*100 points* What is the area of the parallelogram?

The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

Answer:

The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.

Step-by-step explanation:

Answer:

The scale factor is a proportional relationship.   The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship. Enlargements have a scale factor greater than 1.  Reductions have a scale factor between 0 and 1. The proportion should be preserved.

Hope this Helps!

Answer:

50

Step-by-step explanation:

Fractions are division problems. :) You have to complete that first to solve the equation (PEMDAS).

48/6 = 8

42 + 8 = 50

The sum of 106 and h can be written as an expression in the following way:   106 + h

This expression represents the sum of the two numbers, 106 and h. We can simplify this expression by combining like terms, but since h is a variable and 106 is a constant, we cannot combine them. Therefore, the expression remains as 106 + h.

In conclusion, the sum of 106 and h is represented by the expression 106 + h.

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Answer:

f(x) = 0.5x

Step-by-step explanation:

For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).

Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.

p = f(x) / x

p = -2 / -4

p = 1/2 = 0.5

We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.

f(x) = 0.5x

Answer:

5b-5

Step-by-step explanation:

Replace a with a=5/6 * b

A) The value of x in log₄(x² - 12x + 48) = 2, is x = 4 OR x = 8

B) The value of x in 27^(4x-6) =(1/9)^(2x-7), is x = 2

From the question, we are to solve the given equations

The given equation is log₄(x² - 12x + 48) = 2

From one of the laws of logarithm, we have that

logₐ x = n ⇒ x = aⁿ

Thus,

log₄(x² - 12x + 48) = 2 becomes

(x² - 12x + 48) = 4²

x² - 12x + 48 = 16

x² - 12x + 48 - 16 = 0

x² - 12x + 32 = 0

Solve the quadratic equation

x² - 12x + 32 = 0

x² - 8x - 4x + 32 = 0

x(x - 8) -4(x - 8) = 0

(x - 4)(x - 8) = 0

x - 4 = 0 OR x - 8 = 0

x = 4 OR x = 8

B) 27^(4x-6) =(1/9)^(2x-7)

Solve for x

27^(4x-6) =(1/9)^(2x-7)

Express the bases in index form

3^3(4x-6) =(3)^-2(2x-7)

Equate the powers

3(4x - 6) = -2(2x - 7)

12x - 18 = -4x + 14

12x + 4x = 14 + 18

16x = 32

Divide both sides by 16

16x/16 = 32/16

x = 2

Hence, the value of x is 2

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The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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Answer:  D(3) = 4 miles according to the graph.

Step-by-step explanation:

Look for the 3 on the time scale at the bottom of the graph. Follow the grid line straight up to where it meets the graphed line. Follow the grid line to the distance scale at the left to find the value at that point. It is 4 miles.

Answer:

11) 49 in.²

13) 4.515 m²

Step-by-step explanation:

11) area of square = (side)²

area = (7 in.)² = 7 in. × 7 in. = 49 in.²

13) area of triangle = base × height/2

area = 4.3 m × 2.1 m / 2 = 4.515 m²

Answer:28 x 4

Step-by-step explanation: 28 x 4 = 112

Answer: y = 7x

Step-by-step explanation:

y = rate(x)

28 = ?(4)

28/ 4 = 7 so 7 times 4 = 28

y= 7(x)

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

Step-by-step explanation:

I went onto desmos to see if any were parallel or perpendicular and I don't think that any of them are, so your answer is correct.

Answer:I’m guessing the second one

Step-by-step explanation:

I thinking that because if u add it all up also this is just a thought

Answer:

B

Step-by-step explanation:

the British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.

and it is outdated. your teacher and the manufacturer should use joules as metric.

1 BTU ≈ 1055 joules

anyway, so, the solution has several parts.

we need to find how many pounds of water are in a gallon.

and then multiply by the amount of gallons (20 000) and the amount of degrees (2 from 70 to 72).

and after a little search on the internet we get

1 gallon of water = 8.34 pounds

so, we need to warm

20000×8.34 pounds of water by 2 degrees F.

that is

20000 × 8.34 × 2 = 333,600 BTU

if we use only the rounded value of pounds per gallons (8.3), this would be

20000 × 8.3 × 2 = 332,000 BTU

so in any case, B is the right answer (as being the closest to the real result), which is the situation with any size classification of devices : reality is somewhere close by, but never meets the exact specifications.

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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9514 1404 393

Answer:

  57, 58, 75, 78, 85, 87 (no repeats)

  add 55, 77, 88 to the above list if repeats are allowed.

Step-by-step explanation:

With no repeating digits, there are 3 ways to choose the first digit, and 2 ways to choose the second digit, for a total of 3×2 = 6 possible numbers

  57, 58, 75, 78, 85, 87

If the digits can be repeated, than you can add 55, 77, 88 to that list:

  55, 57, 58, 75, 77, 78, 85, 87, 88

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))

A store sold 22 colored shirts and 8 white shirts.

Let x be the number of colored shorts and y be the number of white shirts.

A store sold 14 more colored shirts than white shirts.

so, we get an equation,

x = y + 14                       ....................(1)

The white shirts cost $9.95, and the colored shirts cost $10.50. The store sold $310.60 worth of shirts.

So we get an equation,

10.50x + 9.95y = 310.60           .............(2)

Substitute above value of x in equation (2)

10.50(y + 14) + 9.95y = 310.60          

10.50y + 147 + 9.95y = 310.60          

20.45y = 310.60 - 147

20.45y = 163.6

y = 8

Substitute above value of y in equation (1)

So, x = 8 + 14

x = 22

Therefore, a store sold 22 colored shirts and 8 white shirts.

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Two factors that need to be controlled to keep this test fair are the temperature and the sample volume.

The control variables are those variables that should be kept constant in order to avoid interfering with the free flow of the experiment.

For the provided test, it is important that the temperature of the environment where the test sample is kept is controlled throughout the duration of the experiment so that some results are not affected by this. Also, the sample volume should be controlled for fair outcomes.

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The given figure is a square-based pyramid.

The volume of this pyramid is given by the formula:

Where s is the length of the side of the base, and h is the height of the pyramid.

In this figure, s=4 cm and h=6 cm. By replacing these values we obtain:

The answer is V=32 cm^3

Answer: 97350

Step-by-step explanation:

The numbers (3251)(30) are separated by using parentheses by multiplying the numbers we get 97350.

When we notice two or more numbers together that exist divided by parentheses, then the parentheses exist pointing us to multiply.  In math, multiplying indicates adding equivalent groups. When we multiply, the number of things in the group rises. The two elements and the product exist as regions of a multiplication problem.

Given: (3251)(30)

Here, the numbers are separated by using parentheses, then the parentheses exist pointing us to multiply.

Therefore, by multiplying the numbers we get

(3,251)(30) = 97350

Therefore, the correct answer is 97350.

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The value of x has a z-score of three is 20

The given parameters are:

Mean = 2

Standard deviation = 6

z = 3

The z-score is calculated as:

\(z = \frac{x - \mu}{\sigma}\)

So, we have:

\(3 = \frac{x -2}{6}\)

Multiply through by 6

18 = x - 2

Add 2 to both sides

x = 20

Hence, the value of x has a z-score of three is 20

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Answer:

The number of cows and the number of ducks is equal

Step-by-step explanation:

4c + 2d = 3(c + d)

4c + 2d = 3c + 3d

4c - 3c = 3d - 2d

c = d

To solve this question, use the Binomial probability formula.

The formula is given by

Where:

n = the number of trials

x = the sample we aim to try

p = the probability of success

In this question:

n = 16

x = 9

p = 0.5

Substituting in the equation:

And the combination formula:

Then:

Answer: The probability is 0.1746.

Answer:

1. 420

I cannot figure out the second half. I apologise.

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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