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mote1985 [20]
3 years ago
9

The ratio of cats to dogs at the animal shelteris 6:7. If there are a total of 91 cats and dogs, how many of each are there?

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0
There are 42 cats, and 49 dogs at animal shelters because I know that 6:7 will have total 13 parts, and I just need to take 91 divided for 13 to get 7 for each part, and to find how many cats are there; I just need to take 7 times 6 to get 42 cats, and take 91 subtract for 42 to get 49 dogs. Hope it help!
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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.
Dennis_Churaev [7]

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

       

7 0
3 years ago
PLS HELP ASAP!!
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Answer:

D

Step-by-step explanation:

A = P(1 + \frac{r}{n})^{nt}\\

[5000* (1+0.125)]/12 =234.375, rounds up to $234.38

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3 years ago
“Solve each inequality and graph its solution. Show work.”
Cloud [144]

Answer:

p or p >6

Step-by-step explanation:

Given

|-5-p| > 11

Required

Solve and graph

|-5-p| > 11

Remove absolute bracket

-5 - p > 11 or -5- p

Solve for p

-p > 11 + 5 or -p < -11 + 5

-p > 16 or -p < -6

Divide by -1

p or p >6

<em>See attachment for plot</em>

3 0
3 years ago
When Julio cracked open his piggy bank, he
jok3333 [9.3K]

Answer:

52 quarters, 42 dimes

Step-by-step explanation:

Let's call the number of quarters q, and the number of dimes d.

q+d=94

0.25q+0.1d=17.20

Subtract q from both sides of the first equation to isolate d:

d=94-q

0.25q+0.1(94-q)=17.20

0.25q+9.4-0.1q=17.20

0.15q=7.8

q=52

d=94-q=42

Hope this helps!

5 0
3 years ago
Unghiurile ∢AOB, ∢BOC, ∢COD și ∢DOA sunt unghiuri în jurul punctului O, ∢AOB = 80°, ∢BOC = 140° și CO ⊥ OD.
Sonbull [250]

Answer:

a) ∡AOC = 140 °

∡AOD = 40 °

b) ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC (unghiuri formate din segmentul OC) prin urmare, segmentul OC bisectează ∡AOB

Step-by-step explanation:

a) Calculați măsurile unghiurilor ∢AOC și ∢AOD.

b) Arătați că jumătatea liniei opuse jumătății liniei OC este bisectoarea unghiului ∢AOB

a) Parametrii dați sunt;

∡AOC. ∡BOC. ∡COD și ∡DOA sunt unghiuri în jurul circumferinței unui cerc

∡AOB = 80 ° și ∡BOC = 140 °, segmentul CO este perpendicular pe segmentul DO

Prin urmare, avem;

∡AOB + ∡BOC + ∡AOC = 360 ° (Suma unghiurilor într-un punct = 360 °)

∴ ∡AOC = 360 ° - (∡AOB + ∡BOC) = 360 ° - (80 ° + 140 °) = 140 °

  ∡AOC = 140 °

∡BOC + ∡BOD = 180 ° (Suma unghiurilor unui triunghi = 180 °)

∡BOD = 180 ° - ∡BOC = 180 ° - 140 ° = 40 °

∡BOD = 40 °

∡ BOD + ∡AOD = ∡AOB

∡AOD = ∡AOB - ∡BOD = 80 ° - 40 ° = 40 °

∡AOD = 40 °

b) Deoarece avem ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC = 140 °, avem;

∡AOB = 140 ° + 140 ° = 280 ° = 2 × ∡BOC = 2 × ∡AOC

Prin urmare, segmentul OC bisectează ∡AOB

3 0
3 years ago
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