4. Which best represents the transformation algebraically?
a. (x, y) b. (-x, y)
C.
(-x, -y)- d. (x + 18, y)

The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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Answer:

y = 2x + 5 is an option

The maximum value of P is ______________ at the point (x, y) = (______________).

What is the maximum value of P and its corresponding point (x, y)?

To solve the linear programming problem using the method of corners, we need to examine the feasible region defined by the given constraints and identify the corner points. The objective is to maximize the objective function P = 5x - 6y.

The given constraints are:

1. x + 3y ≤ 15

2. 5x + y ≤ 19

3. x ≥ 0

4. y ≥ 0

We plot the feasible region by graphing the boundary lines defined by each constraint and shading the region that satisfies all the constraints.

Next, we evaluate the objective function at each corner point of the feasible region. The corner points are the vertices of the shaded region.

By substituting the coordinates of each corner point into the objective function P = 5x - 6y, we calculate the corresponding P-values.

The maximum value of P is the highest P-value obtained among all the corner points. Its corresponding point (x, y) represents the coordinates at which the maximum value occurs.

To provide the specific values for the maximum value of P and its corresponding point (x, y), the calculations need to be performed based on the corner points of the feasible region.

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The maximum value of P is 100, attained at the point (15, 30).

Convert the inequalities to equations:

Equation 1: x + 3y = 15

Equation 2: 5x + y = 19

Plot the graph of the feasible region determined by the constraints:

Start by plotting the lines corresponding to the equations.

Determine the feasible region by shading the area that satisfies the given constraints.

The feasible region is bounded by the x-axis, y-axis, and the lines x + 3y = 15 and 5x + y = 19.

Identify the corners of the feasible region:

The corners of the feasible region are the points of intersection between the lines forming the boundary.

In this case, we have three corners: (0, 5), (6, 3), and (15, 30).

Evaluate the objective function P at each corner:

P(0, 5) = 5(0) - 6(5) = -30

P(6, 3) = 5(6) - 6(3) = 12

P(15, 30) = 5(15) - 6(30) = 100

Determine the maximum value of P:

The maximum value of P is 100, which occurs at the point (15, 30).

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Answer:

71.99

Step-by-step explanation:

89.99 x .20=17.998

89.99-17.998=71.992

Round

She paid $71.99

Answer:

The regular price is $1,889.79

Step-by-step explanation:

20% to 0.20

$89.99 divided by 0.20 equals 1,799.80

$1,799.80 plus $89.99 equals $1,889.79

The combined area of dark pieces is 253.5 in².

First, Area of 5 light pieces

= length x width

= 3 3/4 x 39

= 15/4 x 39

= 146.25 in²

Now, Area of board

= L x W

= 29 x 39

= 1131 in²

Thus, the combined area of dark pieces

= 1131 - 146.25 x 6

= 253.5 in²

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Answer:

-3

Step-by-step explanation:

 f(x)=2x^2 - 3x - 2

if x = 1

f(1) = 2(1)^2 - 3(1) - 2

= 4 - 3 - 2

= -3

Hope this helps :)

Pls brainliest...

Answer:

81 in

Step-by-step explanation:

diameter is radius squared

9 × 9 = 81

The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.

The given initial-value problem is a separable differential equation, which can be written as:

dy/dt = -2(t + 1)y²

Integrating both sides, we get:

(1/y) = t² + 2t  + C

where C is the constant of integration.

Since we have an initial condition, we can use it to find the value of C:

y(0) = -1/15
C = -1/15

Solving for C, we get:

C = -1/15

So, the solution to the differential equation is:

(1/y) = t² + 2t -1/15

y = 1 / (t² + 2t -1/15)

The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

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The derivative of the function y = x^2x using logarithmic differentiation is dy/dx = x^2x(2 + 2ln(x)).

To find the derivative of the function y = x^2x using logarithmic differentiation, we follow these steps:

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To find the derivative of the function y = x^(2x) using logarithmic differentiation, we take the natural logarithm of both sides, apply logarithmic properties, and then differentiate implicitly.

Start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(x^(2x))

Apply the power rule of logarithms to simplify the expression:

ln(y) = 2x * ln(x)

Now, differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = 2 * ln(x) + 2x * (1/x)

Simplify the expression:

(1/y) * dy/dx = 2 * ln(x) + 2

Multiply both sides by y to isolate dy/dx:

dy/dx = y * (2 * ln(x) + 2)

Substitute the original value of y = x^(2x) back into the equation:

dy/dx = x^(2x) * (2 * ln(x) + 2)

The derivative of the function y = x^(2x) using logarithmic differentiation is dy/dx = x^(2x) * (2 * ln(x) + 2). Logarithmic differentiation is a useful technique for differentiating functions that involve exponentials or complicated algebraic expressions, as it allows us to simplify the calculation by taking the logarithm of both sides and then differentiating implicitly.

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Answer: u have perpendicular lines

Step-by-step explanation: Hope this helps :)

\(5+2\sqrt{5} , 5-2\sqrt{5}\)    Answer:   5±2\(\sqrt{5}\)

Step-by-step explanation:

x2 -10x=5=0

x2-10x+25=-5+25

(x-5)(x-5)=20

\((x-5)^{2} =\sqrt{20}\)

\(\sqrt{x-5}=\sqrt{20}\)

x-5=±\(\sqrt{20\)

x=5±\(\sqrt{5*4\)

x=5±2\(\sqrt{5}\)

Option (a) and option (b) are the answers for Euler equation

a)Consider the Euler equation ax²y" + bxy' + cy = 0,

where a, b and c are real constants and a 0. Use the change of variables x = et to derive a linear, second order ODE with constant coefficients with respect to t. As per given, the Euler equation is ax²y" + bxy' + cy = 0.

Therefore, change of variable x = et. Using this change of variable, differentiate with respect to t to get y' and y".

$$x=et \\\frac{dx}{dt}

      =e\implies dx

      =edx \\\frac{d}{dt}y

      =\frac{dy}{dx}\cdot\frac{dx}{dt}

      =y'\cdot e \\\frac{d^2}{dt^2}y

      =\frac{d}{dt}\frac{dy}{dt}

      =\frac{d}{dt}\left(\frac{dy}{dx}\cdot\frac{dx}{dt}\right)$$

      =\frac{d}{dx}\left(\frac{dy}{dx}\right)\frac{dx}{dt}+\frac{dy}{dx}\cdot\frac{d}{dt}\left(\frac{dx}{dt}\right)

     =\frac{d^2y}{dx^2}\cdot e^2+y'\cdot e$$

As x=et, therefore,

$\frac{dx}{dt}=e$

$$bxy' = be\cdot y'x \\\implies\frac{bxy'}{x}

           =be\cdot y' \\\implies b\frac{dy}{dx}

           =be\cdot y'$$

$$\frac{dy}{dx}=e\cdot y'$$

$$\frac{d^2y}{dx^2}=e\cdot\frac{d}{dx}\left(e\cdot y'\right)$$

$$=e^2\cdot\frac{d^2y}{dx^2}+e\cdot\frac{dy}{dx}$$

$$\implies \frac{d^2y}{dx^2}=\frac{1}{e}\left[\frac{d^2y}{dx^2}+y'\right]$$

Substituting $x=et$ and replacing $y'$ and $y"$ with the above derivations, we get:

$$a\cdot e^2t^2\cdot \frac{1}{e}\left[\frac{d^2y}{dx^2}+y'\right]+b\cdot e^t\cdot\frac{dy}{dx}+cy=0$$

$$at^2\cdot\frac{d^2y}{dx^2}+\left(bt+c\right)\cdot ty'-a\cdot y'=0$$

$$\boxed{aty''+\left(bt+c\right)y'-ay=0}$$

b)Find the general solution of (x - 3)²y" - 2y = 0 on (0, [infinity]).

Given differential equation is (x - 3)²y" - 2y = 0.

The auxiliary equation will be $(m^2-1)m^0=0$

which gives $m=1$ (repeated root) and $m=-1$.

$$y(x)=c_1 e^{x} + c_2 e^{-x} + c_3 x e^{x}$$

$$y'(x)=c_1 e^{x} - c_2 e^{-x} + c_3 e^{x} + c_3 x e^{x}$$

$$y''(x)=2 c_1 e^{x} + 2 c_3 e^{x} + c_3 x e^{x}$$

$$\boxed{y(x)=c_1 e^{x} + c_2 e^{-x} + c_3 x e^{x}}$$

So, option (a) and option (b) are the answers.

