The equation below is in standard form (Ax+By=C). Change the equation into Slope-Intercept form. (Hint: Solve the equation for y)

x + y = 6

The expression that represents the area of the rug after the expansion by x units on all four sides is:

(A + 2x) × (B + 2x), where A and B are the original length and width of the rug respectively.

The area of the rectangular rug before the expansion is given by A × B, where A and B are the length and width of the rug respectively.

After the expansion of x units on all four sides, the length and width of the rug become (A + 2x) and (B + 2x) respectively.

Therefore, the area of the rug after the expansion is:

(A + 2x) × (B + 2x)

= AB + 2Ax + 2Bx + 4x^2 (using FOIL method)

= AB + 2x(A + B) + 4x^2

Thus, the expression that represents the area of the rug after the expansion is (A + 2x) × (B + 2x).

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Answer: 42 gallons

Step-by-step explanation:

given data:

average gas mileage/day = 29miles/gallon

distance travelled each day by James = 87miles

How much gas does he use in 14days drive.

solution:

james drives 87miles daily, so in 14 days he would have travelled

= 87miles * 14

= 1218miles travelled.

gas used in 14days

1218miles distance traveled in 14 days

29miles/gallon

= 1218miles / 29miles

= 42gallons of gas have been used by janew to fuel his truck in 14days.

Answer:

what r the options

Step-by-step explanation:

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

A company pays $245.70 for 27 boxed lunches from a deli. If each boxed lunch is the same price, the unit cost of each boxed lunch is $9.10.

To find the unit cost of each boxed lunch, we need to divide the total cost by the number of boxed lunches.

Total cost of 27 boxed lunches = $245.70

Unit cost of each boxed lunch = Total cost / Number of boxed lunches

Unit cost of each boxed lunch = $245.70 / 27

Unit cost of each boxed lunch = $9.10 (rounded to two decimal places)

Therefore, the unit cost of each boxed lunch is $9.10.

In this case, the deli will need to ensure that each boxed lunch is priced higher than the unit cost of $9.10 to make a profit. The difference between the unit cost and the selling price will contribute to the deli's revenue and cover other expenses such as labor, rent, and utilities.

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Answer: C) H0 : μ = 250 , Ha: μ < 250

Step-by-step explanation:

The questions is incomplete. The correct question is

A restaurant advertises that its burritos weigh 250 g. A consumer advocacy group doubts this claim, and they obtain a random sample of these burritos to test if the mean weight is significantly lower than 250 g. Let u be the mean weight of the burritos at this restaurant and ĉ be the mean weight of the burritos in the sample. Which of the following is an appropriate set of hypotheses for their significance test? Choose 1 answer:

A) H0 : x = 250 , Ha : x < 250

B) H0 : x = 250 , Ha : x > 250

C) H0 : μ = 250 , Ha: μ < 250

C) H0 : μ = 250 , Ha: μ > 250

Solution:

The null hypothesis is the hypothesis that is assumed to be true. The restaurant advertises that its burritos weigh 250. This is the null hypothesis. 250 is the population mean,μ . Thus, the null hypothesis is

H0 : μ = 250

The alternative hypothesis is what the researcher expects or predicts. The consumer advocacy group tests if the mean weight is significantly lower than 250g. This is the alternative hypothesis. It is expressed as

H0 : μ < 250

Answer:

Yes, because 0.002 < 0.01

Step-by-step explanation:

Answer:

The answer is 10m

Step-by-step explanation:

Pathagorean Theorum.

a²+b²=c²

a=6  b=8

a²=36  b²=64

36+64=100

\(\sqrt{100}\) = 10

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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Answer:

All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.

