Total time taken by Sam before Al caught up with him = 15+10 = 25 minutes

In hours = 25 minutes = 25/60 = 5/12 hrs
Distance covered by Sam = Distance covered by Al = Speed (Sam) * time taken = 3.2*5/12 = 4/3 miles.

Al takes 10 minutes to cover that distance. Therefore,
Al's speed = Distance/time = (4/3)/(10/60) = (4/3)*(60/10) = 8 mph

5 0

3 years ago

How to get 1 2/5 from 14/10

Lesechka [4]

This is a simple simplification problem (ha!).

14/10 is an improper fraction. Since a fraction can also be a division expression, 14 divided by 10 equals 1 with a remainder of 4.

Since we have the answer, we can now produce a mixed fraction of:
4
1 ---
10

Since 4/10 is equal to 2/5,

4 2
1 --- is equal to 1 ---
10 5

5 0

3 years ago

Choose a system of equations with the same solution as the following system:

Lina20 [59]

Answer:

Option A.

Step-by-step explanation:

We are given 6x+2y =-6 ......(1) and 3x-4y=-18 .....(2)

Solving equations (1) and (2) we get

12x+3x =-30, ⇒x= -2 and from equation (1), 2y= -6-6(-2) =6, ⇒ y=3

Therefore, the solution for the given set of equations is x= -2 and y=3

A) Solving the equations 8x+4y = -4 ....... (3)and 17x+2y =-28, we get

8x -34x = -4 -(-56) =52, ⇒-26x =52, ⇒x=-2 and from equation )(3), we get -16+4y =-4, ⇒ y=3

Therefore, the solution x=-2 and y =3 match with the original solution.

B)Solving the equations 12x + 4y = 12 ....... (4)and 21x + 2y = −36, we get

12x -42x = 12 -(-72) =84, ⇒-30x =84, ⇒x=-84/30.

Therefore, the solution x=-84/30 does not match with the original solution.

C) Solving the equations 6x + 8y = −36 ....... (4) and 15x + 6y = −60, we get 18x -60x = -108 -(-240) =132, ⇒-42x =132, ⇒x=-132/42

Therefore, the solution x=--3 do not match with the original solution.

D) Solving the equations 6x + y = 15 ....... (5) and 15x − y = −9, we get 6x +15x = 6, ⇒21x =6, ⇒x=2/7

Therefore, the solution x=2/7 do not match with the original solution.

Therefore, option A) will have the same solution. (Answer)

4 0

3 years ago

Use the completing the square method to find the roots of 2x^2+3x-15=13 include the steps, it would be greatly appreciated thank

Monica [59]

Answer:

The roots are

$x1= \frac{-3+\sqrt{233}}{4}$

$x2= \frac{-3-\sqrt{233}}{4}$

Step-by-step explanation:

we have

$2x^{2}+3x-15=13$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$2x^{2}+3x=13+15$

$2x^{2}+3x=28$

Factor the leading coefficient

$2(x^{2}+(3/2)x)=28$

Complete the square. Remember to balance the equation by adding the same constants to each side

$2(x^{2}+(3/2)x+(9/16))=28+(9/8)$

$2(x^{2}+(3/2)x+(9/16))=233/8$

$(x^{2}+(3/2)x+(9/16))=233/16$

Rewrite as perfect squares

$(x+(3/4))^{2}=233/16$

square root both sides

$(x+\frac{3}{4})=(+/-)\sqrt{\frac{233}{16}}\\ \\(x+\frac{3}{4})=(+/-)\frac{\sqrt{233}}{4}\\ \\x= -\frac{3}{4}(+/-)\frac{\sqrt{233}}{4}$

$x1= -\frac{3}{4}(+)\frac{\sqrt{233}}{4}=\frac{-3+\sqrt{233}}{4}$

$x2= -\frac{3}{4}(-)\frac{\sqrt{233}}{4}=\frac{-3-\sqrt{233}}{4}$

7 0

3 years ago