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3 years ago

I DONT UNDERSTAND HOW TO DO THISSS PLEASE HELP

Mathematics

1 answer:

Fiesta28 [93]3 years ago

5 0

Answer:

inside

Step-by-step explanation:

All of the points on the circle are at distance 25 units from the center. If the questionable point is closer to the center than that, it is inside the circle.

The distance formula can be used.

d = √((x2 -x1)^2 +(y2 -y1)^2)

d = √((5 -(-5))^2 +(-24 -(-8))^2) = √(10^2 +(-16)^2) = √(100 +256) = √356

d ≈ 18.9

The point (5, -24) is inside the circle centered at (-5, -8) with radius 25.

The equation of the circle is equivalent to d=25 using (x1, y1) as the center. It is usually written without the radical:

(x -(-5))^2 +(y -(-8))^2 = 25^2

(x +5)^2 +(y +8)^2 = 625

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miv72 [106K]

we are given equation of line

$y=\frac{2}{3} x+1$

Equation of perpendicular line:

Firstly , we will find slope of line

$y=\frac{2}{3} x+1$

we can compare it with

y=mx+b

we get

$m=\frac{2}{3}$

we know that

slope of perpendicular line will be -1/m

so, slope is

$\frac{-3}{2}$

It passes through point (-4,5)

so, we can use point slope form of line

$y-5=-\frac{3}{2}(x+4)$

we get

$y=-\frac{3}{2}x-1$ ..........Answer

Equation of parallel line:

Firstly , we will find slope of line

$y=\frac{2}{3} x+1$

we can compare it with

y=mx+b

we get

$m=\frac{2}{3}$

we know that

slope of parallel line always equal

so, slope is

$\frac{2}{3}$

It passes through point (-4,-5)

so, we can use point slope form of line

$y+5=\frac{2}{3}(x+4)$

we get

$y=\frac{2}{3}x-\frac{7}{3}$ ............Answer

4 0

4 years ago

Find two numbers given that their sum is 60 and

likoan [24]

Answer:

12 and 48

Step-by-step explanation:

let n be the larger number , then $\frac{1}{4}$ n is the smaller number and their sum is

x + $\frac{1}{4}$ x = 60 ( multiply through by 4 to clear the fraction )

4x + x = 240 , that is

5x = 240 ( divide both sides by 5 )

x = 48

smaller number = $\frac{1}{4}$ × 48 = 12

The 2 numbers are 12 and 48

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3 years ago

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3 years ago

Solve 4 ÷ one fourth = __

olya-2409 [2.1K]

Answer:

Step-by-step explanation:

6 0

3 years ago

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A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 85% confidence inter

Gre4nikov [31]

Answer:

$7.3-1.440\frac{1.2}{\sqrt{830}}=7.240$

$7.3+1.440\frac{1.2}{\sqrt{830}}=7.360$

So on this case the 85% confidence interval would be given by (7.2;7.4)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=7.3$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma =1.2$ represent the population standard deviation

n=830 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.85 or 85%, the value of $\alpha=0.15$ and $\alpha/2 =0.075$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.075,0,1)".And we see that $z_{\alpha/2}=1.440$

Now we have everything in order to replace into formula (1):

$7.3-1.440\frac{1.2}{\sqrt{830}}=7.240$

$7.3+1.440\frac{1.2}{\sqrt{830}}=7.360$

So on this case the 85% confidence interval would be given by (7.2;7.4)

7 0

3 years ago