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finlep [7]
3 years ago
8

Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph

slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)
Mathematics
1 answer:
RSB [31]3 years ago
6 0

Answer:

  54.2 mph

Step-by-step explanation:

Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...

  70² = c² +(c -10)²

  4900 = 2c² -20c +100 . . . . eliminate parentheses

  c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form

  (c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form

  c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical

  c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution

Cynthia's average speed was 54.2 miles per hour.

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(a)<br> Solve.<br> 3x – 4 = x + 5
exis [7]

Answer:

x = 1/2 or 0.5

Step-by-step explanation:

3x - 4 = x +5      (1) subtract x

2x - 4 = 5        (2) subtract 5

2x + 1              (3) divide by 2

x = 1/2 or 0.5

4 0
3 years ago
Please help I need this for a text ASAP.
Sladkaya [172]

The values of x and y are 45 and 8.

<h3>What is a Linear Pair of Angles?</h3>

When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case.

Given:

Measures of two linear pairs of angles which are of equal measures are 2x and 11y + 2.

As the sum of linear pair of angles is 180°, and if they are of equal measures, each angle must be equal to 90°.

To determine the values of x and y we equate the given angles to 90°.

2x = 90°

⇒ x = 45

And 11y+2 = 90°

⇒ 11y = 90-2 = 88

⇒ y = 8

To know more about linear pairs visit:

brainly.com/question/17525542

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8 0
1 year ago
Park Rangers at the North Rim of the Grand Canyon recorded the amounts of rainfall over 12 months. What was the total amount of
myrzilka [38]

Answer:

65.532cm of rainfall over 12 months

Step-by-step explanation

5 0
3 years ago
Consider the following hypothesis test:
Gnom [1K]

Answer:

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

H_0: \mu\leq50\\\\H_a:\mu> 50

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22

The null hypothesis is rejected, as z>zc and falls in the rejection region.

8 0
4 years ago
Consider the line y=9x-8
jasenka [17]

Answer:

y=9x+75

Step-by-step explanation:

since we know that the slope must be the same for two lines to be proportional, we are gonna start there.

so our equation is: y= 9x + b

we need to find b to complete our equation, so substitute in the points we were given.

3 = 9(-8) + b

so now,

3 = -72 + b

now we have to isolate b to find out what it is,

3  =  -72 + b

+72   +72

so now: 75= b

Put that back into the starting equation: y = 9x + 75

7 0
3 years ago
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