Below are two parallel lines with a third line intersecting them.

Answer:

2401

Step-by-step explanation:

khan

Applying the two-tangent theorem, the length of AN is: 21 units.

The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.

More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.

From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.

This implies that the three tangents are congruent. Therefore:

6y - 3 = 29 - 2y

6y + 2y = 29 + 3

8y = 32

y = 32/8

y = 4

AN = 6y - 3

Plug in the value of y

AN = 6(4) - 3

AN = 21 units.

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Answer:

A, undefined

Step-by-step explanation:

The general rule is that vertical lines are undefined slope, because there's literally no change in x values. The vertical line test also fails, meaning there is no slope. Horizontal lines have a slope of 0, while vertical lines don't own any numbers that are important except for x-axis numbers.

If you do y2-y1 over x2-x1, you literally get 1/0 which is nothing. 0/1 = 0, but 1/0 is nothing.

Hope this helps!

Step-by-step explanation:

it is totally simple : you need to put the x-value into every place of the x-variable, and then we calculate.

and then the same for the next x-value. and the next. ...

-2

-2×-2 + 9 = 4 + 9 = 13

0

-2×0 + 9 = 0 + 9 = 9

2

-2×2 + 9 = -4 + 9 = 5

4

-2×4 + 9 = -8 + 9 = 1

The roots of the quadratic-like trigonometric equation according to the quadratic formula are θ₁ ≈ 41.606° and θ₂ ≈ 138.394°, respectively.

In this problem we need to find the roots of a quadratic-like trigonometric equation of the form:

a · sin²θ + b · sin θ + c = 0, where a ≠ 0.

Where a, b, c are real coefficients.

Where we can find them by using the algebraic substitution u = sin θ and the quadratic formula, which is defined below:

u = sin θ = [- b ± √(b² - 4 · a · c)] / (2 · a)

If we know that a = 2, b = 5 and c = - 4, then the roots of the trigonometric equation are, respectively:

u = sin θ = [- 5 ± √[5² - 4 · 2 · (- 4)]] / (2 · 2)

u = sin θ = (- 5 ± √57) / 4

u = sin θ = - 5 / 4 ± √57 / 4

u₁ ≈ 0.664 or u₂ ≈ - 3.137

Since the sine function is a bounded function between - 1 and 1, the only family solutions is u ≈ 0.664. Then, the solutions between 0° and 360°:

θ₁ ≈ 41.606°, θ₂ ≈ 138.394°

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Answer:

n = -13

Step-by-step explanation:

You were doing everything correct but one minor error

-13 - n = 0

you added 13 to both sides which is correct

-13 - n = 0

+13        +13

than you got, n = 13

but you forgot to bring diwn the negative sign with the n

-13 - n = 0

+13        +13

- n = 13 which is basically

-1n = 13

divided both sides by -1 to get n positive

-1n/-1 = 13/-1

Simplified, n = -13

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Answer:

the average number of cars waiting in line L\(q\) is 0.45

Step-by-step explanation:

Given the data in the question;

Cars arrive at an automatic car wash system every 10 minutes on average.

Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour

Washing time for each is 6 minutes per car

Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour

so

P = λ/μ = 6 / 10 = 0.6

Using the length of queue in M/D/1 system since there is only one service bay;

L\(q\) = \(\frac{1}{2}\)[ P² / ( 1 - P ) ]

so we substitute

L\(q\) = \(\frac{1}{2}\)[ (0.6)² / ( 1 - 0.6 ) ]

L\(q\) = \(\frac{1}{2}\)[ 0.36 / 0.4 ]

L\(q\) = \(\frac{1}{2}\)[ 0.9 ]

L\(q\) = 0.45

Therefore, the average number of cars waiting in line L\(q\) is 0.45

The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Given:

f(x) = 2x - 5

g(x) = 4x + 3

(f + g)(x) can be found as,

Therefore, (f + g)(x)=6x-2.

Answer:

B

Step-by-step explanation:

Answer:

18² + 24² = x²

Step-by-step explanation:

Using the Pythagorean theorem, with legs a and b, and hypotenuse c, the equation is:

a² + b² = c²

If the legs measure 18 and 24, and the hypotenuse has length x, then you get:

18² + 24² = x²

Answer:

D

Step-by-step explanation:

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

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Answer:

3.78

Step-by-step explanation:

Answer:

    Step-by-step explanation:

D

The volume of the tower is 224 in³, which is not listed among the given options.

To find the volume of the rectangular block, we need to multiply its length, width, and height. Therefore, the volume of the single block is:
8 x 3.5 x 2 = 56 cubic inches.
Since we are stacking four blocks to create a tower, we need to multiply the volume of a single block by 4.

Thus, the volume of the tower is:
56 x 4 = 224 cubic inches.
The volume of a rectangular block can be found using the formula,

V = length × width × height.

In this case, the length is 8 inches, the width is 3.5 inches, and the height is 2 inches.

V = 8 × 3.5 × 2 V

= 28 × 2 V

= 56 in³

Now that we know the volume of one block, we can find the volume of the tower created by stacking four blocks. Tower volume = block volume × number of blocks Tower volume = 56 in³ × 4 Tower volume = 224 in³

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True, When assessing schedule feasibility, a systems analyst must consider the interaction between time and costs.

When assessing the viability of scheduling a project, an organisation determines the anticipated completion time. The feasibility analysis assists in identifying any potential obstacles the proposed project may encounter, such as: Internal project constraints, including those related to technology, finances, and resources

The expansion and acceptance of project management training have undergone significant changes over the past few years, and it is projected that these developments will continue and accelerate. And as project management becomes more popular, feasibility studies become more important. It may be exhilarating to begin a difficult, extensive project that will have a significant influence on your organization.

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Answer:

59 im pretty sure

Step-by-step explanation:

Answer:

Q6) They are the same.

bi) 1/6, 1/3, 5/12, 1/2

bii) 4/12, 1/2, 2/3, 5/6

Step-by-step explanation:

For Q6, both fractions (5/10 and 10/20) can be simplified to 1/2. This means they are both the same.

For b, I would find a common denominator and then compare them.

3x-1=4x+8-x

3x -4x +x = 8+1

4x -4x = 9

0x =9

x= 9/0 which is undefined .

In-state corresponds to students who are residents of the same state as the university, out-of-state corresponds to students from different states, and foreign corresponds to students from countries other than the university's country.

To match the vocabulary word with its corresponding example in the context of the state university survey, we need to understand the terms and their meanings.

Here are the vocabulary words and their corresponding examples:

Vocabulary Word: In-state

Example: A student who is a resident of the same state where the university is located.

They pay lower tuition fees compared to out-of-state or foreign students.

Vocabulary Word: Out-of-state

Example: A student who is not a resident of the state where the university is located.

They typically pay higher tuition fees compared to in-state students.

Vocabulary Word: Foreign

Example: A student who is from a country other than the country where the university is located.

They are international students who may have different visa requirements and tuition fees.

To match these vocabulary words with their corresponding examples:

In-state: A student from the same state as the university, paying lower tuition fees.

Out-of-state: A student from a different state than the university, paying higher tuition fees.

Foreign: A student from a country other than the country where the university is located, with potential differences in visa requirements and tuition fees.

By associating each vocabulary word with its respective example, we can accurately describe the three categories of students based on their residency and origin in the context of the state university's survey.

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The function that describes his distance from the finish line after x minutes is given by, f(x) = 3-x/2.

Given that a student is running a 3 kilometer race.

He runs 1 kilometer every 2 minutes.

So in 1 minute he runs 1/2 kilometers.

So in x minutes he runs x/2 kilometers.

So his distance from finish line of 3 kilometers race after x minutes = 3-x/2

So the suitable function which shows the his distance he runs after x minutes from finish line is given by,

f(x) = 3-x/2

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The equation

d = 5h

relates time (h) in hours and the accumulated snow (d) in centimeters.

Replacing with d = 1, and solving for h, we get:

1 = 5h

1/5 = h

0.2 = h

It takes 0.2 hours for 1 cm of snow to accumulate in the yard

Replacing with h = 1, and solving for d, we get:

d = 5(1)

d = 5

5 centimeters of snow accumulate per hour

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Answer:

The exponential function is

\(y = {2}^{x} \)

Answer:

1). y= -4+ 4x

2). y= 3+ x/2

Step-by-step explanation:

hope this helps !

The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Answer:

Step-by-step explanation:

The number is 60:

Divide the amount and decimal of the percentage to be extracted

Case 1

\(\frac{21}{0.35} =60\)

Case 2

\(\frac{54}{0.9} =60\)

Now the 55% of this number is:

\(60(0.55)=33\)

Hope this helps

Answer:

she will need 8.4 so just get 9

If each box has 500 sheets, Megan should purchase 9 packs if she needs 4200 sheets of paper. ​

The area of arithmetic operations encompasses the study of numbers and their operations, which are essential to all other branches of mathematics. These systems use the four operations of addition, subtraction, multiplication, and division as their foundation. ​

It is given that, Megan purchases 4200 sheets of paper because each box has 500 sheets. ​

Suppose x be the number of packs,

Applying division to select how to share pack equitably among a group, divide the object into equal halves or groups.

The number of packs needed will be,

x=4200/500

x=8.4 ≈ 9

Thus, she should buy 9 packs if each pack has 500 sheets​.

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