The owner of a video game store creates the expression −2x2 28x 20 to represent the store's weekly profit in dollars, where x represents the price of a new video game. choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine that price. −2(x − 7)2 118; x = $7 −2(x − 7)2 118; x = $118 −2(x2 − 14x) 20; x = $14 −2(x2 − 14x − 10); x = $10

Answers

Answer 1

The given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]price is $7 option first is correct.

What is a quadratic expression?

A quadratic expression is a second-degree algebraic expression represented by the:

[tex]\rm ax^2+bx+c=0[/tex] ........(1)

Where a, b, and c are the constants and  

We have a quadratic expression:

[tex]\rm f(x)=-2x^2+28x+20[/tex]

Convert it to perfect square by perfect square trinomial:

[tex]\rm f(x)=-2(x^2+14x)+20[/tex]  

[tex]\rm f(x)=-2(x^2+14x+49-49)+20[/tex]   (adding and subtracting by 49)

[tex]\rm f(x)=-2(x-7)^2+2(49)+20[/tex]

[tex]\rm f(x)=-2(x-7)^2+118[/tex]

Here [tex]\rm (x-7)^2[/tex] is the positive term and -2 is the negative term so in order to get the highest weekly profit it should be zero, so

[tex]\rm -2(x-7)^2=0[/tex]

x = $7

Thus, the given expression is equivalent to [tex]\rm -2(x-7)^2+118[/tex]  and the price is $7.

Learn more about quadratic expression here:

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Answer 2

Answer:

First option A.  −2(x − 7)^2 + 118; x = $7

Step-by-step explanation:

Took the test and it's correct, trust me :)


Related Questions

If ABCDE is translated 7 units to the right and 2 units up, what will happen to the polygon?

Answers

Answer:

D.

Step-by-step explanation:

It will move but stay the same size. You are translating the shape to a different spot, not adding onto its size.

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I hope this helps!

-No one

PLS HELP
Ignore everything above and below the simplify question

Answers

I think it’s 1/6 or 0.16, those two are basically the same thing

i should know how to do this but its spring break and im scared and bored 8th grade math

Answers

Answer:

19 is B

Step-by-step explanation:

7/8 x 8x = 7x

7/8 x 16 = 14

Factor the trinomial 6x^{2} + 5x - 25. Which of the following is a factor?

Answers

Answer:

its (3x-5)

Step-by-step explanation:

Answer:

C. (3x - 5)

Step-by-step explanation:

1. Find a solution pair that gives the sum of b (5):

-10 + 15 = 5

2. Break the expression into groups:

(6x² - 10x) + (15x - 25)

3. Factor out the common factor in each group:

2x(3x - 5) + 5(3x - 5)

4. Factor out the common pair (3x - 5) using the distributive property:

(3x - 5)(2x + 5)

hope this helps!

What are the gradients and y intercepts of the following equation

y= x/4 + 3

Answers

Answer:

gradient:  1/4; y-intercept:  3

Step-by-step explanation:

In math, 'gradient' is another word for slope.

Here we have y = (1/4)x + 3.  The coefficient of x is the slope or gradient:  1/4.  The y - intercept is 3:  (0, 3).

Answer:

Step-by-step explanation:

The equation is in y = mx + b form.

Here, m is the slope or gradient and b is the y-intercept.

[tex]y =\dfrac{1}{4}x+3\\\\\\Gradient =\dfrac{1}{4}[/tex]

y-intercept = 3

Find the area of the shape shown below. ​ ​

Answers

Answer:

12 cm²

Step-by-step explanation:

Area of triangle: bh/2 = (2)(3)/2 = 3

Area of square: bh = (2)(3) = 6

Total area of the shape = 2 triangles + 1 square

Total area = 2(3) + 6 = 12 cm²

I hope this helps!

Answer:

12

Step-by-step explanation:

You can find the area of the shape 2 different ways.

I'll show you both ways.

First Way: find the area of each individual shape that makes it up then add them together

We can find the area by finding the area of the rectangle and then the two triangles and then adding the two multiples together

Area of a rectangle = length × width

Length = 3 and width = 2

So area = 3 × 2 = 6

Now to find the area of the triangles

Area of a triangle = 1/2bh

Where b = base length and h = height

The base length is 2 and the height is 3

So area = 1/2 × 2 × 3 = 3

There are two triangles and they both have the same dimensions

So the area of both triangles = 2 × 3 = 6

Finally we add the areas together to get the total area

Total Area = 6 + 6 = 12cm²

Second way : Use the area of a trapezoid formula:

The shape shown is a trapezoid so we could also use the area of a trapezoid formula.

Formula : [tex]A=\frac{a+b}{2} h[/tex]

where a and b = base lengths and h = height

The base lengths appear to be 2 and 6 and the height is 3

So a = 2 , b = 6 and h = 3

Which means [tex]A=\frac{2+6}{2} 3[/tex]

Simplify addition

[tex]A=\frac{8}{2} 3[/tex]

simplify division

A = (4)3

Then multiply
A = 12cm²

On the following unit circle, \thetaθtheta is in radians.
A unit circle with an angle from the positive x-axis to a ray labeled theta. The point where the ray intersects the circle is labeled 0.83, negative 0.55 and is in the fourth quadrant.
A unit circle with an angle from the positive x-axis to a ray labeled theta. The point where the ray intersects the circle is labeled 0.83, negative 0.55 and is in the fourth quadrant.
Without a calculator, evaluate the following expressions to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

cos(π+θ)=-cos θ=-(0.83)/1=-0.83

cos (2π-θ)=cos θ=0.83/1=0.83

Answer:

5/4

Step-by-step explanation:

Describe how to compare the two ratios 5:8 to 7:9. Tell each step to set up the ratios, then explain what to do to be able to compare the ratios. Finally make sure to answer how the ratios compare. ~ 100 POINTS AND ILL GIVE YOU BRAINLIEST IF YOU ANSWER CORRECTLY AND 5 SENTENCES NEEDED

Answers

Answer:

5/8 is smaller.

Step-by-step explanation:

A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777

Then to compare them you see which is smaller or bigger.

0.77777  is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.

Steps:-

First rewriteThen convert to fractionsThen divide both

[tex]\\ \rm\rightarrowtail 5:8::7;9[/tex]

[tex]\\ \rm\rightarrowtail 5/8:7/9[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{5(9)}{8(9)}:\dfrac{7(8)}{9(8)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{45}{72}:\dfrac{56}{72}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{45}{56}[/tex]

Second one is bigger

help me pls i really need help​

Answers

Step-by-step explanation:

m<2: 65°( vertically opposite angle)

m<3: 180°-65°=115°(sum of straight line)

m<4: 180°- 65° = 115° (sum of straight line)

Draw a line between 5 and 6.

m<5: 180°- m<7=180-115=65

m<7 = m<4=115°(corresponding angle)

m<8 = m<5 =65°(vertically opposite angle)

m<6=m<7=115°( vertically opposite angle)

in this way 10,11,12 will be find.

Please feel free to ask if you have any questions

Please Mark me as Brainliest .

Thanks

Step-by-step explanation:

correct this answer

mark a brain less

$1500 at 8.5% for 6 months. What is the interest?

Answers

Answer:63.75

Step-by-step explanation: 1500x0.085x0.5=63.75

calculate the side lengths using the given scale.

Answers

Answer:

x = 9 m

y = 1 m

Step-by-step explanation:

6/1 = x/1.5

x = 1.5 × 6

x = 9

6/1 = 6/y

6y = 6

y = 1

Tom is exchanging money for his trip to india. the exchange rate of us dollars to indian rupees is 1:45.897. tom needs 11,550 rupees. the currency exchange service he is using charges a fee of 7.25% after the exchange is made. how many us dollars will it cost tom to get the rupees he wants? round to the nearest dollar. a. $235 b. $252 c. $263 d. $270

Answers

The total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.

How to calculate the percentage?

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

To calculate the percentage part of number, multiply it with the original number and divide with 100.

Tom is exchanging money for his trip to india. The exchange rate of us dollars to indian rupees is,

[tex]r=\dfrac{1}{45.897}[/tex]

Tom needs 11,550 rupees. The dollars need for 11550 Indian rupees are,

[tex]n=\dfrac{11550}{45.897}\\n=251.65[/tex]

The currency exchange service he is using charges a fee of 7.25% after the exchange is made. Thus the total dollar requied after the service charge is,

[tex]n=251.65+\dfrac{7.25}{100}\times251.65\\n=251.65+18.245\\n=269.895\\n\approx270[/tex]

Thus, the total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.

Learn more about the percentage here;

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You are calculating how many seats there are at Wrigley
Field in Chicago, Illinois. You count that there are 1,487 rows
Each row has 28 seats.
How many seats are there in the whole field?

Answers

Answer:

41,636

Step-by-step explanation:

Easy, on each row, there are 28 seats, and we know there's 1487 rows in total.

Hence, number of rows multiplied by number of seats counted

   1487 × 28

   =41,636

(Dang, that's alot of seats then)

   

How many edges does this shape have?

A. 6
B. 12
C. 16
D. 18

Answers

Answer:

B. 12

Step-by-step explanation:

Edges are the straight lines

Hi please help me out I’m really struggling with geometry rn and I can’t afford to buy the tutor thing

Answers

Alright let's solve this problem step by step:

Question 1: Find the perimeterDefinition of Perimeter: basically all the side lengths added up

   The figure is made up triangles

      ⇒ however, we do not know the slanted line that goes from the tip to

           the edge of the base.

           ⇒ we can use the Pythagorean Theorem to help us

                 [tex]2^2 + (5.7)^2 = slanted-line^2\\slanted-line = 6.04[/tex]

   Perimeter = 6.04 + 6.04 + 6.04 + 6.04 + 6.04 + 4 + 4 + 4 + 4 + 4

                      = 50.2 inches

Question 2: Find the slant heightDefinition of Slant height: is the distance measured along a lateral face from the base to the tip along the "center" of the face.

         *look at image attached to better understand this definition

           ⇒ Slant height = 5.7inches

Question 3: Find the Lateral AreaDefinition of Lateral Area: area of the non-base faces only

   Lateral Area = 5 * (Area of Triangle Faces)    

                         = [tex]5 *(\frac{1}{2} *5.7 * 4) = 5*2*5.7 = 5 * 11.4[/tex]

                         = 57 in^2

Hope that helps!

What type of ballots are used when voting for president in the United States?

preference ballots

traditional ballots

alternative ballots

conventional ballots

Answers

Answer:

preference ballot

Step-by-step explanation:

A preference ballot is a ballot in which the voter ranks the choices in order of preference.

Answer:

Traditional ballots

Step-by-step explanation:

i took the test

Find the ratios and reduce them in their lowest terms .
8cm and 8mm​

Answers

Answer:

Hope the picture will help you

You roll a number cube ten times and it lands on a 5 two times. What is the theoretical probability that it lands on a 5 on your next roll?​

Answers

Answer:

2/10 = 1/5

Step-by-step explanation:

It landed five 2 times and you rolled it 10 times

100 points please help fast asap
Find the dimensions of the actual swimming pool.

A drawing plan includes a rectangular swimming pool with a length of 1/2 ft and a width of 1/4 ft. The actual pool will be enlarged by a scale factor of 80/1.

Answers

Answer:

length: 40, width: 20

Step-by-step explanation:

length = 1/2×80/1 = 40

width = 1/4 × 80/1 = 20

hope this helps =)

A local hamburger shop sold a combined total of 394 hamburgers and cheeseburgers on Wednesday. There were 56 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday?

Answers

Answer:

Step-by-step explanation:

Total number of Hamburgers and Cheeseburgers = 394

Let the number of hamburgers = x

x + x - 56 = 394                           Combine the left

2x - 56 = 394                               Add 56 to both sides

2x - 56 + 56 = 394 + 56              Combine

2x = 450                                       Divide both sides by 2

2x/2 = 450/2

x = 225

Answer

225 hamburgers  were sold169 Cheeseburgers sold

solve for x -3(x + 5) = -9

Answers

Answer:

[tex]\tt x=-2[/tex]

Step-by-step explanation:

[tex]\tt -3(x + 5) = -9[/tex]

Step (1) :- Distribute

[tex]\tt -3x-15=-9[/tex]

Step (2) :- Add 15 to both sides

[tex]\tt -3x-15+15=-9+15[/tex]

Step (3) :- Simplify

[tex]\tt -3x=6[/tex]

Step (4) :- Divide both sides by -3:-

[tex]\tt \cfrac{-3x}{-3}=\cfrac{6}{-3}[/tex]

[tex]\tt x=-2\;\; \bf Answer[/tex]

____

Answer:

[tex] \sf:\implies \quad {\pmb{\sf x = -2}} [/tex]

Solution:

Let's solve the given problem step by step :

[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]

First, distribute the given problem :

[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]

[tex] \sf:\implies \quad - (3 \times x) - (3 \times 5) = - 9[/tex]

Add 15 to both sides :

[tex] \sf:\implies \quad - 3x - 15 = - 9[/tex]

[tex] \sf:\implies \quad - 3x - 15 + 15 = - 9 + 15[/tex]

On simplifying :

[tex] \sf:\implies \quad -3x-15+15 = -9+15[/tex]

[tex] \sf:\implies \quad - 3x = 6[/tex]

Dividing both sides with same factor :

[tex] \sf:\implies \quad - 3x = 6[/tex]

[tex] \sf:\implies \quad \dfrac{ - 3x}{ - 3} = \dfrac{6}{ - 3} [/tex]

[tex] \sf:\implies \boxed{ \pmb{ \sf\quad x = - 2}}[/tex]

The box-and-whisker plot below
represents some data set. What is the value of the first quartile?

