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topjm [15]
3 years ago
6

What is the value of y in the solution to the following system of equations ?

Mathematics
1 answer:
Katen [24]3 years ago
4 0
We can use substitution method to solve for this system of equations. We calculate as follows:

<span>2x – 6y = –14
-6y = -14 -2x
y = x/3 + 7/3

 </span>5x – 3y = –11
 5x – 3(x/3 + 7/3) = –11
5x - x + 7 = -11
4x = -11 -7
4x = -18
x = -9/2
y = -9/2(3) + 7/3
y = 5/6
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Find the area of the composite figure​
ehidna [41]
<h3>62.5 cm^2</h3>

The figure is a trapezoid, albeit not possessing the same lengths for the left and right sides. If I'm not mistaken, it has another name or term. But I forgot.

Anyway, to solve the problem, let us chop-chop or break the figure into two parts or two polygons that we are familiar with - a rectangle and a triangle. See the attached image for a clearer presentation.

After breaking the original polygon into two parts as portrayed by the red broken line, we are also going to divide the equivalent value of each side.

Remember, a rectangle has two pairs of common sides. Since the upper side of the polygon has a length of 10 cm, then, the length of the lower side (the side at the left side of the broken line) is 10, too. The same goes for the length of the left side which is 5 cm, and therefore the length of the broken line is 5 cm. Please refer to the attached image, particularly the figures in green.

From the standpoint of the triangle, based on thee figure, it has a height of 5 cm and a base of 5 cm (15 cm- 10 cm). Did you get it? If yes, let's continue.

Solving Time! :D

1. Solve for the area of the rectangle.

\begin{gathered}A_{rectangle}=L\times W\\=5\ cm \times 10\ cm\\=\bold{50\ cm^2}\end{gathered}

Arectangle=L×W=5 cm×10 cm=50 cm²

2. Solve for the area of the triangle.

\begin{gathered}A_{triangle}=\dfrac{b\times h}{2}\\=\dfrac{5\ cm\times5\ cm}{2}\\=\dfrac{25\ cm^2}{2}\\=\bold{12.5\ cm^2}\end{gathered}

Atriangle=2b×h=25 cm×5 cm=225 cm²=12.5 cm²

3. Combine (add) the two areas to find the area of the original figure.

\begin{gathered}A_{composite\ figure}=A_{rectangle}+A_{triangle}\\=50\ cm^2 +12.5\ cm^2\\=\bold{62.5\ cm^2}\end{gathered}

Acomposite figure=Arectangle+Atriangle=50 cm²+12.5 cm2=62.5 cm

If there's a Latex Error, Please click the second image attached below :)

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2 years ago
Spencer rolled a number cube 50 times and recorded the results in this table. Outcome Number 1 8 2 10 3 7 4 7 5 9 6 9 What is th
hram777 [196]
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5 0
3 years ago
The equation 9 y minus 6 x = 36 is written in standard form. What is the first step when writing an equivalent equation which so
enot [183]

Answer:

D. Subtract 9y from both sides of the equation.

Step-by-step explanation:

A. Divide both sides of the equation by 36.

B. Multiply both sides of the equation by 6.

C. Add 9y to both sides of the equation.

D. Subtract 9y from both sides of the equation.

Given:

9y - 6x = 36

To solve for x

Step 1: subtract 9y from both sides

9y - 6x - 9y = 36 - 9y

- 6x = 36 - 9y

Step 2: Divide both sides by -6

- 6x / -6 = (36 - 9y) / - 6

x = (36 - 9y) / - 6

The answer is

x = (36 - 9y) / - 6

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I hope this is helpful

8 0
3 years ago
I need this question sovled asap y=200x+35,000
Svetradugi [14.3K]

Answer: look at the picture

Step-by-step explanation: Hope this help :D

6 0
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