Use the distributive property to factor the expression below.
54x²y - 12x²y²

After 3 years, the value of the car will be approximately $20,959.34.

The depreciation of an asset is the reduction in the value of the asset over time due to wear and tear, obsolescence, or other factors. The depreciation equation is used to calculate the amount by which the value of an asset decreases each year.

The value of the car after 3 years can be represented by the following equation:

V = 26600 * (1 - 0.09)^3

Where V is the value of the car after 3 years and 0.09 is the depreciation rate per year.

Solving this equation gives us a value of V = $20,959.34.

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Answer:20044.9886

Step-by-step explanation:

The number 25209 rounded to the largest place value is 30000.

Every digit in a number has a place value, which is a numerical value determined by the digit's position.

Step 1: First, decide which location value has the highest worth.

The number that is farthest to the left has the highest place value.

Providing the value is not zero.

In the number 25209,

2 is the largest place value.

Step 2: Next, take a look at the number that is closest to the largest place value.

The greatest place value remains the same if the number is 0, 1, 2, 3, or 4.

The highest place value increases by one if the number to the right is a 5, 6, 7, or 9.

We have number 5 to the right of 2.

The number rounded to the largest place value is 30000.

Therefore, the required number is 30000.

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The amount of fabric used on a headband and wristband for each player is $30.97.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

She uses 759.56 inches of fabric on headbands for 31 players and 3 coaches.

Per person = 759.56/(31 + 3) = $22.34

As per the given,

267.53 inches of fabric on wristbands for just the players.

Per player = 267.53/31 = $8.63

Total material of per player = $22.34 + $8.63

⇒ $30.97

Hence "Each player's wristband and headband cost $30.97 worth of cloth".

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Answer:

A(W)=500-19W

177W = 500 - 19W

177W + 19W = 500

196W = 500

W = 2.5

Therefore, Amny needs to save for 2.5 weeks

Step-by-step explanation:

the probability of an archer hitting her target is 83%.The mean of x is 16.6 (16.6 targets hit).

The probability of the archer hitting her target is 83%. This means that for each shot she takes, the probability of her hitting her target is 0.83. Since she has 20 shots to take, the expected number of targets hit is 20 x 0.83, which is 16.6.

The mean of x, which is the number of targets hit, is therefore 16.6. This can be calculated by taking the probability of success (0.83) multiplied by the number of trials (20), which gives the expected value of 16.6.

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The volume of the crater is 64800000 m³

From the question, we are to determine the volume of the crater.

From the given information,

d = 2∛(V/0.3)

To determine the volume,

First, we will solve for V in the equation

d = 2∛(V/0.3)

Divide both sides by 2

d/2 = ∛(V/0.3)

Take the cube of both sides

(d/2)³ = V/0.3

Then,

V = 0.3(d/2)³

Now, substitute the value of the diameter

d = 1200m

Then,

V = 0.3(1200/2)³

V = 0.3(600)³

V = 64800000 m³

Hence, the volume is 64800000 m³

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Answer: x = 18

Step-by-step explanation: If you do 108 divided by 6, you get 18.

I'm not sure whether this is what you wanted for an answer, but here.

Answer:

[tex] \sf \: x = - 18[/tex]

Step-by-step explanation:

Given equation,

→ -108 = 6x

Now the value of x will be,

→ -108 = 6x

→ 6x = -108

→ x = -108/6

→ [ x = -18 ]

Hence, the value of x is -18.

Answer:

2 terms

Step-by-step explanation:

An algebraic expression may be composed of one or more terms. A term of an expression may be a constant, a variable, a product of more than two variables (xy), or a product of a variable and a constant.

Answer:

This because the root cancel each other

Answer: The first three terms of the sequence are: 1^2+1=2, 2^2+1=5, 3^2+1=10

The tenth term of the sequence is: 10^2+1=101.

Step-by-step explanation: To find the first three terms of a number sequence in which the nth term is n^2+1:

For the first term, set n equal to 1 and substitute it into the formula: 1^2 + 1 = 2

For the second term, set n equal to 2 and substitute it into the formula: 2^2 + 1 = 5

For the third term, set n equal to 3 and substitute it into the formula: 3^2 + 1 = 10

To find the tenth term of the same sequence, set n equal to 10 and substitute it into the formula: 10^2 + 1 = 101.

In a cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants and has a local minimum at x = -2 and a local maximum at x = 0, then values of a and b is 12 and 0 respectively. If integrate of f(x)dx = 32 from 0 to 1, then value of k is 27.

The given cubic polynomial function is

f(x) = 4x³ + ax² + bx + k

f'(x) = 12x² + 2ax + b

f''(x) = 24x + 2a

At local maximum f' = 0

f'(0) = 12×(0)² + 2a×(0) + b = 0

b = 0

At local minimum, f' = 0

That is f'(-2) = 0 and f''(-2) > 0

f'(-2) = 12×(-2)² + 2a×(-2) + b = 0

48 - 4a + b = 0

4a - b = 48  

a = 12

Therefore, f(x) =  4x³ + 12x² + k

Integrate f(x)dx = 32 from 0 to 1, that is

∫₀¹ f(x)dx = 32

∫₀¹ (4x³ + 12x² + k) dx = 32

[ x⁴ + 4x³ + kx ]₀¹ = 32

(1⁴ - 0⁴) + 4(1³ - 0³) + k(1 - 0) = 32

1 + 4 + k = 32

k = 27

-- The question is incomplete, answering to the question below--

"A cubic polynomial function f is defined by f(x) = 4x³ + ax² + bx + k, where a, b, k, are constants. The function f has a local minimum at x = -2 and a local maximum at x = 0.

A. Find the values of a and b

B. If you integrate f(x)dx = 32 from 0 to 1, what is the value of k?"

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Answer:

(6,0)

Step-by-step explanation:

Solving a system of equations is finding where 2 (or more) lines intersect.

Graph the lines:

y = x/6 - 1

and

y = -2/3x + 4

(linked)

Look at where they intersect (meet).

(6,0)

The value of x would be [tex]x=\frac{12}{5}[/tex].

Calculus is a branch of mathematics that focuses on the study of change, or the rate of change of a given function. It involves the use of derivatives, integrals, and limits to solve problems in physics, engineering, economics, and other sciences. Calculus is used to describe the behavior of objects under changing conditions, such as velocity, acceleration, and force. It is also used to optimize systems and to solve equations involving functions of several variables. Calculus provides a powerful tool for analyzing and understanding the physical world.
             [tex]\frac{5}{6} x-4=-2[/tex]
Now, combining  [tex]\frac{5}{6}[/tex] and x we get

             [tex]\frac{5x}{6} -4=-2[/tex]

So,

           [tex]\frac{5x}{6} -4=-2\\\\\frac{5x}{6} =2\\\\x=\frac{12}{5}[/tex]

Hence, [tex]x=\frac{12}{5}[/tex].

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The coordinates of J are (-2, -7) , hence the correct option is C.

What is translation?

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.The translated forms (or the image) seem to be an equivalent size because the original shape, indicating that they're congruent. They’ve merely shifted in one or additional directions.

Main body:

Given that, J’(-7, -3) is the image of J after translation (x, y) → (x - 5, y + 4)

We have, x-5 = -7

x = -2

And, y+4 = -3

y = -7

Hence, We get the coordinates of J are (-2, -7).

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Answer:

D. SSA

Step-by-step explanation:

SSA doesn't work because it can produce 2 different triangles that wouldn't be congruent. The angle of the 3rd side without restriction could change, changing the size of the figure. The image attached can help you understand this.

both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities. The resultant remains the same at 3.2 *10^4 Tm

It is possible for the line integral to go around the loop in either direction (clockwise or counterclockwise), the vector area dS to point in either of the two normal directions and Ienc, which is the net current passing through the surface S, to be positive in either direction—but both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities.

The resultant remains the same at 3.2 *10^4 Tm

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Answer:

the number of positive real roots is one

the number of negative real roots is one

I not sure I was right

Step-by-step explanation:

[tex]x^{3} +5x^{2} -3x+7[/tex]

it changed the sign in the second to the third term，so,it was one root

[tex]-x^{3} +5x^{2} +3x+7[/tex]

Change the coefficients of odd items, and the signs of the first to second items change, so there is also a root.

Answer:

Step-by-step explanation:

Descartes' Rule of Signs tells us the maximum number of positive and negative real roots in a polynomial function.

Positive root case

[tex]\begin{aligned}p(x)&=(x)^3+5(x)^2-3(x)+7\\ &=+x^3+5x^2-3x+7\end{aligned}[/tex]

Check the signs of the coefficients. As there are 2 sign changes, the maximum possible number of positive roots is 2.

However, as some pairs of roots may be complex, count down by two's to find the complete list of the possible number of roots.

So there may be as many as 2 real roots or there might also be no real roots (zero).

Negative root case

[tex]\begin{aligned}p(-x)&=(-x)^3+5(-x)^2-3(-x)+7\\&=-x^3+5x^2+3x+7\end{aligned}[/tex]

Check the signs of the coefficients.  As there is one sign change, the maximum possible number of negative roots is 1.  We can't count down by two's since this would give us a negative number. Therefore, there is exactly 1 negative root.

Note:  There is one real negative root of the given function at x ≈ -5.74 and two complex roots at x = 0.37 + 1.04i  and  x = 0.37 - 1.04i.

Answer:

x=138

Step-by-step explanation:

The question is a high school Mathematics problem. It involves using inequalities to solve a practical problem about a shipping container's weight limit. The answer found was that a maximum of 138 crates can be added to the container.

In this Mathematics problem, we have a shipping container that can hold a maximum weight of 27500 kilograms and there are already shipments totaling 6800 kilograms inside. We want to find out how many 150-kilogram crates (let's call this number 'x') can be added to the container without exceeding the maximum allowable weight.

Firstly, we build an inequality. The total weight of the container should not exceed 27500 kilograms, so we have:

6800 (the weight of the already loaded shipments) + 150*x (the weight of the x crates) ≤ 27500

This simplifies to:

150*x ≤ 20700 (because 27500-6800=20700)

Finally, to solve the inequality for 'x', divide throughout by 150:

x ≤ 138 (because 20700/150=138)

So, 138 is the maximum number of 150-kilogram crates that can be loaded into the shipping container without violating the weight constraint.

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There is a correlation that is likely for the number of car accidents and the weather as wet pavement and rainfall leads to more accidents.

The size and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is expressed as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

Weather-related issues will have an impact on our roads and reduce tire traction. Once more, it is advised to slow down while driving on slick roads, increase our following distance, and take more time to slow down when coming to a stop.

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Answer:

mandatory pay raises

Step-by-step explanation:

The month they would have the same amount of money is 2 months.

The linear equation that can be used to represent the total amount of money saved by each person is

Total amount saved = amount started with + (amount deposited per month x number of months)

Amount saved by Tonya = $60 + $20m

Amount saved by Jull = $20 + $40m

When they save the same amount of money, the two two above equations would be equal:

60 + 20m = 20 + 40m

In order to determine the value of m, take the following steps:

60 - 20 = 40m - 20m

40 = 20m

m = 40 / 20

m = 2

Substitute for m in the equation that represents the total amount of money saved by Tonya:

$60 + $20(2)

$60 + $40 = $100

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I do not have any information about you or your beliefs, experiences, or actions.. I do not have the ability to make judgments or assumptions about you or any other individual, you should provide more context as well as fix the category your question is listed under, you might have better results.

The probability is 0.07777.

What does probability mean?

The number of desired outcomes divided by the total number of outcomes yields a probability.

We are attempting to determine the likelihood, out of 10, that the first chip will be white and the second won't be green while assuming that one chip is white and two are green.

1/10 of the time, the initial chip will be white. If the first chip is white, there is a 7/9 chance that the second chip will be a color other than green. The desired probability is therefore provided by:

Ten chips are present.

white 1

red 4

green 2

Blue 3

the likelihood of selecting the W chip is one in ten, or 0.10

There are now only 9 chips left (the first chip was not replaced)

Selecting a non-green chip has a probability of (9-2)/9 = 7/9 = 0.7777.

you multiply the two probabilities to obtain the overall probability at this point.

probability is 0.1 to 0.7776.

The probability is equal to 0.07777, which implies that it must be less than 0.1.

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Answer:

1

Step-by-step explanation:

the height is 2/3ft because it makes a right angle with the surface

base is 3 ft

area: 1/2 x 3 x 2/3 = 1 ft^2

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Answer: 89.69

Step-by-step explanation:

-10.5 + m/ 11.57 = -2.748

First, we add 10.5 on both sides

m/ 11.57 = 7.752

Then we multiply both sides by 11.57

m = 89.69064, or we can simplify it be 89.69

The difference of 4h5k and -7hk5 Not possible.

Which of the following provides an example of to calculate the difference between 4h5k and -7h5k

Changing the situation 4h^5k - (-7hk^5)= 4h^5k +7hk^5

Making the distinction

4h^5k - (-7hk^5)

= 4h^5k +7hk^5

assemble similar phrases

Take note of similar phrases is  hk(4h^4+7k^5)

There can be no difference, therefore.

= hk(4h^4+7k^5)

As a result, the difference is Not possible.

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The Angle ∠MTU from the figure is 65°

The study of shapes and their measurements falls under the umbrella of geometry, a subfield of mathematics. It also emphasizes how the shapes are arranged in relation to one another and their spatial characteristics. We are aware that geometry is divided into 2D and 3D categories. All geometrical shapes are first created by the intersection of points, lines, rays, and plane surfaces. The distance measured between two lines is referred to as a "Angle" when the rays or lines converge at a single point.

Given,

∠STM=31X-3;

∠MTU=20X+5;

∠STU=155°;

From the figure we can say that

∠STU= ∠STM+∠MTU;

⇒ 155=31x-3+20x+5;

⇒155=51x+2;

⇒x=3;

Now substitute x in ∠MTU;

⇒∠MTU=20(3)+5=65°

The Angle ∠MTU from the figure is 65°

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Answer:

I) 70°

II) 120°

Step-by-step explanation:

In a regular polygon the sum of all its internal angles is equal to

180° × (n – 2)

where:

n = number of sides of the polygon

Answer:

[tex] \sf \: \frac{29m - 15}{25} \: (or)1 \frac{4}{25}m - \frac{3}{5} [/tex]

Step-by-step explanation:

Given expression,

→ 1 2/5m - 3/5(2/5m + 1)

Simplifying the given expression,

→ 1 2/5m - 3/5(2/5m + 1)

→ (7/5)m - 3/5(2/5m + 1)

→ (7/5)m - (6/25)m - (3/5)

→ (35/25)m - (6/25)m - (3/5)

→ ((35 - 6)/25)m - (3/5)

→ (29/25)m - (3/5)

→ (29m - 15)/25

→ 1 4/25m - (3/5)

Hence, answer is 1 4/25m - (3/5).

Answer:

55.5 as a fraction is 111/2.

Answer: 55.5 as a fraction is 111/2.

Step-by-step explanation: