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3 years ago

Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1.

Mathematics

1 answer:

qwelly [4]3 years ago

3 0

Answer:

The equation is $y=x-9$

Step-by-step explanation:

If we want a line parallel to the line in the problem it will have the same slope. The equation given in the problem is already in slope intercept form so we can take the slope for the new equation directly from this equation.

The slope-intercept form of a linear equation is: $y=mx+b$

Where m is the slope and b is the y-intercept value.

$y=1x-2$

Therefore the slope is

$m=1$

We can now use the point-slope formula to write the equation of the parallel line:

The point-slope formula states:

$(y-y1)=m(x-x1)$

Where m is the slope and $(x1,y1)$ is a point the line passes through.

Substituting the information from the problem gives:

$(y- (-7)=1(x-2)$

$(y+7)=1(x-2)$

Or, we can solve for y to put the equation in slope-intercept form:

$y+7=x-2$

$y+7-7=x-2-7$

$y+0=x-9$

$y=x-9$

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Bob's age is 4 times greater than Susanne's age. Dakota is three years younger than Susanne. The sum of Bob's, Susanne's, and Da

Ratling [72]

Susanne is 16 years old.

b = Bob's age

s = Susanne's age

d = Dakota's age

Bob's age is 4 times greater than Susanne's age:

b = 4s

Dakota is three years younger than Susanne:

d = s - 3

The sum of Bob's, Susanne's, and Dakota's ages is 93:

b + s + d = 93

solve these equations:

b = 4s

d = s - 3

b + s + d = 93

and get:

b = 64 years

s = 16 years

(remember that s = Susanne)

d = 13 years

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3 years ago

In 2015 as part of the General Social Survey, 1289 randomly selected American adults responded to this question:

Radda [10]

Answer:

B (0.312, 0.364)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

1289 randomly selected American adults responded to this question. This means that $n = 1289$ .

Of the respondents, 436 replied that America is doing about the right amount. This means that $\pi = \frac{436}{1289} = 0.3382$ .

Determine a 95% confidence interval for the proportion of all the registered voters who will vote for the Republican Party. 

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 - 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.312$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3382 + 1.96\sqrt{\frac{0.3382*0.6618}{1289}} = 0.364$

The 95% confidence interval is:

B (0.312, 0.364)

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3 years ago

Which statements are true? Check all that apply.

mariarad [96]

Answer:

A, B, and C

Step-by-step explanation:

A) We can see if this is a horizontal line if its slope is 0. Slope is change in y divided by change in x, so: slope = $\frac{7-7}{3-(-2)} =\frac{0}{5} =0$ . Thus, this is a horizontal line and the statement is correct.

B) Any equation of the form x = k, where k is a constant, will always be a straight line. Let's see if it goes through (-8, 3) by plugging in the values of -8 in for x and 3 in for y in the equation.

Clearly, we don't have a y, so we just put in the -8 for the x: -8 = -8. Since this is a true statement, we know that x = -8 does go through (-8, 3). So, this is a true statement.

C) We can see if this is a vertical line if its slope is undefined (for example, if the denominator is 0, it's undefined). Slope = $\frac{5-(-7)}{0-0} =\frac{12}{0}$ = undefined. So, this is a vertical line and the statement is true.

D) As a basic fact, any point on a horizontal line will have the same y coordinate. However, their x coordinates may vary. Thus, the statement is false.

So, the answers are A, B, and C.

Hope this helps!

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3 years ago

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What’s the difference betweeen relative frequency and frequency

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Answer: Summary: 1. Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated. ... On the other hand, relative frequency is determined by using simple division

Step-by-step explanation:

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3 years ago

Camilo estimates the weight of the dog . The veterinarian says that the dog weighs 84 pounds . The percent error in Camillo's es

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Answer:

The estimated weight is in the range:

75.6 pounds $\leq$ Weight $\leq$ 92.4 pounds

Step-by-step explanation:

Since, the maximum error is 10%.

Therefore, the maximum and minimum vales will be 10% more and 10% less than 84 pounds, respectively.

For Maximum Limit:

$Weight_{max}$ = (1.1)(84 pounds)

$Weight_{max}$ = 92.4 pounds

For Minimum Limit:

$Weight_{min}$ = (0.9)(84 pounds)

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Hence, the estimated weight is in the range:

75.6 pounds $\leq$ Weight $\leq$ 92.4 pounds

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3 years ago

Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1.​

Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1.