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Flauer [41]
2 years ago
13

PLEASE HELP OMG!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
Monica [59]2 years ago
3 0

Answer:

D. (14, 10)

Step-by-step explanation:

Let's use the first equation for this

x = y + 4

Meaning whatever values we are given, x has to be the value of y + 4

So if the y value is 1, the x value has to be 5

A. (6, 10) | 10 + 4 is not 6

B. (9, 5) | 5 + 4 is 9

B is a possible answer

C. (10, 6) | 6 + 4 is 10

C is also a possible answer

D. (14, 10) | 10 + 4 is 14

D is also a possible answer

After going off of the first equation we realize that all of them are possible answers with exception of A, and now we have to base ourselves off of the 2nd equation

2x - 3y = -2

Let's try with B first

2(9) - 3(5) = -2

18 - 15 = -2

B is not the correct answer since 18 - 15 = 3 and not -2

Let's try with C now

2(10) - 3(6) = -2

20 - 18 = -2

C is not the correct answer since 20 - 18 = 2 and not -2

Let's try with D now

2(14) - 3(10) = -2

28 - 30 = -2

D is the correct answer because 28 - 30 = -2

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In triangle KLM, if K is congruent to L, KL = 9x - 40, LM = 7x - 37, & KM = 3x + 23, find x & the measure of each angle.
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Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°

<u>Step-by-step explanation:</u>

Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL

 KM ≅ LM

3x + 23 = 7x - 37

       23 = 4x - 37

       60 = 4x

        15 = x

KM = LM = 3x + 23

               = 3(15) + 23

               = 45 + 23

               = 68

KL = 9x - 40

    = 9(15) - 40

    = 135 - 40

    = 95

Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.

  • Since N is the midpoint of KL and KL = 95, then NL = 47.5
  • Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse

Use trig to solve for ∠L (which equals ∠K):

cos ∠L = \frac{adjacent}{hypotenuse}

cos ∠L = \frac{47.5}{68}

      ∠L = cos⁻¹ (\frac{47.5}{68})

      ∠L = 45.7  

Triangle sum Theorem:

∠K + ∠L + ∠M = 180°    

45.7 + 45.7 + ∠M = 180

       91.4     + ∠M = 180

                      ∠M = 88.6

       

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Then, R=15.

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