What is another way to write the absolute value inequality

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer: If the new or compared value is P% more than the reference value, you can calculate the reference value as follows:

Reference value = New or compared value / (1 + P/100)

For example, if the new value is 120% of the reference value, then P = 20 and the reference value can be calculated as:

Reference value = New value / (1 + 20/100) = New value / 1.2

If the new or compared value is P% less than the reference value, you can calculate the reference value as follows:

Reference value = New or compared value / (1 - P/100)

For example, if the new value is 80% of the reference value, then P = 20 and the reference value can be calculated as:

Reference value = New value / (1 - 20/100) = New value / 0.8

Step-by-step explanation:

The guy wire is 111 ft long.

The length of the guy wire, to the nearest foot is: 207 ft.

After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.

Required:

Length of the guy wire (AE)

First, find AB:

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

AB/11 = (35 + 2)/2

AB/11 = 37/2

AB = (37 × 11)/2

AB = 203.5 ft

AE = √(AB² + BE²)

AE = √(203.5² + 37²)

AE = 207 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is: 207 ft.

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Answer:

\(A)58\)

Step-by-step explanation:

\([Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\\)

\(Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58\)

\(Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58\)

An

346100

Step-by-step explanation:

The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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The equation M = 8 + 8 represents the given information. Maria has 16 scarves.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's let "M" represent the number of scarves that Maria has.

According to the problem, "Maria has 8 more scarves than Lucy." We know that Lucy has 8 scarves. So, Maria has 8 more than that.

We can represent this information in an equation:

M = 8 + 8

We add 8 to Lucy's 8 scarves to get the total number of scarves that Maria has, which is 16.

So, Maria has 16 scarves.

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The required Maria has 16 scarves, and the expression models the situation is given as M = 8 + L.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's use the variable "M" to represent the number of scarves that Maria has. Since Maria has 8 more scarves than Lucy, and Lucy has 8 scarves, we can write an equation as,

M = 8 + L

where L is the number of scarves that Lucy has. Substituting L = 8 into this equation, we get:

M = 8 + 8

M = 16

Therefore, Maria has 16 scarves.

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Answer:

A

Step-by-step explanation:

All the other exponential equations have a base greater than 1 except A and c is a linear equation with positive slope

Answer:

A

Step-by-step explanation:

5 - \(\frac{3}{2}\) x ≥ \(\frac{1}{3}\)

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

30 - 9x ≥ 2 ( subtract 30 from both sides )

- 9x ≥ - 28

divide both sides by - 9 , reversing the symbol as a result of dividing by a negative quantity.

x ≤ \(\frac{28}{9}\)

Answer: Net pay is what you are paid after having taxes withdrawn from that pay. Harry may have earned more money than his net pay but there are state and federal taxes he must pay from his earnings before getting his payment. The government takes out the amount of taxes he owes from the money he name this week and he is then given the rest.

Answer:When you change the position and speed of the ball in the carnival

game, you transfer energy to the ball. Energy is the ability of a person

or an object to do work or to cause a change. When you do work on an

object, some of your energy is transferred to the object. You can think

of work as the transfer of energy. In fact, both work and energy are

measured in the same unit, the joule.

The man in the photograph above converts one form of energy

into another form when he uses his muscles to toss the ball. You can

think of the man and the ball as a system, or a group of objects that

affect one another. Energy can be transferred from the man to the

ball, but the total amount of energy in the system does not change

Step-by-step explanation:

The number of elements in the Q complement set, n(Q') is 7

From the question, we are to determine the number of elements that are in the given set.

To find n(Q'),

First, we will determine the elements in Q'

NOTE: Q' means Q complement, that is, the elements that are present in the universal set but not in Q

The universal set is

ξ = {numbers between 3 and 19}

That is,

ξ = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}

From the given information,

Q = {3, 5, 6, 7, 9, 10, 12, 13, 17, 18}

Therefore,

Q' = {4, 8, 11, 14, 15, 16, 19}

The value of n(Q') is the number of elements in the q' set

That is,

n(Q') = 7

Hence, n(Q') = 7

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The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer:

2,4 3,5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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The value of x in the triangle is 10

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The sum of the three angles in a triangle is 180°.

Therefore

(5x - 5)° + 8x + (6x - 5) =180

5x-5+8x+6x-5 = 180

collect like terms

5x+8x+6x-5-5 = 180

19x = 180+10

19x = 190

divide both sides by 19

x = 190/19

x= 10

therefore the value of x is 10

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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a. exponential function is\(y = 397,000*(1+0.03)^t\) b. Rounding to the nearest thousand, the population after 15 years will be 605,000

A mathematical function with the following formula is an exponential function:

\(f(x) = a^x\)

where x: input variable and an is a positive constant known as the base. As x increases or decreases, the value of the function either rises or falls exponentially. In other words, the function always increases or decreases at a rate that is proportionate to its current value.

a. The formula: can be used to create an exponential function that depicts the population after t years.

\(y = y 0 * (1 + r)^t\)

where t: number of years, r: yearly growth rate expressed as a decimal, and y 0 is the initial population.

The initial population in this instance is 397,000, and the yearly growth rate is 3%, or 0.03 in decimal form. The exponential function that depicts the population after t years is as follows:

\(y = 397,000 * (1 + 0.03)^t\)

b. We may change the exponential function we discovered in part a to include t = 15 to determine the population after 15 years:

\(y = 397,000 * (1 + 0.03)^(15)y = 605,464\)

After 15 years, the population will be roughly 605,000, to the nearest thousand.

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Standard Deviation for given set of data is 0.25634797778466.

What is standard deviation?

Given that,

Sample size :12.3,11.9,12.5,12.1,12.6,11.9,12.2,12.1

Count, N: 8

Sum, submission x: 97.6

Mean, x: 12.2

Variance, s2:  0.065714285714286

s^2 = Σ(xi - x)^2/N - 1

= (12.3 - 12.2)2 + ... + (12.1 - 12.2)^2/8 - 1

= 0.46/7

=  0.065714285714286

s =  √0.065714285714286

=  0.25634797778466

Standard Deviation for given set of data is 0.25634797778466.

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Answer:

Here to get the points thanks for recommending this ur so nice.

Step-by-step explanation:

Answer:

r = 15

Step-by-step explanation:

Line segments DG and GM add up to DM:

r + 3 + 4r - 28 = 50

5r - 25 = 50

5r = 75

r = 15

Answer:

15

Step-by-step explanation:

Given:

Solution:

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Answer: $521.50

Step-by-step explanation:

58 hours worked

40 hours regular x $7.45 = $298

6 hours holiday  x $7.45 x 2 = $89.40

58 - 46 = 12 hours overtime x $7.45 x 1.5 = $134.10

$298 + $89.40 + $134.10 = $521.50

Answer:

the answer to this is a

Step-by-step explanation:

i did it

Answer:

Given,

CB=X

CD=3

CA=3+7=10

HERE,

\( {(cb)}^{2} = cd \times ca \\ {x}^{2} = 3 \times 10 \\ {x}^{2} = 30 \\ x = \sqrt{30} \)

Hope this helps...

Good luck on your assignment..

The value of x is: x= √30.

Here, we have,

from the given figure, we get,

let, angle C = Ф

then, from triangle BCD,

cos Ф = 3/x

and, from triangle ABC,

cos Ф = x/10

so, we have,

3/x = x/10

=> x² = 10×3

=> x² = 30

=> x= √30

Hence, The value of x is: x= √30.

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