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xenn [34]
3 years ago
12

Use the distributive property to write an expression that is equivalent to each given property.

Mathematics
1 answer:
Nadya [2.5K]3 years ago
3 0

Answer:

-6x+12

-9+5a

7x+63

8y-4/5x-12

Step-by-step explanation:

To solve these all you have to do is take the number outside of the parenthesis and multiply them by each term.

-3(2x)-3(-4) All I did here was expand the problem to show what i mean by terms.

-6x+12

Do this for each problem.

0.1(-90)+0.1(50a)

-9+5a

-7(-x)-7(-9) For this one you are taking negatives times negatives so each answer will be positive.

7x+63

4/5(10y)+4/5(-x)+4/5(-15)

8y-4/5x-12

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If the parallelogram is dilated by a factor V what is the new area​
Dahasolnce [82]

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Area V

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by
a_sh-v [17]

Answer:

Dimension of the box is 16.1\times 7.1\times 2.45

The volume of the box is 280.05 in³.

Step-by-step explanation:          

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the box?

Solution :

Let h be the height of the box which is the side length of a corner square.

According to question,

A sheet of cardboard 21 in. by 12 in. by cutting congruent squares from the corners and folding up the sides.

The length of the box is L=21-2h

The width of the box is W=12-2h

The volume of the box is V=L\times W\times H

V=(21-2h)\times (12-2h)\times h

V=(21-2h)\times (12h-2h^2)

V=252h-42h^2-24h^2+4h^3

V=4h^3-66h^2+252h

To maximize the volume we find derivative of volume and put it to zero.

V'=12h^2-132h+252

0=12h^2-132h+252

Solving by quadratic formula,

h=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

h=\frac{-(-132)\pm\sqrt{132^2-4(12)(252)}}{2(12)}

h=\frac{132\pm72.99}{24}

h=2.45,8.54

Now, substitute the value of h in the volume,

V=4h^3-66h^2+252h

When, h=2.45

V=4(2.45)^3-66(2.45)^2+252(2.45)

V\approx 280.05

When, h=8.54

V=4(8.54)^3-66(8.54)^2+252(8.54)

V\approx -170.06

Rejecting the negative volume as it is not possible.

Therefore, The volume of the box is 280.05 in³.

The dimension of the box is

The height of the box is h=2.45

The length of the box is L=21-2(2.45)=16.1

The width of the box is W=12-2(2.45)=7.1

So, Dimension of the box is 16.1\times 7.1\times 2.45

6 0
3 years ago
What is the lcm and gcf of 36 and 45
Rina8888 [55]
I got your answer! I will tell you right now. Your GCF is 9 and your LCM is 180! Your very much welcome!! Good luck for you! :)
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3 years ago
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