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SVETLANKA909090 [29]
2 years ago
5

AJKL and ALMN are shown.

Mathematics
1 answer:
seropon [69]2 years ago
7 0

Answer:

mLNM=63

Step-by-step explanation:

triangle JKL is isocelese so mKJL and KLJ are the same

180-72=108

108/2=54

so both mKLJ and mMLN are equal

and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other

so 180-54=126

126/2=63

mLNM=63

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ANSWER FOR BRAINLIEST
tester [92]

The numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

Since a furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week, and each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor, to determine, if a chair yields a profit of $ 65 and a table yields a profit of $ 90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit, the following calculation should be done:

16 chairs; 24 tables

Time used = 16 x 12 + 24 x 15 = 192 + 360 = 552

Wood used = 16 x 8 + 24 x 20 = 128 + 480 = 608  

15 chairs; 18 tables

Time used = 15 x 12 + 18 x 15 = 180 + 270 = 450

Wood used = 15 x 8 + 18 x 20 = 120 + 360 = 480  

12 chairs; 28 tables

Time used = 12 x 12 + 28 x 15 = 144 + 420 = 564

Wood used = 12 x 8 + 28 x 20 = 96 + 540 = 636  

18 chairs; 20 tables

Time used = 18 x 12 + 20 x 15 = 216 + 300 = 516

Wood used = 18 x 8 + 20 x 20 = 144 + 400 = 544

Therefore, the only option that meets the requirements of time and wood used is that of 15 chairs and 18 tables, whose economic benefit will be the following:

15 x 65 + 18 x 90 = X

975 + 1,620 = X

2,595 = X

Therefore, the numbers of chairs and tables that should be produced each week in order to maximize the company's profit is 15 chairs and 18 tables.

7 0
2 years ago
Read 2 more answers
Find an equation of the sphere which contains points A(1, 3, 2) and B(4, 3, 7) and the distance between A and B is equal to the
Marina86 [1]

Answer:

The answer is 8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2

Step-by-step explanation:

First we need to find diameter of the sphere. The distance point A and point B is:

d=\sqrt{(4-1)^2+(3-3)^2+(7-2)^2} \\d=\sqrt{3^2+0^2+5^2} \\d=\sqrt{34} \\d=5.83

d/2=r=2.92

radius of the sphere is 2.92 units

and the center of the sphere is:

C=((4+1)/2,(3+3)/2,(7+2)/2)

C=(2.5,3,4.5)

We can write the equation of the sphere as:

r^2=(x-2.5)^2+(y-3)^2+(z-4.5)^2\\8.5=(x-2.5)^2+(y-3)^2+(z-4.5)^2

4 0
3 years ago
The diagram shows the curve with equation y = ( 1 + x ) cosx.
r-ruslan [8.4K]

Answer:

y = 1, 1.319, 1.024, 0

Step-by-step explanation:

Given equation:

y=(1+x)\cos x

\textsf{when}\:x=0:

\begin{aligned} \implies y & =(1+0)\cos 0\\\implies y & = 1\end{aligned}

\textsf{when}\:x=\dfrac{\pi}{6}:

\begin{aligned} \implies y & =\left(1+\frac{\pi}{6}\right)\cos \left(\frac{\pi}{6}\right)\\\implies y & = 1.319\: \sf (3\:dp)\end{aligned}

\textsf{when}\:x=\dfrac{\pi}{3}:

\begin{aligned} \implies y & =\left(1+\frac{\pi}{3}\right)\cos \left(\frac{\pi}{3}\right)\\\implies y & = 1.024\: \sf (3\:dp)\end{aligned}

\textsf{when}\:x=\dfrac{\pi}{2}:

\begin{aligned} \implies y & =\left(1+\frac{\pi}{2}\right)\cos \left(\frac{\pi}{2}\right)\\\implies y & = 0\end{aligned}

8 0
1 year ago
An equation of the horizontal line that passes through the point (-2,5)
Greeley [361]
Y=5 it's a horizontal lines so b in y=mx+b would have to be 5 and since it's horizonal, it doesn't have a slope so it's just y=5
8 0
3 years ago
Find the population variance of: 4 6 8 9 9 <br><br> round to the nearest hundredth
soldi70 [24.7K]

Answer:

Step-by-step explanation:

To find the population variance, we first need the mean:

\bar{x}=\frac{4+6+8+9+9}{5}=\frac{36}{5}=7.2 so the mean is 7.2. To find the population variance (which is almost exactly the same as the sample variance except for a small difference in the denominators of the formula) we have to take each number minus the mean, and then square the difference. Add together all these squared numbers and then divide by the number of numbers. Like this:

(4-7.2)^2=10.24\\(6-7.2)^2=1.44\\(8-7.2)^2=.64\\(9-7.2)^2=3.24\\(9-7.2)^2=3.24

Add together those numbers and divide them by 5:

\sigma=\frac{10.24+1.44+.64+3.24+3.24}{5}=\frac{18.8}{5}=3.76

5 0
2 years ago
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