What is the equation of the function in vertex form? Substitute numerical values for a,h and k,

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]

         [tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]

x₂ = 620

[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]

         [tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]

Compute the average rate of change as follows:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

                                      [tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Answer:3.2 ft

Step-by-step explanation:

sin 32°=[tex]\frac{yz}{6}[/tex]

cross multiply

sin 32° x 6=yz

0.5299 x 6 =yz

yz=3.1795

≅3.2ft

Answer:

301.59

Step-by-step explanation:

your answer was almost right you just forgot to multiply by 9

Answer:

Options (1), (2) and (5)

Step-by-step explanation:

Outcomes from the quadratic function given in the graph,

1). Negative y-intercept of the graph represents the loss to the store when x = 0 Or the loss when no clerk is working.

2). Peak of the parabola represents a point (vertex) with x-coordinate as number of clerks working = 4 and y-coordinate as maximum profit earned by the store = $400,000

3). x-intercept of the graph shows the number of clerks working at store when profit earned by the store is zero.

Graph reveals that the store is in loss when number of clerks is zero and 8.

Summarizing these outcomes from the graph,

Options (1), (2), (5) are the correct options.

The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.

Which statements are true based on the model?

Answer:

The original width was 94.71 cm

Step-by-step explanation:

Given:

new smaller area = 1.2m^2

Decrease in length of the rectangular sheet = 34.5cm

Therefore:

1. the final width of the sheet is given as

2X^2 = 1.2 m^2

X^2 - 0.6 m^2

X^2 = 10000 * 0.6 cm

X = 77.46 cm (this is the width)

2. The length of the sheet

= 2 * 77.46

= 154.92 cm.

3. Initial length of the sheet

= 154.92 + 34.5

= 189.42 cm.

4. Initial width of the sheet ( original ).

= 189.42 / 2

= 94.71 cm.

5. Initial area of the sheet

= 94.71 * 189.92

= 17939.9 cm^2

New area of the sheet

= 79.46 * 154.92

= 12000.1 cm^2

Difference between the initial and new area

= 17939.9 - 12000.1

= 5939.86 cm^2

Percentage of area decrease

= 5939.86 ' 17939.9

= 33.1%

Answer:

Step-by-step explanation:

number of likely voters = 2022

candidate A = 49%

candidate B = 46%

margin of error = 5%

using the concept of a confidence interval to explain

from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.

also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL

Answer: x = 9[tex]\sqrt{2\\}[/tex], y =18

Step-by-step explanation:

cuz

Answer:

to be honest I'm not sure how to do

Answer:

[tex]x \leq -7[/tex]

The graph has a closed circle.

–7 is part of the solution.

Step-by-step explanation:

Given

[tex]15 \geq 22 + x[/tex]

Required

Select 3 options from the given list of options

[tex]15 \geq 22 + x[/tex]

Subtract 22 from both sides

[tex]15 - 22 \geq 22 - 22+ x[/tex]

[tex]-7 \geq x[/tex]

Swap positions of the expression; Note that the inequality sign will change

[tex]x \leq -7[/tex]

This means  x less-than-or-equal-to negative 7

There are two options left to select;

The inequality sign in [tex]x \leq -7[/tex] implies that the graph has a close circle.

Inequality signs such as [tex]\leq[/tex] and  [tex]\geq[/tex] signifies a close circle

There is only one option left to select;

Lastly;

Split the expression [tex]x \leq -7[/tex] into two

We have:

[tex]x < -7[/tex] or [tex]x = -7[/tex]

Because [tex]x = 7[/tex],

Then, -7 is also a part of the solution

Answer:

B) x less-than-or-equal-to negative 7

C) The graph has a closed circle.

E) –7 is part of the solution.

Step-by-step explanation:

Im not 100% sure but i am 95% sure they r

Answer:

∠ IAC = 98°

Step-by-step explanation:

The sum of the exterior angle = 360°

∠ HCB = 180° - 46° = 134° ( adjacent angles )

Thus

∠ IAC + 128° + 134° = 360°, that is

∠ IAC + 262° = 360° ( subtract 262° from both sides )

∠ IAC = 98°

Answer:

<IAC=°98

Step-by-step explanation:

<DHA + CHA = 180 SUPPLEMENTARY ANGLE

128 +CHA=180

<CHA=52

<CHA + <HAC+<ACH=180 b/c it is triangle

46 +52+HAC= 180

<HAC= 180-98

<HAC= 82

<HAC + <IAC= 180. Supplementary angle

82+<IAC=180

<IAC=180-82

<IAC=98

Answer:

4,500 Codes

Step-by-step explanation:

Given that, the access code consists of 4 digits.

Since, the First digit cannot be zero, and the last digit has to be even.

Therefore, Locks can only use numbers (0-9), which means the first digit has 9 possible outcomes ( 1-9),

the 2nd has 10 possible outcomes (0-10),

the same with the 3rd (0-10) and

finally the 4th has only 5 possible outcomes (0,2,4,6,8),

which we assume that zero is not excluded.

Finally, Mulitply 9 x 10 x 10 x 5 = 4,500.

