A book publisher found that the cost to produce 1000 calculus textbooks is $26,300, while the cost to produce 2000 calculus textbooks is $52,900. Assume that the cost C(x) is a linear function of x, the number of textbooks produced. What is the marginal cost of a calculus textbook?

Answer:

Positive roots = 1 or 0

Negative roots = 0, 2, or 4

Complex roots = 0, 2, 4, or 6

Step-by-step explanation:

We are given the polynomial:

f(x) = -x⁶ - x⁵ - x⁴ - 4x³ − 12x² + 12

Now, by inspection, the highest degree is 6 and as such the polynomial is therefore a polynomial with more than 2 as a degree.

Applying Descartes Rule of Signs to the polynomial :

f(x) = -x⁶ - x⁵ - x⁴ - 4x³ − 12x² + 12

Signs are: - - - - - +

There is only 1 sign change and thus, it means there is 1 or 0 positive roots

To find number of negative roots, we will use f(-x);

f(−x) = -(−x)⁶ - (−x)⁵ - (−x)⁴ - 4(−x)³ − 12(−x)² + 12(−x)

f(-x) = -x⁶ + x⁵ - x⁴ + 4x³ − 12x² - 12

Signs are: - + - + - -

There are 4 sign changes and thus, it means there are 4, 2 or 0 negative roots

Thus; Complex roots = 0, 2, 4, or 6

Answer:

is it multiple choice?

Step-by-step explanation:

The area of the rectangle given is 24 square centimeters. Hence, The area of the shaded triangle will be 12 square centimeters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The area of the rectangle given is 24 square centimeters.

The area of the rectangle = length × Width

                            24 = a x b

Also,  a = 24/b

The area of the shaded region is equal to the area of the triangle.

So, The area of the triangle = 1/2 x b x h

                                            = 1/2 x (a) x b

                                             = 1/2 x 24

                                             = 12

Hence, The area of the shaded triangle will be 12 square centimeters.

Learn more about the area;

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Answer:

maybe is b

Step-by-step explanation:

but just wait to other people

Answer:

x = 26

2x = 52

(5x - 2) = 128°

Step-by-step explanation:

✔️According to the exterior angle theorem of a ∆, thus:

(5x - 2)° = 2x° + 76°

Solve for x

5x - 2 = 2x + 76

Collect like terms

5x - 2x = 2 + 76

3x = 78

Divide both sides by 3

x = 26

✔️2x

Plug in the value of x

2(26) = 52°

✔️5x - 2

Plug in the value of x

5x - 2 = 5(26) - 2

= 128°

Answer: Number 9 is 200, number 10 is 40%, number 11 is 80%

Step-by-step explanation:

Answer:

$3.20

Step-by-step explanation:

Answer:

a = 82

Step-by-step explanation:

Both angles form to create a supplementary angle. A supplementary angle is when two angles add up to be 180 degrees. We can write an equation and solve.

98 + a = 180

a = 82

Best of Luck!

Answer:

[tex]x = 9.4[/tex]

[tex]y = 17.7[/tex]

Step-by-step explanation:

Given: The figure

Required: Find x and y

The relationship between length x, length 15 and angle 32 is as follows:

[tex]tan \theta = \frac{opp}{adj}[/tex]

So, we have:

[tex]tan\ 32= \frac{x}{15}[/tex]

Cross multiply:

[tex]x =15*tan\ 32[/tex]

[tex]x = 15 * 0.6248693519[/tex]

[tex]x = 9.3730402785[/tex]

[tex]x = 9.4[/tex] --- approximated

Similarly:

The relationship between length y, length 15 and angle 32 is as follows:

[tex]cos \theta = \frac{adj}{hyp}[/tex]

So, we have:

[tex]cos\ 32= \frac{15}{y}[/tex]

Cross Multiply:

[tex]y * cos\ 32= 15[/tex]

Solve for y

[tex]y = \frac{15}{cos\ 32}[/tex]

[tex]y = \frac{15}{0.84804809615}[/tex]

[tex]y = 17.6876760506[/tex]

[tex]y = 17.7[/tex] --- approximated

Answer:

I think x = 4.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3x + x +10 + 5x + 2x + 2 =56

(3x + x + 5x + 2x) + (10 + 2) = 56 (Combine Like Terms)

11x + 12 = 56

11x + 12 = 56

Step 2: Subtract 12 from both sides.

11x + 12 − 12 = 56 − 12

11x = 44

Step 3: Divide both sides by 11.

11x/11 = 44/11

x = 4

Answer:

20 ÷ 10 = 2

or

20 ÷ 2 = 10

Step-by-step explanation:

multiplication is the opposite of division

Answer:

the answer is 45 I believe because it is the same exact as j

Answer:

Based on the number of cookies each girl made and if Kristina and Liz made the same number of cookies, then Heather made 4.2 dozen cookies.