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we can estimate that the proportion of defectives being produced by the machine is around 0.316.

What is proportion?

A comparison between the size, number, or amount of one thing or group with that of another. In our class, there are three boys for everyone lady.

If the random sample of size 2 yields 2 defects, that means both items in the sample were defective. Let p be the proportion of defectives being produced by the machine.

The probability of selecting a defective item on the first draw is p, and the probability of selecting a defective item on the second draw is also p (assuming sampling without replacement).

Since both items were defective, the probability of this happening is p * p = p².

So,

p² = (number of samples with 2 defects) / (total number of samples)

We don't know the values of these numbers, but we can use them to estimate p. For example, if we had a total of 100 samples and 10 of them had 2 defects, then:

p² = 10/100 = 0.1

p ≈ √(0.1) ≈ 0.316

Hence, we can estimate that the proportion of defectives being produced by the machine is around 0.316.

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Answer:

Your answer is 17.5 hours

Step-by-step explanation:

Simply multiply 2.5 and 7 to get your answer.

You have to multiply the number of hours by the number of days to get the correct product or answer.

The probability that the next spin lands on red is

The table of values is given as:

Red = 4

Blue = 3

Green = 20

Yellow = 14

Purple = 16

The probability that the next spin lands on red is:

P(Red) = Red/Total

This gives

P(Red) = 4/(4+3+20+14+16)

Evaluate

P(Red) = 7%

Hence, the probability that the next spin lands on red is

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Answer:8%

Step-by-step explanation:

Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

To make 12 pancakes, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk.

We can use proportions to figure out how much of each ingredient Dan will need. If 240g of plain flour, 2 eggs, and 600ml of milk are enough to make 8 pancakes, then we can set up the following ratios:

Plain flour: 240g/8 pancakes = x/12 pancakes

Eggs: 2/8 pancakes = y/12 pancakes

Milk: 600ml/8 pancakes = z/12 pancakes

Solving for x, y, and z in each of these ratios, we get x = 360g of plain flour, y = 3 eggs, and z = 900ml of milk. Therefore, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

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The given equation is expressed as

- 8 = 8(y - 5)

To solve for y, we would divide both sides of the equation by 8. We have

- 8/8 = 8/8(y - 5)

- 1 = y - 5

Adding 5 to both sides of the equation, we have

- 1 + 5 = y - 5 + 5

4 = y

y = 4

The only value that is a solution is

y = 4

The other values are not solutions

Thus,

y

8 No

9 No

- 2 No

4 Yes

Answer:

-1= -8    0= -3     1= 2     2= 7

Step-by-step explanation:

Plug the x values in and solve to get Y.

The ladder reaches approximately 8.66 feet up the wall.

To find out how far up the wall the ladder reaches, we need to use the Pythagorean theorem. The theorem states that the square of the hypotenuse (in this case, the length of the ladder) is equal to the sum of the squares of the other two sides (the distance of the base of the ladder from the wall and the height the ladder reaches on the wall).

So, if the base of the ladder is 5 feet from the wall, and the ladder is, say, 10 feet long, we can use the Pythagorean theorem to find out the height the ladder reaches on the wall. The equation would be:

10^2 = 5^2 + x^2

(where x is the height the ladder reaches on the wall)

Simplifying the equation, we get:

100 = 25 + x^2

75 = x^2

x = sqrt(75)

x ≈ 8.66 feet

Therefore, the ladder reaches approximately 8.66 feet up the wall.

In summary, we can use the Pythagorean theorem to determine the height the ladder reaches on the wall, given the distance of the base of the ladder from the wall and the length of the ladder itself.
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Answer:

14.5

Step-by-step explanation:

10 + (2 x 3)2 ÷ 4 × (3 x 1/2)

10 + (6)2 / 4 * (1.5)

10 + 12 / 4 * 1.5

10 + 3 * 1.5

10 + 4.5

14.5

Answer:

20.5

Step-by-step explanation:

10 + 12 ÷ 4 x 7/2

10 + 3 x 7/2

10 + 21/2

10 + 10.5

20.5

Part a: Kinko's income is $280.

Part b: Kinko's optimal consumption will change due to the increased price of leather jackets, but the specific values cannot be determined without further calculations.

To find Kinko's income, we need to determine his budget line based on his current consumption and the price of whips. Kinko is consuming 4 whips and 16 leather jackets, and the price of whips is $6.

The budget line equation is given by: Px * x + Py * y = I, where Px is the price of whips, Py is the price of leather jackets, x is the consumption of whips, y is the consumption of leather jackets, and I is the income.

Since Kinko spends all his money on whips and leather jackets, his income equals the total expenditure on these goods. Thus, the budget line equation becomes: 6x + 16y = I.

We can substitute Kinko's consumption values into the equation: 6 * 4 + 16 * 16 = I.

Simplifying, we have: 24 + 256 = I.

Therefore, Kinko's income is $280.

To visualize this, we can plot Kinko's indifference curves and the budget line on a graph with whips (x) on the horizontal axis and leather jackets (y) on the vertical axis.

The budget line represents all the affordable combinations of whips and leather jackets given Kinko's income and the prices. The indifference curves represent Kinko's preferences, showing the combinations of whips and leather jackets that provide him with the same level of utility.

Part b:

If the price of leather jackets increases by 16 times, the new price of leather jackets becomes $16 * Py = $16 * 1 = $16.

To determine Kinko's optimal consumption, we need to find the new tangency point between an indifference curve and the new budget line. Since Kinko's utility function is non-standard, we need to use calculus to find the optimal consumption bundle.

Using the Lagrange multiplier method, we set up the following optimization problem:

Maximize U(x, y) = min{x½ + y½, x/4 + y}

Subject to the constraint: Px * x + Py * y = I, where Px = $6 and Py = $16.

By solving the optimization problem, we can find the new optimal consumption bundle in terms of whips (x) and leather jackets (y).

However, without the specific values for x and y, it is not possible to provide the exact optimal consumption bundle in one line.

The solution would involve finding the tangency point between the new budget line (with the increased price of leather jackets) and the indifference curves, and determining the corresponding values of x and y.

Therefore, without further information, we can only state that Kinko's optimal consumption will change due to the change in the price of leather jackets, but we cannot provide the specific values without additional calculations.

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\(\bf{\dfrac{1}{2}(27+6)10 }\)

Add 27 and 6 to get 33.

\(\bf{\dfrac{1}{2}(33)(10) }\)

Multiply 1/2 by 3 to get 33/2.

\(\bf{\dfrac{33}{2}(10) }\)

Express 33/2 (10) as a single fraction.

\(\bf{\dfrac{(33)(10)}{2} }\)

Multiply 33 and 10 to get 330.

\(\bf{\dfrac{330}{2} }\)

Divide 330 by 2 to get 165.

\(\bf{165 \ \ \to \ \ \ Answer}\)

Check the picture below.

The given integral ∫(4x^2 + 4x + 2) dx can be evaluated to obtain an expression in the form P arctan(ax + b) + c, where P, a, b, and c are constants. The common divisor of P and q is 1, and the value of P is 9.

In the given expression, the integral of 4x^2 is (4/3)x^3, the integral of 4x is 2x^2, and the integral of 2 is 2x. Summing up these integrals, we get (4/3)x^3 + 2x^2 + 2x + C, where C is the constant of integration.

To express this in the form P arctan(ax + b) + c, we need to manipulate the expression further. We can rewrite (4/3)x^3 + 2x^2 + 2x as (4/3)x^3 + (6/3)x^2 + (6/3)x, which simplifies to (4/3)x^3 + (6/3)(x^2 + x).

Comparing this with the form arctan(ax + b), we can see that a = √(6/3) and b = 1. Therefore, the expression becomes 9 arctans (√(6/3)x + 1) + C, where C is the constant of integration.

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Answer:

agree

Step-by-step explanation:

Answer:

B

Step-by-step explanation: