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3 years ago

15

Use the Pythagorean Theorem to find x Round to the nearest tenth?

1 answer:

NemiM [27]3 years ago

6 0

Answer: last option. 9.2

Step-by-step explanation:

The pythagoreon theorm tells us, a^2+b^2 = c^2. We can substitute these values, so 7^2 + 6^2 = x^2 => 49+36 = x^2 => root of 85. The root of 85 is 9.219 something so you can round 9.219 to 9.2.

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Find a polynomial with integer coefficients that satisfies the given conditions.

stepladder [879]

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
\\\\\\
\textit{also recall that }~~~i^2=-1\\\\
-------------------------------\\\\
\begin{cases}
x=5+i\implies &x-5-i=0\\
x=5-i\implies &x-5+i=0
\end{cases}
\\\\\\
(x-5-i)(x-5+i)=\stackrel{\textit{original polynomial}}{0}
\\\\\\\
[(x-5)~~-~~i]~[(x-5)~~+~~i]=0\implies [(x-5)^2~~-~~i^2]=0
\\\\\\
(x^2-10x+25)~~-~~(-1)=0\implies x^2-10x+25+1=y
\\\\\\
x^2-10x+26=y$

8 0

3 years ago

A pump can fill a swimming pool in 8 hours. The pool also has a drain that can empty the pool in 10 hours. If someone turns on t

cluponka [151]

Answer:

40 hours will it take for the pool to fill.

Step-by-step explanation:

A pump can fill a swimming pool in 8 hours.

Work done by pump to fill in 1 hour is $\frac{1}{8}$

The pool also has a drain that can empty the pool in 10 hours.

Work done by pump to drain in 1 hour is $\frac{1}{10}$

If someone turns on the pump to fill the pool, but forgets to shut the drain.

Work done by both pipe in 1 hour is

$W=\frac{1}{8}-\frac{1}{10}$

$W=\frac{10-8}{80}$

$W=\frac{2}{80}$

$W=\frac{1}{40}$

Both pipe filled $\frac{1}{40}$ part of pool in hours = 1

Both pipe filled complete pool in hours = $\frac{1}{\frac{1}{40}}=40$

Therefore, 40 hours will it take for the pool to fill.

7 0

3 years ago

In a game the player wins if he rolls a 6 on a number cube. If the number cube is rolled 18 times, then what is a reasonable pre

SVETLANKA909090 [29]

If the number cube is rolled 18 times, then the number of unsuccessful rolls = 90 unsuccessful rolls.

<u>Step-by-step explanation</u>:

<u>step 1</u>: A cube has six faces and each face is numbered from 1 to 6.

<u>step 2</u>: The win in the game requires the number 6, when a cube is rolled.

<u>step 3</u>: On rolling a cube, the outcomes are (1,2,3,4,5, and 6).

<u>step 4</u>: Out of these outcomes, 5 are unsuccessful rolls (1,2,3,4,5) and 1 is a successful roll (6).

<u>step 5</u>: If the cube is rolled 18 times,

then the number of unsuccessful rolls = 18 * 5 unsuccessful rolls

= 90 unsuccessful rolls.

8 0

3 years ago

Find the area of a triangle with sides 8 equals 5 b equals 8 and C equals 11

IceJOKER [234]

I round the answer to the second digit and get 18.33

4 0

4 years ago

Let x²y +ay² = b be an Implicitly defined function, where a and b are fixed Constants; find dy/dx

geniusboy [140]

The value of the differential with respect to x is -xy/x²+ay

<h3>Implicit differentiation</h3>

Given the following function

x²y +ay² = b

We are to differentiate implicitly with respect to x

x²dy/dx + 2xy + 2aydy/dx = 0

(2x²+2ay)dy/dx = -2xy
dy/dx = -xy/x²+ay

Hence the value of the differential with respect to x is -xy/x²+ay

Learn more on implicit differentiation here: brainly.com/question/25081524

#SPJ1

3 0

2 years ago