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Gnom [1K]
2 years ago
9

Find the value of x in isosceles trapezoid ABCD Given AC=3x-16 and BD=10x-86

Mathematics
1 answer:
Nastasia [14]2 years ago
7 0
X = 10
(WORK SHOWN BELOW)

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Solve the system by substitution: <br> 3x + 2y = 26<br> Y=x + 3
Orlov [11]

Answer:

x = 4

Step-by-step explanation:

3x + 2y = 26

y = x + 3

Plug in the equation for y

3x + 2(x + 3) = 26

Multiply the 2 with what is in the parantheses

3x + 2x + 6 = 26

Combine like terms and solve for x

5x + 6 = 26

5x = 20

x = 4

5 0
3 years ago
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You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the
Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0
3 years ago
The rule that best supports your answer to Question 5 would be:
mixas84 [53]
Sense the two triangles are congruent you would use CPCTC.
6 0
3 years ago
Which graph best represents the equation x+2y=4
RUDIKE [14]
You didn’t show a picture of the graph, although the equation would be y=-1/2x+2
so every two x spaces forward you should go down one y space and the y should start at 2 when x = 0
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What makes apparent magnitude different from absolute brightness? Give an example in your response.
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Apparent magnitude isn’t the actual brightness, it’s what the brightness appears to be from earth, absolute brightness is the actual brightness an example is our sun it appears bright on earth but in space it is so much more brighter
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