Answers

Answer: 77 is right.

Step-by-step explanation:

In the given box-and-whisker plot, the value of first quartile is 85.

What is a box and whisker plot?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

From the given box and whisker plot,

Minimum=77

Maximum=92

First Quartile=85

Median=87

Third Quartile=89

Therefore, in the given box-and-whisker plot, the value of first quartile is 85.

Learn more about the box plot here:

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Mrs. Evans gave her class a 100-page reading assignment. After 2 days, Kya and
Chase each have 64 pages left to read.
Each student writes a function f(t) to model the pages left to read, where t is the
number of days since the assignment was given.
Kya writes an exponential function that fits the data.
Chase writes a linear function that fits the data.
Drag equations to the table to show the functions they wrote

Answers

Answer:

kya- y= 100·(0.8)^t

chase= 100-18t

Step-by-step explanation:

I did the work on imagine math

The exponential function that fits the data is y= 100·(0.8)^t

What are exponential functions?

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

We are given that Mrs. Evans gave her class a 100-page reading assignment.

Since 2 days, Kya and Chase each have 64 pages left to read.

Each student writes a function f(t) to model the pages left to read, where t is the number of days since the assignment was given.

Kya writes an exponential function that fits the data as;

y= 100·(0.8)^t

Chase writes a linear function that fits the data as;

chase= 100-18t

Learn more about function here:

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2(3x+2)=6x+4 linear equations

Answers

Answer:

0 or 6x+4=6x+4  (Technically no slope at all!!)

Step-by-step explanation:

You need to do distributive property and then solve for x!!

meaning the 2(3x+2) has to get distributive property process.

6x+4=6x+4

That shall be equal together!!! (You could stop here!!)


If continue:

6x-6x=4-4

0=0

What does s equal? (Write your answer like this: s = __)

Answers

Answer:

S= -15/5

the slashes are supposed to be fractions.

Step-by-step explanation:

Please help me ASAP.

Answers

The 3 inside angles of a triangle need to equal 180.


X = 180 - 70 - 20 = 90


x = 90 degrees

Use the function f(x) = x2 − 2x 8 and the graph of g(x) to determine the difference between the maximum value of g(x) and the minimum value of f(x). a parabola that opens down and passes through 0 comma 3, 3 comma 12, and 5 comma 8 2 5 7 12

Answers

The difference between the maximum value of g(x) and the minimum value of f(x) is 5.

Given function is:

[tex]f(x)=x^{2} -2x+8[/tex]......(1)

What is the general form of a quadratic equation?

The general form of a quadratic equation is [tex]ax^{2} +bx+c=0[/tex] with [tex]a\neq 0[/tex].

As we know the minimum value of a quadratic function is [tex]\frac{4ac-b^{2} }{4a}[/tex] when a>0

For f(x) a>0 so minimum value of f(x) = [tex]\frac{4*1*8-(-2)^2}{4*1}[/tex]=7

From the graph, the maximum value of g(x) =12

So, the difference between the maximum value of g(x) and the minimum value of f(x) =12-7 =5

Hence, the difference between the maximum value of g(x) and the minimum value of f(x) is 5.

To get more about quadratic functions visit:

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how do i find angle measurements

Answers

Answer:

if youre doing this on paper use a protractor

Step-by-step explanation:

place the straight line ontop of the side you're trying to read the angle from and go in a clockwise direction when using the compass until you find the angle degree.  hope that helps:-)

3w + 4x – 15y + 6w + 7x + 7y
5w + 3y + 9x + 2x - 11y + 4w
7x - 3y + 12w + 5y - 3w + 4x
4w + 3x – y + 5w - 14x - 7y
how many of these are equal?

Answers

Answer:

3w, 4x, 4w, 7y, 7x, 3y,  5w,

Step-by-step explanation:

Find x . Round your answer to the nearest tenth of a degree.

Answers

Answer:

x ≈ 59.0°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{30}{18}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{30}{18}[/tex] ) ≈ 59.0° ( to the nearest tenth )

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