A function and its inverse are shown on the same graph. Complete the sentences to compare the functions.

The y-intercept of f(x) has the same value as the ___

f(x)
The function(x) has a range including all values
greater than or equal to 0; therefore the, ____ does also.

The number that will produce a rational number when multiplied by 1/5 is A. 10.

A rational number is one that can be written in the form of a fraction where the denominator isn't 0. This number is an integer and does not repeat infinitely.

When 1/5 is multiplied by 10 we get:

= 1/5 x 10

= 2

2 is a rational number so option A is correct.

The full question is:

Which number produces a rational number when multiplied by 1/5?

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to get the equation of any straight line, we simply need two points off of it, let's use those two points from the table in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{13})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-17}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-17}-\stackrel{y1}{13}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-30}{6 +4} \implies \cfrac{ -30 }{ 10 }\implies -3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{-3}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-13=-3(x+4)\implies y-13=-3x-12\implies y=-3x+1[/tex]

Answer:

(B

The given system of equations are:

y=x^2+3x+3y=x

2

+3x+3 (1)

and y=x^2+x+2y=x

2

+x+2 (2)

Subtracting equation (2) from (1), we get

0=2x+10=2x+1

⇒2x=-12x=−1

⇒x={\frac{-1}{2}}x=

2

−1

⇒x=-0.5x=−0.5

Now, substituting the value of x=-0.5 in equation (2), we get

y=0.25-0.5+2y=0.25−0.5+2

⇒y=1.7y=1.7

Thus, the values of x and y are -0.5 and 1.7.

Therefore, the approximate solution of the given system of the equation is (-0.5, 1.7).

Hence, option (B) is correct.

The slope and the y intercept of the line on the graph is -1/4 and 1.

A straight line function is what can be written in the form of

y =mx +c

where m is the slope and c is the intercept on y axis.

The intercept on the y axis , c = 1

at x = 4 , y=0

and at x = 0, y =1

The slope can be calculated as

y = mx+1

0 = 4m +1

m = -1/4

Therefore the slope and the y intercept of the line on the graph is -1/4 and 1.

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Answer:

The item has a 9% sales tax.

Step-by-step explanation:

Given the following question:

We are given an item that costs 490 dollars before tax, the sales tax of the item is $44.10, which means the item will cost $534.10 in total. Assuming what you are asking is to find the percentage of the sales tax we will use the formula to calculate percentages, and then add that answer to our before cost to confirm our answer.

Formula to calculate percentages:

[tex]\frac{p\times n}{100}[/tex]
[tex]p=9[/tex]
[tex]\frac{9\times490}{100}[/tex]
[tex]9\times490=4410[/tex]
[tex]4410\div100=44.1=44.10[/tex]
[tex]490+44.10=534.10[/tex]
[tex]=534.10[/tex]

Our sales tax percentage is 9%.

Hope this helps.

Using a dot plot, it is found that the number of dots of each point are given as follows:

The dot plot shows the number of times each measure appears in the data-set.

In this problem, one measure has a value of 1/8, hence:

The value [tex]\frac{1}{8}[/tex] will have one dot above it.

Two measures have a value of 1/4, hence:

The value [tex]\frac{1}{4}[/tex] will have two dots above it.

Three measures have a value of 3/8, hence:

The value [tex]\frac{3}{8}[/tex] will have three dots above it.

Five measures have a value of 1/2, hence:

The value [tex]\frac{1}{2}[/tex] will have five dots above it.

Two measures have a value of 5/8, hence:

The value [tex]\frac{5}{8}[/tex] will have two dots above it.

Three measures have a value of 3/4, hence:

The value [tex]\frac{3}{4}[/tex] will have three dots above it.

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Answer:

1 2 3 5 2 3

Step-by-step explanation:

Let's take this problem step-by-step:

Let's first set up some variables:

Let's examine the information given:

          ⇒ average child is 75 pounds

          ⇒ average adult is 150 pounds

                 ⇒ therefore: [tex]75c + 150a\leq 1500[/tex]

          ⇒ therefore: [tex]c + a \leq 14[/tex]

Let's graph the equations:

 [tex]75c+150a\leq 1500\\c+a\leq 14[/tex]

    ⇒ look at the image attached

The point at which the two graphs intersect:

  ⇒ is the solution that represents the amount of children and adults and

      their combine weight

With the horizontal axis being the # of children and vertical axis being the # of adults:

 ⇒ the solution is 8 children and 6 adults

Answer: 8 children and 6 adults

Hope that helped!

Step-by-step explanation:

2, 2, 3, 4, 5, 5, 5, 6, 6, 7, 9, 10

_

2+2+3+4+5+5+5+6+6+7+9+10 = 64 ÷ 12 = 5.3

_

Mean: 5.3

Median: 5

Answer:

28

Step-by-step explanation:

Circumference = 2*pi*r

r = 1/2*diameter = 4.5

pi = 3.14

Circumference = 2*(3.14)*(4.5) = 28.26 = 28

Answer:

279 miles

Step-by-step explanation:

31 miles/gal  *  9 gallons = 279 miles

The expressions for (h+g)(x) and (h-g)(x) and evaluate (h-g) (4) is 9x-3 ,  x+3 and 7

A function is defined as the law that build relation between a dependent variable and an independent variable.

It is given that

functions g and h are defined for all real numbers x as follows.

g(x) = 5x

h(x) = 4x-3

the expressions for (h+g)(x)= ?

(h+g)(x)= 5x+4x-3

(h+g)(x)= 9x-3

and (h-g)(x) = ?

(h-g)(x) = 5x - 4x +3

(h-g)(x) = x+3

and evaluate (h-g) (4).

(h-g)(x) = x+3

at x = 4

(h-g)(4) = 4+3 = 7

Therefore the value for the functions have been determined.

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Answer:

$0.60 per pound

Step-by-step explanation:

Dollars per pound :

The attached graph shows that the system of equation has no solution since there is no point of intersection

Inequalities are expressions not separated by an equal sign

Given the following inequalities

2y < -12x + 4

y <- 6x +4

_________________

2y < -6x + 4

y <- 6x +4.

Find the y-intercept. When x = 0

y < -6(0) + 4

y < 4

Plot the graphs and determine the point of intersection

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Answer:

392

Step-by-step explanation:

hope this helps!!

The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have three linear equations in three variables:

x - y - z = 0 ..(1)

2x - y + 2z = 1 ..(2)

x - y + z = -2 ..(3)

From the equation (1):

[tex]\rm x=y+z[/tex]

Plug this value in the equation (2) and (3):

[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]

After solving we get:

z = -1

y = 5

Plug the above two values in equation (1) we get:

x = 4

Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.

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Answer:

3.5x10^4 is 50 times larger than 7x10^2

Step-by-step explanation:

3.5x10^4 is 35,000 (move decimal 4 places to the right)

7x10^2 is 700 (7.0 move decimal 2 places to the right)

700x50=35,000 which shows that 35,000 is 50 times larger than 700

The points mean that the temperature at 11 am and 7 pm is 6 degree Celsius

The given parameters are:

The points are given as:

(x, y) = (-1,6) and (7,6)

-1 represents 11 am and 7 represents 7 pm.

The points mean that:

The temperature at 11 am and 7 pm is 6 degree Celsius

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Answer:

12 years

Step-by-step explanation:

1 inch = two years

6x2=12

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 5x + 6 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + 3x + 2x + 6 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {x}^{}( x+ 3) + 2(x + 3)= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: {}^{}( x+ 2)(x + 3)= 0[/tex]

[tex] \begin{cases} \sf \: x = - 2 \: \: \: \: \: \: \: \sf if \: (x + 2) = 0 \\ \\ \sf \: x = - 3 \: \: \: \: \: \: \: if \: (x + 3) = 0\end{cases} [/tex]

I hope that helps ~

Answer:

See below

Step-by-step explanation:

The CENTER will de directly between the two given points

h, k   = -1,7

so...so far the circle eq is

  (x+1)^2 + ( y-7)^2

the RADIUS is  1/2 of the distance between the given points

1/2  d = (using distance formula) = 1/2 sqrt 80     = 4.472

then the equation of the circle in standard form

 (x+1)^2  + (y-7)^2 = 20          

Answer:  93 boxes will be needed

Step-by-step explanation:

     If each box holds 16 paperweights, and 1,486 need to be packaged, we will divide 1,486 by 16.

1,486 / 16 = 92.875

    We will assume you cannot have 0.875 of a box, so we will round up to:

              93 boxes will be needed

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Answer:

2 733.25 + 7270 = 10 003.25

Step-by-step explanation:

192 * 36 = 6 912 +358 = 7 270

45425 - 36000 ( allowed miles for 3 years )

9 425 * 0.29 = 2 733.25

Answer:

see the attachment photo!

Answer:

  C.  (1, -1/2)

Step-by-step explanation:

The midpoint of a line segment has coordinates that are the average of the end point coordinates.

__

  M = (A +B)/2 . . . . . . midpoint of segment between A(1, 4) and B(1, -5)

  M = ((1, 4) +(1, -5))/2 = (1 +1, 4 -5)/2 = (2, -1)/2

  M = (1, -1/2)

The midpoint of the vertical line segment is (1, -1/2).

_____

Additional comment

The midpoint will always be on the line segment. Since this line segment is vertical with x = 1, the x-coordinate of the midpoint must be 1.

Answer:

es kunno.............................