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3 years ago

In the figure, AB = 15.8, 11.9 10.2, 8.4 inches and AC = 18.7, 15.5, 14.3, 13.1 inches.

Mathematics

1 answer:

TEA [102]3 years ago

7 0

Tan=oposite/adjacent=AB/BC
tan(40)=AB/10
10tan(40)=AB≈8.391
so AB=8.4

use pythagorean theorem to find the hypotnhuse

reemember
a²+b²=c²
so
10²+8.4²=c²
100+70.56=c²
170.56=c²
sqrt both sides
13.0599=c so 13.1

AB=8.4 inches
AC=13.1 inches

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Let's start by using distributive multiplication:

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$15x^2 +(35x-12x)-28\\\\15x^2+23x-28$

Now, $15x^2+23x-28$ is equal to:

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In this sense:

$15x^2+23x-28=15x^2-ax-b$

In order to satisfied the equality:

$23x=-ax\hspace{10}(1)\\\\and\\\\-28=-b\hspace{10}(2)$

Hence, from (1), let's solve for a:

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And from (2), let's solve for b:

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Let's verify the result evaluating the values of a and b into the original equation:

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As you can see, the values satisfy the equation, therefore, we can conclude they are correct.

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