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murzikaleks [220]
3 years ago
6

4. Solve the following system of equations for x.

Mathematics
1 answer:
Ber [7]3 years ago
5 0

We are given the system of equations -:

\large{ \begin{cases} 2x + 3y =  - 14 \\ y = 6x + 22 \end{cases}}

Since the second equation is y-isolated equation. It can be substituted as y = 6x+22 in the first equation.

\large{2x + 3(6x + 22) =  - 14}

Expand 3 in the expression so we can combine like terms and isolate x-variable.

\large{2x + 18x + 66 =  - 14}

Then combine like terms.

\large{20x + 66 =  - 14}

Get rid of 66 from the left side by subtracting both sides by itself.

\large{20x + 66 - 66 =  - 14 - 66} \\  \large{20x =  - 80}

To finally isolate the variable, divide both sides by 20 so we can leave x only on the left side.

\large{ \frac{20x}{20}  =  \frac{ - 80}{20} }

Simplify to the simplest form.

\large{x =  - 4}

Normally, we have to find the y-value too but since we only find x-value. The answer is x = -4.

Answer

  • x = -4

I hope this helps! If you have any questions or doubts regarding my answer, explanation or system of equations, feel free to ask!

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Answer:

V ≈ 8.67x10^7 ft^3

Step-by-step explanation:

We know that the volume of a pyramid is V= (lwh)/3

Since it is a square pyramid, it means that the length and the width are the same:

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So, the volume is :

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V = 86736214.158 ft^3

V ≈ 8.67x10^7 ft^3

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Two similar pyramids have base areas of 12.2 cm2 and 16 cm2. The surface area of the larger pyramid is 56 cm2. What is the surfa
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Given =

Two similar pyramid have base area of 12.2 cm² and 16 cm².

surface area of the larger pyramid = 56 cm²

find out the surface area of the smaller pyramid

To proof =

Let us assume that the surface  area of the smaller pyramid be x.

as surface area of the larger pyramid is 56 cm²

Two similar pyramid have base area of 12.2 cm² and 16 cm².

by using ratio and proportion

we have

ratio of the base area of the pyramids : ratio of the surface area  of the pyramids

\frac{12.2}{16} : \frac{x}{56}

x = 12.2 ×56×\frac{1}{16}

by solvingthe above terms

we get

x =42.7cm²

Hence the surface area of the smaller pyramid be 42.7cm²

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