The area of the trapezoid is 42square kilometers. What is the trapezoid's height, h?

Answer:

x = 8

Hope this helps!

Step-by-step explanation:

( 2x + 42 )° + ( 4x )° = 90°  ( right angle )

6x + 42 = 90

6x = 90 - 42

6x = 48

x = 8

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

The curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 can be found by setting the two equations equal to each other:

x² + y² = y² + z² = 20

The intersection of the two cylinders is a circle.

To determine the radius of this circle, we use either of the two equations and solve for one variable in terms of the other two:

y² + z² = 20y²

= 20 - z²y

= ±sqrt(20 - z²)

If we substitute this expression for y into the equation x² + y² = 25, we can solve for x in terms of z:

x² + (20 - z²)

= 25x²

= 5 + z²x

= ±sqrt(5 + z²)

Thus, the curve of intersection can be expressed parametrically as follows:

r(t) = (x(t), y(t), z(t)) = (sqrt(5 + t²), sqrt(20 - t²), t)for -2sqrt(5) ≤ t ≤ 2sqrt(5)

At the point (3, 4, 2), t = 2.

To find the tangent vector to the curve at this point, we take the derivative of the position vector:

r'(t) = (x'(t), y'(t), z'(t)) = (t/sqrt(5 + t²), -t/sqrt(20 - t²), 1)

at t = 2:r'(2) = (2/sqrt(9), -2/sqrt(16), 1) = (2/3, -1/2, 1)

Finally, we obtain the vector equation of the tangent line by using the point-normal form of the equation of a line:

L(t) = r(2) + t r'(2)L(t)

     = (3, 4, 2) + t (2/3, -1/2, 1)L(t)

     = (2/3)t + 3, (-1/2)t + 4, t + 2

Therefore, a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2) is:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

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Answer:

The property is the water cycle

Answer:

a

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

2/3 mi

Step-by-step explanation:

Multiply the length of one side of a square by 4 to find the perimeter.

(1/6)(4) = 4/6

Simplify. The common factor is 2.

4/6 = 2/3

We introduced three conditions that should be met before we construct a confidence interval for an unknown population proportion: Random, Normal, and Independent.

There are three crucial requirements that must be met in order to establish a confidence interval. These are Independent, Random, and Normal.

Any survey is carried out objectively.

It is required to assure randomness. An independent choice is equally likely to be made in a random sample. Similar to how the confidence interval is built, normal is used to confirm which phenomena are being employed or to correct the approach if necessary. In a similar vein, independent is crucial because it contains the facts to be analyzed. For the purpose of calculating the standard deviation, independent is used.

Therefore, it's crucial to consider the Random, Normal, and Independent criteria while building a confidence interval.

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Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.

Step-by-step explanation: I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions ! Hope this helped

The vector space C (complex numbers) is two-dimensional over R (real numbers) and one-dimensional over C (complex numbers).

To prove that C is two-dimensional over R, we need to show that any complex number can be uniquely represented as a linear combination of two real numbers. Since a complex number z can be written as z = a + bi, where a and b are real numbers, we can express z as z = a(1) + b(i), where 1 and i are the basis vectors. This implies that C is spanned by the two real numbers 1 and i, making it two-dimensional over R.

On the other hand, to prove that C is one-dimensional over C, we need to show that any complex number can be uniquely represented as a scalar multiple of a single complex number. Since any complex number z can be written as z = a + bi, where a and b are real numbers, we can express z as z = (a + bi)(1), where 1 is the basis vector. This shows that C can be spanned by the complex number 1, making it one-dimensional over C.

In summary, C is two-dimensional over R because it can be spanned by the two real numbers 1 and i, and it is one-dimensional over C because it can be spanned by the complex number 1.

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Answer:

hhahahahahahah

Step-by-step explanation:

Answer:

The correct answer is 308

Hoped I helped

can u give me a brainliest

The final logic gate circuit consists of three NAND gates connected to an AND gate.

To draw the logic gate circuit for the given Boolean expression ((a b)' and (b.c)' and (a c)')', follow these steps:

1. Identify the basic operations in the expression: The given expression has three operations: (a b)', (b.c)', and (a c)'.

2. Draw the basic gates for each operation:
  - For (a b)', use a NAND gate with inputs a and b.
  - For (b.c)', use a NAND gate with inputs b and c.
  - For (a c)', use a NAND gate with inputs a and c.

3. Connect the outputs of the three basic gates to an AND gate, since the expression requires the outputs to be ANDed together.

So, the final logic gate circuit consists of three NAND gates connected to an AND gate. The inputs of the first NAND gate are a and b, the inputs of the second NAND gate are b and c, and the inputs of the third NAND gate are a and c. The outputs of these three NAND gates are connected to the inputs of the AND gate, and the output of the AND gate represents the final result of the Boolean expression.