Answer:

Step-by-step explanation:

[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]

Answer:

14.0 square meters

Step-by-step explanation:

The average cost of weekly groceries is $124.50."  The statistical measurement are they most likely claiming is Mean

The correct option is (B)

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.

As per the situation we have given average cost of groceries.

The mean is also the average sum of data divided by total number of data.

Hence, The statistical measurement is Mean.

Learn more about mean here:

https://brainly.com/question/15323584

#SPJ2

Answer:

D (8z-4)*(-7)

Step-by-step explanation:

Given:

-56z+28

D (8z-4)*(-7)

-56z+28

Therefore, option D is the equivalent expression

Finding the equivalent expression by solving each option and eliminating the wrong option

​A 1/2*(-28z+14)

=-28z+14/2

=-14z+7

B (-1.4z+0.7) /* 40

Two signs ( division and multiplication)

Using multiplication,we have

-56z+28

Using division, we have

0.035z + 0.0175

C (14-7z)*(-4)

-56+28z

D (8z-4)*(-7)

-56z+28

E -2(-28z-14)

56z+28

Answer:

B and D

trust me

Step-by-step explanation:

the first answer is 72 as it is it

Answer:

The answer is 8.

Step-by-step explanation:

The product of 12 and 3 is 36. One-fourth of 36 is 9. 5 subtracted from 9 is 4.

Answer:

x=7/10

Step-by-step explanation:

2/5=4/10

11/10=x+4/10

11/10-4/10=x

7/10=x

Answer:

x=7/10 or 0.7

Step-by-step explanation:

I turned the fractions into decimals

so

1.1=x+0.4

subtract 0.4 from 1.1 to get 0.7

Turn it into a fraction which is 7/10

Answer:

[tex]A.\ \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

Step-by-step explanation:

Given

Let the two triangles be A and B

Sides of A: 4, 6 and 8.5

Sides of B: 6, 9 and 12.5

Required

Which set of ratio determines the dilation

To determine the dilation of  a triangle over another;

We simply divide the side of a triangle by a similar side on the other triangle;

From the given parameters,

A ------------------B

4 is similar to 6

6 is similar to 9

8.5 is similar to 12.5

Ratio of dilation is as follows;

[tex]Dilation = \frac{4}{6}[/tex]

[tex]Dilation = \frac{6}{9}[/tex]

[tex]Dilation = \frac{8.5}{12.5}[/tex]

Combining the above ratios;

[tex]Dilation = \frac{4}{6} = \frac{6}{9} = \frac{8.5}{12.5}[/tex]

From the list of given options, the correct option is A,

Answer:

a

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:

3x – 5 + 5 = 1 + 5

Simplify: 3x=6

Divide each side by 3 to isolate and solve for x:

3x/3=6/3

Simplify: x=2

Answer: The sum is 127

Step-by-step explanation:

A 2-digit number N = ab can be written as (where a and b are single-digit numbers)

a*10 + b.

Now, we want that:

(a + 2)*(b + 2) = a*10 + b.

So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)

We have:

(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b

a*b + 2*b - b + 4 = a*10 - a*2

a*b + 4 + b = a*8

a*b + 4 + b - a*8 = 0.

Now we can give one of the variables different values, and see if the equation has solutions:

>a = 1:

1*b + 4 + b - 8 = 0

2*b - 4 = 0

b = 4/2 = 2

Then the number 12 has the property.

> if a = 2:

2*b + 4 + b -16 = 0

3b -12 = 0

b = 12/3 = 4

The number 24 has the property.

>a = 3 is already known, here the solution is 35.

>a = 4.

4*b + 4 + b - 8*4 = 0

5*b + 4 - 32 = 0

5*b = 28

b = 28/5

this is not an integer, so here we do not have a solution.

>if a = 5.

5*b + 4 + b - 8*5 = 0

6b + 4 - 40 = 0

6b - 36 = 0

b = 36/6 = 6

So the number 56 also has the property.

>if a = 6

6*b + 4 + b - 8*6 = 0

7b + 4 - 48 = 0

7b - 44 = 0

b = 44/7 this is not an integer, so here we do not have any solution.

>if a = 7

7*b + 4 + b -8*7 = 0

8b -52 = 0

b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.

>if a = 8

8*b + 4 + b -8*8 = 0

9*b + 4 - 64 = 0

9*b = 60

b = 60/9 this is not an integer, so we here do not have any solution:

>if a = 9

9*b + 4 + b - 8*9 = 0

10b + 4 - 72 = 0

10b -68 = 0

b = 68/10 again, this is not an integer.

