How did I get my answer?
3+2=25
5+4=81
2+2=16

The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;

12 feet

The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.

The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;

tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)

The side facing the angle is the distance from the bottom to the point where the ladder touches the building.

The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.

Therefore; tan(θ) = 18/12 = x/8

Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2

18/12 = x/8

x = 18/12 × 8 = 12

The distance, x = 12 feet

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Answer:

12?

Step-by-step explanation:

I'm not too sure! I am in the middle of taking the test right now.

Answer:

The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.

The formula for finding the number of permutations of n objects taken r at a time without repetition is:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being chosen.

In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:

P(10, 4) = 10! / (10 - 4)!

P(10, 4) = 10! / 6!

P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)

P(10, 4) = 10,080

Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.

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The graph of its image after the composition is shown in graph.

We have to given that;

XY with endpoints are,

⇒ X (-3, 1) and Y (4,-5)

Now, After Translation (x, y)→(x, y + 2) we get;

X = (- 3, 1)

X' = (- 3, 1 + 2) = (- 3, 3)

Y = (4, - 5)

Y' = (4, - 3)

And, After Rotation: 90° about the origin.

That is, (x, y) = (y, - x)

The points of image are,

X'' = (3, 3)

Y'' = (- 3, - 4)

Thus, The graph of its image after the composition is shown in graph.

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The measure of the angle BCA is 50 degrees.

The angles at the circumference subtended by the same arc are equal.

The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.

Therefore, let's use the theorem to find the angle ∠BCA in the circle.

Hence,

∠BCA = ∠BOA

Finally,

∠BCA =  50 degrees.

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The complete solution to the system is 25/17, 61/17, 2/17 respectively.

Using the Gauss-Jordan elimination method to find the solution of the system of linear equations represented by the given augmented matrix:

Starting matrix:

[1 -2/3 -1/3 | 1]

[1 -2 6 | -17]

[-3 -7 3 | -43]

Add Row 1 to Row 2 and Row 3:

[1 -2/3 -1/3 | 1]

[0 -4/3 17/3 | -18]

[0 -1 0 | -40]

Multiply Row 2 by -3/4:

[1 -2/3 -1/3 | 1]

[0 1 -17/4 | 27/2]

[0 -1 0 | -40]

Add Row 1 to Row 2 and Row 3:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 -17/4 | -13/2]

Multiply row 3 by -4/17:

[1 0 -7/4 | 19/2]

[0 1 -17/4 | 27/2]

[0 0 1 | 2/17]

Add Row 3 to Row 1 and Row 2:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

Therefore, the solution of the system of linear equations is:

x = 25/17

y = 61/17

z = 2/17

So the solution is [25/17, 61/17, 2/17].

Thus the completed augmented matrix is:

[1 0 0 | 25/17]

[0 1 0 | 61/17]

[0 0 1 | 2/17]

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The solution to the system of equations is given as follows:

Considering the augmented matrix, the system of equations is defined as follows:

Adding the first and third equations, we have that:

-4x - 6y = -36.

From the second equation, we have that:

2x + 3y = 18.

The addition equation is a multiple of this equation, hence the system has an infinite number of solutions.

From the second equation, we have that:

2x + 3y = 18.

x + 1.5y = 9

x = 9 - 1.5y.

The definition for z is given as follows:

z = x + y - 7.

Hence the variable y is:

y = z - x + 7.

The variable x is of:

x = 9 - 1.5(z - x + 7)

x = 9 - 1.5z + 1.5x - 10.5

0.5x = 1.5 + 1.5z

x = 3z + 3.

The variable y is:

y = z - 3z - 3 + 7

y = -2z + 4.

Hence the solution is:

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The slope of the line passing through the given points is -2.5.

To find the slope of a line passing through two points, we need to use the formula:

Slope = (Change in y) / (Change in x

We can choose any two points from the given table to find the slope of the line. Let's choose the points (4, 19) and (6, 14).

Change in y = 14 - 19 = -5

Change in x = 6 - 4 = 2

Slope = (-5) / 2 = -2.5

Therefore, the slope of the line passing through the given points is -2.5.

The slope of a line represents the steepness of the line. If the slope is positive, the line is increasing as we move from left to right. If the slope is negative, the line is decreasing as we move from left to right. A slope of 0 represents a horizontal line, while an undefined slope represents a vertical line.

In this case, the slope of -2.5 indicates that the line is decreasing at a moderate rate as we move from left to right. The higher the absolute value of the slope, the steeper the line.

It is important to note that the slope is constant for any two points on a straight line. Therefore, we can choose any other two points from the table to find the slope, and we will get the same result.

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Answer:

Step-by-step explanation:

X is the horizontal line and Y is the vertical line. :)

The ratios associated to the line segment QR are QP : PR = 1 : 4 and QP : QR = 1 : 5.

In this problem we find a line segment defined by points Q(x, y) = (1, 7) and R(x, y) = (- 9, - 8) and whose partition point is P(x, y) = (- 1, 4), whose ratios must be found. First, find the lengths of line segments QP and PR by Pythagorean theorem:

QP = √[(- 1 - 1)² + (4 - 7)²]

QP = √[(- 2)² + (- 3)²]

QP = √13

PR = √[[- 9 - (- 1)]² + (- 8 - 4)²]

PR = √[(- 8)² + (- 12)²]

PR = 4√13

QR = 5√13

Second, determine the ratios:

QP : PR = √13 : 4√13

QP : PR = 1 : 4

QP : QR = √13 : 5√13

QP : QR = 1 : 5

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The correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction and 4/7 is incorrect answer

The pupil made an error in their addition of 3/5 and 1/2, resulting in an incorrect answer of 4/7.

To solve the task correctly, we need to find a common denominator for 3/5 and 1/2.

The least common multiple of 5 and 2 is 10, so we can rewrite the fractions with a denominator of 10 as follows:

3/5 = 6/10

1/2 = 5/10

Now we can add the fractions:

6/10 + 5/10 = 11/10

Hence, the correct answer to the fraction task is 3/5 + 1/2 = 11/10 expressed as a fraction.

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When t = 0, the value of n is approximately 3.93 million. The estimated number of people who moved to another state in 2005 is approximately 1.68 million. The predicted number of people who moved to another state in 2014 is approximately 6.81 million.

we need to substitute the given values of t (years since 1990) into the equation n = 0.03t² - 0.6t + 3.93. Let's calculate the values accordingly:

a. When t = 0 (which corresponds to the year 1990), we substitute this value into the equation:

n = 0.03(0)² - 0.6(0) + 3.93

n = 0 + 0 + 3.93

n ≈ 3.93

So, when t = 0, the value of n is approximately 3.93 million. In this context, it means that in the year 1990, around 3.93 million people moved to another state.

b. To estimate the number of people who moved to another state in 2005 (t = 2005 - 1990 = 15), we substitute this value into the equation:

n = 0.03(15)² - 0.6(15) + 3.93

n = 0.03(225) - 9 + 3.93

n = 6.75 - 9 + 3.93

n ≈ 1.68

Therefore, the estimated number of people who moved to another state in 2005 is approximately 1.68 million.

c. To predict the number of people who moved to another state in 2014 (t = 2014 - 1990 = 24), we substitute this value into the equation:

n = 0.03(24)² - 0.6(24) + 3.93

n = 0.03(576) - 14.4 + 3.93

n = 17.28 - 14.4 + 3.93

n ≈ 6.81

Hence, the predicted number of people who moved to another state in 2014 is approximately 6.81 million.

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Given two points (7,-2) and (-3,-10), we can determine the slope of the line passing through them as follows:

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

slope = (-10 - (-2)) / (-3 - 7)

slope = -8 / -10

slope = 4 / 5

Since we want a line perpendicular to this line, we need to find its negative reciprocal. The negative reciprocal of 4/5 is -5/4.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the point (-8,-12), we can substitute the values into the equation:

y - (-12) = -5/4(x - (-8))

y + 12 = -5/4(x + 8)

Simplifying, we get:

y + 12 = -5/4x - 10

y = -5/4x - 22

Therefore, the equation of the perpendicular line passing through the point (-8,-12) is y = -5/4x - 22 in point-slope form.

Answer: 4:20 and 13:65

Step-by-step explanation: First one is 4 x 5 and second one you would do 65/5

The earthquake registered 3.6 on the Richter scale.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

R = log(A/0.0001)

The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:

R = log(0.3954/0.0001)

R = 3.6.

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Realized income is NOT part of your budget.

Income that has really been received or generated within a certain period is referred to as realized income. It stands for the money that has been made or acquired through a variety of sources, including work, investments, or commercial ventures.

Realized income is a crucial part of a budget since it shows the actual cash that a person or organization has available for budgeting and financial planning.

The income is what may be used for a variety of costs, savings, investments, or other financial objectives.

In order to appropriately reflect the financial resources available for controlling spending and making financial decisions, realized income is often included as part of a budget.

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The correct probability from the two-way table is given as follows:

B. P(120 lb | 2,000 - 2,500 cal) is different of P(120 lb).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Then the probabilities are given as follows:

Hence statement B is true.

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1. In the short run, the firms in the competitive industry will earn positive profits because the market price is higher than the minimum of the average cost curve. The Option A.

2. If the market price is P4, the individual firm in a competitive industry will earn zero profit. The Option B

3. Firm would be encouraged to enter this market for all price that exceeds P4. The Option D,

When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).

This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.

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The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).

The area of a rectangle is expressed as:

Area = length × width

Given that,  the length of the pen will be 2 feet longer than the width, so the width is x feet and the length can be expressed as (x + 2) feet.

Using area of rectangle:

Area = length × width

1680 = (x + 2) × x

Simplify

1680 = x² + 2x

x² + 2x - 1680 = 0

Solve for x:

Using factoring

(x + 42)(x - 40) = 0

Hence:

x + 42 = 0 or x - 40 = 0

x = -42 or x = 40

Since we are dealing with dimensions, we use the positive value:

The valid solution is x = 40.

This represents the width of the horse pen.

The length can be found by adding 2 to the width:

Length = x + 2

Plug in x = 40

= 40 + 2

= 42

Therefore, the length is 42 feets.

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Factor of x ^2+7x−18 is (x−2)(x+9).

We have,

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

so, we have,

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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complete question:

Factor completely x² - 7x + 18.

Prime

(x-9)(x-2)

(x-9)(x+2)

(x + 9)(x+2)

Answer:

1,000 - 50x > 600

-50x > -400

$0.00 < x < $8.00

Answer:

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2

Answer:

90Y + 36

Step-by-step explanation:

just multiply the length by the width.

9 X (8y + 4 + 2y)

= 9 X (10y + 4)

= 90Y + 36

The unknown angle measure is 70 degrees.

We are given that;

The values 40° 70° 110° 180°

Now,

One possible equation to find the unknown angle measure is:

180 - 40 - 70 = ?

This equation is based on the fact that the sum of the angles in a triangle is 180 degrees. To solve for ?, we can subtract 40 and 70 from both sides of the equation:

180 - 40 - 70 = ? - 40 - 70 180 - 110 = ? 70 = ?

The solution is ? = 70 degrees.

Therefore, by equation the answer will be 70 degrees.

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The probability of just thunder is 0.196.

We have,

The probability of rain P(A) = 1/2

The probability of thunder and raining P(A ∩ B) = 1/3

The probability of rain and thunder P(A U B) = 11/30

Now,

Using the addition rule of probability.

P(A U B) = P(A) + P(B) - P(A∩B)

Substituting.

11/30 = 1/2 + P(B) - 1/3

11/30 - 1/2 + 1/3 = P(B)

P(B) = 0.196

The probability of just thunder is 0.196.

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The volume of small solid is 24 cm³ and volume of big solid is 216 cm³.

Given that

Height of small solid = 4 cm = h₁

Width of small solid = 2 cm = w₁

Length of small solid = 3 cm = L₁

Width of big solid = 6 cm = w₂

Let,

Height of small solid = h₂

Length of small solid = L₂

Since we know that volume of solid  = length x width x height

Therefore,  volume of small solid = 4x2x3 = 24 cm³

Since both the solids are similar,

So,

⇒ w₁/w₂ = h₁/h₂

⇒     2/6 = 4/h₂

⇒     h₂ = 12 cm

Also,

w₁/w₂ = L₁/L₂

⇒2/6 = 3/L₂

⇒    L₂= 9 cm

Hence , the volume of big box = 6x12x9

                                                   = 216 cm³

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