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3 years ago

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ABC has A(-3,6),B(2,1),and C(9,5) as its vertices the length of side AB is units . The length of side BC is ?units . The length

of side AC is ? Units .ABC ?

1 answer:

yawa3891 [41]3 years ago

6 0

Answer:

The length of side AB is $\sqrt{50}$ units.

The length of side BC is $\sqrt{65}$ units.

The length of side AC is $\sqrt{145}$ units.

Step-by-step explanation:

To find the length of each side, we use the formula for the distance between two points.

Distance between two points:

Points $(x_1,y_1)$ and $(x_2,y_2)$ . The distance between them is given by:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Side AB:

Points $A(-3,6),B(2,1)$ . So the distance between them is:

$D = \sqrt{(2-(-3))^2 + (1-6)^2} = \sqrt{50}$

The length of side AB is $\sqrt{50}$ units.

Side BC:

Points $C(9,5),B(2,1)$ . So the distance between them is:

$D = \sqrt{(2-9)^2 + (1-5)^2} = \sqrt{65}$

The length of side BC is $\sqrt{65}$ units.

Side AC:

Points $A(-3,6),C(9,5)$ . So the distance between them is:

$D = \sqrt{(9-(-3))^2 + (5-6)^2} = \sqrt{145}$

The length of side AC is $\sqrt{145}$ units.

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ANEK [815]

Answer:

Given that,

R = 3x + 9y

Also, given that,

y = 6

R = 7

We have to find the value of x

For that, you can to put 6 and 7 to the equation instead of y and R respectively.

R = 3x + 9y

7 = 3x + 9 × 6

7 = 3x + 54

7 - 54 = 3x

- 47 = 3x

$\frac{-47}{3} = \frac{3x}{3}$

$\frac{-47}{3}=x$

Hope this helps you :-)

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2 years ago

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true

kvv77 [185]

Answer:

99.74% probability that the sample proportion will be less than 0.1

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 276, p = 0.06$

So

$\mu = E(X) = np = 276*0.06 = 16.56$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{276*0.06*0.94} = 3.9454$

What is the probability that the sample proportion will be less than 0.1

This is the pvalue of Z when X = 0.1*276 = 27.6. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{27.6 - 16.56}{3.9454}$

$Z = 2.8$

$Z = 2.8$ has a pvalue of 0.9974

99.74% probability that the sample proportion will be less than 0.1

5 0

4 years ago

Kera earns $12 per hour at her job. Every day she also earns $15 for walking her neighbor’s dog. She has decided to save all of

worty [1.4K]

Answer:

nah

Step-by-step explanation:

4 0

3 years ago

The equation giving a family of ellipsoids is u = (x^2)/(a^2) + (y^2)/(b^2) + (z^2)/(c^2) . Find the unit vector normal to each

Fynjy0 [20]

Answer:

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Step-by-step explanation:

Given equation of ellipsoids,

$u\ =\ \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}$

The vector normal to the given equation of ellipsoid will be given by

$\vec{n}\ =\textrm{gradient of u}$

$=\bigtriangledown u$

$=\ (\dfrac{\partial{}}{\partial{x}}\hat{i}+ \dfrac{\partial{}}{\partial{y}}\hat{j}+ \dfrac{\partial{}}{\partial{z}}\hat{k})(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2})$

$=\ \dfrac{\partial{(\dfrac{x^2}{a^2})}}{\partial{x}}\hat{i}+\dfrac{\partial{(\dfrac{y^2}{b^2})}}{\partial{y}}\hat{j}+\dfrac{\partial{(\dfrac{z^2}{c^2})}}{\partial{z}}\hat{k}$

$=\ \dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}$

Hence, the unit normal vector can be given by,

$\hat{n}\ =\ \dfrac{\vec{n}}{\left|\vec{n}\right|}$

$=\ \dfrac{\dfrac{2x}{a^2}\hat{i}+\ \dfrac{2y}{b^2}\hat{j}+\ \dfrac{2z}{c^2}\hat{k}}{\sqrt{(\dfrac{2x}{a^2})^2+(\dfrac{2y}{b^2})^2+(\dfrac{2z}{c^2})^2}}$

$=\ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

Hence, the unit vector normal to each point of the given ellipsoid surface is

$\hat{n}\ =\ \ \dfrac{\dfrac{x}{a^2}\hat{i}+\ \dfrac{y}{b^2}\hat{j}+\ \dfrac{z}{c^2}\hat{k}}{\sqrt{(\dfrac{x}{a^2})^2+(\dfrac{y}{b^2})^2+(\dfrac{z}{c^2})^2}}$

3 0

3 years ago

Vera is using her phone. Its battery lifw is down to 2/5 and it drains another 1/9 fraction every hour. How long will her batter

just olya [345]

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Battery drains at the rate of 1/9 every hour.

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So, 1/9 y = 3/5

y = 27/5

y = 5 + 2/5 hours

y = 5 hrs and 24 mins

So battery will last another 5 hrs and 24 mins.

hope this helps:)

4 0

3 years ago