Two landscapers must mow a rectangular lawn that measures 95 feet by 170 feet. Each wants to mow no more than half of the lawn. The first starts by mowing around the outside of the lawn. The mower has a 24-inch cut. How wide a strip must the first landscaper mow on each of the four sides in order to mow no more than half of the lawn? (Round your answer to three decimal places.) Approximate the required number of trips around the lawn the first landscaper must take. (Round your answer to one decimal place.)

Answer: Top right corner (northeast corner)

Angle IAE = Angle DAH

These two angles are vertical angles as shown in the diagram below. Vertical angles are always congruent.

Answer:

181 bagels

Step-by-step explanation:

Well how much money did they have to raise more to get to $950? It is $360.45. So now we take $360.45 and divide it by 2 and we get 180.225. But if we round 180.225 they would have to sell at least 181 bagels to raise $950 dollars.

Answer:

181 is the correct answer

Step-by-step explanation:

1. The equation of the line perpendicular to 2x – 7y = 14 and passing through (-5, 7) is 7x + 2y = -9.

2. The equation of the line with a slope of 5/3 and passing through (-2, -4) is y + 4 = (5/3)(x + 2).

3. The equation of the line passing through (0, -5) and parallel to 3y = 6x – 4 is 3y = 6x - 5.

4. The equations 5y – 2x = 4 and 4x = 5y + 10 are not parallel but rather represent the same line.

1. To find the equation of a line perpendicular to 2x – 7y = 14, we need to determine the negative reciprocal of the slope. Rearranging the given equation into slope-intercept form (y = mx + b), we have -7y = -2x + 14, which simplifies to y = (2/7)x - 2. The slope of this line is 2/7, so the slope of the perpendicular line is -7/2. Using the point-slope form (y - y₁ = m(x - x₁)) with (-5, 7) as the given point, we substitute the values to get y - 7 = (-7/2)(x - (-5)). Simplifying further gives the equation 7x + 2y = -9.

2. The equation of a line with a slope of 5/3 and passing through (-2, -4) can be found using the point-slope form. Substituting the given values into the equation y - y₁ = m(x - x₁), we have y - (-4) = (5/3)(x - (-2)). Simplifying yields y + 4 = (5/3)(x + 2).

3. To find the equation of a line parallel to 3y = 6x - 4 and passing through (0, -5), we use the same slope as the given line, which is 6/3 = 2. Using the point-slope form, we substitute the values into y - y₁ = m(x - x₁), resulting in y - (-5) = 2(x - 0). Simplifying gives the equation 2x - y = 5.

4. To prove that the equations 5y - 2x = 4 and 4x = 5y + 10 are parallel, we need to compare their slopes. Rearranging the first equation into slope-intercept form, we have 5y = 2x + 4, which simplifies to y = (2/5)x + 4/5. The slope of this line is 2/5. Rearranging the second equation, we get 5y = -4x + 10, which simplifies to y = (-4/5)x + 2. The slope of this line is -4/5. Since the slopes are not equal, the lines are not parallel; instead, they represent the same line.

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Answer:

A. 1/2

Step-by-step explanation:

3/16   /    3/8

3/3 = 1

16/8 = 2

1/2

Answer: 1/2

Step-by-step explanation:

3/16 divided by 3/8

To divide by a fraction multiply by the reciprocal of that fraction

3/16 x 8/3

Reduce the numbers with the GCF (3)

1/16 x 8

Reduce the numbers with the GCF (8)

1/2 or 0.5

Interest-free or below-market interest loans are a taxable benefit, and their value must be included in the employee's gross income. For federal tax purposes, the rate charged on the loan should be equal to or greater than the Applicable Federal Rate (AFR) set by the IRS.

If the loan's interest rate is lower than the AFR, the difference between the AFR and the loan rate is considered a gift or taxable interest. If the borrower is an employee, the taxable interest is compensation and must be reported as such.

On September 1, 2021, Carol Mason received a $150,000 loan from her employer at a 1% interest rate. The relevant prescribed rate was 2 % in Q3 and 3% in Q4. We must calculate the benefit's value. There are two ways to calculate the value of a taxable benefit: the loan's interest-rate differential method and the loan's principal-amount method.Let's start with the interest-rate differential method.The difference between the interest rate on the loan and the prescribed rate on the day the loan was made, multiplied by the loan principal and divided by the number of days remaining in the year, is the amount of taxable interest using this method.

