Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
Oy=2x-2
Oy = 2x + 2
Oy=x+2
Oy=x-2

Distance of the house from the base of the cliff is 282.27 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From the figure attached,

AB = Height of the cliff = 60 m

Let the distance between the base of the cliff and the house 'C' = x m

If the angle of depression = 12°

Then angle of elevation of the top of the cliff from the house = 12°

Now from right triangle ABC,

tan12=60/x

x=60/tan 12

x=60/0.21256

x = 282.27 m

Therefore, distance of the house from the base of the cliff is 282.27 m.

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The circumference of the circle is 110 m.

Let us assume that the wire has been cut into two equal halves thus the radius of the circle would be 35 m/2 = 17.5 m

Then;

C = 2πr

C = circumference

r = radius

"pi" is a mathematical constant approximately equal to 3.14 and "r" is the radius of the circle. If the diameter of the circle is known, the radius can be calculated by dividing the diameter by 2.

C = 2 * 3.142 * 17.5

C = 110 m as we can see here

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1. The plane travelled a distance of 471.239 ft

2. The plane would travel further by 6283.185 ft

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]

Part 1:

Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times

The total distance travelled by plane is [tex]15*2\pi *15[/tex]

[tex]=150\pi[/tex]

= 471.239 ft

Part 2:

Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.

The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])

If he increases the length by 10 ft, The cord will now be 60 ft.

The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])

Now,

100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])

= 100 * (2*(60-50))*[tex]\pi[/tex])

= 100 * 2 * 10 * [tex]\pi[/tex]

= 2000 * [tex]\pi[/tex]

= 6283.185 ft

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Answer:

Step-by-step explanation:

You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.

Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.

I used x to represent what we are looking for:

6.5% of $400 = x

0.065 * 400 = $26

12.5% of 100 = x

0.125 * 100 = $12.5

x of 650 = 130

130/650 = 0.2 which equals 20%

x of $4.50 = $5.40

5.40/4.50 = 1.2 which equals 120%

x of $28 = $8.40

8.40/28 = 0.3 which equals 30%

56% of x = $21.84

21.84/0.56 = 39

55% of x = $495

495/0.55 = 900

x of 400 = 120

120/400 = 0.3 which equals 30%

4% of 975 = x

0.04 * 975 = 39

Answer:

See below

Step-by-step explanation:

a. 6.5% of $400:

[tex]= \frac{65}{100}[/tex]× ($400)

= $260

b. 12.5% of $100:

[tex]= \frac{12.5}{100}[/tex] × ($100)

= $12.5

c. 130 is what percent of 650:

[tex]=\frac{130}{650}[/tex]×100%
= 20%

d. $5.40 is what percent of $4.50:

[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%

e. $8.40 is what percent of $28:

[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%

f. 56% of what number is $21.84:

=[tex]\frac{56}{100}[/tex]× number = $21.84

∴ Number = [tex]\frac{100}{56}[/tex]×$21.84

                 = $39

g. $495 is 55% of what number:

= $495 = [tex]\frac{55}{100}[/tex]× Number

∴Number = [tex]\frac{100}{55}[/tex]×($495)

                 = $900

h. 120 is what percent of 400:

= [tex]\frac{120}{400}[/tex]×100%
= 30%

i. 4% of 975 is what number:

= [tex]\frac{4}{100}[/tex]×975

= 39

Answer:

3rd choice  (x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - -8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = -8

k = 11

r = 2

(x + 8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

The answer is C. (x+8)² + (y-11)² = 4

Answer:

Step-by-step explanation:

The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).

The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.

For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.

So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.

Step-by-step explanation:

answer is in the picture

The difference in cost between a one-line ad and a four-line ad is 0

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

c(x) = 40 x ≤ 5

c(x) = 40 + 7(x-4), x>5)

For one line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 1 is in the domain of x ≤ 5

For four line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 4 is in the domain of x ≤ 5

So, we have

C(1) = 40 and C(4) = 40

The difference, it

Difference = 40 - 40

Evaluate

Difference = 0

Hence, the difference is 0

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The piecewise function for the given problem is;

C(x) = $61.29                           x ≥ 400

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.

First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;

47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;

C(x) = 61.29

Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

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The positive coterminal angle less than 360° is, 55°

Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).

To find a positive angle that is coterminal with -1025°,

we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.

Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:

= -1,025° + 1080°

=   55°

Since this angle is less than 360°,

Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.

