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3 years ago

An amusement park wants to install a zipline that is 500 feet long and slopes

Mathematics

1 answer:

Mila [183]3 years ago

8 0

Answer:

Check attachment for solution

Step-by-step explanation:

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1. In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ. Also, AY = 7, BZ = 8, and XZ

Varvara68 [4.7K]

Answer:

Part 1) The perimeter of triangle ABC is 24 units

Part 2) $y=97\°$

Step-by-step explanation:

Part 1) we know that

The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side

see the attached figure to better understand the problem

Applying the midpoint theorem

step 1

Find the value of BC

$BC=\frac{1}{2}XY$

$XY=2AY$ ---> because A is the midpoint

substitute the given value of AY

$XY=2(7)=14\ units$

$BC=\frac{1}{2}(14)=7\ units$

step 2

Find the value of AC

$AC=\frac{1}{2}YZ$

$YZ=2BZ$ ---> because B is the midpoint

substitute the given value of BZ

$YZ=2(8)=16\ units$

$AC=\frac{1}{2}(16)=8\ units$

step 3

Find the value of AB

$AB=\frac{1}{2}XZ$

substitute the given value of XZ

$AB=\frac{1}{2}(18)=9\ units$

step 4

Find the perimeter of triangle ABC

$P=AB+BC+AC$

substitute

$P=9+7+8=24\ units$

Part 2) Find the measure of angle y

step 1

Find the measure of angle z

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

$55\°+42\°+z=180\°$

solve for z

$97\°+z=180\°$

$z=180\°-97\°$

$z=83\°$

step 2

Find the measure of angle y

we know that

$z+y=180\°$ ----> by supplementary angles (form a linear pair)

we have

$z=83\°$

substitute

$83\°+y=180\°$

solve for y

$y=180\°-83\°$

$y=97\°$

6 0

3 years ago

100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −

xxTIMURxx [149]

Let's see

$\\ \rm\rightarrowtail y=6x^2-25x+11$

Graph attached

vertex(-2,-13)

Axis of symmetry

x=-2

7 0

2 years ago

Read 2 more answers

If the minute hand of a clock is 20 degrees behind the hour hand at this moment, then in 18 minutes, the minute hand will be how

Fantom [35]

79 degreeeeeeeeesssss

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3 years ago

Solve for this equation: 500:10||x:50

Y_Kistochka [10]

x=10 and pls give me a thanks

7 0

3 years ago

#7 plz help me!! Need to finish before tmmrw. THANK YOU SOOOO MUCH

Alina [70]

I really hope this is right

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3 years ago