A farmer wants to build a rectangular pen using 20 feet of fencing, but the length is to be 4 feet more than the width. What is the length of the pen, in feet?

9514 1404 393

Answer:

  $46.38

Step-by-step explanation:

When a 20% tip is added to the bill, the result is the bill being multiplied by a factor of (1 + 20%) = 1.20.

  1.20 × 38.65 = 46.38

Marina's total with the tip is $46.38.

Answer:

y = 6h  h = hour

Step-by-step explanation:

Answer:

2,4,5 got it right on egde2021

Step-by-step explanation:

Answer:

Part A) -3, 4 Part C) 12 i think

Step-by-step explanation:

Answer:

Part A-(3,4)

Part B- 2 units

Step-by-step explanation:

Part A- (x,y)--->(-x,y)

Solution

(a)Given a pendulum bob swings back and forth,

The graph of the horizontal position versus time is shown below

The vertical axis represents the horizontal position f(t)

The algebric expression \(cot(sin^{(-1)}\sqrt{(x^2}\)simplifies to sqrt(1 - |x|^2) / |x|.

The expression "cot(sin^(-1)(sqrt(x^2)))" involves trigonometric and square root functions. Let's break it down step by step to simplify the expression.

Inside the square root: x^2.

The square root of x^2 is |x| (the absolute value of x), as the square root eliminates the square and keeps the positive value.

The expression sin^(-1)(sqrt(x^2)) is equivalent to arcsin(sqrt(x^2)).

Since we already know that the square root of x^2 is |x|, we can rewrite the expression as arcsin(|x|).

Now, we have cot(arcsin(|x|)).

The cotangent (cot) of an angle is equal to the reciprocal of the tangent (tan) of the same angle.

So, cot(arcsin(|x|)) can be written as 1 / tan(arcsin(|x|)).

Using the inverse trigonometric identity, tan(arcsin(x)) = x / sqrt(1 - x^2), we can simplify further.

In our case, x = |x|.

Therefore, tan(arcsin(|x|)) = |x| / sqrt(1 - |x|^2).

Substituting this result back into the expression, we have 1 / (|x| / sqrt(1 - |x|^2)).

To divide by a fraction, we multiply by its reciprocal.

Hence, the final simplification of the expression is sqrt(1 - |x|^2) / |x|.

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Answer:

90

Step-by-step explanation:

18/9=2

2 x 45=90

Answer:

D

Step-by-step explanation:

f(x)=-x(x-4)

f(x)=-x²+4x

-x²+4x=0

x(-x+4)=0

x=0, x=4

(2)

4x²-x-3=0

(4x²+3x)-(4x-3)=0

x(4x+3)-1(4x+3)=0

x=1, x=-3/4

use a divider to find the length of the middle line then use

Answer:

41.93 degrees

Step-by-step explanation:

Answer:

Equation.

Step-by-step explanation:

The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.

Whereas if the two equation are not equal then it is known as inequality.

Thus, the given statement is correctly filled with equation.

the surface area of the cylinder is approximately 471 dm².

Now, For the surface area of the cylinder, we need to find the lateral area  and the area of the two circular bases.

Since, The formula for the lateral area of a cylinder is

L = 2πrh,

where r is the radius of the cylinder and h is the height.

In this case, the diameter is 10 dm,

So the radius is 5 dm.

And the height is also 10 dm.

Therefore, the lateral area is:

L = 2πrh

L = 2π(5 dm)(10 dm)

L = 100π dm²

The formula for the area of a circle is

A = πr²,

where r is the radius.

In this case, the radius is 5 dm,

So the area of each base is:

A = πr²

A = π(5 dm)²

A = 25π dm²

To find the total surface area, we add the lateral area and the area of the two bases:

SA = 2(Area of Base) + Lateral Area

SA = 2(25π dm²) + 100π dm²

SA = 50π dm² + 100π dm²

SA = 150π dm²

Substitute pi as 3.14, we can calculate:

SA ≈ 150(3.14) dm²

SA ≈ 471 dm²

Therefore, the surface area of the cylinder is approximately 471 dm².

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Answer:

306

Step-by-step explanation:

An outlier is a number that is not near the other numbers

306 is not near the other numbers

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.

2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.

3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.

4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.

5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.

6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.

A system of equations involves using more than one equation solved simultaneously.

