Answer:
Step-by-step explanation:
Answer:
1) 
2) 
Step-by-step explanation:
Please ignore the squiggle in the middle of the page.
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Answer:
<h2>x = 3</h2>
Step-by-step explanation:
Look at the picture.
We have the triangles 45° - 45° - 90° and 30° - 60° - 90°.
The sides of those triangles are in ratio:
1 : 1 : √2 and 1 : √3 : 2
Therefore
If AC = 6√2 then AB = BC = 6
If BC = 6 then x = 6 : 2 = 3
Answer:
8
Step-by-step explanation:
Let's just call the number x for simplicity.
So, 7x is 8 less than x².
Putting this into an equation would look like this
x² - 8 = 7x
It looks like we'll have to factor this to solve. Before we do that we need to move the 7x to the left side so that everything is together.
x² - 7x -8 = 0
Now, we can proceed. To factor we first need to find the factors of -8.
The factors of -8 are
-2 ⋅ 4, -4 ⋅ 2, -1 ⋅ 8, 1 ⋅ -8.
We need to find the pair of factors that adds up to -7. The only ones that do are -1 and 8.
So now that we have these we can create a pair of binomials using them. This will give us the factored form of this equation.
( x + 1 ) ( x - 8 )
To find the solutions we will have to set them to 0 and solve each of these binomials individually.
x - 1 = 0
x = 1
So, one of the solutions is 1. It's not the one we want, since it's positive.
x - 8 = 0
x = 8
This is the one we want since it is positive.
