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elena-14-01-66 [18.8K]
3 years ago
9

Please Help!!!!! Which method can you use to prove these triangles congruent?

Mathematics
1 answer:
Trava [24]3 years ago
6 0

Answer: The HL Theorem.

Step-by-step explanation: We are given that the triangles have a congruent 90 degree angle and two congruent sides. This would indicate towards SAS but in this case, that doesn't work because the angle is not in between the two congruent sides. We know that the triangles are right, and that their hypotenuses are congruent and that one leg is congruent. Thus, the answer must be HL (hypotenuse & leg).

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Based on the data given in the picture, calculate the area of the car track...
Verizon [17]

Refer to the diagram below. We need to find the areas of the green and blue regions, then subtract to get the area of the orange track only.

The larger green region is composed of a rectangle of dimensions 200 meters by 4+42+4 = 50 meters, along with two semicircles that combine to make a full circle. This circle has radius 25 meters.

The green rectangle has area 200*50 = 10000 square meters. The green semicircles combine to form an area of pi*r^2 = pi*25^2 = 625pi square meters. In total, the full green area is 10000+625pi square meters. I'm leaving things in terms of pi for now. The approximation will come later.

The blue area is the same story, but smaller dimensions. The blue rectangle has dimensions 200 meters by 42 meters, so its area is 200*42 = 8400 square meters. The blue semicircular pieces combine to a circle with area pi*r^2 = pi*21^2 = 441pi square meters. In total, the blue region has area 8400+441pi square meters.

After we figure out the green and blue areas, we subtract to get the orange region's area, which is the area of the track only.

orange area = (green) - (blue)

track area = (10000+625pi) - (8400+441pi)

track area = 10000+625pi - 8400-441pi

track area = (10000-8400) + (625pi - 441pi)

track area = 184pi + 1600 is the exact area in terms of pi

track area = 2178.05304826052 is the approximate area when you use the pi constant built into your calculator. If you use pi = 3.14 instead, then you'll get 2177.76 as the approximate answer. I think its better to use the more accurate version of pi. Of course, be sure to listen/follow your teachers instructions.

4 0
3 years ago
What is the equation of a line that passes through point R(−4, −3) and has a slope of 7?
Ymorist [56]
M = 7 is the given slope
(x,y) = (-4,-3) is the given point

Turn to slope-intercept form and use these values to find b

y = mx+b
-3 = 7(-4)+b ... plug in the given values
-3 = -28+b
-3+28 = -28+b+28
25 = b
b = 25

since we know that m = 7 and b = 25, the equation y = mx+b turns into y = 7x+25

The final answer is choice A

6 0
3 years ago
Please help! Change 3/8 to a decimal fraction.
arsen [322]

Answer:

0.375

Step-by-step explanation:

0.125 x 3 = 0.375

6 0
3 years ago
Read 2 more answers
HELP FAST 100 POINTS <br> MUCH SHOW WORK
Svet_ta [14]

Step-by-step explanation:

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5 0
3 years ago
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Find all exact solutions that exist on the interval [0, 2π).<br> 1 − 2 tan(ω) = tan2(ω)<br><br> w =
Fofino [41]

A possible solution: First add 1 to both sides and reduce the RHS via the Pytagorean identity.

1-2\tan\omega=\tan^2\omega\implies2-2\tan\omega=1+\tan^2\omega=\sec^2\omega

Rewrite \tan and \sec in terms of \sin and \cos:

\implies2\left(1-\dfrac{\sin\omega}{\cos\omega}\right)=\dfrac1{\cos^2\omega}

Multiply both sides by \cos^2\theta:

\implies2(\cos^2\omega-\sin\omega\cos\omega)=1

\implies2\cos^2\omega-1=2\sin\omega\cos\omega

Use the double angle identities:

\implies\cos2\omega=\sin2\omega

Divide both sides by \cos2\omega:

\implies1=\dfrac{\sin2\omega}{\cos2\omega}=\tan2\omega

Now, \tan2\omega=1 for 2\omega=\dfrac\pi4+n\pi, or \omega=\dfrac\pi8+\dfrac{n\pi}2, where n is any integer. \omega will fall in the interval [0,2\pi) for n=1,2,3,4, which means we have

\omega=\dfrac\pi8,\dfrac{5\pi}8,\dfrac{9\pi}8,\dfrac{13\pi}8

6 0
3 years ago
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