Makayla leans a 18 foot ladder aginst a wall so that it forms and angle of 64 degrees with the ground. what the horizontal distance between the base of the ladder and the wall

The reference angle of 13π/8 is 3π/8 and the sketch of the angle is attached

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

Angle = 13π/8

Rewrite as

θ = 13π/8

The above angle is in the fourth quadrant

So, we subtract it from 2π to calculate the reference angle

Using the above as a guide, we have the following:

Reference angle = 2π - 13π/8

Evaluate the difference

Reference angle = 3π/8

Hence, the reference angle is 3π/8 and the sketch of the angle is added as an attachment

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The size of angle EAD is 40°.

To find the size of angle EAD, we can use the information given in the diagram and apply some basic trigonometry principles. Let's go step by step.

First, we notice that triangle CDB is a right triangle since angle CDB is given as 90°. We also know that angle DCB is 40°. This means that angle CBD can be found by subtracting 40° from 90°:

angle CBD = 90° - 40° = 50°.

Since E is the midpoint of DB, we can conclude that angle CBE is also 50°, as it is vertically opposite to angle CBD.

Now, let's consider triangle ADE. We know that angle EAD is the angle we're trying to find. We can use the fact that the angles in a triangle add up to 180° to write the equation:

angle EAD + angle ADE + angle DEA = 180°.

Since E is the midpoint of DB, we can conclude that angle ADE is equal to angle CDE. Angle DEA is equal to angle CEA. Therefore, we can rewrite the equation as:

angle EAD + angle CDE + angle CEA = 180°.

We can substitute the values we know: angle CDE is 90° (since it's a right angle), and angle CEA is 50° (since it's vertically opposite to angle CEB).

angle EAD + 90° + 50° = 180°.

Simplifying the equation:

angle EAD = 180° - 90° - 50° = 40°.

Therefore, the size of angle EAD is 40°.

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If the events A and B are mutually exclusive, meaning they cannot occur simultaneously, then the probability of both events occurring together is zero. In this case, the formula simplifies to P(A or B) = P(A) + P(B).

The probability that either event A or event B will occur can be calculated using the addition rule of probability. According to this rule, the probability of either event A or event B occurring is equal to the sum of the individual probabilities of each event minus the probability of both events occurring together.

In other words, P(A or B) = P(A) + P(B) - P(A and B)



However, if the events A and B are not mutually exclusive, then the probability of both events occurring together needs to be subtracted from the sum of their individual probabilities to avoid double-counting.

So, the final answer to the question "What is the probability that either event will occur?" depends on the specific probabilities of events A and B and whether they are mutually exclusive or not.

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The values of the distance are;

1. 4. 49 feet

2. 7. 73 feet

We need to know the trigonometric identities and their ratios. We have;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Now, substitute the values, we have;

1. Adjacent = d

Hypotenuse = 12

Angle = 68 degrees

cos 68 = adjacent/hypotenuse

cos 68 = d/12

cross multiply the values, we get;

d = 4. 49 feet

2.

cos 25 = 7/x

cross multiply the values, we have;

x = 7/0. 9063

divide the values, we get;

x = 7. 73 feet

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The possible trigonometric ratios for the angle θ are given as follows:

A. [tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

B. [tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex] and [tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

The sine for the angle θ is given as follows:

sin(θ) = 2/3.

The identity relating the sine and the cosine is given as follows:

sin²(θ) + cos²(θ) = 1.

Hence the cosine of the angle is given as follows:

cos²(θ) = 1 - 4/9

cos²(θ) = 5/9

[tex]\cos{\theta} = \pm \frac{\sqrt{5}}{3}[/tex]

The tangent is given by the division of the sine by the cosine, hence it is calculated as follows:

[tex]\tan{\theta} = \frac{2}{\sqrt{5}}[/tex]

(if the cosine is negative, the tangent is then negative, as the sine is positive).

The secant is the division of one by the cosine, that is, it is the inverse fraction of the cosine, hence:

[tex]\sec{\theta} = \frac{3}{\sqrt{5}}[/tex]

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Answer:

y = (1)(1.004)^^(84)

y ≈ 1.610

Therefore, the balance of the investment account after 7 years, assuming an initial principal of 1 dollar, is approximately 1.610 dollars.

