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prohojiy [21]
3 years ago
10

Solve each question and check your solution -2(3x-4)=4(x+3)+6

Mathematics
1 answer:
agasfer [191]3 years ago
8 0

Answer:

x = -1

Step-by-step explanation:

-2(3x-4)=4(x+3)+6

Distribute

-6x +8 = 4x +12 +6

Combine like terms

-6x +8 = 4x+18

Add 6x to each side

-6x+6x +8 = 4x+6x +18

8 = 10x+18

Subtract 18 from each side

8-18 =10x+18-18

-10 = 10x

Divide each side by 10

-10/10 = 10x/10

-1 =x

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<h3>Calculate the volume of the sphere</h3>

To start finding the volume of this sphere, we get the following data:

  • π = 3
  • r = 2 ft²

To find the volume we apply the following formula:

  • \boldsymbol{\sf{V= \dfrac{3}{4}\pi r^{2}  }}, where
  • v = volume
  • π  = pi
  • r = radius

We substitute our data in the formula and solve:

Substituting values into the equation

  • \boldsymbol{\sf{V=\dfrac{3}{4}*3*(2 \ ft)^{3}  }}

Calculate exponent cubed

  • \boldsymbol{\sf{V=\dfrac{3}{4}*3*8 \ ft^{3}  }}

Multiplying

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Therefore, the volume of the sphere is 32 ft³.

8 0
2 years ago
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Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them earn up to $400 by payi
LenKa [72]

Answer:

25m + 10b = 400

Step-by-step explanation:

Total amount that can be earned = $ 400

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Amount earned per hour on babysitting = $10

Amount earned for mowing one lawn is $ 25, so amount earned for mowing m lawns will be $ 25m

Amount earned for one hour of babysitting is $ 10, so amount earned for babysitting for b hours will be $ 10b

Total amount earned = Amount earned from mowing m lawns + Amount earned from babysitting for b hours

Using the values from above, we can set up the equation as:

400 = 25m + 10b

or

25m + 10b = 400

This equation represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.

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3 years ago
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Answer:

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Step-by-step explanation:

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To find a unit rate, we divide the quantity of cords of wood by the time.

This gives us the complex fraction.

\frac{ \frac{6}{5} }{ \frac{4}{5} }

This is the same as

\frac{6}{5}  \div  \frac{4}{5}

To divide two fractions, we multiply by the reciprocal of the second fraction.

\frac{6}{5}   \times   \frac{5}{4}

\frac{3}{1}   \times   \frac{1}{2}

This simplifies to:

\frac{3}{2}  = 1 \frac{1}{2}

The unit rate is 1.5 cords per hour

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Answer:

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