Mathematics, 26.10.2021 21:40 erica11223344

I need help please thank you

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Answer from: jacckiie4069

b = 12

Step-by-step explanation:

hi! so this looks like a right triangle because it has a right angle which is 90 degrees! that means we can use the Pythagorean theorem to solve for the missing leg.

The Pythagorean theorem: $a^{2} + b^{2} = c^{2}$

a and b will be the two shorter legs, so it does not matter which of the two legs are which! in this problem, 5 and b (the missing leg) are the two shorter legs! c is always the hypotenuse, which is the sloped-looking line. in this problem, 13 is the hypotenuse! this line is the longest side on every right triangle!

Let's solve for the missing leg now!

1) first, we need to plug in the missing numbers into the equation

$5^{2} + b^{2} = 13^{2}$

2) next, let's simplify the problem

$25 + b^{2} = 169$

3) now, let's isolate the variable, b

$b^{2} = 144$

4) finally, we have to take the square root of b so it will be b not $b^{2}$

b = 12

Let's plug in our answer to the equation to check if it is correct!

$5^{2} + 12^{2} = 13^{2}$

25 + 144 = 169

169 = 169 hooray!

you do not have to do all of this work if you memorize the Pythagorean triples!

(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) , (9, 40, 41)these are automatic matches! for example: $3^{2} + 4^{2} = 5^{2} -- 9 + 16 = 25 -- 25 = 25$

comment or message if you have any questions :)

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

answer: ur v dumb

step-by-step explanation:

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