To begin, we must calculate the relevant prescribed rate for Carol's loan. It is 2% in Q3 (July 1, 2021, to September 30, 2021) and 3% in Q4 (October 1, 2021, to December 31, 2021). Since Carol received the loan on September 1, 2021, she would be liable for the 2% interest rate for the rest of Q3 and the 3% rate for the rest of the year (Q4).2% for 30 days in September and 3% for 91 days in Q4 are the equivalent annual rates.The interest rate differential can be calculated using the formula below:($150,000 × (3 percent – 1 percent) ÷ 365 × 122) + ($150,000 × 2 percent ÷ 365 × 243) = $1,017.81.Carol would need to report $1,017.81 as taxable interest on her 2021 tax return using the interest rate differential method.

The loan principal amount method is the second approach. The loan principal method assumes that the loan was provided on the first day of the year and repaid on the last day of the year using the prescribed rate interest.Carol's loan has a principal of $150,000. The interest on the loan at the prescribed rate for Q3 (2%) and Q4 (3%) can be calculated using this method. The total interest on the loan is the sum of the two interests.To determine the taxable interest using the principal amount method, multiply the average prescribed rate of 2.5% by the $150,000 loan principal, then divide by 12 months. Carol would need to report $3,750 as taxable interest on her 2021 tax return using the principal amount method.

The amount of benefit to be included in Carol’s tax return for 2021 is $1,017.81 if the interest rate differential method is used. If the principal amount method is used, the amount of benefit to be included in Carol’s tax return for 2021 is $3,750. Thus, the correct option among the given options is D) $250.

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If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.

To solve the dual of the given problem using the dual simplex algorithm, we first need to rewrite the primal problem in standard form. The primal problem is as follows:

Maximize: z = 11x + x + 6w

Subject to:

6x + 15x - 3w ≥ 60

3x + 2x + w ≤ 21

2x + 3x - w = 34

x ≥ 0, y ≥ 0, w ≥ 0

The dual problem will have the following form:

Minimize: w = 60y + 21z + 34u

Subject to:

6y + 3u + 2v ≥ 11

15y + 2u + 3v + u + v ≥ 1

-3y + v = 6

y ≥ 0, u ≥ 0, v unrestricted

Now, we can apply the dual simplex algorithm to solve the dual problem. The steps involved in the dual simplex algorithm include:

Start with an initial feasible solution.

Check for optimality.

If not optimal, select a pivot column and pivot row.

Perform row operations to make the pivot element 1 and all other elements in the pivot column 0.

Repeat steps 2-4 until the optimal solution is reached.

The detailed calculations and iterations involved in the dual simplex algorithm can be quite lengthy and involve complex matrix operations. It would be best to use a specialized software or linear programming solver to perform these calculations accurately and efficiently.

If you have access to a linear programming solver or software like Excel Solver or MATLAB's Optimization Toolbox, you can enter the dual problem and use the solver to obtain the optimal solution.

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Starstruck Inc. should report approximately $8,767 as the amount of interest expense on its income statement for the year ended December 31, 2021.

To calculate the amount of interest expense that Starstruck Inc. should report on its income statement for the year ended December 31, 2021, we need to determine the interest accrued for the 14-month period from November 1, 2020, to December 31, 2021.

The formula to calculate interest expense is:

Interest Expense = Principal * Interest Rate * Time

Principal = $300,000

Interest Rate = 8% per year

Since the note is an 8-month note, we need to calculate the interest for the 14-month period.

We can use the following formula to calculate the time in years:

Time = Number of days / Days in a year

Number of days from November 1, 2020 to December 31, 2021 = 426 days

Days in a year = 365 days

Time = 426 / 365

Now we can calculate the interest expense:

Interest Expense = $300,000 * 8% * (426 / 365)

Interest Expense ≈ $8,767.12

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Answer: B

Step-by-step explanation:

Both plant and animal cells have vacuoles, cell membrane, nucleus, and mitochondria.

Answer:

lesser x =-4

greater x =1/2

Answer:

-44

Step-by-step explanation:

Answer:

15w - 15y - 36

Step-by-step explanation:

Combine like terms

In this case the only two terms would be numbers without variable and numbers with the variable w

First lets combine the numbers with no variable which are -16 and -20. you subtract these two -16 - 20 = -36 and get -36

Now lets combine like terms for w, it doesn't matter which order you go in exactly but in the case I will do

1. combine 8w and 7w, since these are both positive you will add the together

8w + 7w = 15w

2. Now combine -11y and -4y, since these are both negative you will subtract them and get -15y

Answer:

Numbers: 6 and -2

Step-by-step explanation:

Equations

This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.

