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In circle N, KL ≅ ML. What is the measure of ?

pentagon [3]

This is the concept of geometry, for us to get the value of JM we will requires to get the value of x first;
From the diagram we have been told that;
KL=ML
KL=7x+7
ML=8x-3
thus;
8x-3=7x+7
collecting the like terms we get;
8x-7x=7+3
x=10
But, JM=13x+2
substituting the value of x in JM we get:
JM=13(10)+2
JM=130+2
JM=132
The answer is 132°

3 0

3 years ago

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What is the constant of proportionality between y and x in the graph

VMariaS [17]

Answer:

y/x =2/3

Step-by-step explanation:

you just need see at one point. for example: (3, 2)

4 0

2 years ago

Solve this proportion 9/v = 3/2 a. {6} b. {7.3} c. {4.4} d. {1.3} What percent of 151 is 119.5? a. 129.8% b. 126.4% c. 79.1% d.

Roman55 [17]

V = ( 9*2 ) / 3 ;
v = 18 / 3 ;
v = 6 ;
a. is the right answer;

( 119.5 / 151 ) * 100 = 11950 / 151 = 79.1 ;

The percent is 79.1%;

c. is the right answer;

1 - (40/100)*1 = 1 - 2 / 5 = 3 / 5 = 0.60 ;
d. is the right answer.

6 0

3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago

Compute the number of vinyl tiles, measuring 10 in. each side, needed to tile a kitchen measuring 20 ft. by 16 ft.

weqwewe [10]

(20*16 ft^2)(144 in^2/ft^2)(tiles/(10*10 in^2)

320ft^2(144in^2/ft^2)(tiles/100in^2)=460.8 tiles

However tiles are quantized integer units so 461 tiles will be needed to tile the kitchen.

5 0

3 years ago

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