Solve the equation using mental math 6 and 6/7 sequels and + 5and 3/7

in the figure below trianglePQM and triangleQRP are right triangles. the measure of lineQM is 6 and the measure of lineQP is 8.

Kipish [7]

Answer:

Option 4 is correct. The length of PR is 6.4 units.

Step-by-step explanation:

From the given figure it is noticed that the triangle PQR and triangle MQR.

Let the length of PR be x.

Pythagoras formula

$hypotenuse^2=base^2+perpendicular^2$

Use pythagoras formula for triangle PQM.

$PM^2=QM^2+PQ^2$

$PM^2=(6)^2+(8)^2$

$PM^2=36+64$

$PM^2=100$

$PM=10$

The value of PM is 10. The length of PR is x, so the length of MR is (10-x).

Use pythagoras formula for triangle PQR.

$PQ^2=QR^2+PR^2$

$(8)^2=QR^2+x^2$

$64-x^2=QR^2$ .....(1)

Use pythagoras formula for triangle MQR.

$MQ^2=QR^2+MR^2$

$(6)^2=QR^2+(10-x)^2$

$36=QR^2+x^2-20x+100$

$36-x^2+20x-100=QR^2$ .... (2)

From equation (1) and (2) we get

$36-x^2+20x-100=64-x^2$

$20x-64=64$

$20x=128$

$x=6.4$

Therefore length of PR is 6.4 units and option 4 is correct.

3 0

3 years ago

Please help will give brainliest.

Olenka [21]

-1/7 is the correct answer for slope

4 0

2 years ago

Which of the following expressions is 8x + 16 not equivalent

yKpoI14uk [10]

10x-2x-20+4 is incorrect

5 0

3 years ago

In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H? 42°

Vinvika [58]

The complete question is shown in the attached image

Answer:
measure angle H = 42°

Explanation:
There is a theorem that states that:
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"

In the given, we have:
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H

Based on the above rule:
measure angle E = measure angle D + measure angle H

We are given that:
angle E = 87°
angle D = 45°

Substitute with the givens in the above rule and solve for the measure of angle H as follows:
angle E = angle D + angle H
87° = 45° + measure angle H
measure angle H = 87° - 45°
measure angle H = 42°

Hope this helps :)

3 0

3 years ago

Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30 degrees. To the nearest foot,

Firlakuza [10]

The problem says that Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30 degrees. So, you can calculate the height asked, by following this procedure:

Tan(α)=Opposite leg/Adjacent leg

α=30°
Opposite leg=x
Adjacent leg=200 feet

When you substitute these values into the formula above (Tan(α)=Opposite leg/Adjacent leg), you have:

Tan(α)=Opposite leg/Adjacent leg
Tan(30°)=x/200

You must clear "x":

x=200xTan(30°)

Therefore, the value of "x" is:

x=115 feet

How high above the ground the is the helicopter?

The answer is: 115 feet

4 0

3 years ago