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2 years ago

Simplify: ? (10x = 105 - (12x – 247)

Mathematics

1 answer:

Greeley [361]2 years ago

7 0

Answer:

x = 16

Step-by-step explanation:

10x = 105 - (12x - 247) //Distribute - sign

10x = 105 - 12x + 247 // Add 12x & combine like terms

10x + 12x = 352

22x = 352 //Divide 22

x = 352/22

x = 16

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You use 4 gallons of water on 30 plants in your garden. At that rate, how much water will it take to water 45 plants?

Wewaii [24]

Write a proportion like so:

4 gallons/30 plants= x gallons/45 plants

Cross multiply to find the value of x
4*45= 180
180/30= 6=x

Final answer: 6 gallons

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2 years ago

Read 2 more answers

Use the box method to distribute and simplify (-5x-2)(-2x^2+6x).

Mkey [24]

Answer:

$10x^{3} - 26x^{2} - 12x$

Step-by-step explanation:

1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd.

$10x^{3} - 30x^{2} + 4x^{2} -12x$

2) Collect like terms.

$10x^{3} + (-30x^{2} +4x^{2} )-12x$

3) Simplify.

$10x^{3} - 26x^{2} -12x$

Therefor, the answer is, 10x^3 - 26x^2 - 12x.

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2 years ago

An ice cream store has the pricing shown below. You want to determine the best value. The height of the cone is 4.5 in and the d

nignag [31]

Solution:

Step 1:

We will calculate the volume of ice cream in the single scoop

The volume of the ice cream will be

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{2}{3}\pi r^3 \\ r=\frac{2in}{2}=1in(cone) \\ h=4.5in \\ r=\frac{3in}{2}=1.5in(radius\text{ of the hemisphere\rparen} \end{gathered}$

By substituting the values, we will have

$\begin{gathered} V=\frac{1}{3}\pi r^{2}h+\frac{2}{3}\pi r^{3} \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+\frac{2}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{14} \\ V=\frac{165}{14} \\ V=11.79in^3 \end{gathered}$

Step 2:

We will use the formula below to calculate the volume of the two scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{4}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5in+\frac{4}{3}\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{99}{7} \\ V=\frac{132}{7} \\ V=18.86in^3 \end{gathered}$

Step 3:

We will use the formula below to calculate the volume of the three scoops of ic cream

$\begin{gathered} V=\frac{1}{3}\pi r^2h+\frac{6}{3}\pi r^3 \\ V=\frac{1}{3}\times\frac{22}{7}\times1^2\times4.5+2\times\frac{22}{7}\times1.5^3 \\ V=\frac{33}{7}+\frac{297}{14} \\ V=\frac{363}{14} \\ V=25.93in^3 \end{gathered}$

For the first ice cream with one scoop

$\begin{gathered} 1in^3=\frac{3.50}{11.79} \\ 1in^3=\text{ \$}0.30 \end{gathered}$

For the second ice cream with two scoops

$\begin{gathered} 1in^3=\frac{4.50}{18.86} \\ 1in^3=\text{ \$}0.24 \end{gathered}$

For the third ice cream with three scoops

$\begin{gathered} 1in^3=\frac{5.50}{25.93} \\ 1in^3=\text{ \$}0.21 \end{gathered}$

Hence,

The final answer is

The triple sold at $5.50 has the best value because it has the lowest price of $0.21 per cubic inch of the ice cream

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7 months ago

A bakery offers a sale price of $3.45 for 4 muffins. What is the price per dozen?

Vlad [161]

Answer:

Cost of 4 muffins = $3.45

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Step-by-step explanation:

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2 years ago

A car is traveling at 45mph. What is the equation that models the total distance d traveled after h. What is the graph of the eq

Ostrovityanka [42]

D=45h

For example: 45mph times 2 hours equals 90 miles traveled

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2 years ago

Simplify: ? (10x = 105 - (12x – 247)​

Simplify: ? (10x = 105 - (12x – 247)