If y varies directly as x, and y = 25 when x = 5, find y when x = 25.

Mathematics

2 answers:

s344n2d4d5 [400]3 years ago

8 0

It would be 125 so A

dezoksy [38]3 years ago

5 0

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ \rule{31em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} y=25\\ x=5 \end{cases}\implies 25=k5\implies \cfrac{25}{5}=k \\[2em] 5=k\hspace{20em}\boxed{y=5x} \\[2em] \textit{when x = 25, what is \underline{y}?}\qquad y=5(25)\implies y=125$

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If G = {(-1, 7),(-8, 2),(0, 0),(6, 6)), then the range of G is

lana66690 [7]

Answer:

$\{0, 2, 6, 7\}$

Step-by-step explanation:

You are given the relation $G = \{(-1, 7),(-8, 2),(0, 0),(6, 6)\}$

This means that

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The input values of this relation are $-1,\ -8,\ 0,\ 6$ , so the domain of this relation is $\{-8,-1,0,6\}$

The output values of this relation are $7,\ 2,\ 0,\ 6$ , so the range of this relation is $\{0, 2, 6, 7\}$

8 0

3 years ago

How to solve this :') please help

blsea [12.9K]

Answer:

3/2

Step-by-step explanation:

sin(3π/4 - β) = sin(3π/4)cosβ - cos(3π/4)sinπ =

$\sin(\frac{3\pi}{4}-\beta)=\sin(\frac{3\pi}{4})\cos\beta-\cos\frac{3\pi}{4}\sin\beta\\=\frac{1}{\sqrt{2}}\cos\beta-(-\frac{1}{\sqrt{2}})\sin\beta\\\\=\frac{1}{\sqrt{2}}(\cos\beta +\sin\beta)\\\\\sin^2(\frac{3\pi}{4}-\beta)=\frac{1}{2}\cos\beta +\sin\beta)^2=\frac{1}{2}(\cos^2\beta +\sin^2\beta+2\sin\beta\cos\beta\\=\frac{1}{2}(1+\sin2\beta)=\frac{1}{2}(1-\frac{1}{5}) = \frac{2}{5}\\$