Hello!
To solve this problem, we will use a system of equations. We will have one number be x and the other y. We will use substitutions to solve for each variable.
x+y=9
x=2y-9
To solve for the two numbers, we need to solve the top equation. The second equation shows that x=2y-9. In the first equation, we can replace 2y-9 for x and solve.
2y-9+y=9
3y-9=9
3y=18
y=6
We now know the value of y. Now we need to find x. We can plug in 6 for y in the second equation to find x.
x=2·6-9
x=12-9
x=3
Just to check, we will plug these two numbers into the first equation.
3+6=9
9=9
Our two numbers are three and six.
I hope this helps!
Answer:
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2(z - 5) + (z - 8) =
= 2z - 10 + z - 8 =
= 2z + z - 10 - 8 = <u>3</u><u>z</u><u> </u><u>-</u><u> </u><u>1</u><u>8</u> ← the end
8 x 64 = (8 x 60) + (8 x 4)=
<h3>
Answer: n = -11</h3>
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Explanation:
Since x-2 is a factor of f(x), this means f(2) = 0.
More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
So if we plugged x = 2 into f(x), we'd get
f(x) = x^3+x^2+nx+10
f(2) = 2^3+2^2+n(2)+10
f(2) = 8+4+2n+10
f(2) = 2n+22
Set this equal to 0 and solve for n
2n+22 = 0
2n = -22
n = -22/2
n = -11 is the answer
Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10
Plug x = 2 into that updated f(x) function to find....
f(x) = x^3+x^2-11x+10
f(2) = 2^3+2^2-11(2)+10
f(2) = 8+4-22+10
f(2) = 0
Which confirms our answer.
