Astudent's work to solve an equation is shown.
1/8(40x+16)=9x−7(2x−1)−5 5x+2=9x−14x+7−5 5x+2=5x+2 2=2
the student solved the equation because the original equation has solution(s).
select the options that makes the above statements true.
question 5 options:
correctly
incorrectly
no solution
one solution
infinitely many solutions

the student solved the equation incorrectly because the original equation has one solution

Step-by-step explanation:

1/8(40x + 16) = 9x − 7(2x − 1) − 5

use the distributive property a(b + c) = ab + ac

(1/8)(40x) + (1/8)(16) = 9x + (-7)(2x) + (-7)(-1)

5x +2 = 9x − 14x + 7 − 5       combine like terms

5x + 2 = (9x - 14x) + (7 - 5)

here the student make mistake 9x - 14x = 5x

5x+2=-5x+2    add 5x to both sides and subtract 2 from both sides

5x + 5x + 2 - 2 = -5x + 5x + 2 - 2

10x = 0          divide both sides by 10

10x/10 = 0/10

x = 0

any options?

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1