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3 years ago

Two buses leave a station at the same time and travel in opposite directions. One bus travels

Mathematics

1 answer:

natima [27]3 years ago

4 0

Answer:

63 miles per hour

54 miles per hour

Step-by-step explanation:

Let the two buses be represented as bus A and bus B.

bus A and bus B leave a station at the same time and travel in opposite directions.

Let the speed of bus A be A miles per hour.

Let the speed of bus B be B miles per hour.

One bus travels 9 miles/hour slower than the other.

Let bus A be the faster bus.

This means that the speed of bus B is B = A - 9

If the two buses are 585 miles apart after 5hours, this means that after 5hours, the total distance travelled by bus A and bus B is 585 miles.

Distance travelled by bus A in 5 hours = speed × time = 5A

Distance travelled by bus B in 5 hours = speed × time = 5B

5A + 5B = 585 - - - - - -1

Substituting B = A - 9 in equation 1

5A + 5(A - 9) = 585

5A + 5A - 45 = 585

10A = 585 + 45 = 630

A = 630/10 = 63 miles per hour

B = A - 9 = 63 - 9 = 54 miles per hour

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the lines are below are parallel . if the slope of the green line is - 2/3 , what is the slope of the red line?

lina2011 [118]

If the two lines a re parallel, they would have the same slop which means the red line would have a slope of - 2/3

3 0

3 years ago

A SOLUTION CONTAINS 60% WATER, 15% BLEACH AND THE

Allushta [10]

Answer:

20 ounces of cleaner

Step-by-step explanation:

Water 48 oz is 60% of unknown total. 60% = 3/5. Create equation and solve

48= 3x/5. 240= 3x. 80 = x

Total of water, bleach and cleaner is 80 ounces

60% + 15% = 75%

100% - 75%= 25% cleaner

.25 × 80 = 20 ounces

6 0

2 years ago

Is X=[−14−32] the inverse of A=[15−25310−110]?

Elis [28]

The product of the matrices is an identity matrix. Therefore, X and A are inverse of each other.

The matrices are given as:

$X = \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]$

$A = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right]$

To check the matrices are inverse, we calculate their products.

$A \times X = \left[\begin{array}{cc}\frac 15&\frac 3{10}\\-\frac 25 &-\frac 1{10}\end{array}\right] \times \left[\begin{array}{cc}-1&-3\\4&2\end{array}\right]$

Multiply the rows of A by the column of X.

This gives

$A \times X = \left[\begin{array}{cc}\frac 15 \times -1 + \frac{3}{10} \times 4&\frac 15 \times -3 + \frac{3}{10} \times 2\\ -\frac 25 \times -1 - \frac{1}{10} \times 4&-\frac 25 \times -3 + -\frac{1}{10} \times 2\end{array}\right]$

$A \times X = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

The product of A and X is an identity matrix.

This means that; both matrix are inverse of each other