. A rectangle’s length is twice its width. Its perimeter is 156 meters. What is the rectangle’s length?

a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.

b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5

c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is  3.

What is Function?

A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.

Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.

a. The equation for g(x) is:

g(x) = 6((x+5)/2)³

When 3 is put in for x, the output is:

g(3) = 6((3+5)/2)³= 6(4)³ = 384

b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:

Putting this in equation form, we get:

g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5

c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:

g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3

Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).

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The total surface area of this cone is equal to 735.1 square meters.

Mathematically, the total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Where:

Substituting the given parameters into the total surface area (TSA) (SA) of a cone formula, we have the following;

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

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Answer:

If you want it simplified, it is 3x + 14!

Hope it helps!

Answer: 37

Step-by-step explanation:

let x be the number of students who pass "fante". Then the number of students who passed "Ga" will be x + 6.

with the added information that 8 students passed both we can say:

(x + x + 6) - 8 = 60

2x + 6 = 68

2x = 62

x = 31

.: x + 6 = "only Ga pass" = 37

The question does not make it clear if it is asking for students who *only* passed Ga, or students who passed Ga + those who passed both. I'll assume the former though. Otherwise the answer would be 37 + 8 = 45 students

Answer: 4 people

Step-by-step explanation:

As you can see the money spent is on one side of the graph and the people attending on the other. Try to go along the line of where 60 is and find where the line meets the line on 60. Look down and you can see 4.

Answer:

216 in^3

Step-by-step explanation:

Volume = 6 in. * 4 in. * 9 in. = 216 in^3

Answer: 0.1 decimal 1/9 fraction

Step-by-step explanation:

Answer:

0.1 or 1/9 i think so but I am sure

The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:

Total cost of cement rings = Cost of each cement ring x Number of cement rings used

Total cost of cement rings = 28 x 2500 = RS. 70,000

Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]

Cost of digging out the well = 500 x 9.798 = RS. 4,899

Total cost of the well = RS. 74,899

Total cost of cement rings = 2500 x 28 = RS. 70,000

Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

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Answer: x = y

Step-by-step explanation:

x and y are angles with vertical sides, and angles with vertical sides are always equal

The equation that represents this situation is $6t - $450 ≥ $1000.

The number of tickets that should be sold is 242.

The form of the equation is:

total revenue - total cost ≥ $1000

(cost of one ticket x number of tickets sold) -  cost of pizza and drinks ≥ $1000

($6 x t) - ($200 + $250) ≥ $1000

$6t - $450 ≥ $1000

$6t ≥ $1000 + $450

$6t ≥ $1450

t ≥ $1450 / 6t

t ≥ 242

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The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.

To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.

First, we'll calculate the cost at Suttons Shop:

Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.

If she buys 1 bag of compost, it will cost her £2.25.

If she buys 2 bags of compost, it will cost her £3.25.

Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.

So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.

The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.

Next, we'll calculate the cost at Greens Garden Shop:

Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.

Each bag at Greens Garden Shop costs £4.99.

So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.

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I know, I answer quick. What do you expect I'm Johnny Sins to help you with your homework. :)

Anyways,

The height of the nth bounce can be calculated using the formula:

h_n = h_1 * 0.68^(n-1)

Where h_1 is the height of the first bounce, h_n is the height of the nth bounce, and 0.68 is the percentage of the height lost with each successive bounce.

Substituting the given values, we have:

h_9 = 5 * 0.68^(9-1)

h_9 = 5 * 0.68^8

h_9 = 5 * 0.265

h_9 = 1.325

So the height of the 9th bounce would be approximately 1.3 feet, rounded to the nearest tenth.

_________________________________________________________

Thanks for the support, love you brother!

Love Johnny Sins

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Answer: 1/m^2n^2

Step-by-step explanation: when dividing powers, we subtract.

so, the top would all cancel out

and we would be left with only m^-2n^-2.

to get rid of the negative we put the number into the denominator.

so m^-2n^-2 would become 1/m^2n^2.

Answer:

x = 4

The missing angle is 28°

Step-by-step explanation:

7x + 62 = 90  These angles are complementary which means that they add to 90°

7x + 62 = 90  Subtract 62 from both sides of the equation

7x = 28  Divide both sides by 7

x = 4

Answer:

Step-by-step explanation:

well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.

No, f(x, y) = 3x - 3y^2 is not a harmonic function.

A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
                                                                            ∂²f/∂x² + ∂²f/∂y² = 0.

Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0

Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.

As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.

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Answer:

304

Step-by-step explanation

it was on my quiz

Answer:

The number 304 is exactly halfway between 61 and 547.

Step-by-step explanation:

To find the halfway point between two given numbers we can simply add them together then divide them by 2.

Note:

let [tex]N[/tex] be the number that is halfway

[tex]N=\frac{547+61}{2}[/tex]

[tex]N=\frac{608}{2}[/tex]

[tex]N=304[/tex]

The resulting expression of the algebraic expression  is 13r²(2rs + 4r³ - 3s⁴).

option C.

The resulting expression of the algebraic expression given as

26r³s + 52r^(5) - 39r²s⁴

can be determined by finding the highest common factor here and factorize out.

The highest common factor of the letters is r²

Factors of 26 = 1, 2, 13, 26

Factors of 39 = 1, 3, 13, 39

Factors of 52 = 1, 2, 4, 13, 26, 52

The highest common factor for the 3 numbers is 13.

Thus, in total, the highest common factor for the algebraic expression is 13r².

Finally, we have;

13r²(2rs + 4r³ - 3s⁴)

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The complete question is below:

Factor  26r³s + 52r^(5) - 39r²s⁴

The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In this context, an equation that models the situation is given by:

y = mx + c

340 = 28x + 102

28x = 340 - 102

28x = 238

x = 238/28

x = 8.5 gallons of gasoline.

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The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C

From the information given, we have that;

We also have that the function is;

h(x) =-(x)(x-13)

Given that the distance is 3 inches

Substitute the values, we have;

h(3)= -(3)(3-13)

substract the values

h(3) = (-3)(-10)

multiply the values

h(3) = 30 inches

Hence, the value is 30 inches

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There 144 four digit numbers are made up of four consecutive numbers from 1 to 9

We can approach this problem by counting the number of ways we can choose four consecutive numbers from 1-9 and then arranging them in a four-digit number.

Here we have to use combination

There are 6 possible sets of four consecutive numbers in the range 1-9

= {1,2,3,4}, {2,3,4,5}, {3,4,5,6}, {4,5,6,7}, {5,6,7,8}, and {6,7,8,9}.

For each set, there are 4! = 24 ways to arrange the four numbers into a four-digit number.

So the total number of four-digit numbers made up of four consecutive numbers from 1-9 is:

6 sets × 24 arrangements per set = 144

Therefore, there are 144 such four-digit numbers.

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These are the four points that are exactly 5 units away from point W. To find points that are 5 units from point W, which is located at (-5, -3).

To find points that are 5 units from point W, which is located at (-5, -3), we need to find all points that are a distance of 5 units away from (-5, -3) using the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the distance between two points) is equal to the sum of the squares of the lengths of the other two sides

Given a point (x, y), the distance between that point and point W can be found using the formula:

distance = sqrt((x + 5)^2 + (y + 3)^2)

Setting this distance equal to 5 and solving for x and y, we get the following points:

(0, -8), (-10, -8), (0, 2), and (-10, 2).

These are the four points that are exactly 5 units away from point W.

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A quadratic equation with -1 and 5 as its roots is x^2 - 4x - 5 = 0 by multiplying the terms.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

Derive factor from the roots

x = -1    and    x = 5

x + 1 = 0  and  x - 5 = 0

Now, (x+1)(x-5) = 0

 x(x - 5) + 1(x - 5) = 0

x^2 - 5x + x - 5 = 0

 x^2 - 4x - 5 = 0

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Answer:

The expressions are identical, as shown by two methods:  1) equation rearrangement and 2) mathematical calculations.

Step-by-step explanation:

2(x + 5) + 3x

Let's simplify this expression.

2(x + 5) + 3x  

2x + 10 + 3x    [remove parentheses]

5x + 10              [combine like terms]

This matches the other expression.

5x + 10

Several values of x are calculated for both expressions and are shown on the attached table.  Each expression results in the same value for a given value of x.  This comparison also holds for negative numbers.

The total surface area is π[(4/3)x]² + π(4/3)x². The base area is greater than the lateral area.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

Given the cone. The surface area (SA) is given by the equation:

SA = πr² + πrs

where r is the radius of the cone and s is the slant height.

Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x

Hence:

SA = πr² + πrs

substituting:

SA = π[(4/3)x]² + π(4/3)x(x)

SA = π[(4/3)x]² + π(4/3)x²

The base area = π[(4/3)x]², the lateral area =  π(4/3)x²

The base area is greater than the lateral area.

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An appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Since the data represents the average time employees spent online, the y-axis of the bar graph should represent time in minutes.

To choose an appropriate scale for the y-axis.

we need to consider the range of values in the data set.

The lowest value is 15 minutes

and the highest value is 60 minutes

Range of values is 60 - 15 = 45 minutes.

It's best to choose a scale that divides the range of values into equal intervals.

One possible option is to use a scale where each unit represents 5 minutes of time. This would allow us to represent the data accurately without making the bars too small or too large.

Therefore, an appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.

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Answer:

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Step-by-step explanation:

-5(y + 0.2) = 25  Distribute the -5

-5(y) + -5(0.2) = 25   Adding a negative is the same as subtracting a positive

-5y - 1 = 25   add 1 to both sides

-5y - 1 + 1 = 25 + 1

-5y = 26  Divide both sides by -5

[tex]\frac{-5y}{-5}[/tex] = [tex]\frac{26}{-5}[/tex]

y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal

Answer: To solve the equation -5(y + 0.2) = 25, we need to isolate y by performing the following steps:

Distribute the -5 to the expression inside the parenthesis:

-5 * y - 5 * 0.2 = 25

-5y - 1 = 25

Add 1 to both sides of the equation to isolate -5y on one side:

-5y - 1 + 1 = 25 + 1

-5y = 26

Divide both sides of the equation by -5 to find y:

(-5y) / -5 = 26 / -5

y = -5.2

So, the solution to the equation -5(y + 0.2) = 25 is y = -5.2.

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

[tex]h\left(x\right)=\frac{1}{2}x-14\\h\left(-4\right)=-4/2-14=-2-14=-16[/tex]

The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments.

The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments. This is because the area of the smaller square inscribed in the larger square is equal to the product of the side lengths of the smaller square. If a vertex of the smaller square is located on the side of the larger square, the side of the larger square is divided into two segments with one segment having length and the other having length . The side length of the larger square is then equal to the sum of the lengths of the two segments plus the side length of the smaller square, which is . Therefore, the side length of the larger square minus the sum of the lengths of the two segments is equal to the side length of the smaller square, or the value of is equal to two segments.

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