Which of the following ordered pairs are solutions to the system of equations below?
(3x + 5y = 14
y = 1/2x + 5)
O (2.4)
0 (-2,4)
O (2,6)
O (-2,6)

If the functions f(x) and g(x) are equal, then the value of x is 3

The definition of the functions f(x) and g(x) are given as

f(x) = -2x + 4

g(x) = 2x - 8

The question states that:

The values of the functions are equal

This implies that we set the functions f(x) and g(x) equal to one another

This is represented as

f(x) = g(x)

Next, we substitute the equations of the above functions in f(x) = g(x)

So, we have the following equation

-2x + 4 = 2x - 8

Collect the like terms

So, we have

2x + 2x = 8 + 4

Evaluate the like terms in the above equation

So, we have

4x = 12

Divide both sides of the equation by 4

x = 3

We calculate the value of x to be 3

This means that the value of x if the functions have the same value is 3

Recall that:

f(x) = -2x + 4

g(x) = 2x - 8

So, we plot the graphs of the functions

See attachment for the graph of the functions

Read more about functions at

https://brainly.com/question/2946572

#SPJ1

Answer: 7 1/2 miles mire

Step-by-step explanation:

\(m\angle ABC=24^{\circ}\) by the inscribed angle theorem.

Answer:= 24

Step-by-step explanation:

by the inscribed angle theorem.

The right choice is (C) 91. The correlation between the variables x and y is significant.

Using a regression line, it is possible to predict a student's score if they study seven hours.

A regression line usually looks like this:

y = α + βx

In this case, Y is the dependent variable, and X is the independent variable.

The equation for regression is:

y = 56.114 + 5.044 x

Determine the value of y as follows for x = 7:

y = 56.114 + 5.044 x

= 56.114 + (5.044 * 7)

= 91.422

≈ 91

Consequently, a student who studied for seven hours received a score of 91.

To learn more about dependent variable here

https://brainly.com/question/1479694

#SPJ4

Full Question = The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. What is the best predicted value for y given x = 7? Assume that the variables x and y have a significant correlation.

Hours, x 3 5 2 8 2 4 4 5 6 3

Scores, y 65 80 60 88 66 78 85 90 90 71

Choose one answer.

A. 89

B. 90

C. 91

D. 92

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

learn more about similar triangles from

https://brainly.com/question/14285697

#SPJ1

After regrouping 1 tenth into 10 hundredths; we have; 1 whole, 5 tenths, and 10 hundredths, After crossing out 3 tenths and 2 hundredths,; what we have left is; 1 whole, 2 tenths, and 8 hundredths. the result is; 1.28

Given data :

The model can be used as follows;

The model shows a total of 1 whole and 6

tenths. After regrouping 1 tenth into 10

hundredths, there is 1 whole, 5 tenths, and

10 hundredths. After crossing out 3 tenths

and 2 hundredths, there is 1 whole, 2 tenths, and 8 hundredths.

According to the question;

After regrouping 1 tenth into 10 hundredths; we have; 1 whole, 5 tenths, and 10 hundredths

After crossing out 3 tenths

and 2 hundredths,; what we have left is; 1 whole, 2 tenths, and 8 hundredths.

Ultimately, the result is; 1.28

Learn more about Place value refer to :

https://brainly.com/question/25137147

#SPJ1

The Horizontal Line Test determines whether or not a function is one-to-one.

Create a graph of the function you want to test.

Cross the graph with horizontal lines.

Examine the graph to see if any horizontal lines intersect it more than once.

The function is one-to-one if no horizontal line meets the graph more than once.

The function is not one-to-one if any horizontal line intersects the graph more than once.

"The Horizontal Line Test is used to determine whether a function is one-to-one" is correct.

The Horizontal Line Test is a graphical approach for determining whether or not a function is one-to-one.

A function is said to be one-to-one (or injective) if each element in its range corresponds to a unique element in the function.

To put it another way, no two elements in the function's domain should map to the same element in the range.

To use the Horizontal Line Test, we draw a horizontal line over the function graph.

The function is one-to-one if the horizontal line touches the graph of the function at exactly one spot for each horizontal position.

If the horizontal line meets the function's graph at more than one place for any horizontal location, the function is not one-to-one.

It should be noted that not all functions are one-to-one.

For instance, consider the quadratic function

For example, a quadratic function like \(y = x^2\) is not one-to-one because different values of x can produce the same value of y.

On the other hand, a straight line function like y = mx + b is always one-to-one because it has a constant slope and does not intersect itself.

For similar question on Horizontal Line.

https://brainly.com/question/25081736

#SPJ11

Answer:

x = cos 135° = - (√2) / 2

Step-by-step explanation:

x = cos 135° = - √2/2

Answer:

  a) -12x -3

  b) 12x +9

Step-by-step explanation:

Put the argument into the function expression and simplify.

a) f(-x) = 12(-x) -3 = -12x -3

__

b) f(x+1) = 12(x+1) -3 = 12x +9

Answer:

$59.94

Step-by-step explanation:

So for this question, you need to find 8% of 748.

You can do this by multiplying .08 by 748:

.08(748) = 59.94

Answer:

149.6

Step-by-step explanation:

I. First we will find the value of a

II. Then we need to find b

we substitute the value of a

we apply natural logarithm on both sides

The value of b is 4

b=4

III.

IV.

We will use the natural logarithm

V.

Then for e

Then we substitute

we simplify

ANSWER

a=27

b=4

c=1/16

d=2

e=1/3

De acuerdo con la información podemos inferir que la población se refiere a los habitantes de la ciudad y la muestra es 40,000 personas.

Para identificar la información faltante debemos tener en cuenta la información del enunciado. En este caso nos dicen que quieren implementar una revista en una ciudad determinada y para identificar los temas de la revista debemos hacer una encuesta.

En este caso, la entrevista se realiza a 40,000 personas por lo que esta sería la muestra debido a que no podríamos realizar la encuesta a cada una de las personas que es habitante de la ciudad.

Nota: Esta pregunta está incompleta. Aquí está la información completa:

Aprenda más sobre población y muestra en: https://brainly.com/question/22903538

#SPJ1

Answer:

C. (x-3)(x+2)(x+1)

Step-by-step explanation:

We can use the rational roots test to help factor out the original equation.

The leading term is 1 and the constant is 6

p/q= 6/1

Now we find factors (all these are plus and minus)

1,2,3,6

1

We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function

Factor, (x+1)

Now we have (x+1)(x^2-x-6)

Factor this with whatever method you perfer, I use AC method

Find two that are a product of -6 and add to -1 (-3 and 2)

We get (x+1)(x-3)(x+2)

C

Answer:

\(\boxed{C}\)

Step-by-step explanation:

Let's solve all of the option and see which equals x³-7x-6

Option A)

\((x-4)(x-2)(x+1)\)

=> \((x^2-6x+8)(x+1)\)

=> \(x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1\)

So, A is not correct

Option B)

\((x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6\)

This is also not correct

Option C)    ← Correct

\((x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6\)

This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!

Answer:

m=3 I think not sure

Step-by-step explanation:

Answer:

1500 millimeters

Step-by-step explanation:

1 meter = 1000 millimeters

1.5 meters = 1500 millimeters

Answer:

Part 1) \(LN=5.5\ units\)

Part 2) \(MN=2\ units\)

Step-by-step explanation:

Part 1) What is the length of LN?

To find out the length LN subtract the coordinate of L from the coordinate of N

so

\(LN=3-(-2.5)\\LN=3+2.5\\LN=5.5\ units\)

Part 2) What is the length of MN?

To find out the length MN subtract the coordinate of M from the coordinate of N

so

\(MN=3-(1)\\MN=2\ units\)

Answer:

120

Step-by-step explanation:

Simply do (7.5*8*4)/2=240/2=120

Answer:

To find the volume of this prism, we must first find the area of the triangle and then multiply the area of the triangle by the prism's width.

We must know the formula for the area of a triangle;

A = BH

Where b is the base, and h is the height.

In this case, 4 is the base and 7.5 is the height, so we plug this into our formula:-

A = BH

A = 4(7.5)

A = 30

Now we must multiply the area of the triangle with the prism's length which is 8.

30(area of triangle) x 8(width of prism)

= 240 cubic meters (240^3 meters) is your volume.

Graph 1:

Slope: -3

X-Intercept: -1

Y-Intercept: -3

Graph 2:

Slope: 2

X-Intercept: 3

Y-Intercept: -6

Graph 3:

Slope: 3/2

X-Intercept: -4

Y-Intercept: 6

Graph 4:

Slope: -2/3

X-Intercept: 3

Y-Intercept: 2

*The picture is a bit blurry so I'm guessing the intervals are going by ones. Sorry if I'm wrong

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  standard deviation is  \(\sigma = 2.45\)  

Step-by-step explanation:

From the given data we can compute the expected mean for each random values as follows

          \(E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6\)

So  

          \(E(x) = 0 + 0.6 + 0.8 + 0.6\)

          \(E(x) = 2\)

The  

             \(E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6\)

So  

        \(E(X^2) = 0 + 1.2 + 3.2 + 3.6\)

        \(E(X^2) = 8\)

Now  the variance is  mathematically evaluated as

         \(Var (X) = E(X^2 ) -[E(X]^2\)

Substituting value  

        \(Var (X) = 8-4\)

        \(Var (X) = 6\)

The standard deviation is mathematically evaluated as

       \(\sigma = \sqrt{Var(x)}\)

      \(\sigma = \sqrt{4}\)

      \(\sigma = 2\)

Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

Read more about signal

https://brainly.com/question/14699772

#SPJ1

sharon spent 23/20 hour doing her homework than reading.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Sharon spent reading the book = \(1 \frac{1}{4}\) = 5/4 hours

                                                     = 25/20 hours

Sharon spend doing homework = \(2 \frac{2}{5}\) = 12/5 hours

                                                      = 48/20 hours

So, the difference between both activities

= 48/20- 25/20

= 23/20

Hence, sharon spent 23/20 hour doing her homework than reading.

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ1

Answer:

(16.75x) + 50

Step-by-step explanation:

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

For more such questions on profit function

https://brainly.com/question/16866047

#SPJ8

Given:

The two models for the two polynomials.

To find:

The sum of the given polynomials.

Solution:

From the given figure, it clear that

\(\text{First polynomial}=a^2+a+2\)

\(\text{Second polynomial}=-a-1\)

Adding both polynomials, we get

\(Sum=a^2+a+2+(-a-1)\)

\(Sum=a^2+a+2-a-1\)

\(Sum=a^2+1\)

Therefore, the correct option is A.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

For more such question on function. visit :

https://brainly.com/question/11624077

#SPJ8

The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².

From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.

It should be noted that 15% of the material will be:

= 15% × 115.4

= 17.31 ft²

It should be noted that 20% of the material will be:

= 20% × 115.4

= 23.08 ft²

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

Answer:

$1000

Step-by-step explanation:

It would be $1000 in total of all the people attending the party. This is because, you need to multiply, 50 and 20! The answer will be 1000.

Answer:

D' = (5, 2)

Step-by-step explanation:

Try to join D and the origin using a line. Counterclockwise means in an opposite direction of rotation of the clock hands. So draw another line towards the right which is perpendicular to the previous line to fine the answer. Remember the length of the lines should be equal.

Answer:

If ET is 20 then DS should be 30 which makes RS 90

Step-by-step explanation:

Hope this helps. :)