Jesse's reading rate per day = 30 pages

Amir's reading rate per day = 35 pages

The number of pages read by Jesse, y = 30 + 30x

The number of pages read by Amir, y = 35x

Where x = the number of days they have been reading

y = 30 + 30x and y = 35x

35x  = 30 + 30x

35x - 30x = 30

5x = 30

x = 6 (30/5)

y = 30 + 30x

y = 30 + 30(6)

y = 210

y = 35x

y = 35(6)

y = 210

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Answer:

27

Step-by-step explanation:

3x - 2x²

3 × -3 = -9

2 × -3 = -6

-9 - (-6²)

-9 - (-36)

-9 + 36

36 - 9

36 - 9 = 27

Step-by-step explanation:

Answer: its d

Step-by-step explanation:

Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

Answer:

You are right, it is C. -7/3

Step-by-step explanation:

Rise/run - to get from point (2, 5) to (5, -2), you go down 7 and right 3.

But it seems you already know this :)

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

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The Stafford loan will have a higher balance of $36.53 at the time of repayment.

The correct option is C.

The formula:

PV = PMT/i[1 - {1/(1+i)ⁿ]

PV denotes the loan sum.

PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)

To compare the balances of the two loans at the time of repayment, we need to calculate the total amount owed for each loan.

For the Unsubsidized Stafford Loan:

The total loan amount is $6,720, and the annual interest rate is 3.99%, compounded monthly.

Therefore, the monthly interest rate is 3.99% / 12 = 0.3325%. The loan has a grace period of 6 months, so interest will not start accruing until 6 months after graduation.

The loan will be repaid over a period of 10 years, or 120 months.

Using the formula for the future value of an annuity, the total amount owed for the Unsubsidized Stafford Loan is:

FV = PMT x [(1 + r)ⁿ - 1] / r

where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

We can solve PMT using a loan repayment calculator, such as the one found on bankrate.com, and we get a monthly payment of $73.80. Plugging this into the formula, we get:

FV = $73.80 x [(1 + 0.003325)¹¹⁴ - 1] / 0.003325

FV = $9,222.41

Therefore, the total amount owed for the Unsubsidized Stafford Loan at the time of repayment is $9,222.41.

For the PLUS Loan:

The loan amount is $7,241.17, and the annual interest rate is 4.99%, compounded monthly. Therefore, the monthly interest rate is 4.99% / 12 = 0.4158%. Interest starts accruing immediately, and the loan will be repaid over a period of 10 years, or 120 months.

Using the same formula, the total amount owed for the PLUS Loan is:

FV = PMT x [(1 + r)ⁿ- 1] / r

Again, using a loan repayment calculator, we get a monthly payment of $78.93. Plugging this into the formula, we get:

FV = $78.93 x [(1 + 0.004158)^120 - 1] / 0.004158

FV = $9,258.94

Therefore, the total amount owed for the PLUS Loan at the time of repayment is $9,258.94.

Comparing the two loan amounts, we see that the Unsubsidized Stafford Loan will have a higher balance of $36.53 ($9,222.41 - $9,258.94) at the time of repayment.

Therefore, the answer is:

The Stafford loan will have a higher balance of $36.53 at the time of repayment.

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The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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The shaded area for the inequality y > -3-(5/4)x is given below.

The inequality is the relation between two expressions showing the relationships such as greater than, lower than, greater than equals to, and lower than equals to.

The given inequality is -5x-4y<12

solving this inequality for y

-5x-4y<12

⇒ -4y<12+5x

⇒y > (12+5x)/(-4)

⇒y > -3-(5/4)x

the line y= -3-(5/4)x has y intersection at (0,-3) and  x intersection at (-12/5,0).

The inequality y > -3-(5/4)x show that this will be above the straight line y = -3-(5/4)x as if we put (0,0) in the inequality, the inequality will be 0>-3 which is true that shows that the region contains (0,0).

Therefore the shaded area for the inequality y > -3-(5/4)x is given below.

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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Answer:

4.5 hours

Step-by-step explanation:

fbdjdbercyTxxivdu

Answer:

Basically You are asking how many hours we need to reach 7:00, if we are at 2:30, so: we need 4hours, to reach 6:30, and and extra 30minutes to reach 7:00pm. The answer is 4hours and 30minutes.

The volume of the triangular pyramid, with a base area of 12 and a height of 25, is equal to 100 cubic units.

To calculate the volume of a triangular pyramid, we need the values of the base area and the height. Given that a = 12 and h = 25, we can proceed with the calculation.

The formula for the volume of a triangular pyramid is (1/3) * base area * height. Since we know the base area is equal to a, we can substitute the values into the formula.

Volume = (1/3) * a * h

Plugging in the given values, we have:

Volume = (1/3) * 12 * 25

Simplifying the expression further:

Volume = (1/3) * 300

Volume = 100

Therefore, the volume of the triangular pyramid, with a base area of 12 and a height of 25, is equal to 100 cubic units.

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