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Step-by-step explanation:

Simplifying

8x + -2(3x + -4 + 2y) + -12x = 0

Reorder the terms:

8x + -2(-4 + 3x + 2y) + -12x = 0

8x + (-4 * -2 + 3x * -2 + 2y * -2) + -12x = 0

8x + (8 + -6x + -4y) + -12x = 0

Reorder the terms:

8 + 8x + -6x + -12x + -4y = 0

Combine like terms: 8x + -6x = 2x

8 + 2x + -12x + -4y = 0

Combine like terms: 2x + -12x = -10x

8 + -10x + -4y = 0

Solving

8 + -10x + -4y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -10x + -8 + -4y = 0 + -8

Reorder the terms:

8 + -8 + -10x + -4y = 0 + -8

Combine like terms: 8 + -8 = 0

0 + -10x + -4y = 0 + -8

-10x + -4y = 0 + -8

Combine like terms: 0 + -8 = -8

-10x + -4y = -8

Add '4y' to each side of the equation.

-10x + -4y + 4y = -8 + 4y

Combine like terms: -4y + 4y = 0

-10x + 0 = -8 + 4y

-10x = -8 + 4y

Divide each side by '-10'.

x = 0.8 + -0.4y

Simplifying

x = 0.8 + -0.4y

Answer:

wht is it called

Step-by-step explanation:

cause irdk

Answer:

i=10

Step-by-step explanation:

5i+4=14+4i

5i-4i=14-4

i=10

The number of real roots for the function​s are

From the question, we have the following parameters that can be used in our computation:

The graphs

The number of real roots of a function​ is the number of times the function intersects with the x-axis

This in other words means the zeros of the function

Using the above as a guide, we have the roots of the graphs to be

Graph 1 = 4

Graph 2 = 1

Graph 3 = 2

Graph 4 = 0

Graph 5 = 1

Graph 6 = 1

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a.) That includes saturation flux density

b.) The approximate values for these limits depend on the specific materials used in the transformer.

c.) The fundamental transformer design equation is: V = 4.44 * f * B * A * N

d.) Inrush is a transient phenomenon that occurs when a transformer is energized

a) The fundamental design limits of a transformer based on material properties include the saturation flux density and the maximum allowable current density.

b) The approximate values for these limits depend on the specific materials used in the transformer. For example, the saturation flux density for silicon steel, a commonly used material for transformer cores, is around 2 tesla, while the maximum allowable current density is typically around 4 A/mm2.

c) The fundamental transformer design equation is:

V = 4.44 * f * B * A * N

where V is the voltage induced in the winding, f is the frequency of the alternating current, B is the flux density in the core, A is the cross-sectional area of the core, and N is the number of turns in the winding.

d) Inrush is a transient phenomenon that occurs when a transformer is energized. It is caused by the sudden magnetization of the transformer core and can result in a high inrush current, which can damage the transformer windings and other components. To protect against inrush, transformers are typically equipped with fuses, circuit breakers, or other protective devices.

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The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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Answer: 9(2x-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find KLR, we subtract MLR from KLM. We get left with 2x+14=KLR. With this, we can see that 36 degrees = 2x+14.

Now you just solve.

Answer:

81

Step-by-step explanation:

63×135=8505

8505÷105=81#

In 63 pounds, there are equivalent 81 dollars.

A unit conversion expresses the same property as a different unit of measurement.

For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

Given is that -

1 pound = Rs.135

1 dollar = Rs. 105

Now, we can write that 1 rupee as -

Rs. 1 = 1/105 dollar

So, in 1 pound we can write -

1 pound = 135 x 1/105 dollars

63 pounds = 63 x 135 x 1/105 = 81 dollars

Therefore, in 63 pounds, there are equivalent 81 dollars.

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Answer:

B

Step-by-step explanation:

The type of solution set in the equation 3 – 1∕2x = –1∕2x + 3 is infinitely many solutions

From the question, we have the following parameters that can be used in our computation:

3 – 1∕2x = –1∕2x + 3

This equation can be expressed as

3 – 1∕2x = 3 – 1∕2x

An equation that has infinitely many solutions is represented as:

a + bx = a + bx

The above means that both sides of the equations are the same

Both sides of the equation 3 – 1∕2x = 3 – 1∕2x are the same

Hence, the equation that has infinitely many solutions is 3 – 1∕2x = 3 – 1∕2x

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The possible angles between two unit vectors u and v if ||u x v|| = √3/2 are 60 degree.

