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OverLord2011 [107]
3 years ago
5

The angles in a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times a

s large as the smallest angle. Find the measures of all three angles.
Mathematics
1 answer:
umka21 [38]3 years ago
4 0

Answer:

The measure of the three angles are 120°, 20° and 40°

Step-by-step explanation:

Let

x ----> the measure of the first angle

y ---> the measure of the second angle (smallest angle)

z ---> the measure of the third angle

Remember that

The sum of the angles in a triangle must be equal to 180 degrees

so

x+y+z=180 ----> equation A

x=y+100 -----> equation B

z=2y ------> equation C

solve the system by substitution

substitute equation B and equation C in equation A

(y+100)+y+(2y)=180

solve for y

4y+100=180

4y=180-100

4y=80

y=20\°

<em>Find the value of x</em>

x=y+100  ---- x=20+100=120\°

<em>Find the value of z</em>

z=2y ----> z=2(20)=40\°

therefore

The measure of the three angles are 120°, 20° and 40°

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3 years ago
If 2x + 5 = 82, then 12x = ?<br> A 5<br> B<br> 10<br> C 15<br> D 20
KengaRu [80]

Answer:

2x= 38.5

Step-by-step explanation:

I'm not sure where u got 12x but 2 x = 38.5:

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subtract 5 for 82

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A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed
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Try this solution:

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Step-by-step explanation:

- The basic formula used in this task is S=V*t, where S - distance, V - speed, t - time.

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- the upstream speed is: V-Vc.

- according to the described above the distance for downstream is S1=(V+Vc)*t1, where t1=10; the distance for upstream is S2=(V-Vc)*t2, where t2=70.

- for whole travel down- and upstream: S=S1+S2.

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\left \{ {{(70(V-V_c)=10(V+V_c)} \atop {70(V-V_c)+10(V+V_c)=210}} \right.

V - the speed of the boat in still water - 6 miles per hour, Vc - the speed of the current - 4.5 miles per hour. All the details for the system of the equations are in the attachment.

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4 years ago
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