Step-by-step explanation:

In order to find the number of cookies that Heather made, you need to set up two equations that represent the number of cookies that Kristina and Liz each made.  Since Kristina made 2.4 dozen less than 6 times as many dozen as Heather, we can represent that with the equation  6c - 2.4.  Since Liz made 1.8 dozen more than 5 times as many dozen as Heather, we can represent that with the equation 5c + 1.8.  We can set both equations equal to each other since Liz and Kristina made the same number, so 6c - 2.4 = 5c + 1.8.  Solving for 'c', which represents how many dozen cookies Heather made, we get 4.2  

Answer:

COEFFICENT

Step-by-step explanation:

Answer:

Xbox $544.00 sales tax: 38.08 after tax: 582.08

Airpods $125:00 sales tax: 8.75 after tax: 133.75

Answer:

Xbox before tax: $544.00

Sales Tax: 38.08

Total Price: $582.08

Airpods before tax: $125.00

Sales Tax: $8.75

Total Price: $133.75

Step-by-step explanation:

take .07 and multiply it by 544.00 and you get 38.08. Then add 38.08 and you get 582.08.

Then take .07 and multiply it by 125.00 and you get 8.75. Then add 8.75 to 125.00 and you get 133.75.

(6,-7)

multiply Midpoint by 2

Answer:

hello your question is incomplete attached below is the complete question

answer : 2/13    6/13

               6/13    3/13

Step-by-step explanation:

Firstly we will calculate the orthogonal basis L in R^2

attached below is the detailed solution

also assuming β to be the standard ordered basis

hence the matrix A of the reflection in the Line L in R2 =

2/13    6/13

6/13    3/13

The matrix A of the reflection in line L is given by  [tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]  and this can be determined by first evaluating the value of [tex]\rm R^2[/tex] by using the given data.

The orthogonal basis L in [tex]\rm R^2[/tex] is given by:

[tex]r = [u_1,u_2] =\left[\dfrac{1}{\sqrt{39} }\binom{6}{3}, \dfrac{1}{\sqrt{39} }\binom{3}{-6}\right][/tex]

[tex]\rm T(u_1)=u_1[/tex]

[tex]\rm T(u_2)=0[/tex]

[tex]\rm [T]_r = \begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}[/tex]

[tex]\rm Q = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]

Now, matrix A is given by the formula:

[tex]\rm A=Q[T]_rQ^{-1}[/tex]

Now, substitute the value of known terms in the above equation.

[tex]\rm A = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]

Simplify the above expression.

[tex]\rm A = \dfrac{1}{{39} }\begin{bmatrix}6 & 18\\ 18 & 9\end{bmatrix}[/tex]

[tex]\rm A = \dfrac{3}{{39} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]

[tex]\rm A = \dfrac{1}{{13} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]

Multiply by 1/13 in the matrix.

[tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]

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Answer:

b 8%

Step-by-step explanation:

40 divide by 500 is 0.08 to find percentage you just multiply your number by 100 to get it

Answer:

B) 8%

Step-by-step explanation:

Easy way to solve these type of problems is to divide.

40/500=0.08.

0.08 conversion to percentage is 8%

Answer:

The candy bar would cost 1.50 cents and the bag of chips would be a 1.00

Step-by-step explanation:

Answer:

1.50 times 10=15 for cream bars, and 5 packs of chips each will be $1 which is 5 packs of chips so it it will be 15 cream bars+5 packs of chips =$20

Step-by-step explanation:

Answer:

the answer is -1/2

Step-by-step explanation:

Answer:

See attachment :D

Step-by-step explanation:

y = 2/3x + 2

This is in slope-intercept form, y = mx+b. m is the slope, 2/3, and b is the y- intercept, 2. So you know the line intersects with the y-axis at (0,2). The slope is 2/3. So you can move up two points, then over three. Because it's a positive slope, you move right. This leaves you at point (0,3). Connect a line between these two points.

The line intersects with points (-3,0) and (0,2).

Hope this is helpful ^^ Good luck with your test :D

Answer: 4,000

Step-by-step explanation: 12,000 - 8,000 = 4,000 Hope it helped!! :)

Answer:

The flight to Portland takes 10.6 hours.

Step-by-step explanation:

To find the time of flight to Portland we need to calculate the distance traveled by using the equation:

[tex] x = v*t [/tex]

Where:

v: is the speed = 204 mph (return flight)

t: is the time = 12 h (return flight)

[tex] x = v*t = 204 mi/h*12 h = 2448 mi [/tex]

Now, we can find the time of flight to Portland using v = 232 mph:

[tex]t = \frac{x}{v} = \frac{2448 mi}{232 mi/h} = 10.6 h[/tex]

Therefore, the flight to Portland takes 10.6 hours.

I hope it helps you!                      

Answer:

g = 21

h = 8

Step-by-step explanation:

3g + 5 + 6g - 14 = 180 (since they are adjacent angles and will equal 180)

Simplify to get g = 21.

Substitute 21 for g in 3g + 5 and set that equal to 9h - 4 and solve for h to get 8 (since they are opposite angles and will equal each other)

Answer:g=21 h = 8

Step-by-step explanation:

That's a rhombus supposedly so the opposite angles are congruent.

This means 9h-4=3g+5 Also the opposite sides of a rhombus add up to 180 degrees, so 3g+5+6g-14=180

9g=,189 g = 21

now plug this into the first equation

9h-4=3(21)+5

9h-4=63+5

9h=72

h=8

Answer:

6

Step-by-step explanation: