Use a let statement
first
let x and x + 2 be the number so you write it like this
<u>let x = the first consecutive integer
</u><u>let x + 2 = the second consecutive integer
</u>
second
x(x+2)=323
x^2 + 2x = 323
-323 -323
x^2 + 2x -323 = 0
third
try to factor -323 so it is 19 and -17
(x + 19) (x - 17) = 0
x = 19
x = -17
hope this help
In order for the triangle to be isosceles, we have to set two lengths of the triangle equal to each other.
Let's take the lengths 5x-12 and x+20 and set them equal to each other.
5x - 12 = x + 20
Combine like terms by moving them over to their respective sides.
Subtract x from both sides of the equation.
4x - 12 = 20
Add 12 to both sides of the equation.
4x = 32
Divide both sides by 4.
x = 8
Check your answer by substituting.
5x - 12 = x + 20
5(8) - 12 = 8 + 20
40 - 12 = 28
28 = 28
Solution: x = 8
If you are reflecting across the line y = x, then the x value becomes the y-vale and the y-value becomes the x-value. So the answer would be (6, -1) (Just trade places with x and y.)
Answer:

Step-by-step explanation:
In essence, one needs to work their way backwards to solve this problem. Use the information to construct the function.
The function has verticle asymptotes at (x = 4) and (x = 5). This means that the denominator must have (x - 4) and (x - 5) in it. This is because a verticle asymptote indicates that the function cannot have a value at these points, the function jumps at these points. This is because the denominator of a fraction cannot be (0), the values (x - 4) and (x - 5) ensure this. Since if (x) equals (4) or (5) in this situation, the denominator would be (0) because of the zero product property (this states that any number times zero equals zero). So far we have assembled the function as the following:

The function has x-intercepts at (6, 0), and (0, 10). This means that the numerator must equal (0) when (x) is (6) or (10). Using similar logic that was applied to find the denominator, one can conclude that the numerator must be (
). Now one has this much of the function assembled

Finally one has to include the y-intercept of (0, 120). Currently, the y-intercept is (60). This is found by multiplying the constants together. (6 * 10) equals (60). One has to multiply this by (2) to get (120). Therefore, one must multiply the numerator by (2) in order to make the y-intercept (120). Thus the final function is the following:

Answer:
5
Step-by-step explanation: