The scale factor of an object is the ratio of the lengths of two corresponding sides of two similar objects.

True

False

Answer:

There are many ways we can write \(5^{11}\) one of them being that we just write 11 fives being multiplied against each other like the following:

\(5*5*5*5*5*5*5*5*5*5*5\)

This can seem very repetitive which is why powers are a lot more helpful.  We can also rewrite \(5^{11}\) using the power in the bottom of a fraction.  The way that we do this is put \(5^{-11}\) on the bottom which can then be flipped to the top with a positive power and will be the same.

\(\frac{1}{5^{-11}}\)

The final way that we can rewrite \(5^{11}\) is by using several different powers.  We can do \(5^6*5^5\) which will equal the same thing as \(5^{11}\) because the base is the same and what we basically do is just add up the powers together to get back to 11.

\(5^6*5^5\)

Answer:the answer above is correct

Step-by-step explanation:

Answer:

10

Step-by-step explanation: You would have to multiply 2 by itself 50 times.

The value of the given expression is 32.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 2⁵

Evaluate using the Power rule:

mⁿ = m *m* m* m* m*m.......n times

Thus, the Value of the expression 2⁵ will be:

2⁵ = 2 * 2 * 2 * 2 * 2

2⁵ = 32

Therefore, The value of the given expression is 32.

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Answer:

C

Step-by-step explanation:

step by step fr

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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Answer:

Area is π(Pi) × Radius².

Soo, 3,14×5×5=78,54

I hope this is right

ii) the cost of fencing the land is Rs. 32,000. iii) the area of the land remaining for farming is 150,000 sq.m - 600 sq.m - 1200 sq.m - 9π sq.m.

i) Here is a rough figure depicting the land, fence, farm house, well, and path:

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               |       Farm House (20m x 30m)             |

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               |            Path (5m width)               |

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               |                                         |

               |                 Well                    |

               |                                         |

               |                                         |

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               |_________________________________________|

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               |                                         |

               |                                         |

               |                                         |

               |                                         |

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               |_________________________________________|

ii) The cost of fencing can be calculated by finding the perimeter of the land and multiplying it by the cost per meter. The perimeter of a rectangle is given by the formula P = 2(length + breadth).

Perimeter = 2(500m + 300m) = 2(800m) = 1600m

Cost of fencing = Perimeter * Cost per meter = 1600m * Rs.20 = Rs. 32,000

Therefore, the cost of fencing the land is Rs. 32,000.

iii) The area of the land remaining for farming can be calculated by subtracting the area of the farm house, the path around it, and the well from the total area of the land.

Area of the land = Length * Breadth = 500m * 300m = 150,000 sq.m

Area of the farm house = Length * Breadth = 20m * 30m = 600 sq.m

Area of the path around the farm house = (Length + 2width) * (Breadth + 2width) = (20m + 25m) * (30m + 25m) = 30m * 40m = 1200 sq.m

Area of the well = π * radius^2 = π * (3m)^2 = 9π sq.m

Area remaining for farming = Area of the land - Area of the farm house - Area of the path - Area of the well

= 150,000 sq.m - 600 sq.m - 1200 sq.m - 9π sq.m

Therefore, the area of the land remaining for farming is 150,000 sq.m - 600 sq.m - 1200 sq.m - 9π sq.m.

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Answer: NO SOLUTION

Step-by-step explanation:

6x + 4x - 1 = 2(5x + 4)

10x - 1 = 2(5x+4)

10x - 1 = 10x + 8

-1 = 8

NO SOLUTION

Answer:

5m/s^2

Step-by-step explanation:

Acceleration = Change in velocity/time.

= 50 - 10

------------

8

= 40/8

= 5

Answer:

5 m/s²

Step-by-step explanation:

v = 50 m/s

u = 10 m/s

t = 8 s

\(a = \frac{v - u}{t} \)

a = (50 - 10) ÷ 8

a = 40 ÷ 8

a = 5 m/s²

D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.

Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.

We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:

(PDP^(-1))^2 = PDP^(-1) + 1.

Expanding the square and applying the matrix multiplication rules, we get:

PD^2P^(-1) = PDP^(-1) + 1.

Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:

P(D^2)P^(-1) = PDP^(-1) + 1.

Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:

D^2 = D + 1.

This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.

Therefore, the correct answer is D) A^2 = A + 1.

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The particular antiderivative that satisfies the given condition is: C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000

To find the particular antiderivative (or integral) of the given derivative \(C''(x) = 4x^2 - 3x\)  that satisfies the condition C(0) = 2000, we need to integrate the given function twice.

First, we integrate C''(x) to find C'(x):

\(C'(x) = ∫ (4x^2 - 3x) dx\)

To find the antiderivative of \(4x^2\), we use the power rule for integration: the power of x increases by 1 and is divided by the new power. Similarly, the antiderivative of -3x is \(-(3/2)x^2\).

\(C'(x) = ∫ (4x^2 - 3x) dx = (4/3)x^3 - (3/2)x^2 + K1\)

Here, K1 is the constant of integration. Next, we integrate C'(x) to find C(x):

\(C(x) = ∫ (C'(x)) dx = ∫ ((4/3)x^3 - (3/2)x^2 + K1) dx\)

To find the antiderivative of \((4/3)x^3\), we again use the power rule for integration. Similarly, the antiderivative of \(-(3/2)x^2\) is \(-(3/2)(1/3)x^3\).

The constant of integration K1 will also be integrated with respect to x, resulting in another constant of integration, K2.

\(C(x) = (1/3)(4/3)x^4 - (1/2)(3/2)x^3 + K1x + K2\)

Simplifying further, we have:

\(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + K2\)

Now, we can apply the initial condition C(0) = 2000 to find the particular solution for K2:

\(C(0) = (4/9)(0)^4 - (9/8)(0)^3 + K1(0) + K2 = 2000\)

Since all the terms involving x become zero when x = 0, we have:

K2 = 2000

Therefore, the particular antiderivative that satisfies the given condition is: \(C(x) = (4/9)x^4 - (9/8)x^3 + K1x + 2000\)

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The question is asking for a number answer that is rounded to the nearest meter. This means that the answer should be given in whole meters, and rounded to the closest meter.

For example, if the answer is 3.7 meters, it should be rounded up to 4 meters, and if the answer is 3.3 meters, it should be rounded down to 3 meters.

In order to provide an accurate answer, it is important to know what measurement is being asked for. If it is a distance, such as the length of a room or the height of a building, the answer should be given in meters and rounded to the nearest whole meter.

If it is a weight or volume, the answer may be given in a different unit of measurement, such as kilograms or liters, but still rounded to the nearest whole unit.

Overall, rounding to the nearest meter ensures that the answer is easy to understand and provides a clear picture of the measurement being taken.

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Answer:

radius=d/2 = 8/2 = 4inch.

Step-by-step explanation:

area = πr²

16π(inch)². or 352/7 (inch)².

hope this helps you.

Hello There!

\(GraceRosalia\) is here to help you!

We are given that

d=8 in.

We know that the radius is 1/2 of d or r=d/2. So the radius is 4.

However, we have to find the area.

The formula for the area of a circle is:

A=\(\pi\)\(r^{2}\)

We know that r=4, so all we have to do is plug it into the formula:

A=\(\pi (4)^{2}\)

Remember that only the radius is squared.

A=\(\pi *16\)

A=50.265

Let's round to the nearest tenth:

A=50.3

Hope this helps you!

\(GraceRosalia\)

Let me know if you have any questions!

Answer: B

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

I got it correct on a test!! Hope this helps!!

Answer:

Rs.184.80

Step-by-step explanation:

Total cp =(cp + overhead,expenses)

Total cp =150 + 12% of 150

Total,cp = 150 + 12/100 × 150 = Rs 168

Given that , gain = 10%

Therefore, Sp = 110/100 × 168 = Rs 184.80

Answer:

4.329

Step-by-step explanation:

Answer: \(-144vw^2\)

Step-by-step explanation:

\(\left(4v\cdot \:3w\right)\left(-2w\cdot \:3\right)\cdot \:2\)

\(=-4v\cdot \:3w\cdot \:2w\cdot \:3\cdot \:2\)

\(=-144vww\)

\(=-144vw^2\)

Answer

Step-by-step explanation:

16v^3w^7

Answer:

see explanation

Step-by-step explanation:

(3)

the values of q decrease as the values of p increase.

this indicates an inverse relationship between the quantities, that is

q = \(\frac{k}{p}\) ← k is the constant of variation

to find k use any ordered pair from the table.

