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vlada-n [284]
3 years ago
7

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 ?
Mathematics
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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Given that
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 :-)

Let me know if you have any other questions :-)

3 0
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]

Battery is down currently = 2/5

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

Remaining battery life of Vera = 1 -2/5 = 3/5

Let y we the number of hours battery will last.

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
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