5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4

The length of the extension ladder that is against the outside wall of the house is 22.58 feet.

What is the length of the ladder?

The ladder forms a right triangle when it is placed up against a home. The hypotenuse of a ladder is its length. The base of the ladder is where the distance from the house to the base begins. The length is the distance from the home.

Here, we have

Given: An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77

To find the length of the ladder, Sin would be used:

Sin = opposite / hypotenuse

Sin77 = 22 / h

h = 22 / 0.9743 = 22.58 feet

Hence, the length of the extension ladder that is against the outside wall of the house is 22.58 feet.

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Answer:

yES

Step-by-step explanation:

The approximate diameter of the sphere is 29.3 cm, the correct option is C.

To find the approximate diameter of the sphere, we can use the formula for the volume of a sphere and solve for the diameter.

The following equation determines a sphere's volume:

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

where r is the sphere's radius and V is its volume.

We are given the volume of the sphere as 3600 cubic centimeters. If we use this value as a substitute in the formula, we get:

3600 = [tex]\frac{4}{3} \pi r^{3}[/tex]

Multiplying both sides by [tex]\frac{3}{4}\pi[/tex], we get:

r³ = ([tex]\frac{3}{4}\pi[/tex]) × 3600

r³ = 8100

If you take the cube-root of both sides, you get:

r = [tex]8100^{1/3}[/tex]

r ≈ 14.6 cm

So, the radius of the sphere is approximately 14.6 cm.

The sphere's diameter is twice its radius. Therefore, the approximate diameter of the sphere is:

d = 2r

d= = 2 × 14.6

d ≈ 29.3 cm

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The complete question is:

The volume of a sphere is 3600 cubic centimeters. What is the approximate diameter of this sphere?

Volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

A) 9.5 cm

B) 19 cm

C) 29.3 cm

D) 14.6 cm

Hence, equation of parabola is  option b, y = -2(x + 3)² - 2

A parabola is a U-shaped curve that is created by graphing a quadratic function.

It is a type of conic section, which is formed when a plane intersects a cone.

The general equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants.

The value of the parameter a determines the shape and orientation of the parabola. If a > 0, the parabola opens upwards and has a minimum point. If a < 0, the parabola opens downwards and has a maximum point.

The equation of parabola is:-

y = a(x - h)² + k

hence applying value in given equation-

y = -2(x - (-3))² - 2

y = -2(x + 3)² - 2

hence option b y = -2(x + 3)² - 2 is the correct answer.

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The complete question is :-

Hence, equation of parabola is  option b, y = -2(x + 3)² - 2

A quadratic function graphed as a U-shaped curve is called a parabola.

It is a particular kind of conic section that is created when a plane crosses a cone.

Y = ax² + bx + c is the general equation of a parabola, where a, b, and c are constants.

The parabola's shape and orientation depend on the value of the parameter a. The parabola has an upward opening and a minimum point if a > 0. The parabola has a maximum point and opens downward if a 0.

The equation of parabola is:-

y = a(x - h)² + k

hence applying value in given equation-

y = -2(x - (-3))² - 2

y = -2(x + 3)² - 2

hence option b y = -2(x + 3)² - 2 is the correct answer.

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complete question is:

The triangle proportionality theorem indicates that Maria and Juan properly divides the plot of land

The triangle proportionality theorem which is known as Thales Theorem states that the segment drawn joining two of the sides of a triangle and parallel to the third side divides the other two sides proportionately.

The parallel lines with which Maria and Juan uses to divide the 300 feet long side into six sides of the same length, indicates that length of each division on the Shady Lane is 50 feet, therefore, the length of each division on the Oak Creek will also be the same.

The slope of the the divisions on Maria's Plan is steeper than the slopes on the division on Juan's Plan such that the length of each division on Oak Lane is longer for Juan, than for Maria.

However, the triangle proportionality theorem, and the width of each division on Shady Lane indicates that the width of each division is 50 feet.

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Triangle DEF as shown ion figure D(-4, 6), E(2,6), F(0,8) translate by a factor of 1/2, So the new vertex are: D' (-2, 3), E' (1, 3), F' (0, 4)

Triangle is commonly represented by a graph in which the three points are labeled as A, B, and C, and the three line segments are labeled as AB, AC, and BC. The graph of a triangle typically looks like below figure.

The new coordinates of each vertex of the triangle after scaling by 1/2.

For vertex D:

x-coordinate = -4, y-coordinate = 6

New x-coordinate = (1/2) × (-4) = -2

New y-coordinate = (1/2) × 6 = 3

So the new coordinates for D' are (-2, 3)

For vertex E:

E (2, 6) ⇒ 1/2 × (2, 6) ⇒ (1, 3)

So the new coordinates for E' are (1, 3)

For vertex F:

F (0, 8) ⇒ 1/2 × (0, 8) ⇒ (0, 4)

So the new coordinates for F' are (0, 4)

D(-4, 6), E(2,6), F(0,8)  ⇒   D' (-2, 3), E' (1, 3), F' (0, 4)

Finally, plot the new points on the same coordinate plane and connect them to form the new triangle. You should see that the new triangle is a smaller version of the original triangle, with all sides and angles scaled down by a factor of 1/2.

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The equation of its axis of symmetry is x = 4.

What is axis of symmetry?

The axis of symmetry is a line that divides a symmetrical object or shape into two mirror-image halves. In mathematics, the axis of symmetry is often used in the context of graphs of equations, particularly quadratic equations

The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the parabola.

If a quadratic equation has zeros at x = 3 and x = 5, then its factored form is:

(x - 3)(x - 5) = 0

Expanding this expression, we get:

x^{2} - 8x + 15 = 0

This is the standard form of a quadratic equation: ax^{2} + bx + c = 0, where a = 1, b = -8, and c = 15.