So the numbers with the property are:

12, 24, 35 and 56

And the sum is:

12 + 24 + 35 + 56 =  127

Answer:

6 possible integers

Step-by-step explanation:

Given

A decreasing geometric sequence

[tex]Ratio = \frac{m}{7}[/tex]

Required

Determine the possible integer values of m

Assume the first term of the sequence to be positive integer x;

The next sequence will be [tex]x * \frac{m}{7}[/tex]

The next will be; [tex]x * (\frac{m}{7})^2[/tex]

The nth term will be [tex]x * (\frac{m}{7})^{n-1}[/tex]

For each of the successive terms to be less than the previous term;

then [tex]\frac{m}{7}[/tex] must be a proper fraction;

This implies that:

[tex]0 < m < 7[/tex]

Where 7 is the denominator

The sets of [tex]0 < m < 7[/tex] is [tex]\{1,2,3,4,5,6\}[/tex] and their are 6 items in this set

Hence, there are 6 possible integer

Answer:

A. Undefined slope (no slope)

B. [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

A slope is rise over run.

The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.

However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.

Hope this helped!

Answer:

the function is decreasing at the domain values: (-∞,1)

Step-by-step explanation:

the function is decreasing in the domain values from -∞ until 1, the lowest point with no increase or decrease:

which in interval notation can be written as: (-∞,1)

I hope this helps, but if I didn't answer the question or answered wrongly I will try again.

Answer:

The equation of a circle centered in the point (a, b) and with a radius R.

(x - a)^2 + (y - b)^2 = R^2

Then, if you move the circle to the left, then you are decreasing the value of b.

Where b = 0 means that the center of the circle lies on the y-axis.

When you move the graph to the right you will be increasing the value of b.

Answer:

The variable h changes as the center of the circle moves horizontally. The sign of h is negative when the center is to the left of the y-axis and positive when it is to the right of the y-axis. The sign of the variable h flips when the center moves across the y-axis.

Step-by-step explanation:

plato answer from Equation of a Circle: Tutorial :)

This link will take you to a quizlet that is on this lesson with the other answers and test question answers!!

https://quizlet.com/519491317/geometry-b-unit-7-flash-cards/#:~:text=Move%20the%20center%20of%20the%20circle%20vertically%20so%20it%20lies,of%20the%20circle%20moves%20vertically.

Answer:

∠ G ≈ 38.9°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos G = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{GH}{GI}[/tex] = [tex]\frac{7}{9}[/tex] , thus

∠ G = [tex]cos^{-1}[/tex] ([tex]\frac{7}{9}[/tex] ) ≈ 38.9° ( to the nearest tenth )

Answer:  13.5

Step-by-step explanation:

Find the total volume of the melted cubes:

V₁ = 6³                V₂ = 8³                 V₃ = 12³

    = 216                   = 512                    = 1728

So the new cube will have a volume of 216 + 512 + 1728 = 2456

Volume of the cube = side³

 2456 = s³

[tex]\sqrt[3]{2456} = s[/tex]

    13.5 = s

Answer:

Step-by-step explanation:

The given set of data is 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.

Now the stem - leaf plot will be,

5  4

6  0   1   2   2

7   1   2  4   6    8

8 2   3  4   6    7

9  0   2  5   5   9

Since range of the data = Highest term of the data - Lowest term of the data

                                       = 99 - 54

                                       = 45

Therefore, range of the data set is 45.

The range of the data is 45.

As we know that

Since range of the data = Highest term of the data - Lowest term of the data

= 99 - 54

= 45

Learn more: https://brainly.com/question/10046743?referrer=searchResults

Answer:

(6, 1)

Step-by-step explanation:

x + 2y = 8

1. subtract 2y to get x alone -- x = -2y + 8

2. insert (-2y + 8) as x

2x - 2 = 10

2(-2y + 8) -2 = 10

3. distribute the 2

-4y + 16 - 2 = 10

4. combine like terms

-4y + 14 = 10

5. subtract 14 from both sides

-4y = -4

6. divide by -4

y = 1

7. plug y into any of the two original equations

x + 2(1) = 8

8. simplify

x + 2 = 8

x = 6

9. check answer with second equation

2(6) - 2 = 10

12 - 2 = 10

Step-by-step explanation:

sorry I can only explain as there are no labels to each diagram

The first diagram is single and can solved using triangular formular given as 1/2 ×base × height

A = 1/2 × 5 × 12

A = 30cm^2..

as for the second one...it consist of 2 diagrams which will be solved separately before adding ...it can simply be done using Pythagoras theorem..

To get the smaller part ...out tita is 45degrees while our adjacent is 4 and opposite is x we are to find x which is the height...

using SOH CAH TOA...

WE HAVE TAN45= opp/adj

Tan45= x/ 4

Tan 45 =1 ...so

1 = x/ 4

and x= 4 ...

so...having our height as 4 and base as 4 ..

Area of smaller triangle become 1/2 × 4 × 4

A = 8cm^2 ...

......SOLVING FOR THE SECOND DIAGRAM ..

WE HAVE the height as ( dotted spot + undotted spot ) = 4 + 4 = 8cm

and our base can be gotten from

Tan45 = opp / adj

1 = 8/x ..

x = 8cm ....so the base is 8 and the height is 8

..

The Area becomes 1/2 × 8×8 = 32cm ...

Total area becomes 32cm + 8cm = 40cm^2

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(

−

1

,

10

3

)

Equation Form:

x

=

−

1

,

y

=

10

3

Tap to view steps...

image of graph

Tap to hide graph...

Answer:

D

Step-by-step explanation:

From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.