A salesperson has January sales of $20,000(1,$20,000) and April sales of $80,000 (4,$80,000). What is the rate of change?

Answer:

Step-by-step explanation:

I think you meant 3([7/5]x + 4) - 2(3/2 - [5/4]x).  If that's the case, then identify the LCD:  It is 20.  Multiply both [7/5]x + 4 and 3/2 - [5/4]x by 20 and then divide the resulting expression by 20:

3(28x + 80) - 2(30 - 25x)

------------------------------------

               20

Next, perform the indicated multiplication:

 84x + 240 - 60 + 50x

----------------------------------

                 20

This simplifies to:

 34x + 180        17x + 9

---------------- = ----------------

       20                 10

Next time, please share the answer choices.

Answer:

67x/10 + 9

Step-by-step explanation:

Simplify 7/5x to 7x/5

3(7x/5 + 4) -2(3/2 - 5/4x)

Simplify 5/4x to 5x/4

3(7x/5 + 4) -2(3/2 - 5x/4)

Expand

21x/5 + 12 - 3 + 5x/2

Collect like terms

(21x/5 + 5x/2) + (12 - 3)

Simplify

67x/10 + 9

Answer:

Part 1) h(g)=-4+g ----> the input is g

Part 2) f(h)=-h-7 -----> the input is h

Part 3) g(f)=-2f -----> the input is f

Step-by-step explanation:

Part 1) we have

h(g)=-4+g

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is h(g) or 4+g

the input  is the variable g

Part 2) we have

f(h)=-h-7

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is f(h) or h-7

the input  is the variable h

Part 3) we have

g(f)=-2f

we know that

The input  is the independent variable and the output is the dependent variable

so

the output is g(f) or 2f

the input  is the variable f

Answer: Questions are in different places than other people screen.

h(g) = -4+g     -       The input is G

g(f) = 2f          -       The input is F

f(h) = h - 7      -       The input is H

Step-by-step explanation:

Just put tha answer in nd get a good grade :)

Answer: A

Step-by-step explanation: The converse of a conditional is when the two statements switch spots, for example:

Conditional: If someone like ice cream, they have brown hair

Converse: If someone has brown hair, they like ice cream

The converse of our given conditional would be:

If two lines do not intersect, they are parallel

This eliminates Option D

Next, the converse is false.

Skew lines (example attached) do not intersect and are also not parallel, meaning if two lines do not intersect, they could be either parallel or skew.

This eliminates Option C and B, leaving us with Option A

We want to find the converse statement to one given statement and see if it is true.

We will see that the correct option is a:

If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.

A general statement is written as:

If P then Q.

Where P and Q are two given propositions.

The converse statement to the above shown is:

If Q then P.

For this question, we have the statement:

If two line are parallel, they do not intersect.

Then we can write the converse statement as:

If two lines do not intersect, they are parallel.

Which is false, in 3-dimensions we can have two non-parallel lines that don't intersect each other (parallel lines must not intersect and also live on the same plane).

Then the correct option is the first one:

a: If two lines do not intersect, they are parallel. One statement is false. If two lines do not intersect, they could be skew.

If you want to learn more you can read:

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Answer:

[7, -4, -8]

Step-by-step explanation:

Just simply plug in each choice into the equations to confirm their authenticities.

Answer:

h = (10 ft)(4.01) = 40.1 ft

Step-by-step explanation:

The tangent function relates this elevation to the horizontal distance (10 ft) and the angle of elevation (76 degrees):

                               opp           h

tan 76 degrees = --------- = ------------- = 4.01

                                adj         10 ft

Therefore , h = (10 ft)(4.01) = 40.1 ft

Answer: 40 ft

Step-by-step explanation:

You can find the height of the statue by solving the right triangle.

In this case the adjacent side of the triangle is the horizontal distance to the statue (10 ft). The height of the statue is the opposite side to the angle of 76 °.

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case

[tex]\theta=76\°\\\\opposite = h\\\\adjacent = 10\ ft[/tex]

Therefore

[tex]tan(76) = \frac{h}{10}[/tex]

[tex]h=tan(76) * 10\\\\h=40\ ft[/tex]

Answer:

The rest is 6+3=9 , 9-6=3 , 9-3=6.

