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egoroff_w [7]
4 years ago
7

Sam wants to install a zip line across a ravine. One side is of the ravine is 45 feet tall while the other side is 65 feet. If t

he ravine is 21 feet wide how long must the zip line be?
Mathematics
1 answer:
Umnica [9.8K]4 years ago
6 0
The difference of the heights is 65-45=20 feet, and the length of the ravine is 21 feet.  By the Pythagorean Theorem, the length of the zipline is sqrt(20^2+21^2)=sqrt(841)=29.
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Suppose KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. Prove that A is equidistant from LM and KN.
Neporo4naja [7]

Answer:

This is proved by ASA congruent rule.

 Step-by-step explanation:

Given KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. we have to prove that A is equidistant from LM and KN i.e we have to prove that AP=AQ

we know that the diagonals of parallelogram bisect each other therefore the the bisectors of ∠K and ∠L must be the diagonals.

In ΔAPN and ΔAQL

∠PNA=∠ALQ    (∵alternate angles)  

AN=AL   (∵diagonals of parallelogram bisect each other)

∠PAN=∠LAQ      (∵vertically opposite angles)

∴ By ASA rule ΔAPN ≅ ΔAQL

Hence, by CPCT  i.e Corresponding parts of congruent triangles PA=AQ

Hence, A is equidistant from LM and KN.

7 0
3 years ago
How can you use a scatter plot to find a trend line
Marina CMI [18]
It helps you determine the characteristics of the plot/graph. I am not sure so it is your choose.
8 0
3 years ago
MATH QUESTION!! WILL MARK BRAINLIEST!! PAST DUE HELP ASAP!!!
monitta

Answer:

<em>Proof below</em>

Step-by-step explanation:

<u>Right Triangles</u>

In any right triangle, i.e., where one of its internal angles is 90°, some interesting relations stand. One of the most-used is Pythagora's Theorem.

In a right triangle with shorter sides a and b, and longest side c, called the hypotenuse, the following equation is satisfied:

c^2=a^2+b^2

The image provided in the question shows a line passing through points A(0,4) and B(3,0) that forms a right triangle with both axes.

The origin is marked as C(0,0) and the point M is the midpoint of the segment AB. We have to prove.

CM=\frac{1}{2}AB

First, find the coordinates of the midpoint M(xm,ym):

\displaystyle x_m=\frac{0+3}{2}=1.5

\displaystyle y_m=\frac{4+0}{2}=2

Thus, the midpoint is M( 1.5 , 2 )

Calculate the distance CM:

CM=\sqrt{(1.5-0)^2+(2-0)^2}

CM=\sqrt{2.25+4}=\sqrt{6.25}=2.5

CM=2.5

Now find the distance AB:

AB=\sqrt{(3-0)^2+(4-0)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}

AB=5

AB/2=2.5

It's proven CM is half of AB

3 0
3 years ago
In order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for
Korolek [52]

Answer:

Step-by-steIn order to go to college, Chris goes from working full-time making $30,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000. If Chris makes $35,000 per year after getting his degree, approximately how many years will it take him to recover his investment? *

it would take him 7 years to recover the 35,000 he invested

p explanation:

he was in college two years and it cost him a total of 5000 and he lost 30000 from the two years he worked part time

6 0
3 years ago
In a box of 500 colored balls, 75 are black, 150 are green, 175 are red, 70 are white, and 30 are blue. what are the probabiliti
Oksanka [162]
If we want to select a ball of each colour we have to extract 175+150+75+70+1=471 balls

P=471/500 is the answer
4 0
3 years ago
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