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3 years ago

Slope-intercept from of an equation for the line passes through -1,2 and Parallel to y=2x-3

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

8 0

The equation of the line in slope - intercept form is $y=2 x+4$

Explanation:

The line passes through the points $(-1,2)$ and parallel to the line $y=2x-3$

Since, the line is parallel, the slope is $m=2$

The y - intercept can be determined by substituting the points $(-1,2)$ and $m=2$ in the slope - intercept formula, we get,

$y=mx+b$

$2=(2)(-1)+b$

$2=-2+b$

$4=b$

Thus, the y - intercept is $b=4$

The equation of the line in slope - intercept form can be determined using the formula $y=mx+b$

Thus, substituting $m=2$ and $b=4$ , we get,

$y=2 x+4$

Hence, the equation of the line in slope - intercept form is $y=2 x+4$

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Fabio and Gwen are saving money to buy a new gaming station. They need at least $510 to purchase the new gaming station. Gwen we

vaieri [72.5K]

x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.

Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.

So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.

They need at least $510 to purchase the new gaming station.

Therefore,

12x + 9y ≥ 510

Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.

Therefore,

y ≤ 2x

Also, Fabio will walk at least 25 dogs.

Therefore,

y ≥ 25

Hence, the constraints are:

12x + 9y ≥ 510

y ≤ 2x

y ≥ 25

8 0

3 years ago

20 POINTS<br> Can someone check over these? I have a quiz on it tomorrow :(

Mama L [17]

Looks good! You have the right answers.

However, the graph for 12 and 15 is inaccurate! Because he starts from a stop sign/stop light, the graph's speed should start from the origin!

Not to confuse you or anything, but this means the graph does not follow the description of the problem. Please let your teacher know so s/he can fix the worksheet.

3 0

3 years ago

Here is the histogram of a data distribution. All class widths are 1.

vaieri [72.5K]

The answer is 7 because the mean is an average. So if you add up all the numbers and then divide that number by the amount of numbers listed then that will get you your answer which is 7

4+5+6+7+8+9+10=49
49/7=7

4 0

3 years ago

I have no idea what I’m doing please help!!<br><br> the number 4.121221222... is... *

andriy [413]

Answer:

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5 0

3 years ago

Brent is a researcher for a food company. He is on a team creating a reduced-calorie version of its flagship cracker. The team w

Andre45 [30]

Answer:

Step-by-step explanation:

Hello!

The research team created a cracker with fewer calories. The average content of calories of the new crackers per serving of 6 should be less than 60.

To test it a random sample of 26 samples of the new cracker was taken and the calories per serving were measured.

Then the study variable is

X: calories of a 6 serve sample of the new reduced-calorie version. (cal)

The variable has a normal distribution with a population standard deviation of 0.82 cal.

To test the claim that the new crackers have on average less than 60 calories, the parameter of interest is the population mean (μ) and the hypotheses are:

H₀: μ ≥ 60

H₁: μ < 60

α: 0.01

Since the variable has a normal distribution and the population variance is known, the best statistic to use to conduct the test is a Standard Normal

$Z= \frac{(X[bar]-Mu)}{\frac{Sigma}{\sqrt{n}} } ~N(0;1)$

This test is one tailed to the left, wich means that the null hypothesis will be rejected at low levels of the statistic.

$Z_{\alpha } = Z_{0.01} = -2.334$

If Z ≤ -2.334, the decision is to reject the null hypothesis.

If Z > -2.334, the decision is to not reject the null hypothesis.

Using the data of the sample I've calculated the sample mean.

X[bar]= ∑X/n= 1548.61/26= 59.56 cal

$Z_{H_0}= \frac{(59.56-60)}{\frac{0.82}{\sqrt{26} } } = -2.736$

The observed Z value is less than the critical value, so the decision is to reject the null hypothesis.

At a level of significance of 1%, you can conclude that the population mean of calories of the samples of new crackers is less than 60 cal.

I hope it helps!

6 0

3 years ago