Answer:
500 pts :DDDD
Step-by-step explanation:
1 ) y = mx + b
hmmm 2 is wrong
2) y = -a
+bx+c
I'm unsure about 3 also hmm
3) y = a![x^{y}](https://tex.z-dn.net/?f=x%5E%7By%7D)
In order to get an 81 average,
the student has to get 81x5=405
71+96+90+73+?=405
330+?=405
405-330=75
he needs to get an 75
Answer:
-1/2
Step-by-step explanation:
y = mx + c
y = -1/2x + 3 (rearranged from question)
slope = m
To solve an absolute value equation of the form |X| = k, where X is an expression with a variable and k is a non-negative number or an expression, you must solve the compound equation X = k or X = -k.
The first step is to divide both sides by 9 to get the absolute value of an expression equal to a non-negative number.
9|9 – 8x| = 2x + 3
Divide both sides by 9.
![|9 - 8x| = \dfrac{2x + 3}{9}](https://tex.z-dn.net/?f=%20%7C9%20-%208x%7C%20%3D%20%5Cdfrac%7B2x%20%2B%203%7D%7B9%7D%20)
Now we eliminate the absolute value by rewriting this as a compound equation.
![9 - 8x = \dfrac{2x + 3}{9} ~~~or~~~ 9 - 8x = -\dfrac{2x + 3}{9}](https://tex.z-dn.net/?f=%209%20-%208x%20%3D%20%5Cdfrac%7B2x%20%2B%203%7D%7B9%7D%20~~~or~~~%209%20-%208x%20%3D%20-%5Cdfrac%7B2x%20%2B%203%7D%7B9%7D%20)
We must solve both equations.
Multiply both sides by 9.
![9(9 - 8x) = 2x + 3 ~~~or~~~ 9(9 - 8x) = -(2x + 3)](https://tex.z-dn.net/?f=%209%289%20-%208x%29%20%3D%202x%20%2B%203%20~~~or~~~%209%289%20-%208x%29%20%3D%20-%282x%20%2B%203%29%20)
![81 - 72x = 2x + 3 ~~~or~~~ 81 - 72x = -2x - 3](https://tex.z-dn.net/?f=%2081%20-%2072x%20%3D%202x%20%2B%203%20~~~or~~~%2081%20-%2072x%20%3D%20-2x%20-%203%20)
![-74x = -78 ~~~or~~~ -70x = -84](https://tex.z-dn.net/?f=%20-74x%20%3D%20-78%20~~~or~~~%20-70x%20%3D%20-84%20)
![x = \dfrac{-78}{-74} ~~~or~~~ x = \dfrac{-84}{-70}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B-78%7D%7B-74%7D%20~~~or~~~%20x%20%3D%20%5Cdfrac%7B-84%7D%7B-70%7D%20)
![x = \dfrac{39}{37} ~~~or~~~ x = \dfrac{6}{5}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B39%7D%7B37%7D%20~~~or~~~%20x%20%3D%20%5Cdfrac%7B6%7D%7B5%7D%20)
Answer: x = 39/37 or x = 6/5
To check for extraneous solutions, we plug in each solution into the original equation and check if it works.
Check 39/37:
9|9 – 8(39/37)| = 2(39/37) + 3
|81 - 72(39/37)| = 78/37 + 3
|2997/37 - 2808/37| = 78/37 + 111/37
|189/37| = 189/37
189/37 = 189/37
The solution 39/37 is valid.
Check x = 6/5.
9|9 – 8x| = 2x + 3
9|9 – 8(6/5)| = 2(6/5) + 3
|81 - 72(6/5)| = 12/5 + 15/5
|405/5 - 432/5| = 27/5
|-27/5| = 27/5
27/5 = 27/5
The solution x = 6/5 is also valid.
There are no extraneous solutions.