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Amanda [17]
3 years ago
14

Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.

Mathematics
1 answer:
sattari [20]3 years ago
3 0

Answer:

x=17

Step-by-step explanation:

Hope this helps

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An open box is to be made out of a 12-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corn
Natali5045456 [20]

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

7 0
2 years ago
Evaluate the expression for the given value of the variable.<br><br> |4b-8|+|-1-b^2|+2b^3;b=2
Elena-2011 [213]

In this question we already know the value of 'b' so put the value b=2 in the equation

=|4(2)-8| + |-1-(2)^2| + 2(2)^3

=|8-8| + |-1-4| + 2(8)

=0 -5 +16

=11

4 0
3 years ago
Apply the distributive property to create an equivalent expression. 12(2a - 6b+ 8) = 2 1 ​ (2a−6b+8)
liberstina [14]

Answer:

a+4=11b

Step-by-step explanation:

Distributive property in mathematics means to multiply the sum by a number of two or more add-ons will provide the same result that each add-on multiplies by a single number and then together add the products.

for example a( b+c) = ab+ac

Therefore, applying distributive property in asked eapression

12(2a - 6b+ 8) = 21(2a−6b+8)

24a+72b+96 = 42a-126b+168

198b=18a+72

9a +36=99b

3a+12=33b

a+4=11b

5 0
3 years ago
Use the distributive property to remove the parentheses.
blagie [28]

Answer:

Step-by-step explanation:

10x^2(3x^2 - 5x)                       Remove the brackets (Distributive Property)

10*3*x^2 * x^2 - 5x * 10x^2

30 x^(2 + 2) - 5*10x^(2+1)

30x^4 - 50x^3

6 0
2 years ago
What is the area of a circle whose radius is 4 ft?
pychu [463]
It would be 50.24 ft
BTW in this case I used 3.14 for pi
5 0
3 years ago
Read 2 more answers
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