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3 years ago

Write the equation of the line that passes through the points (-9, -7) and (-4, 4).

Mathematics

1 answer:

Amanda [17]3 years ago

6 0

Answer:

$y-4 = \frac{11}{5} (x+4)$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ to find the slope. Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(4)-(-7)}{(-4)-(-9)} \\m = \frac{4+7}{-4+9} \\m = \frac{11}{5} \\$

Thus, the slope is $\frac{11}{5}$ .

2) Now, use the point-slope formula, or $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. Substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute $\frac{11}{5}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, choose any one of the given points (either one is fine, the equation will represent the same line) and substitute its x and y values into the formula as well. (I chose (-4, 4) as seen below.) Make sure to simplify the double negatives to positives. This gives the following answer in point-slope form:

$y-(4) = \frac{11}{5} (x-(-4))\\y-4 = \frac{11}{5} (x+4)$

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A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The

adelina 88 [10]

Answer:

The 90% confidence level is $19.15< L < 20.85$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 64$

The mean age is $\= x = 20 \ years$

The standard deviation is $\sigma = 4 \ years$

Generally the degree of freedom for this data set is mathematically represented as

$df = n - 1$

substituting values

$df = 64 - 1$

$df = 63$

Given that the level of confidence is 90% the significance level is mathematically evaluated as

$\alpha = 100 - 90$

$\alpha =$ 10 %

$\alpha = 0.10$

Now $\frac{\alpha }{2} = \frac{0.10}{2} = 0.05$

Since we are considering a on tail experiment

The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as

$t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669$

The margin for error is mathematically represented as

$MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

substituting values

$MOE = 1.699 * \frac{4 }{\sqrt{64} }$

$MOE = 0.85$

he 90% confidence interval for the true average age of all students in the university is evaluated as follows

$\= x - MOE < L < \= x + E$

substituting values

$20 - 0. 85 < L < 20 + 0.85$

$19.15< L < 20.85$

4 0

3 years ago

A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after anothe

DedPeter [7]

The thief originally stole 64 plants.

<h3>What is arithmetic?</h3>

In mathematics, it deals with numbers of operations according to the statements.

Here,
Let the number of plants originally stolen by the thief be x.
On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half of the plants that he still had, plus 2 more.

Here,
For gourd 1 the planet is given = 1/2 x
For gourd 2 the planet is given = 1/2 * 1/2 x = 1/4 x
For gourd 3 the planet is given = 1/2*1/4 x = 1/8 x
Total plant given to the gourds = 1/2x +1/4x +1/8x + 2 = 7/x/8x +2
Finally, the thief leaves the nursery with 10 plants
x - 7x/8 + 2 = 10
x/8 = 8
x = 64

Thus, the thief stole 64 plants.

Learn more about arithmetic here:

brainly.com/question/14753192

7 0

2 years ago

You notice a hot air balloon descending. The elevation h

ANEK [815]

Answer:

the domain is 0 x 45 and the range is 0 h 360. The slope is -8, so the change in the height of the ballon is -8 feet per second. The h-intercept is 360, so the height of the ballon when the first noticed it was 360 feet. The x-intercept is 45, so the time it took the hot air balloon to reach the ground was 45 seconds.

Step-by-step explanation:

8 0

3 years ago

Please help with this asap!! Would help a lot for me :)

lisov135 [29]

Answer:

answer 1 = true

answer 2 . Area of shaded part is 87m^2

<em><u>explanation in the pic above</u></em>

3 0

3 years ago

Read 2 more answers

60.April would like to invest $200 in the bank for one year. Three banks all have a nominal APR of 1.5%, but compound the intere

mojhsa [17]

Answer:

$203.02

Step-by-step explanation:

Since the bank in question compounds interest continuously, the following equation should be used to determine the final balance (B) in April's account:

$B= 200*e^{i*t}$

Where "e" is a mathematical constant approximated as 2.7183, "i" is the interest rate (1.5%) and "t" is the investment time in years (1):

$B= 200*e^{0.015*1}$

$B= 203.02$

April's balance would be $203.02 after one year.

5 0

3 years ago