The magnitude of the cross product between two vectors u and v is equal to the area of the parallelogram formed by the two vectors. Since the magnitude of the cross product is ||u x v|| = √3/2, it means that the area of the parallelogram formed by u and v is √3/2.

The area of a parallelogram is given by the formula A = ||u|| ||v|| sin(theta), where theta is the angle between the two vectors. Since both u and v are unit vectors, their magnitudes are 1.

Thus, we can simplify the formula to A = sin(theta)/2.

Therefore, sin(theta) = √3/2, which implies that the value of sin theta is √3/2 when theta = 60°

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Answer:

Step-by-step explanation:

cot θ=11

tan θ=1/11

\(\sin ~2\theta=\frac{2 \tan ~\theta}{1+\tan^2 \theta} =\frac{2*\frac{1}{11} }{1+(\frac{1}{11} )^2}=\frac{22 }{122} \\\\cos~2 \theta=\frac{1-tan^2 \theta}{1+tan^2\theta} =\frac{1-(\frac{1}{11})^2 }{1+(\frac{1}{11} )^2} =\frac{120}{122} =\frac{60}{61} \\tan 2 \theta=\frac{2 tan\theta}{1-tan^2 \theta} =\frac{2*(\frac{1}{11 } )}{1-(\frac{1}{11} )^2} =\frac{2*11}{120} =\frac{11}{60}\)

Answer:

Total is 3

Step-by-step explanation:

AI-generated answer

Let's start by finding out how many marbles John had initially. We can do this by using the information given in the problem.

Let the original number of marbles be x.

John gave away 3/4 of his marbles, which means he has 1/4 of the original number of marbles left. We can express this as:

1/4 x = the number of marbles John has left

If we solve for x, we get:

4/1 * 1/4 x = 4/1 * the number of marbles John has left

x = 4 * the number of marbles John has left

Now we know that John had 4 times the number of marbles he has left.

Next, John receives another bag of marbles containing 2/4 (which is the same as 1/2) of the original number of marbles.

We can express this as:

1/2 x = the number of marbles in the new bag

To find the total number of marbles John has now, we can add the number of marbles he has left to the number of marbles in the new bag:

Total number of marbles = the number of marbles John has left + the number of marbles in the new bag

Total number of marbles = 1/4 x + 1/2 x

Total number of marbles = (1/4 + 1/2) x

Total number of marbles = (3/4) x

We know that x = 4 times the number of marbles John has left, so we can substitute this into the equation:

Total number of marbles = (3/4) * 4 * the number of marbles John has left

Total number of marbles = 3 * the number of marbles John has left

Therefore, the total number of marbles John has now is 3 times the number of marbles he has left.

Tell me in the commets if you didn't understand a word or something in the equation. :)

Answer:

x-int: (-12/9, 0)

y-int: (0, 6)

Step-by-step explanation:

x-int ==> on x-axis when y=0

y-int ==> on y-axis when x=0

9/4x -1/2y = -3

x-int: 9/4x -1/2(0) = -3

9/4x = -3

9x/4 = -3

9x*4/4=-3*4

9x=-12

x=-12/9 ==> x-int: (-12/9, 0)

y-int: 9/4(0) -1/2y = -3

-1/2y = -3

1/2y=3

y/2=3

y=6 ==> y-int: (0, 6)

Answer:

deductive

Step-by-step explanation:

Step-by-step explanation:

Hi there,

m<5 = 100 degrees by the same-side interior angles postulate.

We know that "t" is a straight line and straight lines are equal to 180 degrees, so if m<4=80, we just subtract 80 from 180 to get 100. The Same-Side Interior Angles Postulate rule says "the sum of any pair of same side interior angles will always equal 180 degrees." So, if m<4=80 degrees, then m<5 must equal 100.

Hope this helps.

Answer:

100°, same-side interior angles postulate

Step-by-step explanation:

∠4=80°

∠4+∠5=180° by same-side interior angles postulate

180°-∠4=180°-80°

=100°

∠5=100°

The probability that the product of two randomly selected numbers is even is 3/4 or 75%.

To find the probability that the product of two randomly selected numbers is even, we can consider the possible scenarios in which the product is even.

1. If at least one of the selected numbers is even: In this case, the product will be even regardless of the second number.

2. If both selected numbers are odd: In this case, the product will be odd.

Therefore, the only scenario where the product is not even is when both selected numbers are odd.

Let's assume the set of numbers we are selecting from is the set of positive integers.

The probability of selecting an odd number is 1/2, and since we are selecting two numbers independently, the probability of selecting two odd numbers (and therefore the product being odd) is (1/2) * (1/2) = 1/4.

Therefore, the probability that the product of two randomly selected numbers is even is:

1 - 1/4 = 3/4.

Hence, the probability that the product is even is 3/4 or 75%.

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