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katrin2010 [14]
2 years ago
14

30 points plus brainliest if answered right!

Mathematics
2 answers:
alukav5142 [94]2 years ago
8 0

Answer:

AC = 5, BC = √17, AB = √32

Explanation:

Given points: A(-3, -2), B(1, 2), C(2, -2)

Use distance between two points formula:

\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

AC length:

\sf d =  \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2}  = \sqrt{25+ 0}  = 5

BC length:

\sf d =  \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2}  = \sqrt{1 + 16}  = \sqrt{17}

AB length:

\sf d =  \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2}  = \sqrt{16 + 16}  = \sqrt{32}

Anettt [7]2 years ago
4 0

Answer:

The second choice.

Step-by-step explanation:

The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.

Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.

Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.

Therefore, we are left with the second option.

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Complete the table using the relationship between q and t.
kati45 [8]
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3 years ago
let f(x)= p+ 8/x-q. the line x=4 is a vertical asymptote to the graph of f. what is the value of q and p, if the y intercept is
svlad2 [7]

Answer:

The value of q and p is 4 and -24  respectively.

Step-by-step explanation:

Being f(x)=\frac{p+8}{x-q} , the line x=4 is a vertical asymptote to the graph of f(x).  The line r is an asymptote of a function if the graph of the function is infinitely close to the line r. That is, an asymptote is a line to which a function approaches indefinitely, without ever touching it.

Being a rational function that which can be expressed as the quotient of two polynomials, a vertical asymptote occurs when the denominator is 0, that is, where the function is not defined. In this case:

x - q= 0

Solving:

x= q

Being the line x=4 the vertical asymptote, then

<u><em>4=q</em></u>

Then the function f (x) is:

f(x)=y=\frac{p+8}{x-4}

The y intercept is (0,4). This is, x= 0 and y=4. Replacing:

4=\frac{p+8}{0-4}

Solving:

4=\frac{p+8}{-4}

4*(-4)= p+8

-16= p+8

-16 - 8= p

<u><em>-24= p</em></u>

<u><em>The value of q and p is 4 and -24  respectively.</em></u>

7 0
3 years ago
A trucking firm suspects that the mean life of a certain tire. it uses is less than 33,000 miles. To check the claim, the firm r
Mice21 [21]

Answer:

We accept the alternate hypothesis. We conclude that the mean lifetime of tires is  is less than 33,000 miles.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 33,000 miles

Sample mean, \bar{x} =  32, 450 miles

Sample size, n = 18

Alpha, α = 0.05

Sample standard deviation, s = 1200 miles

a) First, we design the null and the alternate hypothesis

H_{0}: \mu = 33000\text{ miles}\\H_A: \mu < 33000\text{ miles}

b) Level of significance:

\alpha = 0.05

c) We use One-tailed t test to perform this hypothesis.

d) Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} } Putting all the values, we have

t_{stat} = \displaystyle\frac{32450 - 33000}{\frac{1200}{\sqrt{18}} } = -1.9445

Now, t_{critical} \text{ at 0.05 level of significance, 17 degree of freedom } = -1.7396

Rejection area:

t < -1.7396

Since,                  

t_{stat} < t_{critical}

e) We fail to accept the null hypothesis and reject it as the calculated value of t lies in the rejection area.

f) We accept the alternate hypothesis. We conclude that the mean lifetime of tires is  is less than 33,000 miles.

3 0
3 years ago
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