using q = 16 when p = 3 , then

16 = \(\frac{k}{3}\) ( multiply both sides by 3 )

48 = k

q = \(\frac{48}{p}\) ← equation of variation

(4)

the values of q increase as the values of p increase.

this indicates the quantities are in direct variation, that is

q = kp ← k is the constant of variation.

to find k use any ordered pair from the table.

using q = 2 when p = 6 , then

2 = 6k ( divide both sides by 6 )

\(\frac{2}{6}\) = k , that is

k = \(\frac{1}{3}\)

q = \(\frac{1}{3}\) p ← equation of variation

Answer:

Step-by-step explanation:

the formula is named the point slope formula for a reason.   and  you have show both of them in the question , the slope and the point are given

y - y1 = m(x-x1)

so for your answer

y-(-2) = 4(x-5)

y+2 = 4(x-5)    is the right answer

Answer: 21 and 3

Step-by-step explanation:

\(21+3=24\)

21 × 3 = 63

Hopes this helps!

Answer:A) -4/3 B) 1/2 C) -5/4

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

For A) let (x1, y1) = (8, -7), (x2, y2) = (5, -3)

Slope = (-3 -(-7)) / (5 - 8) = 4/-3

For B) let (x1, y1) = (-5, 9), (x2, y2) = (5, 11)

Slope = (11 - 9) / (5 - (-5)) = 2/10 = 1/2

For C) let (x1, y1) = (-8, -4), (x2, y2) = (-4, -9)

Slope = (-9 -(-4)) / (-4 - (-8)) = -5/4

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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Answer:

240 meters

Step-by-step explanation:

Since you dont know the length of any sides you would find the lengths of each side

√(360) = 18.973665961

Since each side equals 18.973665961 you would add that to its self 3 times

18.973665961+18.973665961+18.973665961+18.973665961

that equals which equals 75.894663844

Answer:

Let $x$ be the number of gallons of the 40% antifreeze and $y$ be the number of gallons of the 90% antifreeze. We know that the total amount of antifreeze is 140 gallons, so $x+y=140$. We also know that the final mixture should have 75% pure antifreeze, so the amount of pure antifreeze in the mixture is 0.75(140) = 105 gallons. We can set up a system of equations to solve for $x$ and $y$:

$$0.4x + 0.9y = 105$$

$$x+y = 140$$

Solving the system of equations, we get $x=60$ and $y=80$. Therefore, the chemical company must use 60 gallons of the 40% antifreeze and 80 gallons of the 90% antifreeze.

Here is a step-by-step solution:

1. Let $x$ be the number of gallons of the 40% antifreeze and $y$ be the number of gallons of the 90% antifreeze.

2. Set up a system of equations to represent the given information:

$$x+y = 140$$

$$0.4x + 0.9y = 105$$

3. Solve the system of equations:

$$x = 60$$

$$y = 80$$

4. Therefore, the chemical company must use 60 gallons of the 40% antifreeze and 80 gallons of the 90% antifreeze.

Step-by-step explanation:

To differentiate the function y = (7x^2 - 1) / (4x^3 + 5), we can apply the quotient rule. The derivative is given by y' = (14x(4x^3 + 5) - (7x^2 - 1)(12x^2)) / (4x^3 + 5)^2.

To differentiate the given function y = (7x^2 - 1) / (4x^3 + 5), we use the quotient rule. According to the quotient rule, if we have a function of the form f(x) / g(x), the derivative is given by (f'(x)g(x) - f(x)g'(x)) / (g(x))^2.

In this case, f(x) = 7x^2 - 1 and g(x) = 4x^3 + 5. We differentiate f(x) and g(x) to obtain f'(x) = 14x and g'(x) = 12x^2.

Applying the quotient rule, we have:

y' = [(14x)(4x^3 + 5) - (7x^2 - 1)(12x^2)] / (4x^3 + 5)^2.

Simplifying further, we get:

y' = (56x^4 + 70x - 84x^4 + 12x^4) / (4x^3 + 5)^2.

Combining like terms, we have:

y' = (14x^4 + 70x) / (4x^3 + 5)^2.

Therefore, the derivative of y = (7x^2 - 1) / (4x^3 + 5) is y' = (14x^4 + 70x) / (4x^3 + 5)^2.

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Answer:About 1,012 Inches

Step-by-step explanation: