(c) Solve.<br> x + 1.5 = 2.5y<br> 2y-x=0

Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance be

Oksana_A [137]

<h2>Hello!</h2>

The answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

$x_{FirstCar}=x_o+v*t$

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

$x_{SecondCar}=x_o+(v+14mph)*t$

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles, so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

$RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph$

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

$2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours$

Writing the equation:

$264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph$

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

$SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph$

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

Have a nice day!

7 0

3 years ago

Use the information to solve the triangle. Round your answers to two decimal places. Hint: draw a sketch first to determine if y

tatyana61 [14]

Answer:

A = 40.0 (3 sig. fig)

C = 40

c = 15

Step-by-step explanation:

Using sin law,

sinA/15 = sin100/23

A = 40.0 (3 sig. fig)

Using angle sum of triange,

C = 180 - 40.0 - 100 = 40

Since angleA = angleC, by side equal opp angles, c = 15

6 0

3 years ago

-5x-4y=10

strojnjashka [21]

Answer:

y intercept = $(0, ~-\frac{5}{2} )$

x intercept = $(-2, ~0)$

.

Step-by-step explanation:

$-5x - 5y = 10$

.

y intercept

$\to x = 0$

$-5(0) - 4y = 10$

$-4y = 10$

$y = \frac{10}{-4}$

$y = -\frac{5}{2}$

so, the answer is $(0, ~-\frac{5}{2} )$

.

x intercept

$\to y = 0$

$-5x - 4(0) = 10$

$-5x = 10$

$x = \frac{10}{-5}$

$x = -2$

so, the answer is $(-2, ~0)$

.

Happy to help :)

8 0

3 years ago

Read 2 more answers

NEED HELP show your work<br><br> Simplify the expression √8x^5 / z1

satela [25.4K]

Answer:

3/4

Step-by-step explanation:

8 0

2 years ago

Calvin thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags

Strike441 [17]

Answer:

a) There are no evidence that Calvin is correct.

b) There are evidence that Calvin is correct.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 1 ounce

Sample size, n = 23

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 1\text{ ounce}\\H_A: \mu < 1\text{ ounce}$

P-value = 0.086

a) Significance level = 5% = 0.05

Since

P-value > Significance level

We fail to reject the null hypothesis and accept it. Thus, the chips bag contain one ounce of product. Thus, there are no evidence that Calvin is correct.

b) Significance level = 10% = 0.10

Since

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, the chips bag contain less than one ounce of product. Thus, there are evidence that Calvin is correct.

7 0

3 years ago

(c) Solve. x + 1.5 = 2.5y 2y-x=0