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Yuki888 [10]
3 years ago
14

The area of a rectangular patio is 27 5 8 square meters. The width of the patio is 3 1 4 meters. What is the length? Enter your

answer as a mixed number in simplest form.
Mathematics
1 answer:
DedPeter [7]3 years ago
8 0

Answer:

Step-by-step explanation:

L and W are length and width, respectively.

W = 3¼ = 13/4

Area = LW = 27⅝ = 221/8 m²

L = area/W = (221/8)/(13/4) = (221/8)(4/13) + 221/26 = 17/2 = 8½ m

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General solutions of sin(x-90)+cos(x+270)=-1<br> {both 90 and 270 are in degrees}
mixer [17]

Answer:

\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.

Step-by-step explanation:

Given:

\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1

First, note that

\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x

So, the equation is

-\cos x+\sin x= -1

Multiply this equation by \frac{\sqrt{2}}{2}:

-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}

The general solution is

x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.

4 0
3 years ago
The next model of a sports car will cost 12.7% less than the current model. The current model costs $49,000 . How much will the
Wittaler [7]
Percentage of a number.

$49,000 x .127 = $6,223 is the decrease
$49,000 - $6,223 = $42,777
4 0
2 years ago
Read 2 more answers
Which equation represents a function?
Maurinko [17]

All the answers except C has a Vertical Line when graphed. It must pass the Vertical line test in order to be a function.

Vertical Line Test: If you can draw a vertical line anywhere on a graph so that it hits the graph in more  than one spot, then the graph is NOT a function.

C.) can pass the test since it's a horizontal line.

Hope this helps!

6 0
2 years ago
What is 2/3 of the distance between the points U (-1,4) and B (8,5)
BlackZzzverrR [31]

Answer:

<h2>         6.037</h2>

Step-by-step explanation:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\U (-1,4)\quad\implies\quad x_1=-1\,,\ \ y_1=4 \\\\B (8,5)\quad\implies\quad x_2=8\,,\ \ y_2=5\\\\\frac12d=\frac23\sqrt{(8+1)^2+(5-4)^2}=\frac23\sqrt{81+1}=\frac23\sqrt{82}\approx6.037

7 0
3 years ago
How to solve and the answer
algol13

A reciprocal just flips the fraction

1. \frac{4}{3}

2.\frac{11}{1}

3. Before it is flipped it is \frac{9}{1} but it turns into \frac{1}{9}


Hope this helps!

6 0
2 years ago
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