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4 years ago

Ray QM is the angle bisector of angle NQR. If angle PQN = 7x + 15 and angle NQM = 4x, what is the value of x?

Mathematics

1 answer:

Ksivusya [100]4 years ago

5 0

Answer:

x = 2.7

Step-by-step explanation:

From the question given above, the following data were obtained:

QM = angle bisector of angle PQR

Angle PQN = 7x + 15

Angle NQM = 4x

x =?

Since QM is the angular bisector, it means that it bisect PQR into two equal angle i.e 45° each.

See attachment for diagram.

Thus, we can obtain the value of x as follow:

7x + 15 + 4x + 45= 90° (angle in a right angle triangle)

7x + 4x + 15 + 45= 90

11x + 60 = 90

Collect like terms

11x = 90 – 60

11x = 30

Divide both side by 11

x = 30/11

x = 2.7

Therefore, the value of x is 2.7

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3 years ago

Alex was biking along a 48 mile trail. First half of the time he was biking twice as fast as the second half of the time. If he

nydimaria [60]

Answer:

The speed in the first part is 16 mph.

Step-by-step explanation:

The total distance is 48 miles. The total time is 4 hours.

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.

In the first part of the trip he was traveling at twice the speed, or 2s, for distance 48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part of trip:

48 - d = 2s * 2

d + 4s = 48 Equation 1

Second part of the trip:

d = s * 2

d = 2s Equation 2

Equations 1 and 2 form a system of equations in two unknowns, d and s.

d + 4s = 48

d = 2s

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48

s = 8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) = 16.

The speed in the first part is 16 mph.

Check:

d = 2s = 2(8) = 16

48 - d = 48 - 16 = 32

The second part is 16 miles. The first part is 32 miles.

16 miles at 8 mph takes 2 hours.

32 miles at 16 mph takes 2 hours.

2 hours + 2 hours = 4 hours.

Our answer is correct.

Answer: The speed in the first part is 16 mph.

7 0

4 years ago

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered

LenaWriter [7]

This is the concept of algebra, given that ab^4=12 and a^5b^5=7776, the value if a will be found as follows:
ab^4=12
a=12/b^4
also;
a^5=7776/b^5
thus;
a=(7776/b^5)^(1/5)
a=6/b
thus the value of a will be:
6/b=12/b^4
dividing both sides by b we get:
6=12/b^3
multiplying both sides by b^3 we get
6b^3=12
b^3=2
hence;
b=2^(1/3)

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4 years ago