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lara31 [8.8K]
3 years ago
13

Complete the statement of congruence for the triangles.

Mathematics
1 answer:
Hoochie [10]3 years ago
3 0

If you are proving a congruence of triangles then you need to match the corresponding parts to the triangle you are proving congruent.

BAC would then be congruent to MJR because of the corresponding angles

B is the same angle as M

A is the same angle as J

C is the same angle as R

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The straight line with equation y=3/4x makes an acute angle theta with the x-axis.
yanalaym [24]
The angle is arctan(3/4) => sin(2t) = sin(2arctan(3/4)) =
2sin(arctan(3/4))cos(arctan(3/4)) 

Let z = arctan(3/4) => tan(z) = 3/4 

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<span>cos(2t) = cos^2(t) - sin^2(t) = cos^2(z) - sin^2(z) = (4/5)^2 - (3/5)^2 = (16 - 9)/25

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The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500
natali 33 [55]
You did not include the questions, but I will give you two questions related with this same statement, and so you will learn how to work with it.

Also, you made a little (but important) typo.

The right equation for the annual income is: I = - 425x^2 + 45500 - 650000

1) Determine <span>the youngest age for which the average income of a lawyer is $450,000

=> I = 450,000 = - 425x^2 + 45,500x - 650,000

=> 425x^2 - 45,000x + 650,000 + 450,000 = 0

=> 425x^2 - 45,000x + 1,100,000 = 0

You can use the quatratic equation to solve that equation:

x = [ 45,000 +/- √ { (45,000)^2 - 4(425)(1,100,000)} ] / (2*425)

x = 38.29 and x = 67.59

So, the youngest age is 38.29 years

2) Other question is what is the maximum average annual income a layer</span> can earn.

That means you have to find the maximum for the function - 425x^2 + 45500x - 650000

As you are in college you can use derivatives to find maxima or minima.

+> - 425*2 x + 45500 = 0

=> x = 45500 / 900 = 50.55

=> I = - 425 (50.55)^2 + 45500(50.55) - 650000 = 564,021. <--- maximum average annual income
3 0
3 years ago
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