However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:

[tex]x+y=4\qquad\qquad [1][/tex]

[tex]x.y=-12\qquad\qquad [2][/tex]

Solving [1] for y:

[tex]y=4-x[/tex]

Substituting in [2]

[tex]x(4-x)=-12[/tex]

Operating:

[tex]4x-x^2=-12[/tex]

Rearranging:

[tex]x^2-4x-12=0[/tex]

Solving with the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

With a=1, b=-4, c=-12:

[tex]\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}[/tex]

[tex]\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}[/tex]

[tex]\displaystyle x=\frac{4\pm 8}{2}[/tex]

The solutions are:

[tex]\displaystyle x=\frac{4+ 8}{2}=6[/tex]

[tex]\displaystyle x=\frac{4- 8}{2}=-2[/tex]

This confirms the preliminary results.

Numbers: 6 and -2

Answer:

1.x=4​+5y/3

​2.x=3y−9

​​

Step-by-step explanation:

The required coordinates of endpoint S are (8, -2).

Given that the midpoint of Rs is M (1, 2) and one endpoint is R(-6, 6). We need to find the coordinates of endpoint S.Let the coordinates of the endpoint S be (x, y).Now, the formula for the midpoint of a line is:(x₁+x₂/2 , y₁+y₂/2)M(1, 2)=R(-6, 6)+ S(x, y)/2⇒ (x - 6)/2 = 1 ....(1)and (y + 6)/2 = 2....(2)

Solving the above equations we get,x - 6 = 2⇒ x = 8and y + 6 = 4⇒ y = -2So, the coordinates of endpoint S are (8, -2).

Hence, the required coordinates of endpoint S are (8, -2).

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We are given three conic sections: a parabola, a hyperbola, and a new conic section with its center at point K(1, -1) and passes through points L(0, 0) and M(-1, 1). We need to determine the correct letter(s) that represent these conic sections.

To identify the conic sections, let's analyze the given information. The center of the new conic section is at point K(1, -1), and it passes through points L(0, 0) and M(-1, 1).

Since a parabola is determined by its focus and directrix, and a hyperbola has two foci, it is unlikely that either of these conic sections can be uniquely determined based on the given information.

Therefore, without additional information about the nature of the conic sections (e.g., the eccentricity for hyperbola or the vertex and axis of symmetry for parabola), we cannot definitively determine the correct letter(s) to represent these conic sections. It is possible that the correct letter(s) could be CO, L, or none of them.

In conclusion, without further information, we cannot determine the exact conic sections represented by the given points.

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Answer:

im not in high school sorry

Step-by-step explanation:

Answer:

The inequality would be x < 7

Step-by-step explanation:

I did this problem and I'm not sure what the "x | x" is so I ignored it, and it is right I checked. I'm pretty sure you know this answer by now but I was just trying to help.

Answer:

the answer is 64 because you should multiply it by it self for three times

Answer:

68

Step-by-step explanation:

because 4×4×4 =68

and I think it will helpful answer.

The solution is: y=2.3x, is the equations can be used to represent the proportional relationship between the number of apps, x, and the total earnings, y.

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.

Given that ,

100 apps downloads leads to $230.00 then we need to get earnings for 1 app download by dividing the total earnings by the number of apps

Earning per download=230.00/100=2.30

When we have x apps downs, the earnings will be equivalent to 2.3x

The total earning, y will then be

y=2.3x

Hence, The solution is: y=2.3x, is the equations can be used to represent the proportional relationship between the number of apps, x, and the total earnings, y.

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The optimal solution for the given linear programming problem using the graphical solution procedure is at (A, B) = (6, 2) with the objective function value of -4.

To find the optimal solution graphically, we plot the feasible region determined by the constraints. In this case, the feasible region is a polygon bounded by the lines 2A + 3B = 12, A + 4B ≤ 21, 2A + B ≥ 7, 3A + 1.5B ≤ 21, and -2A + 6B ≥ 0. We then evaluate the objective function -2A - B at the vertices of the feasible region to determine the optimal solution. The vertex that gives the minimum value of the objective function is the optimal solution. By calculating the objective function at each vertex, we find that the minimum value of -4 is obtained at (A, B) = (6, 2). This means that the optimal solution is to set A = 6 and B = 2, and the objective function value at this point is -4. For part (b), to determine the amount of slack or surplus for each constraint, we evaluate the constraints at the optimal solution (A, B) = (6, 2). For the constraint 1A + 4B ≤ 21, the left-hand side is 1(6) + 4(2) = 14, which indicates a slack of 7 (21 - 14). For the constraint 2A + 1B ≥ 7, the left-hand side is 2(6) + 1(2) = 14, which indicates a surplus of 7 (14 - 7). For the constraint 3A + 1.5B ≤ 21, the left-hand side is 3(6) + 1.5(2) = 20, which indicates a slack of 1 (21 - 20). Lastly, for the constraint -2A + 6B ≥ 0, the left-hand side is -2(6) + 6(2) = 4, which indicates a surplus of 4 (4 - 0). These slack and surplus values represent the amount by which the left-hand side of each constraint falls short or exceeds the right-hand side at the optimal solution. A positive slack indicates that the constraint is not fully utilized, while a positive surplus indicates that the constraint is exceeded.

