Plz help ASAP!! Explain your answer! I will mark at brainliest!!!

Mathematics

1 answer:

Rina8888 [55]3 years ago

3 0

Answer:

A. 16.12 ft B. 9.64 ft

Step-by-step explanation:

For both of these, you need Pythagorean's Theorem because we have right triangles. In part A, we are given 2 legs and are asked to find the length of the hypotenuse:

$14^2+8^2=PR^2$ and

$196+64=PR^2$

and PR = 16.12 ft

In part B, we are given the length of the hypotenuse and side PQ remains the same:

$14^2+QR^2=17^2$ and

$196+QR^2=289$

$QR^2=289-196$ so

QR = 9.64 ft

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The sum of two numbers is 9 and the sum of their squares is 41. What is the larger number?

Sonbull [250]

The larger number is 5.

<u><em>Explanation</em></u>

Lets assume, the larger number is $a$ and the smaller number is $b$

As the sum of two numbers is 9, so...

$a+b= 9 ...............................(1)$

Now, the sum of their squares is 41, so....

$a^2 + b^2 = 41 .......................................(2)$

First, solving equation (1) for $b$ ....

$b=9-a$

Now, plugging this $b=9-a$ into equation (2) , we will get...

$a^2 +(9-a)^2 = 41\\ \\ a^2 +81-18a+a^2 =41 \\ \\ 2a^2-18a+81 =41 \\ \\ 2a^2-18a+40=0\\ \\ 2(a^2 -9a+20)=0\\ \\ a^2 -9a+20=0\\ \\ (a-5)(a-4)=0\\ \\ a=5,4$