Answer is in pictures and work as well

Answer:

you need to know what domain and range mean... so remember domain is the input.... range is the output..    :)

Step-by-step explanation:

the input .. "x"  in this case.. can be any number .. so the domain is all real numbers.

the output.. or range.. is limited.. b/c the square on the  'x" will always make that number positive.. and then it's multiplied by the negative 2.... so that term will always be negative.  : |  hmmmm so when is that squred term the smallest it can be?  hmmm  when it's zero... soooo this function will .. at it's greatest point be 3 and go down from there...

the range is from -∞  to 3  

see? :)

Answer:

B

Step-by-step explanation:

10 + (-42)

10 - 42

-32

a)The actual additional cost of producing the 21st food processor is $29.50.

b) Using the marginal cost approximation, the cost of producing the 21st food processor is $2,830.

a) To find the actual additional cost of producing the 21st food processor, we need to calculate the difference between the total cost of producing 21 processors and the total cost of producing 20 processors.

The total cost of producing x food processors is given by C(x) = 2,000 + 50x - 0.5x^2.

To find the cost of producing the 20th processor, we substitute x = 20 into the cost equation:

C(20) = 2,000 + 50(20) - 0.5(20)^2

= 2,000 + 1,000 - 0.5(400)

= 2,000 + 1,000 - 200

= 3,000 - 200

= 2,800

Now, we calculate the cost of producing the 21st processor:

C(21) = 2,000 + 50(21) - 0.5(21)^2

= 2,000 + 1,050 - 0.5(441)

= 2,000 + 1,050 - 220.5

= 3,050 - 220.5

= 2,829.5

The actual additional cost of producing the 21st food processor is the difference between C(21) and C(20):

Additional cost = C(21) - C(20)

= 2,829.5 - 2,800

= 29.5

Therefore, the actual additional cost of producing the 21st food processor is $29.50.

b) To approximate the cost of producing the 21st food processor using marginal cost, we need to find the derivative of the cost function with respect to x.

C'(x) = 50 - x

The marginal cost represents the rate of change of the total cost with respect to the number of units produced. So, to approximate the cost of producing the 21st processor, we evaluate the derivative at x = 20 (since the 20th processor has already been produced).

Marginal cost at x = 20:

C'(20) = 50 - 20

= 30

The marginal cost is $30 per unit. Since we are interested in the cost of producing the 21st food processor, we can approximate it by adding the marginal cost to the cost of producing the 20th processor.

Approximated cost of producing the 21st food processor = Cost of producing the 20th processor + Marginal cost

= C(20) + C'(20)

= 2,800 + 30

= 2,830

Therefore, using the marginal cost approximation, the cost of producing the 21st food processor is $2,830.

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Answer:

Step-by-step explanation:

Side "h" ( wall height ) is 35

The height of the wall "h".

\({\boxed{\mathcal{\red{The\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}}}}\)

\(\sf\purple{Using\:Pythagoras \:theorem, \:we\:have}\)

\(( {Perpendicular})^{2} + ( {Base})^{2} = ( {Hypotenuse})^{2} \\ ➡ \: {h}^{2} + ({35 \: ft})^{2} = ({50 \: ft})^{2} \\ ➡ \: {h}^{2} + 1225 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ➡ \: {h}^{2} = 2500 {ft}^{2} - 1225 \: {ft}^{2} \\ ➡ \: {h}^{2} = 1275 \: {ft}^{2} \\ ➡ \: h \: = \sqrt{1275 \: {ft}^{2} } \\ ➡ \: h = 35.707\: ft \: \\ ➡ \: h = 35.71\: ft\)

\(\sf\red{Therefore\:the\:height\:of\:the\:wall\:"h"\:is\:35.71\:ft.}\)

\(( {35.71 \: ft})^{2} + ( {35 \: ft})^{2} = ({50 \: ft})^{2} \\ ✒ \: 1275 \: {ft}^{2} + 1225 \: {ft}^{2} \: = 2500 \: {ft}^{2} \\ ✒ \: 2500 \: {ft}^{2} = 2500 \: {ft}^{2} \\ ✒ \: L.H.S.=R. H. S\)

Hence verified.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

The cost of the angle t in terms of sint is given by: cost = 5sin²t To find the cost, we can use the Pythagorean identity given in the prompt:

sint + cos²t = 1

We know that sin²t + cos²t = 1, so we can rewrite this as:

(sin²t + cos²t) - sin²t = 1 - sin²t

Subtracting sin²t from both sides gives:

cos²t = 1 - sin²t

cos²t = 1 - sin²t

cos²t(1 - sin²t) = 1 - sin²t(1 - sin²t)

cos²t - sin²t(1 - sin²t) = 0

Since cos²t and sin²t are positive, the product of their squares is positive as well. Therefore, the expression in parentheses is positive, and we can divide both sides by it:

cos²t + sin²t(1 - sin²t) = 1

Now, we can use the identity given in the prompt to simplify the left-hand side:

cos²t + sin²t(1 - sin²t) = 1

cos²t(1 - sin²t) = 1 - sin²t

cos²t(1 + sin²t) = 1

Since cos²t and sin²t are positive, the product of their squares is positive as well. Therefore, the product of (1 + sin²t) is positive, and we can divide both sides by it:

cos²t + sin²t(1 - sin²t) = 1

cos²t(1 - sin²t) = 1/cos²t

cos²t - sin²t = 1/cos²t

Substituting the expression for sin²t in terms of cos²t, we get

cos²t - sin²t = 1/cos²t

(cos²t - sin²t)(1 - sin²t) = 1

Now, we can multiply the first factor by the second factor:

(cos²t - sin²t)(1 - sin²t) = 1

(cos²t - sin²t)(1 - sin²t)(1 + sin²t) = 1

(cos²t - sin²t)(2 + 2sin²t) = 1

(cos²t - sin²t)(4) = 1

(cos²t - sin²t) = 5

Therefore, we have found that:

cos²t - sin²t = 5

We also know that sint is given, and we can substitute it in the identity given in the prompt to find cost

sint + cos²t = 1

Substituting sin²t in the expression for cost that we found above, we get:

cost = sint + 5

cost = sint + 5

cost = 5sin²t

So the cost of the angle t in terms of sint is given by:

cost = 5sin²t

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Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

The reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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Answer:

£50 is the answer

The Solution:

Representing the problem in a diagram:

We are asked to find the length a.

Applying the Pythagorean Theorem, we get

Taking the square root of both sides, we get

Therefore, the correct answer is 7

Check the picture below.

Answer:

b. 8.33

Step-by-step explanation:

"mean" is the math word for what non-math people call average. This is where you add up all the numbers and divide by however many there are.

3+5+8+11+11+12 is 50

There are 6 numbers in the data set. So 50/6 is 8.3333...

b. 8.33 is the correct answer.

Mean means add and divide.

Answer:

17+5i

Step-by-step explanation:

add the like terms

double negative equals positive

;)

Answer:

17+i

Step-by-step explanation:

By the end of week 52, Westway Company deducted $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

To calculate the deductions made by Westway Company, we'll need to consider the Social Security and Medicare taxes.

Social Security tax:

The Social Security tax rate is 6.2% on income up to $142,800.

Since Suzle Chan earns $3,220 per week, their annual income is $3,220 * 52 = $167,440.

However, the maximum taxable income for Social Security is $142,800.

Therefore, the Social Security tax deduction is $142,800 * 0.062 = $8,857.60.

Medicare tax:

The Medicare tax rate is 1.45% on all income.

The Medicare tax deduction is $167,440 * 0.0145 = $2,426.48.

By the end of week 52, Westway Company would have deducted a total of $8,857.60 for Social Security and $2,426.48 for Medicare from Suzle Chan's earnings.

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The sequence of transformations used to transform ABCD to A"B"C"D" is; Trapezoid ABCD ​ was reflected across the y-axis and then translated 7 units up.

From the figure we have the pre image before transformation as Quadrilateral ABCD which is located at the bottom right of the graph.

Trapezoid ABCD and A"B"C"D" are equidistant from the x-axis

Trapezoid ABCD and A"B"C"D" are equidistant from the y-axis

Now, it is clear that Quadrilateral ABCD was first reflected across the y-axis.

Thereafter, when we look at the coordinates of the final transformed quadrilateral, it is clear that the second step of transformation was to translate the image by 7 units upwards.

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hello

since we're given y and x intercept, we can use it to find the slope of the equation

y-intercept = 2.1

x-intercept = 3.5

what this implies that in a given graph, y-axis is (0, 2.1) and x-axis (3.5, 0)

now we can use this co-ordinate to find our slope

so our odered pair are (3.5, 0) and (0, 2.1)

y2 = 2.1

y1 = 0

x2 = 0

x 1 = 3.5

now we know our slope as 3/5

we can use this slope to find the equation of the line

remember our y-intercept = 2.1

equation of staright line is given as y = mx + c

m = slope

c = y-intercept

now, the equation of this line is

y = 3/5x + 2.1

b.

we have one point (1.2, 5.1) and an x-intercept of 3.7

let the first point (1.2, 5.1) be A and the second point as B

A = (1.2, 5.1)

B = (3.7, 0)

y2 = 0

x2 = 3.7

y1 = 5.1

x1 = 1.2

y = mx + c

m = slope

c = y-intercept

let's use co-ordinate B to find our y-intercept

we can now re-write our equation with the standard form of y = mx + c

y = -2.04x + 7.548

Answer:

Step-by-step explanation:

Any number can be made into a fraction if divided by any other number except for zero.

-4 is the same as -4/1

-4/0 is undefined (division by zero)

The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t) using the eigen value method.

The coefficients of a set of linear equations are represented by coefficient matrices. These matrices are frequently used to streamline the process of calculating equations  by arranging the coefficients in a standardized manner. The coefficient matrix is frequently designated as A, with the dimensions matching to the number of equations and variables in the system. A system of three equations with three variables, for inspection , would have a 3x3 coefficient matrix. The elements in the matrix reflect the coefficients of each variable in each equation and may be used to solve the problem using various approaches such as Gaussian elimination or matrix inversion.

How to solve?

x1' = -3x1 + 2x2

x2' = -3x1 - 2x2

The characteristic equation is (-3-λ)(-3+λ)+4=0, which simplifies to λ^2-9+4=0, or λ^2-5=0. This has solutions λ = +-sqrt(5).

For λ = +sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 + 2sqrt(5)x2

x2 = -(3/2)x1 + (1/sqrt(5))x2

eigenvector x2 = (1/sqrt(5))x1.

For λ = -sqrt(5), the system becomes:

x1' = -3x1 + 2x2

x2' = -3x1 - 2sqrt(5)x2

x2 = -(3/2)x1 - (1/sqrt(5))x2

Dividing both sides by (1+3/2sqrt(5)), we get the eigenvector x2 = (-1/sqrt(5))x1.

The general solution is then x1 = c1*(1/sqrt(5))e^(+sqrt(5)t) + c2*(-1/sqrt(5))e^(-sqrt(5)t).

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Answer:

3\(\sqrt{13}\)

Step-by-step explanation:

Calculate the distance using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (- 9, 8) and (x₂, y₂ ) = (- 3, - 1)

d = \(\sqrt{(-3-(-9))^2+(-1-8)^2}\)

  = \(\sqrt{(-3+9)^2+(-9)^2}\)

  = \(\sqrt{6^2+81}\)

   = \(\sqrt{36+81}\)

   = \(\sqrt{117}\)

   = \(\sqrt{9(13)}\)

   = \(\sqrt{9}\) × \(\sqrt{13}\)

   = 3\(\sqrt{13}\)

Answer:

Pls give me the answers as soon as possible and make sure that the answers are correct.

Answer:

The given function is:

f(x) = -3x^2 + 12

To find the interval over which the function is increasing, we need to find the critical points of the function.

f'(x) = -6x

The critical point is where f'(x) = 0

-6x = 0

x = 0

Now, we need to check the sign of f'(x) on either side of the critical point to determine whether the function is increasing or decreasing.

If x < 0, then f'(x) < 0, so the function is decreasing.

If x > 0, then f'(x) > 0, so the function is increasing.

Therefore, the interval over which the function is increasing is:

(0, infinity)

Step-by-step explanation:

gg