Answer:  [tex]y=(x +3)^2 -6[/tex]

Step-by-step explanation:

The equation of a parabola in Vertex form is:

[tex]y=a(x-h)^2+k[/tex]

Where [tex](h,k)[/tex] is the vertex of the parabola

We can rewrite the function [tex]f(x)= x^2 + 6x + 3[/tex] as:

 [tex]y= x^2 + 6x + 3[/tex]

 In order to convert it into vertex form we need to Complete the square:

Take the coefficient of the x term, divide it by 2 and square it:

[tex](\frac{6}{2})=3^2[/tex]

Add and subtract 3² on the right side:

[tex]y= x^2 + 6x+3^2 + 3-3^2[/tex]

Now we must convert the right side to a squared expression, then we get:

 [tex]y=(x +3)^2 -6[/tex]

The percentage of bags contain between 65 and 85 potato chips is 95%.

Step-by-step explanation:

A probability distribution that is symmetric and the data near the mean are more frequent than far is known as a normal distribution. Normal distributions are important in statistics and are often used to represent real-valued random variables.

The formula for finding the percentage of bags using normally distributed is given as

f(x) = (1 / sigma * square root 2 *pi) * e^((-1/2)*((x-u)/sigma))

Substituting the values of mean and standard deviation,

The percentage of bags contain between 65 and 85 potato chips is 95%.

Final answer:

Using the empirical rule, approximately 95% of potato chip bags will contain between 65 and 85 chips, as this range spans two standard deviations away from the mean in a normal distribution.

Explanation:

The question is regarding the percentage of potato chip bags that contain a specific number of chips based on a normal distribution. With a mean of 75 and a standard deviation of 5, the range of chips in the bags is between 65 and 85. To find this percentage, we use the empirical rule, sometimes referred to as the 68-95-99.7 rule, which states that approximately 68% of the data within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Since the range from 65 to 85 chips spans two standard deviations from the mean (65 is 10 chips away from 75 which is two standard deviations as 5*2=10, and the same logic applies for 85), we can say that approximately 95% of the bags will contain between 65 and 85 potato chips.

Answer:

solution = (1.-2)

Step-by-step explanation:

put x= 1 and y = -2 in this system  :  y=-4x+2 and y + 2x = 0

you have :  - 2 = - 4(1)+2  and -2 +2(1)=0

-2=-2 and 0=0 .....right

The required solution of the given system of equations is (1, -2), and a graph of the solution has been shown.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
y=-4x+2 - - - -(1)
y + 2x = 0 - - - (2)

Equating equations,
-4x +2 = -2x
x =  1

Put x = -2 in equation 1
y = -4(1) + 2
y = -2

Thus, the required solution of the given system of equations is (1, -2).

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Answer:

Option B [tex]f(x)=-x^{2}+12x-32[/tex]

Step-by-step explanation:

we know that

For the given values, the quadratic function is a vertical parabola open downward (vertex is a maximum)

The equation in vertex form is equal to

[tex]f(x)=a(x-h)^{2} +k[/tex]

where

(h,k) is the vertex

a is a coefficient

we have

(h,k)=(6,4)

so

[tex]f(x)=a(x-6)^{2} +4[/tex]

Find the value of a

For x=8, y=0 -----> the y-intercept

substitute

[tex]0=a(8-6)^{2} +4[/tex]

[tex]0=a(2)^{2} +4[/tex]

[tex]0=4a +4[/tex]

[tex]a=-1[/tex]

substitute

[tex]f(x)=-(x-6)^{2} +4[/tex]

Convert to standard form

[tex]f(x)=-(x^{2}-12x+36) +4[/tex]

[tex]f(x)=-x^{2}+12x-36+4[/tex]

[tex]f(x)=-x^{2}+12x-32[/tex]

The graph in the attached figure

Answer:

[tex]\large\boxed{\text{no soltion in the set of real numbers}}\\\boxed{n=-\dfrac{3}{8}i\ \vee\ n=\dfrac{3}{8}i\ \text{in the set of complex numbers}}[/tex]

Step-by-step explanation:

[tex]18+128n^2=0\qquad\text{subtract 18 from both sides}\\\\128n^2=-18\qquad\text{divide both sides by 128}\\\\n^2=-\dfrac{18}{128}\\\\n^2=-\dfrac{18:2}{128:2}\\\\n^2=-\dfrac{9}{64}<0\to\bold{ no\ solution\ in\ the\ set\ of\ real\ numbers}\\\\\bold{In\ the\ set\ of\ Complex\ numbers}\\\\i=\sqrt{-1}\\\\n^2=-\dfrac{9}{64}\to n=\pm\sqrt{-\dfrac{9}{64}}\\\\n=\pm\sqrt{\dfrac{9}{64}\cdot(-1)}\\\\n=\pm\sqrt{\dfrac{9}{64}}\cdot\sqrt{-1}\\\\n=\pm\dfrac{\sqrt9}{\sqrt{64}}i\\\\n=\pm\dfrac{3}{8}i[/tex]

Answer:

Step-by-step explanation:

note that the square root of any number can be expressed as  the number raised to a [tex]\frac{1}{2}[/tex] power

i.e √a = [tex]a^{\frac{1}{2} }[/tex]

Applying this to our expression

[tex](\sqrt{x} )^{5}[/tex]

= [tex]x^{\frac{1}{2} * 5 }[/tex]

= [tex]x^{\frac{5}{2}}[/tex]

The Answer Is...

x^5/2

[tex]x^ \frac{5}{2}[/tex]

Answer:

(- [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Step-by-step explanation:

Using the midpoint formula

Given 2 points (x₁, y₁ ) and (x₂, y₂ ), then midpoint is

([tex]\frac{x_{1}+x_{2}  }{2}[/tex], [tex]\frac{y_{1}+y_{2}  }{2}[/tex])

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (- 8, - 4), then midpoint

= ([tex]\frac{-1-8}{2}[/tex], [tex]\frac{5-4}{2}[/tex] )

= ( - [tex]\frac{9}{2}[/tex], [tex]\frac{1}{2}[/tex] )

Answer:-4.5,0.5

Step-by-step explanation:midpoint =x1+x2/2, y1+y2/2

-1+-8/2=x,-4+5/2=y

-9/2=x,1/2=y

-4.5=x, 0.5=y

Answer:

18 square units

Step-by-step explanation:

you multiply the base by the hight after graphing the square.

ANSWER

C) (6,-8)

EXPLANATION

The equations are:

[tex]y = \frac{1}{3}x - 10[/tex]

and

[tex]2x+y=4[/tex]

We substitute the first equation into the second equation to get:

[tex]2x + \frac{1}{3}x - 10 = 4[/tex]

We multiply through by 3 to get:

[tex]6x + x - 30= 12[/tex]

Group similar terms,

[tex]6x + x = 30 + 12[/tex]

[tex]7x = 42[/tex]

Divide both sides by 7 to get,

[tex]x = \frac{42}{7} = 6[/tex]

Put this value of x into the first equation to get;

[tex]y = \frac{1}{3} (6) - 10[/tex]

[tex]y = 2 - 10 = - 8[/tex]

You would need to divide the money by 2 ( both sisters) to get the equal amount they each need to pay. Then include the extra amount Carlotta owes.

The correct equation would be -28 ÷ 2- (-6)

Answer:

a

Step-by-step explanation:

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 5

b = 8

c = x

^^^Plug these numbers into the theorem

[tex]5^{2} +8^{2} =x^{2}[/tex]

simplify

25 + 64 = [tex]x^{2}[/tex]

89 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

√89 = x  

(choice A)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer is first option  √89

Step-by-step explanation:

Points to remember

Pythagorean theorem

For a right triangle,

Base² + Height² = Hypotenuse²

To find the vale of x

From the figure we can see a right triangle,

Base = 8 units and height = 5 units

Hypotenuse² = Base² + Height²

x² = 8² + 5²

 = 64 + 25

 = 89

x = √89

The correct answer is first option  √89

Answer:

It would be (-2,11)

Step-by-step explanation:

I used desmos for this, since it says graphing.

desmos.com/calculator/glijhd4ksg

look at the link to view the graph and solution.

Normally, you would plot points from one line, connect them, then do the same for the other line.

Hope this helps!

When using a graph to find the solution you must look at where the lines intersect. Look at the graph provided below:

As you can see the graph below shows that the two lines intersect at point (-2, 11)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

4444₁₀

Step-by-step explanation:

4×10³=4000  (that's 10 to the power of 3)

4×10²=400

4×10¹=40

4×10⁰=4

4000+400+40+4=4444

Answer:

The range for the equation is all real numbers.

Step-by-step explanation:

The range of an equation is the set of y-values that you can get by plugging in all possible x-values.

Another way to put it is, when you graph the equation, whatever y-values the line produces, is its range.

Graphing y=2x-3, you can see it is a graph with a positive slope that extends from negative infinity y-value to positive infinity x-value.

since its complementary, the sum if both angles equals 90 degrees.

you do x+x+10 so you combine like terms to get 2x+10=90

then you subtract 10 to get

2x=80

and divide by 2

x=40

angle a=50 degrees

angle b=40 degrees

Answer:

m < A = 50 degrees, m < B = 40 degrees.

Step-by-step explanation:

Complementary angles sum to 90 degrees, so:

A + B = 90

As A = B + 10:

B + 10 + B = 90

2B = 80

B = 40.

So A = 40 + 10 = 50.

Answer:

15

Step-by-step explanation:

-225/-15 = 15

A negative divided by a negative is a positive

225/15 = 15

Answer:

15

Step-by-step explanation:

The value of expression -225 divided (-15) :

-225/-15 = 15

Answer:

c)

Step-by-step explanation:

-2 is the slope so that y equals -2x and the y intercept is positive 4 so that the equation is y=-2x+4

Answer:

c)  y = -2x+4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

Substituting in

y = -2x +4

Answer:

89.95 + 4x =628.35

x = 134.60

Step-by-step explanation:

The trip to the dentist had a flat fee plus 4 cavities for a total cost of 628.35

fee + 4 * cost of cavity = 628.35

Let x = the cost of each cavity

89.95 + 4x =628.35

Subtract 89.95 from each side

89.95-89.95 + 4x =628.35-89.95

4x =538.40

Divide each side by 4

4x/4 =538.40/4

x =134.60

Answer: its C. $669

Step-by-step explanation:

B^2 for B = 9 means squaring the value of 9, resulting in 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.

To evaluate B^2 for B = 9, you simply substitute the value of B into the expression and then perform the calculation. Here's how it's done:

B^2 means "B squared," which is equivalent to multiplying B by itself. So, for B = 9, we have:

[tex]\(B^2 = 9^2 = 9 \times 9\)[/tex]

Now, calculate the product:

[tex]\(9 \times 9 = 81\)[/tex]

So, B^2 for B = 9 is equal to 81.

In summary, when you substitute B = 9 into the expression B^2, you get 9^2, which equals 81. Therefore, B^2 for B = 9 is 81.

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Answer:

The numbers are -16,-15 and -14

Step-by-step explanation:

Let

x ----> the first number

x+1 ----> the second number

x+2 ---> the third number

we know that

(1/4)x+(1/5)(x+1)=(1/7)(x+2)-5

Multiply by (4*5*7) both sides

35x+28(x+1)=20(x+2)-140*5

35x+28x+28=20x+40-700

43x=-688

x=-16

so

x+1=16+1=-15

x+2=-16+2=-14

The numbers are -16,-15 and -14

Answer: Second option.

Step-by-step explanation:

Given the function f(x), which is:

[tex]f(x)=x[/tex]

And given the function g(x), which is:

[tex]g(x)=2[/tex]

You need to substiute the function [tex]g(x)=2[/tex]  into the function  [tex]f(x)=x[/tex] in order to find [tex](fog)(x)[/tex].

Therefore, through this procedure, you get this answer:

[tex](fog)(x)=(2)[/tex]

[tex](fog)(x)=2[/tex]

You can observe that this matches with the second option.

For this case we have the following functions:

[tex]f (x) = x\\g (x) = 2[/tex]

We must find [tex](f_ {0} g) (x).[/tex]

By definition of composite functions we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

We substitute g (x) into f (x), then we have:

[tex]f (g (x)) = 2[/tex]

Answer:

[tex]f (g (x)) = 2[/tex]

Option B