is -5.
The slope of a perpendicular line is the negative reciprocal of the original slope.
Using a graphing calculator, we know the y-intercept of the line that is perpendicular to the original line must have a y-intercept of -6 to run through the points (-2, 5).
The equation of the new line is y = -5x - 6.