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Komok [63]
3 years ago
12

Mancuso wants to draw a sector whose area is 2 times the area of the sector shown

Mathematics
1 answer:
Alecsey [184]3 years ago
7 0

Answer:

Multiply the radius (r), by 2 then divide the angle measure, x, by 4.

Step-by-step explanation:

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Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Serhud [2]

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

  • Find the mid-point of a diagonal whose endpoints are given
  • Use this mid-point to find the missing vertex
  • The mid point rule is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ x_{1} = -2 and x_{2} = 7

∴ y_{1} = -3 and y_{2} = 7

- Substitute them in the rule of the mid point to find the

   mid-point of XZ

∴ M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ x_{1} = x and x_{2} = 0

∴ y_{1} = y and y_{2} = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ 2.5=\frac{x+0}{2}

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ 2=\frac{y+5}{2}

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

4 0
3 years ago
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the dista
poizon [28]
The rate of Car A is x
The rate of Car B is x - 5

They travel the same distance. So we can make an equation:

4(x) = 4.5(x-5)

Solve for x.

4(x) = 4.5(x-5)
4x = 4.5x - 22.5

Subtract 4.5x on both sides

-0.5x = -22.5

Divide by -0.5 on both sides
x = 45

But we want the speed of Car B which is x - 5

So Car B's speed is 45 - 5 = 40

Your answer is 40
8 0
3 years ago
Use the distributive property to rewrite the expression 4(3.5 + 2.3).
Fed [463]

Step-by-step explanation:

4x 3.5 + 4x 2.3

14 + 9.2

= 23.2

6 0
2 years ago
Read 2 more answers
The small submarine is at –1,320 feet in relation to sea level. The submarine needs to be 180 feet below sea level in 60 minutes
emmainna [20.7K]

Answer:

The first submarine needs to travel at a rate of [-180 – (-1,320)] ÷ 60 = 19 feet per minute.

The second submarine needs to travel at a rate of [-180 – (-1,440)] ÷ 60 = 21 feet per minute.

21 – 19 = 2, so the second submarine must travel 2 feet per minute faster than the first sub.

3 0
3 years ago
Due tomarrow please help!!!!!!!!!!!!!!!!!!!!!!!!! Identify the independent and dependent variables in the following statement. T
miskamm [114]
The independent variable is the rate that water is flowing into the pool, and the dependent variable is the depth of water in the pool.

I believe this would be the case due to the fact that we are not in control of the flow yet the flow impacts the depth. So flow would be independent while the pool depth would be dependent on the rate of flow.
8 0
3 years ago
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