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Sauron [17]
3 years ago
5

How to find the common ratio of 5,15,45,135

Mathematics
1 answer:
galina1969 [7]3 years ago
6 0

Answer: HOPE THIS HELPED! :D

3 is the common ratio

Step-by-step explanation:

5x3      15

15x3     45

45x3    135

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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
Hey so im also looking for the first answer and the choices were “ is not “ and “ is “
dexar [7]

so the investigator found the skid marks were 75 feet long hmmm what speed will that be?

s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ d=75 \end{cases}\implies s=\sqrt{30(0.7)(75)}\implies s\approx 39.69~\frac{m}{h}

nope, the analysis shows that Charlie was going faster than 35 m/h.

now, assuming Charlie was indeed going at 35 m/h, then his skid marks would have been

s=\sqrt{30fd}~~ \begin{cases} f=\stackrel{friction}{factor}\\ d=\stackrel{skid}{feet}\\[-0.5em] \hrulefill\\ f=\stackrel{dry~day}{0.7}\\ s=35 \end{cases}\implies 35=\sqrt{30(0.7)d} \\\\\\ 35^2=30(0.7)d\implies \cfrac{35^2}{30(0.7)}=d\implies 58~ft\approx d

4 0
2 years ago
Plzz Help me!! Have to have this submitted by tonight!
Aliun [14]
N is the number of the Tshirt
c is the cost
the relationship between the cost and the number of the Tshirt is:
12n+3=c
so if 1 is the number of the tshirt so the cost is
12.1+3=12+3=15
if n=2 c=12.2+3=24+3=27
and etc.....
7 0
3 years ago
Melissa walked at a rate of 88 feet per minute. What was her approximate speed to the nearest tenth of a mile
Illusion [34]

88x60=5280

I believe it's 1 mile.

7 0
3 years ago
Read 2 more answers
Use the triangles above. Find the side lengths and perimeters if x=5.
NeTakaya

First triangle side lengths: 9, 4, 8

First triangle perimeter: 21

Second triangle side lengths: 18, 8, 16

Second triangle perimeter: 42

Please consider brainliest!

✉️ If any further questions, inbox me! ✉️

3 0
3 years ago
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