Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.

b) The corresponding prices are $180 in market 1 and $160 in market 2.

c) If it becomes illegal to discriminate, the profit loss is $50.

d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.

a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.

In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.

For market 1:

MR₁ = dP₁/dQ₁ = -2

For market 2:

MR₂ = dP₂/dQ₂ = -4

Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:

MR₁ = -2 = dC/dQ₁ = 20

MR₂ = -4 = dC/dQ₂ = 20

Solving these equations, we find:

Q₁ = 10

Q₂ = 5

Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.

b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:

For market 1:

P₁ = 200 - 2Q₁ = 200 - 2(10) = 180

For market 2:

P₂ = 180 - 4Q₂ = 180 - 4(5) = 160

Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.

c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.

Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.

Under discrimination:

Profit = Total revenue - Total cost

For market 1:

Total revenue₁ = P₁ \(\times\) Q₁ = 180 \(\times\) 10 = $1

For market 2:

Total revenue₂ = P₂ \(\times\) Q₂ = 160 \(\times\) 5 = $800

Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600

Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300

Profit = Total revenue - Total cost = $2600 - $300 = $2300

Under non-discrimination:

Since the same price is charged in both markets, we take the average price:

Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170

Total revenue = Average price \(\times\) (Q₁ + Q₂) = $170 \(\times\) (10 + 5) = $2550

Total cost remains the same at $300.

Profit = Total revenue - Total cost = $2550 - $300 = $2250

Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.

d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.

This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.

The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.

The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.

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Answer:

12.72792

Step-by-step explanation:

d = √2a = √2 x 9 = 12.72792

Sorry, I don't have too much time to explain the question but I hope this helps!

Answer:

The area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Step-by-step explanation:

From this study,

The surface area of f(x,y) is expressed by:

\(A = \iint_R \sqrt{1 +f^2_x+f^2_y}} \ dA\)

where

\(0 \leq x \leq 2 \ and \ 0 \leq y \leq 2\)

Given that:

f(x,y) = 9 - x²

Thus, \(f_x = -2x\) and   \(f_y = 0\)

However, the area becomes:

\(A = \iint_R \sqrt{1+(-2x)^2+0^2} \ dxdy\)

\(A = \iint_R \sqrt{1+4x^2} \ dxdy\)

From above, replacing x with \(\dfrac{1}{2} \ tan \ u\)

then \(dx = \dfrac{1}{2} sec^2 \ udu\)

∴

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint \sqrt{1 + 4u^2 } \ sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} \iint sec^2 \ udu\)

\(\sqrt{1 + 4x^2 } \ dA= \dfrac{1}{2} ( \sqrt{4x^2 + 1x} + \dfrac{1}{2} In \sqrt{4x^2 + 1}+2x)\)

Hence;

\(\mathsf{A = \int \limits ^2_0 \begin {bmatrix} \dfrac{1}{2}(\sqrt{4x^2 +1 x}+ \dfrac{1}{2} In ( \sqrt{4x^2+1}+2x \end {bmatrix}^2_0 \ dy}\)

\(\mathbf{A = 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Therefore, the area of the surface over R is \(\mathbf{ 2 \sqrt{17} + \dfrac{1}{2} \ In ( \sqrt{17} +4)}\)

Therefore, sin(0) = -√305/41 when 0 is an angle in quadrant IV.

Trigonometry is a branch of mathematics that deals with the study of relationships between the angles and sides of triangles. It is used to solve problems in many fields, including engineering, physics, astronomy, and architecture. Trigonometry involves the use of functions such as sine, cosine, and tangent to relate the angles and sides of a right triangle. It also includes the study of trigonometric identities, equations, and graphs, as well as applications of trigonometry in real-world situations.

Here,

If 0 is an angle in quadrant IV, then cosine is positive and sine is negative. We can use the Pythagorean identity to find the value of sin(0):

sin²(0) + cos²(0) = 1

sin²(0) = 1 - cos²(0)

sin(0) = -√(1 - cos²(0))

substituting the given value of cos(0):

sin(0) = -√(1 - (4√47/41)²)

sin(0) = -√(1 - (16*47/41))

sin(0) = -√(1 - 736/41)

sin(0) = -√(305/41)

sin(0) = -(√305)/√(41)

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The amount of money donated by Jacy is $10.

Given that, Jacy made the first donation Gillermo’s donation was twice Jacy’s donation Rosa’s mother tripled what Aurora had raised so far now Aurora has $120.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the donation given by Jacy be $x.

Divide that amount by 4. One part is Guillermo's and Jacy's donation and three parts is the amount donated by Rosa's mother = 120 ÷ 4 = $30

Divide that amount by 3. One part is for Jacy's donation ($x) and two part is the amount Guillermo donated x = 30/3 = $10

Jacy was the first to donate. So, Jacy donated is $10

Therefore, the amount of money donated by Jacy is $10.

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Answer:

74ft

Step-by-step explanation:

22+22+15+15= 74

Answer:

85º

Step-by-step explanation:

<7=<4 since we know the lines are parallel, and intersected at the same angle

Therefore, <7=85º.

