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iren [92.7K]
3 years ago
12

A car can travel 300 miles in the same amount of time it takes a bus to travel 180 miles. if the rate of the bus is 20 miles per

hour slower than the rate of the car, find the average rate for each
Mathematics
1 answer:
Gnesinka [82]3 years ago
6 0
It would be the bus goes 75 miles per hour while the car is going 95 miles per hour
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1) What is the solution of the given system?
m_a_m_a [10]

Answer:

1  x=-2.5  y = -5.5

2.  x=5  y=1

Step-by-step explanation:

1) What is the solution of the given system?

5x-y=-7

3x-y=-2

Multiply the second equation by -1

-1*(3x-y)=-1(-2)

-3x +y = 2


Now add the first equation to the modified second equation

5x-y=-7

-3x +y = 2

------------------

2x = -5

Divide each side by 2

2x/2 = -5/2

x = -2.5

Now we need to find y

-3x+y =2

-3(-2.5) +y =2

7.5 +y =2

Subtract 7.5 from each side

7.5 -7.5 +y =2-7.5

y = -5.5


2) what is the solution of the given system?

5x+7y=32

8x+6y=46

Divide the second equation by 2

8x/2+6y/2=46/2

4x+3y =23


Multiply the first equation by 4

4 (5x+7y)=32*4

20x+28y = 128


Now multiply the modified 2nd equation by -5

-5(4x+3y )=-5(23 )

-20x -15y = -115


Lets add the new equations together to eliminate x

20x+28y = 128

-20x -15y = -115

---------------------

      13y = 13

Divide each side by 13

13y/13 =13/13

y=1

Now substitute back in to find x

5x+7y=32

5x +7(1) =32

5x +7 =32

Subtract 7 from each side

5x+7-7 =32-7

5x =25

Divide by 5

5x/5 =25/5

x=5





3 0
3 years ago
Point D is the centroid of Triangle ABC. Find CD and CE.<br> DE = 9
sukhopar [10]

Given:

Point D is the centroid of Triangle ABC and DE = 9.

To find:

The measures of CD and CE.

Solution:

We know that, centroid is the intersection of medians and it divides each median in 2:1.

In triangle ABC, CE is a meaning and centroid D divided CE in 2:1. So,

Let the measures of CD and DE are 2x and x respectively.

DE = 9                (Given)

x=9

Now,

CD=2x

CD=2(9)

CD=18

And,

CE=CD+DE

CE=18+9

CE=27

Therefore, the measure of CD is 18 units and the measure of CE is 27 units.

6 0
3 years ago
the length of a rectangle is 3 feet more than twice the width. if the width is increased by four feet the perimeter of the new r
densk [106]

Answer:

The area of the original rectangle  = 189 sq ft.

Step-by-step explanation:

Let, the width of the rectangle = m feet

So, the length of the rectangle =  (2 m + 3)  ft

Now, new width w'  = (m + 4)

Perimeter of new rectangle (P')   = 68 ft

Perimeter of a rectangle = 2 (LENGTH + WIDTH)

⇒68 ft   = 2( L + W')  

or, 68 ft   = 2 [( 2m + 3) + (m + 4)]

or, 2 (3m + 7)  = 68

or, 3m + 7 = 68/2  = 34

⇒ 3m = 34 - 7 = 27

⇒ m = 27/3 = 9

or, m = 9 ft

Hence, the original width  of the rectangle =  9 ft

Original Length of the rectangle = 2m  + 3  = 2(9) + 3 = 21 ft

Now, Area of the Rectangle = LENGTH X WIDTH

=  21 ft  x  9 ft  = 189 sq ft

Hence,the area of the original rectangle  = 189 sq ft.

5 0
3 years ago
Miquel created the table below to show how he uses the money he earns at work
lara [203]

<u>Complete Question with table is attached</u>

<u>Answer:</u>

Miguel will save money of $90 if he earns $120.00

<u>Step-by-step explanation:</u>

The figure attached clearly shows the ratio of his earnings and savings. We have to find what would be the savings amount if he earn $120.00. So, first we have to calculate the percentage of ratio of his earnings and savings. As per the data given in the figure,

If he earns $10.00, he saves $7.50, calculate %amount he saves as below,

           \frac{\$ 7.50}{\$ 10.00} \times 100=0.075 \times 100=75 \%

Likewise, calculate for all given data. If he earns $50.00 then he saves $37.50

           \frac{\$ 37.50}{\$ 50.00} \times 100=0.75 \times 100=75 \%

If he earns  $150.00 and save $112.50,

           \frac{\$ 112.50}{\$ 150.00} \times 100=0.75 \times 100=75 \%

So, from all above, it clearly tells that Miguel saves 75% of amount from his earnings. Now, given earnings as $120.00. By finding 75% of $120.00, we can find his savings in that amount. So,

             \frac{75}{100} \times \$ 120=0.75 \times 120=\$ 90

6 0
3 years ago
Read 2 more answers
PLEASE HELP ME PLEASE HELP ME WITH MY MATH
ryzh [129]
A. I would estimate that 7 in of the ribbon
B. the estimate would be high because the longer the ribbon is the more of the ribbon would have to be cut.
C. 11.7 - 5.25 = 6.45 iris has to cut 6.45 off the longer ribbon for the ribbons to be the same length.
5 0
2 years ago
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