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Leni [432]
3 years ago
12

Using drt what is the Answer to this question a car in a bus set out at 2 PM find the same point headed in the same direction. T

he average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car
Mathematics
1 answer:
Zina [86]3 years ago
3 0

Answer: the rate of the car is 50mph

Step-by-step explanation:

Let x represent the average speed of the bus.

Let y represent the distance travelled by the bus.

The average speed of the car is 30 mph slower than twice the speed of the bus. This means that the average speed of the car would be

2x - 30

Distance = speed × time

Time = distance/speed

Therefore, In 2 hours time,

2 = y/x

2x = y

In two hours the car is 20 miles ahead of the bus. Therefore

2 = (y + 20)/(2x - 30)

2(2x - 30) = y + 20

4x - 60 = y + 20 - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes

4x - 60 = 2x + 20

4x - 2x = 20 + 60

2x = 80

x = 80/2 = 40

The speed of the car would be

2x - 30 = 2 × 40 - 30

= 80 - 30 = 50 mph

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3 years ago
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Nuetrik [128]

Thanks for asking your question!

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8 0
3 years ago
What is the 24th term if the arithmetic sequence where a1 = 8 and a9 = 56
AnnyKZ [126]

Answer:

a_{24} = 146

Step-by-step explanation:

a1 = 8

a9 = 56

Using formula for finding nth term of arithmeric sequence

a_{n} =a_{1} + (n-1)d

We have to find 24th term, therefore n = 24

a_{1} is the first term but we are missing d

d is the difference between the two consecutive terms, lets calculate it first


a9 = 56

Using the above given formula for finding d

put n = 9,  a9= 56

a_{9} =a_{1}+ (9-1)d

56 = 8 + 8d

8d = 48

d = 6


Getting back to main part of finding 24th term

n = 24, d = 6, a1 = 8

put values in nth term formula

a_{n} =a_{1}+ (n-1)d

a_{24} = 8 + (24-1)6

a_{24} = 8 + 138

a_{24} = 146



5 0
3 years ago
The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? {5, 8} {-5, -8} {3, 8} {4, 7} {4, 8}
Savatey [412]
The range is the ouutput from inputing the input
basically
25=k²+2k+1 and 64=k²+2k+1
the values that satisfy both equations (not at the same tim) are the valuess that are the domain
solve each
25=k²+2k+1
minus 25 both sides (or recognize the perfect square trinomial, but anyway)
0=k²+2k-24
factor
0=(k+6)(k-4)
set to zero
k+6=0
k=-6
k-4=0
k=4
k=-6 or 4

64=k²+2k+1
minus 64 both sides
0=k²+2k-63
facor
0=(k-7)(k+9)
set to zer
k-7=0
k=7
k+9=0
k=-9
k=-9 or 7



so the domain has the numbers
-9,-6,4,7
it seems we only want the positive square roots so
answer is {4,7} is the domain
3 0
3 years ago
For what value of x is the rational expression below<br> equal to zero?
krek1111 [17]

Answer:

4

Step-by-step explanation:

It's easy because 4-4=0 and anything divided by zero is zero.

8 0
3 years ago
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