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vichka [17]
3 years ago
14

Triangle ABC is translated to create triangle DFG, as shown below.

Mathematics
1 answer:
Anton [14]3 years ago
5 0

Answer:

x=3

y = 9

Step-by-step explanation:

Given

The translated triangles

Required

Find x and y

We have:

AB = DF

BC = FG

AB = DF means:

3(2x + 10) = 12x + 12

Open bracket

6x + 30 = 12x + 12

Collect like terms

12x - 6x = 30 -12

6x = 18

Divide by 6

x=3

BC = FG means

2y + 12 = 2(2y - 3)

Open bracket

2y + 12 = 4y - 6

Collect like terms

4y - 2y = 12+6

2y = 18

Divide by 2

y = 9

You might be interested in
-3 ≤ 6 <br> add 8 to both sides
yawa3891 [41]

Answer:

-3=5

6=14

so it would be 6

Step-by-step explanation:

8 0
2 years ago
A textbook store sold a combined total of 477 sociology and math textbooks in a week. The number of sociology textbois sold was
denpristay [2]

Answer:

The correct answer is 218 math textbooks and 259 sociology textbooks.

Step-by-step explanation:

To solve this problem, we can make a system of equations. Let the number of sociology textbooks sold be represented by the variable "s" and the number of math textbooks sold be represented by the variable "m". Using these variables, we can make two equations:

s + m = 477

m + 41 = s

There are many ways to solve this system of equations. One approach we can take is substituting the value for s given by the second equation into the first equation. This is modeled below.

s + m = 477

(m + 41) + m = 477

Combining like terms on the left side of the equation yields:

2m + 41 = 477

Subtracting 41 from both sides of the equation gives us:

2m = 436

Finally, dividing both sides of the equation by 2 gives us:

m = 218

To solve for the number of sociology textbooks, we can substitute into either of our original equations.

m + 41 = s

(218) + 41 = s

s = 259

Therefore, your answer is m = 218 and s = 259, or 218 math textbooks and 259 sociology textbooks were sold.

Hope this helps!

6 0
3 years ago
The slope of the line in the graph is
gizmo_the_mogwai [7]

Answer:

the slope of the line in the graph is: 3

the y-intercept is: -4

the equation of the line is: y=3x-4

Step-by-step explanation:

If we find a point on the graph and count it until it reaches other solid point we get that you have to go up three and to the right by one. This solid point I looked at was (0,-4) and counted up to (-1,1). To find the slope, we have to simply count and use "rise over run". The rise is 3 for every 1 we run, making the slope 3/1 which is 3.

the y-intercept is the point on the graph that touches the y-axis on the graph. The only point on the graph that touches the y-axis is -4, making the y-intercept -4.

The equation for a graph is y=mx+b. m would be the slope and b would be the y-intercept. We know that the slope is 3 (m) and that the y-intercept is -4 (b). Putting them together, we get that the equation of the graph is y=3x-4.

6 0
3 years ago
At 6 a.m., the temperature was –8°C. By noon, the temperature had risen 6°C. The temperature at 6 p.m. was –10°C. Which integer
Grace [21]
It’s negative 16 so i guess it’s a negative integer
4 0
3 years ago
Read 2 more answers
Find the area of the figure:  Select one: a. 59.5 yd^2 b. 81 yd^2 c. 58.5 yd^2 d. 55.3 yd^2
lions [1.4K]
Answer would be 58.5 yd^2 .

You should take the base of the triangle multiplied by the height.

Formula: 1/2×base×height

In this case, you know that base is 13yd and height is 9 yd.

So, apply the formula.

Area = 1/2(13yd)(9yd) = 58.5 yd^2

*Do not include the " invisible length as it is not part of the actual triangle.

*Do not include 32yd as it is a hypotenuse and not a base. Hypotenuse is a side that is opposite a right angle triangle.
8 0
3 years ago
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