Answer:
10.91%
Step-by-step explanation:
Take your number: 10.9091
Now find the first 3 decimals: 10.<u>909</u>
If the last (3rd) decimal is 5 or more raise the 2nd decimal: 10.9<u>09</u> → 10.9<u>1</u>
That is 2 decimal places
(if your teacher doesn't want it rounded then just 10.90%)
The <em><u>correct answer</u></em> is:
non-extraneous
Explanation:
An extraneous solution is one that we arrive at that will not work in the equation. For rational equations such as we have, extraneous solutions are ones that will cause the denominator to be 0. For ours, that would mean x=-5.
The equation we have is:
![\frac{3}{x+5}+\frac{1}{5}=\frac{2}{x+5}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bx%2B5%7D%2B%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B2%7D%7Bx%2B5%7D)
We will multiply everything by (x+5) in order to get that off the bottom of the fractions:
![\frac{3}{x+5}\times (x+5)+\frac{1}{5}\times (x+5)=\frac{2}{x+5}\times (x+5) \\ \\3+\frac{x+5}{5}=2](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bx%2B5%7D%5Ctimes%20%28x%2B5%29%2B%5Cfrac%7B1%7D%7B5%7D%5Ctimes%20%28x%2B5%29%3D%5Cfrac%7B2%7D%7Bx%2B5%7D%5Ctimes%20%28x%2B5%29%0A%5C%5C%0A%5C%5C3%2B%5Cfrac%7Bx%2B5%7D%7B5%7D%3D2)
Multiply all terms by 5 to eliminate the fraction:
![3\times 5+\frac{x+5}{5}\times 5=2\times 5 \\ \\15+x+5=10](https://tex.z-dn.net/?f=3%5Ctimes%205%2B%5Cfrac%7Bx%2B5%7D%7B5%7D%5Ctimes%205%3D2%5Ctimes%205%0A%5C%5C%0A%5C%5C15%2Bx%2B5%3D10)
Combine like terms:
20+x = 10
Subtract 20 from each side:
20+x-20 = 10-20
x = -10
Since this is not -5, this is not an extraneous solution.
Answer:
k=-9
Step-by-step explanation:
The given functions are
![h(x) = {x}^{2} + 3](https://tex.z-dn.net/?f=h%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%203)
and
![g(x) = {x}^{2} - 6](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%206)
We want to find the value of k, for which
![g(x) = h(x) + k](https://tex.z-dn.net/?f=g%28x%29%20%3D%20h%28x%29%20%2B%20k)
This means we need to extract g(x) from f(x) to get:
![g(x) = {x}^{2} + 3 - 9](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%203%20-%209)
Or
![g(x) = ( {x}^{2} + 3) + (- 9)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%203%29%20%20%2B%20%28-%209%29)
![g(x) =h(x)+ - 9](https://tex.z-dn.net/?f=g%28x%29%20%3Dh%28x%29%2B%20%20-%209)
Therefore k=-9
Answer:
x = -7
Step-by-step explanation:
4 - 2(x - 3) = 24
Subtract 4 from each side
4-4 - 2(x - 3) = 24-4
-2(x-3) = 20
Divide each side by -2
-2(x-3)/-2 = 20/-2
x-3 = -10
Add 3 to each side
x-3+3 = -10+3
x = -7
Answer:
x = 24.7
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp side/ adj side
tan 20 = 9/x
x tan 20 = 9
x = 9/ tan 20
x = 24.72729678
Round to the nearest tenth
x = 24.7