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The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:

1520.75 liters.

The necessary amount of natural oil is obtained applying the proportions in the context of this problem.

Considering the ratio given in the problem, a rule of three is established, as follows:

7 liters of natural oil - 4 liters of Petrolyn oil.

n liters of natural oil - 869 liters of Petrolyn oil.

Applying cross multiplication, the desired amount is obtained as follows:

4n = 7 x 869

n = 7 x 869/4

n = 1520.75 liters.

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The end behavior of the given fucntion is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

End behavior of a equation is defined as behavior of graph of the function at the ends of the x-axis.

Given, [tex]4x^{5} +1[/tex].

We have to find the end behavior of the graph.

The corresponding graphical representation is given below:

From the graph it is clearly known that as,

Value of x increases ⇒Value of y decreases.

That is x approaches positive infinity and y approaches negative infinity.

i.e., [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex]

Hence, the end behavior of the given equation is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

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Answer: 8

Step-by-step explanation:  9 x 8 = 72

Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.

An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.

Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings

Since 1 rating point is given = 1,800,000

Rating point = 1,800,000 household

Rating point = 10.2 × 1,800,000 household.

Rating point =18360000 household.

Therefore, correct to state that the number of households that watched the show that week are 18360000 household.

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The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.

What is elimination method?

The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.

We are given two equations as

7x + 14y = 28     ....(1)

5x + 10y = 20     ....(2)

Now, on multiplying equation (1) by 10, we get the equation as

70x + 140y = 280     ....(3)

On multiplying equation (2) by 14, we get the equation as

70x + 140y = 280     ....(4)

Since, we are getting the same equations so, the system has infinitely many solutions.

Hence, the value of x is [0,∞] and y is [0,∞].

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The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]

Your system might not require the "0≤x", but it technically should be there.

Answer:

  20 cubic yards

Step-by-step explanation:

You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.

You know that ...

Then the dimensions of the volume being applied are ...

  6 inches = 6/36 yards

  31 feet = 31/3 yards

  34 feet = 34/3 yards

The volume is the product of the dimensions of the space:

  V = LWH

  V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³

About 20 cubic yards are needed to fill the garden.

answer c)

cross x  at x = -2, x = 3, and x = 1

the square root tells us that it bounces off that location rather than intercepting

Answer:s

Step-by-step explanation:

B is significantly more affordable and better than A, renting for $1.62 per square foot.

Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.

To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.

1 yard² = 9 feet²

A rents for $33 per yard squared

hence A rents $33 for 9 feet squared

hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared

Thus, as B is more economical, it is better.

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The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.

A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .

Therefore, the height of the plane can be found as follows:

The situation forms a right angle triangle.

Using trigonometric ratios,

tan 12 = opposite / adjacent

tan 12° = x /  4812

cross multiply

x =  4812 tan 12°

x =  4812 × 0.21255656167

Therefore,

x = 1022.82217476

x = 1023 metres.

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The value equivalent to the expression is (2)√6 and option B is the correct answer.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.

the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.

The given expression is √24.

Find the prime factorization of 24:

2 | 24

2 | 12

2 | 6

3 | 3

  | 1

Thus, √24 can be written as:

√24 = √(2)²(2)3

√24 = (2)√6

Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.

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The sample standard deviation weight of the 50 candies is, 0.07 grams.

The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.

To find the sample standard deviation weight,

we can use the formula:

[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]

where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.

We can first find the sample mean weight:

[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50

[tex]\bar x[/tex] = 0.8456

Next, we can calculate the sample standard deviation:

s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))

s = sqrt(0.0045916)

s = 0.0678

Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.

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Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

Here are the steps to complete the budget, as described in the instructions:

Calculate totals for each type of expense and for each month:

Calculate net income for each month:

Add another column to calculate the percentage of total expenses for each category:

Create two different unique charts:

Label each page tab according to the chart:

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Answer: x=0.545455

Step-by-step explanation:

add 216 to both sides

divided both sides by 1331

take cube root

Answer:

x = 5/2

y = 1/2

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = - 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]

That's our required ratio ~

Answer:

D

Step-by-step explanation:

Front

5x4 = 20

Back

5x4 = 20

Top

5x8 = 40

Bottom

5x8 = 40

Right side

8x4 = 32

Left side

8x4 = 32

Add all the sides

20 + 20 + 40 + 40 + 32 +32 = 184