1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Genrish500 [490]
3 years ago
8

Find the points of intersection of the graphs of the equations.

Mathematics
1 answer:
AURORKA [14]3 years ago
4 0

Answer:

To find the point of intersection, just solve for x and y in the equations

so since x - y = -5

x = y - 5

now that we have a value of x, we will substitute x with in in the other equation

<em>5x + 3y = -9</em>

<em>5(y-5) + 3y = -9</em>

<em>5y - 25 + 3y = -9</em>

<em>8y = 16 </em>

y = 2

now use this value of y in the equation we made for x

<em>x = y - 5</em>

<em>x = 2 - 5</em>

x = -3

Hence, the point of contact is (-3 , 2)

You might be interested in
Find an equation of the line passing through the point (-4,6) that is perpendicular to the line y=7/2x+5. Work please.
kondaur [170]

Answer:

y = -\frac{2}{7}x + 4\frac{6}{7}

Step-by-step explanation:

We are to find the equation of line 1 which passes through point (-4,6)

Line 1 is perpendicular to line 2.

The equation of line 2 is; y = \frac{7}{2}x + 5

The slope of line 2 is  \frac{7}{2}

Because the product of two perpendicular line is -1;

The slope of line 1 is -1 ÷  \frac{7}{2} =  \frac{-2}{7}

Taking another point (x,y) on line 1;

Slope = change in y ÷ change in x

\frac{-2}{7} = \frac{y - 6}{x - -4}

y - 6 =  \frac{-2}{7}(x + 4)

y - 6 =  \frac{-2}{7}x - \frac{8}{7}

y =  \frac{-2}{7} - \frac{8}{7} + 6

y = -\frac{2}{7}x + 4\frac{6}{7}

8 0
3 years ago
Find the intercepts and graph each line.<br><br> a.) x – 4y =− 4<br> b.) 2x + 5y =-10
Snezhnost [94]

Answer:

(1,5) I think that's what it is

4 0
1 year ago
Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, the
fenix001 [56]

Answer:

(a): Marginal pmf of x

P(0) = 0.72

P(1) = 0.28

(b): Marginal pmf of y

P(0) = 0.81

P(1) = 0.19

(c): Mean and Variance of x

E(x) = 0.28

Var(x) = 0.2016

(d): Mean and Variance of y

E(y) = 0.19

Var(y) = 0.1539

(e): The covariance and the coefficient of correlation

Cov(x,y) = 0.0468

r \approx 0.2657

Step-by-step explanation:

Given

<em>x = bottles</em>

<em>y = carton</em>

<em>See attachment for complete question</em>

<em />

Solving (a): Marginal pmf of x

This is calculated as:

P(x) = \sum\limits^{}_y\ P(x,y)

So:

P(0) = P(0,0) + P(0,1)

P(0) = 0.63 + 0.09

P(0) = 0.72

P(1) = P(1,0) + P(1,1)

P(1) = 0.18 + 0.10

P(1) = 0.28

Solving (b): Marginal pmf of y

This is calculated as:

P(y) = \sum\limits^{}_x\ P(x,y)

So:

P(0) = P(0,0) + P(1,0)

P(0) = 0.63 + 0.18

P(0) = 0.81

P(1) = P(0,1) + P(1,1)

P(1) = 0.09 + 0.10

P(1) = 0.19

Solving (c): Mean and Variance of x

Mean is calculated as:

E(x) = \sum( x * P(x))

So, we have:

E(x) = 0 * P(0)  + 1 * P(1)

E(x) = 0 * 0.72  + 1 * 0.28

E(x) = 0   + 0.28

E(x) = 0.28

Variance is calculated as:

Var(x) = E(x^2) - (E(x))^2

Calculate E(x^2)

E(x^2) = \sum( x^2 * P(x))

E(x^2) = 0^2 * 0.72 + 1^2 * 0.28

E(x^2) = 0 + 0.28

E(x^2) = 0.28

So:

Var(x) = E(x^2) - (E(x))^2

Var(x) = 0.28 - 0.28^2

Var(x) = 0.28 - 0.0784

Var(x) = 0.2016

Solving (d): Mean and Variance of y

Mean is calculated as:

E(y) = \sum(y * P(y))

So, we have:

E(y) = 0 * P(0)  + 1 * P(1)

E(y) = 0 * 0.81  + 1 * 0.19

E(y) = 0+0.19

E(y) = 0.19

Variance is calculated as:

Var(y) = E(y^2) - (E(y))^2

Calculate E(y^2)

E(y^2) = \sum(y^2 * P(y))

E(y^2) = 0^2 * 0.81 + 1^2 * 0.19

E(y^2) = 0 + 0.19

E(y^2) = 0.19

So:

Var(y) = E(y^2) - (E(y))^2

Var(y) = 0.19 - 0.19^2

Var(y) = 0.19 - 0.0361

Var(y) = 0.1539

Solving (e): The covariance and the coefficient of correlation

Covariance is calculated as:

COV(x,y) = E(xy) - E(x) * E(y)

Calculate E(xy)

E(xy) = \sum (xy * P(xy))

This gives:

E(xy) = x_0y_0 * P(0,0) + x_1y_0 * P(1,0) +x_0y_1 * P(0,1) + x_1y_1 * P(1,1)

E(xy) = 0*0 * 0.63 + 1*0 * 0.18 +0*1 * 0.09 + 1*1 * 0.1

E(xy) = 0+0+0 + 0.1

E(xy) = 0.1

So:

COV(x,y) = E(xy) - E(x) * E(y)

Cov(x,y) = 0.1 - 0.28 * 0.19

Cov(x,y) = 0.1 - 0.0532

Cov(x,y) = 0.0468

The coefficient of correlation is then calculated as:

r = \frac{Cov(x,y)}{\sqrt{Var(x) * Var(y)}}

r = \frac{0.0468}{\sqrt{0.2016 * 0.1539}}

r = \frac{0.0468}{\sqrt{0.03102624}}

r = \frac{0.0468}{0.17614266944}

r = 0.26569371378

r \approx 0.2657 --- approximated

8 0
3 years ago
the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the
Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

.35+.05x

Let y be the newspaper they sell, then the income will be

y(.35+.05x)

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

y=500-20x

Plugging the value of y in the first expression we have that the income will be

\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}

Then the income is given by the function

f(x)=-x^2+18x+175

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}

no we equate the derivative to zero and solve for x.

\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

4 0
1 year ago
Please help this one doesnt nee and explantion
ICE Princess25 [194]

Answer:

$159.99 * .25 "C"

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • What can you tell about the rate of the two reactions shown in the graph? A. They occurred at the same rate. B. One reaction sta
    15·1 answer
  • A system of linear inequalities is shown below. y ≥ –2x – 3 1 y&lt;2x+1 Which of the following ordered pairs is a solution to th
    7·1 answer
  • A room is 8.5 m long,6.5 m broad and 3.4 m high. It has two doors, each measuring (2 m 1m).Find the cost of painting its four wa
    11·1 answer
  • What’s the measure of angle F?
    14·1 answer
  • Using similar triangles if KLM~ PQR with a scale factor of 3:5, find the perimeter of PQR (With work please)
    8·2 answers
  • If Tammy takes 200 steps to travel 1/4 of a city block, how many steps will she take to travel 4 3/4 city blocks?
    13·2 answers
  • Which expression is equivalent to 4 - (-7)​
    8·2 answers
  • 20 friends to 15 strangers
    7·2 answers
  • I need help doin this please
    10·1 answer
  • Type the correct answer in each box.<br><br> Find the elements of matrix A.<br><br> help PLS!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!