Answer:

  A.  440°, -280°

  B.  17π/6, -7π/6

Step-by-step explanation:

You want angles coterminal with the given angle, one with a positive sign, and one with a negative sign.

Adding an integer multiple of 360° = 2π radians to any angle will give the measure of a coterminal angle.

A positive coterminal angle is ...

  80° +360° = 440°

A negative coterminal angle is ...

  80° -360° = -280°

A positive coterminal angle is ...

  5π/6 +2π = 17π/6

A negative coterminal angle is ...

  5π/6 -2π = -7π/6

__

Additional comment

We have used the smallest multiples of 1 full rotation around the origin. You could choose others. For example, adding 3600° to the first angle will give 3680° as a positive angle coterminal with 80°.

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(a) The inverse variation equation that relates to x and y is  y = -20/x.

(b) The value of y when x = 25 is -0.8 or -4/5

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

(a) To write the inverse variation equation that relates to x and y, we look for the constant k connecting x and y

From the questiuon,

To remove the proprotionality/Variation sign, we introduce a constant k

Given:

Substitute into equation 1 and solve for k

Hence, the equation is y = -20/x.

(b) To find the value of y when x = 25, we subtitute into the equation

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a)

The cost per unit decreasing by 0.00001 for production levels above 12,000.

Given,

From the graph it is clear that the graph passes through the points (12000,0.85) and (38000,0.59).

Now,

If a line passes through two points then the slope of the line is

m = y2 - y1 / x2 - x1

The rate of change in cost per unit for production levels above 12,000 is

m = 0.59 - 0.85 / 38000 - 12000

m = -0.00001

Here negative sign represents the decreasing rate. It means the cost per unit decreasing by 0.00001 for production levels above 12,000.

b)

The function for the domain over [12000, 38000] is :

y = -0.00001x + 0.97

The point slope form of a linear function is,

(y-y1) = m (x - x1)

m = slope.

The slope of the line over [12000, 38000] is -0.00001 and the point is (12000,0.85). So, the function for the domain over [12000, 38000] is

y-0.85 = -0.00001(x-12000)

y =  -0.00001x + 0.97

c)

The cost per unit at the production level of 19,000 is 0.78.

Substitute x=19000 in the above equation, to find the cost per unit at the production level of 19,000.

y = -0.00001(19000) + 0.97

y = 0.78

Thus the cost per unit at the production level of 19,000 is 0.78.

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[tex]x-9z^5+4z+11+2z^5+14=-5z^5-3z+25\\x=2z^5-7z[/tex]

Therefore, it's [tex]2z^5-7z[/tex].

10-10=69.420!!!!!!!!!!

The perimeter of the polygon which is a triangle is

72 units

The perimeter of the polygon is solved using the knowledge of tangents

This is applied as follows

perimeter of the triangle = GH + HL + GJ

GH = (4 + 32 - 15) = 21

HL = 15 + 4 = 19

GJ = 32

plugging in the values we have

perimeter of the triangle = 21 + 19 + 32

perimeter of the triangle = 72 units

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Answer:

9:30

Step-by-step explanation:

The shortest tour from A to B to C and back to A is 50 km.

We have,

A to Zoo and Port and back to A: 10 km

B to Park and Zoo and back to B: 12 km

C to Port and Park and back to C: 13 km

Zoo to Park and Port and back to Zoo: 15 km

To calculate the shortest tour from A to B to C and back to A, we can add up the distances between each pair of stations:

A to Zoo and Port and back to A (10 km)

Zoo to Park and Port and back to Zoo (15 km)

B to Park and Zoo and back to B (12 km)

C to Port and Park and back to C (13 km)

So, Total distance: 10 + 15 + 12 + 13 = 50 km

Therefore, the shortest tour from A to B to C and back to A is 50 km.

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Answer:60

Step-by-step explanation: because I Maltiply 6 by 6 times

no it dose not

your right whats the question

From the graph, we can calculate that 6 seconds after the ball is thrown, it will be 20 meters from the ground again.

The equation is as follows:

d = d0 + v0 * t - (1/2) * g * t²

d =  distance from the ground

d0 = the initial height

v0 =  initial velocity

g  =  acceleration due to gravity = 9.8 m/s²

t=  time

20 = 20 + 15 * t - (1/2) * 9.8 * t^2

We simplify as follows:

0 = -4.9 * t² + 15 * t

We then go ahead to solve  this quadratic equation to find the values of t when the ball is 20 meters from the ground again.

t * (-4.9t + 15) = 0

t = 0 or

-4.9t + 15 = 0.

-4.9t + 15 = 0

-4.9t = -15

t = 3.06 seconds

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The equation of the graph is,

⇒ y = 6x + 2

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

For each by sitting job. Adam charges a fee for his bus fare plus an hourly rate.

And, The graph shows how he calculates the cost of a babysitting job.

Now, By graph;

Two points on the line are (1, 8) and (2, 14).

Now,

Since, The equation of line passes through the points (1, 8) and (2, 14).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (14 - 8)) / (2 - 1)

m = 6 / 1

m = 6

Thus, The equation of line with slope 6 is,

⇒ y - 8 = 6 (x - 1)

⇒ y - 8 = 6x - 6

⇒ y = 6x + 2

Therefore, The equation of line will be;

⇒ y = 6x + 2

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The function [tex]f(x) = \sqrt[3]{2x-1}[/tex] is a cubic root function with a linear transformation applied.

The expression inside the root, 2x-1, is a linear function that scales and shifts the input x. The cubic root function then takes the cube root of the result.

This function is defined for all real numbers x, as the cubic root can be calculated for any real number.

Its graph is a transformed version of the standard cubic root function, skewed and shifted depending on the coefficients in the linear function. The function increases monotonically as x increases, and it is continuous and differentiable everywhere.

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The Complete Question

[tex] f(x)=\sqrt[3]{2x-1}[/tex]

Identify this function and solve

the answer is of the inequality is x>8

The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Line AB is congruent to line CD , proved.

The proof that line AB is congruent to line CD is determined as follows;

If line AB ≅ CD, then will have the following to be true;

Let angle A = x

The value of angle C will be equal to x (alternate angles are equal)

Let angle B = y

The value of angle D will be equal to y (alternate angles are equal)

Let angle m∠AEB = z

The value of m∠DEC will be equal to z (vertical opposite angles are equal).

So line AB is congruent to line CD , proved.

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Ethical guidelines are established to help professional psychologists maintain Professional behavior.

Professional behavior refers to the conduct and standards expected of psychologists in their professional practice. Ethical guidelines provide a framework that outlines the principles, values, and standards that psychologists should follow in their interactions with clients, colleagues, and the broader community.

These guidelines promote ethical behavior by setting expectations for confidentiality, informed consent, competence, integrity, and avoiding conflicts of interest, among other aspects. They ensure that psychologists prioritize the well-being and rights of their clients, maintain professional boundaries, and uphold ethical standards in research and practice.

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The area of the decagon is 3077.68 square meters

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

A decagon with a side of 20 meters

This means that

a = 20

The area of the decagon is then calculated as

A = 2.5a² * √(5 + 2√5)

substitute the known values in the above equation, so, we have the following representation

A = 2.5 * 20² * √(5 + 2√5)

Evaluate

A = 3077.68

Hence, the area of the decagon is 3077.68 square meters

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Complete question

A decagon with a side of 20 meters. What is the area?

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

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Answer: 0

Step-by-step explanation:

To solve the equation (x² + 3x)³ - 16(x² + 3x) - 36 = 0 using substitution, let's make a substitution:

Let u = x² + 3x.

Now, we can rewrite the equation in terms of u:

u³ - 16u - 36 = 0.

Let's solve this equation for u by factoring:

(u - 6)(u² + 6u + 6) = 0.

Now, we have two possible cases:

Case 1: u - 6 = 0.

This gives us u = 6.

Case 2: u² + 6u + 6 = 0.

To solve this quadratic equation, we can use the quadratic formula:

u = (-b ± √(b² - 4ac)) / (2a),

where a = 1, b = 6, and c = 6.

Plugging in these values, we get:

u = (-6 ± √(6² - 4(1)(6))) / (2(1)),

u = (-6 ± √(36 - 24)) / 2,

u = (-6 ± √12) / 2,

u = (-6 ± 2√3) / 2,

u = -3 ± √3.

Now that we have the possible values of u, let's substitute back to find the corresponding values of x:

Case 1: u = 6.

Since u = x² + 3x, we have x² + 3x = 6.

Rearranging, we get x² + 3x - 6 = 0.

Hope it helps!

Answer:

[tex]\frac{3}{4}[/tex] or 75%

Step-by-step explanation:

There are 8 equal-sized sections, 6 being blue. 6/8 = 3/4 = 0.75 which is 75%. That is the probability that the spinner lands on blue.

The value of all the expression which have x = 5 asymptotes are,

⇒ g (x) = 3 log (x - 5)

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ f (x) = (3x + 20) / (x - 5)

We have to given that,

All the expressions are,

⇒ g (x) = 3 log (x - 5)

⇒ f (x) = √(x - 5) + 2

⇒ h (x)= eˣ⁻⁵

⇒ g (x) = log₁₀ (- x + 5) -  4

⇒ h (x) = - ∛(x - 5) + 1

⇒ f (x) = (3x + 20) / (x - 5)

Now, We can check all the expressions for which have x = 5 asymptotes.

Hence, We can substitute x = 5 in each expression and check all expression as which are not defined at x = 5,

⇒ g (x) = 3 log (x - 5)

Substitute x = 5;

⇒ g (x) = 3 log (5 - 5)

⇒ g (x) = 3 log (0)

Which is undefined.

⇒ f (x) = √(x - 5) + 2

Substitute x = 5;

⇒ f (x) = √(5 - 5) + 2

⇒ f (x) = 2

Which is defined.

⇒ h (x)= eˣ⁻⁵

Substitute x = 5;

⇒ h (x)= e⁻⁵

Which is defined.

⇒ g (x) = log₁₀ (- x + 5) -  4

Substitute x = 5;

⇒ g (x) = log₁₀ (- 5 + 5) -  4

⇒ g (x) = log₁₀ (0) -  4

Which is undefined.

⇒ h (x) = - ∛(x - 5) + 1

Substitute x = 5;

⇒ h (x) = - ∛(5 - 5) + 1

⇒ h (x) =  1

Which is defined.

⇒ f (x) = (3x + 20) / (x - 5)

Substitute x = 5;

⇒ f (x) = (3x + 20) / (5 - 5)

⇒ f (x) = (15 + 20) / (0)

Which is undefined.

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Answer: D) 5217

Step 1: Start by finding the three numbers that Julian got from cutting the sheet of paper.

Step 2: We can split the number into three sections: 502, 197, and 2970.

Step 3: Add the three numbers: 502 + 197 + 2970 = 3669

Step 4: The smallest sum Julian can get is 3669 and the answer is D) 5217.

The correct statement is that "Line p must be drawn in plane B."

If a new line, p, is drawn parallel to line /, the statement that is true is "Line p must be drawn in plane B."

To understand this, let's analyze the given information:

Planes A and B are shown.

Line m is shown in plane A.

Line n is shown in plane B.

Line / is the line that connects planes A and B.

When a new line, p, is drawn parallel to line /, it means that line p will also connect planes A and B. However, since line / itself is connecting planes A and B, line p must also lie in plane B to maintain its parallel relationship with line /. This is because parallel lines lie in the same plane.

This ensures that line p remains parallel to line / and maintains its connection between planes A and B.

It is important to note that line p being drawn in plane B does not necessarily imply that it intersects with line n. It simply means that line p lies within plane B and remains parallel to line /.

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The smallest subset containing 7.83 among the common subsets is Q.

We are given that;

The number 7.83

Now,

Subset of a given set is a set whose all elements are in the original set of which it is subset.

So if B is subset of A, then all elements of B are in A but it is not necessary that all elements of A are in B.

If B is subset of A, then A is superset of B.

The smallest subset containing the value 7.83 is the set of rational numbers. A rational number is a number that can be written as a fraction of two integers, such as 7.83 = 783/100. The set of rational numbers is denoted by Q and it is a subset of the set of real numbers R.

Therefore, by subsets the answer will be Q.

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