-4(1 -6b) - 5 ( 2b - 6)= 8b - 7b

Mathematics

2 answers:

Citrus2011 [14]3 years ago

5 0

The answer is b=-2 Hope that helps!!

aksik [14]3 years ago

4 0

-4(1-6b)-5(2b-6)=8b-7b

We move all terms to the left:

-4(1-6b)-5(2b-6)-(8b-7b)=0

We add all the numbers together, and all the variables

-4(-6b+1)-5(2b-6)-(+b)=0

We multiply parentheses

24b-10b-(+b)-4+30=0

We get rid of parentheses

24b-10b-b-4+30=0

We add all the numbers together, and all the variables

13b+26=0

We move all terms containing b to the left, all other terms to the right

13b=-26

b=-26/13

b=-2

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I'm guessing that you know about 45-45-90 and 30-60-90 triangles.

In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is $\sqrt{2}$ times the legs.

In 30-60-90 triangles, the legs are in a ratio of 1: $\sqrt{3}$ :2

In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9 $\sqrt{2}$ because of the ratio of the sides of a 45-45-90 triangle.

The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is $\sqrt{3}$ : 2

We can create an equation to solve for x using these ratios:

$\frac{\sqrt{3} }{2}$ = $\frac{x}{9\sqrt{2} }$