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Answer:

Step-by-step explanation:

0.3x – 2.1 / 2 = 0.4 ​

0.3x - 2.1 = 0.4 (2)

0.3x = 0.8 + 2.1

x = 2.90  

      0.3

x = 9.67

Answer:

x=8

Step-by-step explanation:

48=5(2x-7)+3

Use the distributive property

48=10x-35+3

Combine like terms

48=10x-32

Add 32 to both sides to cancel out the negative 32

80=10x

x=8

Answer:

x = 8

Step-by-step explanation:

Step 1: Write equation

48 = 5(2x - 7) + 3

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

48 = 5(2(8) - 7) + 3

48 = 5(16 - 7) + 3

48 = 5(9) + 3

48 = 45 + 3

48 = 48

Answer:

so 1 dollor for each comic book

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B has the greater slope because it's a drastic incline compared to C and A

Answer:

The better buy is:

$2.12 for 12 oz.

Step-by-step explanation:

$1.49 / 8oz = $0.18625/1oz

$2.12 / 12oz = 0.17667/oz

0.17667 < 0.18625

then:

the better buy is:

$2.12 for 12 oz

Answer:

i think  -12,9 and you multiply it by x,-2

The fields [tex]$\mathbb{Q}[\sqrt[4]{3}]$ and $\mathbb{Q}[\sqrt[4]{3}i]$[/tex] are isomorphic but not equal.

To prove that the fields are isomorphic, we need to find a bijective ring homomorphism between them. Consider the map [tex]$\phi: \mathbb{Q}[\sqrt[4]{3}] \to \mathbb{Q}[\sqrt[4]{3}i]$[/tex] defined by [tex]$\phi(a + b\sqrt[4]{3}) = a + bi\sqrt[4]{3}$ for any $a, b \in \mathbb{Q}$[/tex].

To show that [tex]$\phi$[/tex] is a ring homomorphism, we need to verify that it preserves addition and multiplication. This can be easily verified by applying the properties of complex numbers and the fact that [tex]$\sqrt[4]{3}$[/tex] is a real number.

To show that [tex]$\phi$[/tex] is bijective, we need to show that it is injective and surjective. Injectivity follows from the fact that if [tex]$\phi(a + b\sqrt[4]{3}) = \phi(c + d\sqrt[4]{3})$[/tex]. then [tex]$a + bi\sqrt[4]{3} = c + di\sqrt[4]{3}$[/tex], which implies a = c and b = d.

Surjectivity follows from the fact that for any i[tex]$a + bi\sqrt[4]{3}$[/tex] in [tex]$\mathbb{Q}[\sqrt[4]{3}i]$[/tex], we can find [tex]$a + b\sqrt[4]{3}$[/tex] in [tex]$\mathbb{Q}[\sqrt[4]{3}]$[/tex] such that [tex]$\phi(a + b\sqrt[4]{3}) = a + bi\sqrt[4]{3}$[/tex].

Since we have found a bijective ring homomorphism between the two fields, they are isomorphic. However, they are not equal because [tex]$\sqrt[4]{3}$[/tex] is a real number in [tex]$\mathbb{Q}[\sqrt[4]{3}]$\\[/tex] while [tex]$\sqrt[4]{3}i$[/tex] is an imaginary number in [tex]$\mathbb{Q}[\sqrt[4]{3}i]$[/tex] .

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Answer:

It looks correct!!!!!!!!!

Answer:

    190

Step-by-step explanation:

You want the sum of four 2-digit prime numbers that can be formed from the set of digits {1, 2, 3, 4, 5, 6, 7, 9} using each digit only once.

There are 18 primes in the range 13-97 that have unique digits. These can be paired by the digits they use:

  {23, 59} and {29, 53} . . . . number total = 82

  {41, 67} and {47, 61} . . . . . number total = 108

A set of 4 primes with unique digits can be formed by choosing one of the first two pairs together with one of the second two pairs. For example, one possible choice is ...

  {23, 59, 47, 61}

However you do this, the sum of the four primes will be ...

  82 +108 = 190

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Answer:

A=27/4       B=2.25

Step-by-step explanation:

4 and 1/2 also equals 18/4.

18/4+1/2(18/4)=18/4+9/4

18+9=27

Answer is 27/4

B)=4.5/2=2.25