Marisol traveled 175 miles in 2 ½ hours. What was her average rate of speed?

Let numerator of fraction be x and denominator be y.

∴ Fraction = x/y

★ Part - A :

[tex]:\implies\tt\:\dfrac{x\times 4}{y-2}=2[/tex]

[tex]:\implies\tt\:4x=2(y-2)[/tex]

[tex]:\implies\tt\:4x=2y-4[/tex]

[tex]:\implies\tt\:2y=4x+4[/tex]

[tex]:\implies\bf\:y=2x+2\:\:\dots (1)[/tex]

★ Part - B :

[tex]:\implies\tt\:\dfrac{x+15}{2y-2}=\dfrac{9}{7}[/tex]

[tex]:\implies\tt\:7(x+15)=9(2y-2)[/tex]

[tex]:\implies\tt\:7x+105=18y-18[/tex]

From equation (1)...

[tex]:\implies\tt\:7x+105=18(2x+2)-18[/tex]

[tex]:\implies\tt\:7x+105=36x+38-18[/tex]

[tex]:\implies\tt\:29x=105-18[/tex]

[tex]:\implies\tt\:x=\dfrac{87}{29}[/tex]

[tex]:\implies\boxed{\bf{x=3}}[/tex]

[tex]:\implies\tt\:y=2x+2[/tex]

[tex]:\implies\tt\:y=2(3)+2[/tex]

[tex]:\implies\boxed{\bf{y=8}}[/tex]

∴ Fraction = x/y = 3/8

Answer:  3/8

Step-by-step explanation:

Let x represent the numerator and y represent the denominator.

Equation 1: (4x)/(y - 2) = 2

                  4x = 2(y - 2)        Cross Multiplied

                  4x = 2y - 4           Distributed

                  4x - 2y = -4          Subtracted 2y from both sides

Equation 2: (x + 15)/(2y - 2) = 9/7

                  9(2y - 2) = 7(x+15)           Cross Multiplied

                  18y - 18 = 7x + 105          Distributed

                  -7x + 18y - 18  = 105        Subtracted 7x from both sides

                  -7x + 18y = 123                Added 18 to both sides

Solve the system of equations using Elimination Method:

EQ1:    4x - 2y =  -4     →    9(4x - 2y =  -4)     →      36x - 18y =  -36

EQ2: -7x + 18y = 123   →   1(-7x + 18y = 123)  →      -7x + 18y = 123  

                                                                              29x          =  87

                                                                            ÷29              ÷29

                                                                                  x         =  3

Substitute x = 3 into either equation to solve for y:

EQ1: 4x - 2y = -4

      4(3) - 2y = -4

       12  - 2y = -4

            -2y  = -16

              y  =   8

The numerator (x) = 3

The denominator (y) = 8

The fraction is: 3/8

Answer:

x = 3

Step-by-step explanation:

8x - 12 = 4x

subtract 4 from each side

4x - 12 = 0

add 12 to each side

4x = 12

divide each side by 4

x = 3

Answer:

7.45

Step-by-step explanation:

5*1.49

Hope this helps!

Answer: 7.45

Step-by-step explanation: multiply 1.49$ by 5 and get 7.45

Answer:

Q minus 7

Step-by-step explanation:

Answer:

-6 ≤ x < 0

Step-by-step explanation:

Subtract the 7 on both sides to get x isolated.

Answer:

-6 ≤ x < 0

Step-by-step explanation:

This is the answer because:

1) First, we have to isolate the x

2) In order to isolate the x, you have to subtract 7 from 1 and 7

1 - 7 = -6

7 - 7 = 0

Therefore, the inequality is -6 ≤ x < 0

Hope this helps! :D

Answer:

It will take 12 seconds to be at same distance

The equation is;

8.8x = 6.3x + 30

Step-by-step explanation:

Let the number of seconds it will take be x

Mathematically, distance = speed * time

At x-seconds , Hudson will be at a distance of 8.8 * x = 8.8x ft

At x seconds , Knox will be at a distance of 30 ft + (6.3 * x) = 6.3x + 30feet

So the time it will take them to be at the same distance can be calculated using the equation;

6.3x + 30 = 8.8x

8.8x - 6.3x = 30

2.5x = 30

x = 30/2.5

x = 12 seconds

Answer:

Step-by-step explanation:

It will take 12 seconds to be at same distance

Answer:c

Step-by-step explanation:

Answer:x-9

Step-by-step explanation:

Simplifying

Solving for variable

Move all terms containing x to the left all other terms to the right

Devide each side by 16

X=9

Answer:

the difference between -23.3° and 30.4° is 53.7°F

Step-by-step explanation:

30.4° - (- 23.3° ) = 53.7° F

Answer:

216.66667

Step-by-step explanation:

(0+0+150+250+400+500) / 6 = 216.66667

Answer:

11 and 12

Step-by-step explanation:

Answer:

9.5

Step-by-step explanation:

if you divide them

28.5÷3=9.5

38÷4=9.5

47.5÷5=9.5

57÷6=9.5

the constant proportionality is 9.5. They are equal.

Answer:

For every one inch of water the snow increases by 9.5

Step-by-step explanation:

38 - 28.5 = 9.5

57 - 47.5 = 9.5

Answer:what is the question

Step-by-step explanation:

Answer:

So it will be over at 5:15

Step-by-step explanation: you add them together I think this is how I am supposed to answer this.

Answer:

x=-1 y=-3

............

Answer:

( − 1 , − 3 ) or x= − 1 , y = − 3

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

Since we can't buy 0.68 of a fish and our number must be less than 13.68, we can buy 13 fish.

Step-by-step explanation:

3.29f ≤ 45

3.29f/3.29 ≤ 45/3.29

f ≤ 13.68

0 = 8-2b

Subtract 8 from both sides

-8 = -2b

Divide both sides by-2

B = 4

Answer:

Step-by-step explanation:

Are you solving for b? Just subtract 8 from both sides so it will be -8 = -2b. Then divide 2 on each side and the answer is b=-4

Answer:its a

Step-by-step explanation:

3/4 +2 +2

Answer:

EF = 58

Step-by-step explanation:

Find the diagram of the question attached.

According to the addition postulate;

DE+EF = DF

Given

DE = 47

EF = 3x+10

DF = 9x-39

Substitute into the addition postulate formula and get x

47+3x+10= 9x-39

Collect like terms

3x-9x = -39-10-47

-6x = -96

x = -96/-6

x = 16

Next is to evaluate EF:

EF = 3x+10

EF = 3(16)+10

EF = 48+10

EF = 58

Hence the measure of EF is 58

Answer:

Answer 5 / 32

Step-by-step explanation:

Answer:

600:900

Step-by-step explanation:

Let the ratio be 2x+3x

2x+3x=1500

5x=1500

x=1500/5

x=300

2x = 600          ;         3x = 900

Therefore, 600:900 = 2:3

Answer:

False It has to be the divisor/ the second fraction.

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

If you look at the point (-2,0) you can see that it sits directly on the line above 2. If you also at the point (3,4) you can see that its also sitting directly in the middle, where the line runs through it. Using this information we can use Rise/Run.

Rise/Run = Y/X

from (-2, 0) you rise 4 and you run 5 to the right to land on (3,4).

This is one of many ways you can calculate The slope from a graph!

Hope this helps! :)

Answer:

x = -9

Step-by-step explanation:

Let unknown number = x

Largest 2-digit number  = 99

x * (-11) = 99

         x = 99 ÷ (-11)

       x = -9

Answer:

-9

Step-by-step explanation:

1. The largest 2-digit number is 99

2. So, our problem should look like this: (-11) x ?= 99

3. Divide 99 by -11, and that'll equal -9

hope this helps! <3

Answer:

4(4+9)

Step-by-step explanation:

If you distribute(multiply) the 4 within the parentheses it'll equal 16+36.

Answer:

Andrew has $15 left over each month

Step-by-step explanation:

Inflows=$240+$60=$300/mo.

Outflows=$170+$70+45=$285/mo.

Inflows-Outflows=left over

$300-$285=$15

Answer:

Associative property of addition

Step-by-step explanation:

This is because the associative property of addition states that changing the grouping of addens does not change the sum. In other words, if you rearrange the sums of a expression, the result should remain the same.

Answer:

associatice property of addition

Step-by-step explanation:

Answer:

The indifference point is 50 orders.

Step-by-step explanation:

Giving the following information:

Fundraiser A:

$1.50 for each order places plus $75 as a bonus.

Fundraiser B:

$3.00 for each order placed.

First, we need to structure the fundraisers' formula:

Fundraiser A= 75 + 1.5x

Fundraiser B= 3x

x= number of orders

Now, we equal both formulas and isolate x:

75 + 1.5x = 3x

75/1.5= x

50= x

The indifference point is 50 orders.

Prove:

Fundraiser A= 75 + 1.5*50= $150

Fundraiser B= 3*50= $150

Answer:

B or 4/3 i think

Step-by-step explanation:

hope this helps :3

sorry if im wrong