Answer:

-1/3x + 62/3

Step-by-step explanation:

Interchange the variables:  y = -3x + 62

Swap the sides:  -3y + 62

Move constant:  -3y + 62 = x

Divide and simplify:  -3y = x - 62

Answer: -1/3x + 62/3

Please help me with my answer.  I'm stuck and really need help on it.

Answer:

-3 = slope, 62 = y intercept

Step-by-step explanation:

Im sorry but what I got was x=1.5 I don't know if this helps or not.

If a circle in the xy-plane has the equation above, the point does NOT lie on the exterior of the circle is (5,2) (option c).

Now, let's take a look at the given equation: (x - 2)² + (y + 5)² = 36. We can see that the center of the circle is (2, -5) and its radius is 6, since 6² = 36.

To determine which points do not lie on the exterior of the circle, we need to look for the points that are either inside the circle or on its circumference. In other words, we need to find the points that satisfy the given equation.

Let's plug in the coordinates of each point in the given answer choices into the equation of the circle and see which points satisfy it:

A) (2,1): (2 - 2)² + (1 + 5)² = 36, satisfies the equation.

B) (2,5): (2 - 2)² + (5 + 5)² = 100, satisfies the equation.

C) (5,2): (5 - 2)² + (2 + 5)² = 58, does not satisfy the equation.

D) (-1,1): (-1 - 2)² + (1 + 5)² = 36, satisfies the equation.

Therefore, the answer is C) 5,2, since it does not satisfy the equation of the circle and hence does not lie on the exterior of the circle.

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Complete Question:

If a circle in the xy-plane has the equation (x−2)²+(y+5)²=36, which of the following does NOT lie on the exterior of the circle?

A) 2,1

B) 2,5

C) 5,2

D) -1,1

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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Answer:

$3040 profit made

Step-by-step explanation:

$13×95=$1235 cost to make all the shoes they sold

$45×95=$4275 money she made

$4275-$1235=$3040 profit

Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

The true similarity statement are using Right Triangle Altitude Theorem :

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.

By the Right Triangle Altitude Theorem,

If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.

Using this,

ΔABD similar to ΔBCD

ΔABC similar to ΔADB

ΔABC similar to ΔBDC

Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.

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The complete question is given below.

Answer: 7-8      

Step-by-step explanation:

7-8  A squared + B squared =c Square

        9x9     8x8                                       10x10     12x12        

         81        64                                         100        144

               145                                                    244

Answer:

y = -3x/2 - 1/2

Step-by-step explanation:

slope m = -3/2

-5 = (-3/2)×3+b

or, b = -1/2

putting it into y = mx + b

y = -3x/2 - 1/2

Answered by GAUTHMATH

Answer: 0.655

Step-by-step explanation:

Let X be a random variable that represents percent of fat calories that a person in America consumes each day.

As per given , X is normally distributed with a mean \(\mu=36\) and a standard deviation \(\sigma=10\).

Sample size : n= 16

The probability that the average percent of fat calories consumed is more than 35:

\(P(\overline{X}>35)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{35-36}{\dfrac{10}{\sqrt{16}}})\\\\=P(Z>\dfrac{-1}{\dfrac{10}{4}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>\dfrac{-4}{10})\\\\=P(Z>-0.4)\\\\=P(Z<0.4)\ \ \ [P(Z>-z)=P(Z<z)]\\\\=0.655\ \ \ [\text{By p-value table}]\)

Hence, Required probability =0.655

Answer:2  hope this helps it was right on my test

Step-by-step explanation: it was right on the test i took

$231784 is the  to raise a child from birth to 17 years in a household with an annual income of $78,300.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let y represents  the total cost in dollars f raising a child in the United States from birth to 17 years

x represents the households annual income

We have  y = 1.55x + 110,419

We need to find the value of y for x=78300

y=1.55(78300) + 110,419

y=231784

Hence, $231784 is the  to raise a child from birth to 17 years in a household with an annual income of $78,300.

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Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

chocolate chip 7

walnuts 3.5

Step-by-step explanation:

assume x=chocolate chips

 y=walnuts.

equation

4x + 8y=33

(2x+3y=13)×2

new eq

4x + 8y=33

4x + 6y=26

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

 2y=7

  y=7/2

4x+ 8y = 33

4x + 8(7/2)= 333

4x= 33-28

x=7.00

Answer:

4/3 square feet.

Step-by-step explanation:

To find the area of the replica, you need to use a formula that relates the area of the original figure and the area of the dilated figure by the scale factor1. The formula is:

Area of dilated figure = Area of original figure x (Scale factor)^2

In this case, the area of the original artwork is 12 square feet and the scale factor is 1/3. So, we plug these values into the formula and get:

Area of replica = 12 x (1/3)^2

Area of replica = 12 x 1/9

Area of replica = 4/3

So, the area of the replica is 4/3 square feet.

Hope this helps :)

1. The diagram below shows the net of a pyramid with all its labeled sides.

2. The surface area; S = L + B

3. The total surface area = 22.44 cm².

To calculate the total surface area, we use the formula to find Area = (1/2) x b x h.

After we've found the area, we say

Total surface area = 1/2 x 2.24 x (3 x 4) + (3)²

= 22.44 cm²

The above answers are based on the full questions below;

A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.

1. Draw a net for the pyramid. Label all sides with measurement?

2. Write an expression for the surface area of the pyramid and then find the total surface area

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The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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