Answer:
x = 9,-21
Step-by-step explanation:
Given:
![\displaystyle \large{|x+6|-7=8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C-7%3D8%7D)
Transport -7 to add 8:
![\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D8%2B7%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D15%7D)
Cancel absolute sign and add plus-minus to 15:
![\displaystyle \large{x+6=\pm 15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%2B6%3D%5Cpm%2015%7D)
Transport 6 to subtract ±15:
![\displaystyle \large{x=\pm 15-6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D%5Cpm%2015-6%7D)
Consider:
or ![\displaystyle \large{x = -15-6}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%20%3D%20-15-6%7D)
or ![\displaystyle \large{x=-21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D-21%7D)
Solution:
or ![\displaystyle \large{x=-21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D-21%7D)
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Second Method
Given:
![\displaystyle \large{|x+6|-7=8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C-7%3D8%7D)
Transport -7 to add 8:
![\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D8%2B7%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D15%7D)
Absolute Function Property:
![\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx-a%7C%20%3D%20%5Cbegin%7Bcases%7D%20x-a%20%5C%20%5C%20%28x%20%5Cgeq%20a%29%20%5C%5C%20-x%2Ba%20%5C%20%5C%20%28x%20%3C%20a%29%20%5Cend%7Bcases%7D%7D)
Consider both intervals:
When x ≥ a then:
![\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D15%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7Bx%2B6%3D15%7D)
Transport 6 to subtract 15:
![\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D15-6%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7Bx%3D9%7D)
When x < a then:
![\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%7Cx%2B6%7C%3D15%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B-%28x%2B6%29%3D15%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B-x-6%3D15%7D)
Transport -6 to add 15:
![\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B-x%3D15%2B6%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B-x%3D21%7D)
Transport negative sign to 21:
![\displaystyle \large{x=-21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D-21%7D)
Solution:
or ![\displaystyle \large{x=-21}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7Bx%3D-21%7D)
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Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
Step-by-step explanation:
Because he always do that non sense thing by this true method and always shout it when they will go from their house
Answer:
![13,846\ cones](https://tex.z-dn.net/?f=13%2C846%5C%20cones)
Step-by-step explanation:
Let
x -----> the number of ice cream cones sold 5 years ago
Remember that
![100\%+30\%=130\%=130/100=1.3](https://tex.z-dn.net/?f=100%5C%25%2B30%5C%25%3D130%5C%25%3D130%2F100%3D1.3)
we know that
Sales 5 years ago, multiplied by the 30% increase should equal 18,000 ice cream cones.
so
The linear equation that represent this problem is
![1.30x=18,000](https://tex.z-dn.net/?f=1.30x%3D18%2C000)
Solve for x
Divide by 1.3 both sides
![x=13,846\ cones](https://tex.z-dn.net/?f=x%3D13%2C846%5C%20cones)
Answer:
The measure of angle AGF is
Step-by-step explanation:
Let
x------> the measure of angle CGD
y------> the measure of angle BGC
we know that
-----> equation A
-----> equation B
Substitute equation B in equation A and solve for y
![y+5\°+y+67\°=180\°](https://tex.z-dn.net/?f=y%2B5%5C%C2%B0%2By%2B67%5C%C2%B0%3D180%5C%C2%B0)
![2y=180\°-72\°](https://tex.z-dn.net/?f=2y%3D180%5C%C2%B0-72%5C%C2%B0)
![2y=108\°](https://tex.z-dn.net/?f=2y%3D108%5C%C2%B0)
![y=54\°](https://tex.z-dn.net/?f=y%3D54%5C%C2%B0)
Find the value of x
The measure of angle CGD is
m<AGF=m<CGD -------> by vertical angles
therefore
The measure of angle AGF is
Answer:
is the answer.
Step-by-step explanation:
Well the first thing we would do is simplify all the exponents first inside the parenthesis. So 2^-3 is equal to 1/8. To solve negative exponents you would just divide the number instead of multiply, so 2 divided by 2 divided by 2 is equal to ⅛ or .125
Next would be to do the 2^-9. This would equal 1/512
Now would be to simplify 5^0. Anything to the power of 0 is always one. So now we simplify all the products meaning 7*5*2 and 7*3.
Now we would simplify both fractions.
The picture are pretty much self explanatory. If you have any questions feel free to ask in the comments - Mark
Also when you have the chance please mark me brainliest.