To find the x-coordinate of the vertex of the parabola, we can use the formula:

x = -b/2a

Substituting the values of a and b, we get:

x = -(-8)/(2*1) = 4

Therefore, the axis of symmetry is a vertical line passing through x = 4. The equation of this line is simply:

x = 4

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Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?

A "verb" is defined as "a word or group of words that express an action (such as eat), an event (such as happen), or a state (such as exist)" in the Oxford Learners' Dictionary. A verb is defined as "a word or phrase that describes an action, condition, or experience" by the Cambridge Dictionary.

Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?

Note: The verb "arrive" is in the Present Simple tense because it is a general statement about buses arriving at the same time. The verb "is" is in the Present Simple tense because it is a general question about the probability. The verb "come" is in the Present Simple tense because it is a general question about the first bus. The verb "is" could also be in the Present Continuous tense, i.e., "Will the first bus be from the north?" depending on the context and intended meaning. However, in this case, both Present Simple and Present Continuous are grammatically correct. The correct tense to use depends on the specific context and meaning intended. Please provide more context or clarify if you have a specific intended meaning or scenario in mind. I'll be happy to help you further.

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From the calculation, we have the total area of the figure as shown to be 86 cm^2.

The area of a triangle is the amount of space that is enclosed within the three sides of a triangle. It can be calculated using the formula:

A = 1/2 * b * h

where A is the area of the triangle, b is the length of the base of the triangle, and h is the height of the triangle, which is the perpendicular distance from the base to the opposite vertex.

We know that;

Tan 45 = h/10

h = 10 cm

Then;

Tan 30 = 10/10 + x

0.58 = 10/10 + x

0.58(10 + x) = 10

5.8 + 0.58x = 10

x = 7.2 cm

Thus;

The area of the first triangle = 1/2 * 10 * 10

= 50 cm^2

The area of the second triangle = 1/2 * 7.2 * 10

= 36cm^2

Total area = 86 cm^2

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Answer:

Two

Step-by-step explanation:

Trangles are labled n named alphabetically therefore on the bigger triangle D comes first than E and E comes forsr than R wich means that itvis triangle DER not any ather way around.

On the second triangle A comes first than N and N comes first then T thetefore it is triangle ANT

Answer:

Option A is the correct answer

Triangle RED IS SIMILAR TO TRIANGLE TAN

Answer:

A

Step-by-step explanation:

I added a photo of my notes (the angles I've marked as equal are cross angles)

[tex]w = 180° - 30° - x°[/tex]

[tex]w = 150° - x°[/tex]

The cost of Veronica's supper was $11.92, plus an additional 8% tax of $0.954 and a 15% gratuity on top of tax of $2.0681, for a total price of $14.94.

We first need to figure out the tax and tip amounts and add them to the initial cost to get the final price of Veronica's dinner.

Let's first figure out the tax amount. The cost of the meal is multiplied by the 8% tax rate to determine the tax:

Tax = 11.92 * 0.08 = 0.954

Hence, the meal's tax is $0.954.

Next, let's figure out how much to tip. We multiply the price of the meal plus the tax by the 15% tip percentage to determine the tip:

Tip = (11.92 + 0.954) x 0.15 = 2.0681

Thus, $2.0681 is the total tip for the lunch, tax included.

The original price of the meal, the tax, and the tip can now be added to determine the final price:

Total Cost: 11.92 plus 0.9544 plus 2.0681

Veronica's total bill, rounded to the nearest cent, is therefore $14.94.

In conclusion, Veronica's dinner cost $11.92, plus an additional 8% tax of $0.954 and a 15% tip on top of the meal plus tax of $2.0681, for a total of $14.94.

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Answer:

-57

Step-by-step explanation:

matrix multiplication

Step-by-step explanation:

[tex] \frac{ \frac{1}{7} }{ \frac{2}{5} } = \frac{1}{7} \times \frac{5}{2 } = \frac{5}{14} \\ [/tex]

Answer: 5/14

Step-by-step explanation:

It would help if you used the KCF (Keep, Change, Flip) method. First, you write 1/7 as a fraction, then change the division sign to a multiplication sign, and flip the fraction 2/5 to 5/2. Then multiply 1/7 by 5/2 to get 5/14.

This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.

This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.

However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.

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Answer:

To calculate the amount in the IRA at retirement, we can use the formula for the future value of an annuity:

S = PMT * (((1 + r)^n - 1) / r)

Where:

PMT = the monthly payment (in dollars)

r = the monthly interest rate (APR/12)

n = the number of months (45 years * 12 months/year)

Substituting the given values, we get:

PMT = $50

r = 0.06/12 = 0.005

n = 45 * 12 = 540

S = $50 * (((1 + 0.005)^540 - 1) / 0.005) = $204,055.57

So the IRA will contain $204,055.57 at retirement.

The total deposits made over the time period is:

Total deposits = 540 * $50 = $27,000

Therefore, the amount in the IRA at retirement ($204,055.57) is significantly higher than the total deposits made over the time period ($27,000). This demonstrates the power of compound interest over a long time horizon

Step-by-step explanation:

If u have other qstns too, feel free to ask me on my sn ap

the side CD will be 27 units.

What is parallelogram?

A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.

Here CD=AB

2x+13=5x-8

3x = 13+8

x= 21/3

x=7

CD= 2*7+13=14+13=27

Hence the side CD will be 27 units.

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We can conclude by answering the provided question that We get a equation sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5

An equation in mathematics is a declaration that states the equivalence of two expressions. An equation is made up of two parts that are separated by a mathematical equation (=). For example, the argument "2x + 3 = 9" asserts that the sentence "2x + 3" equals the number "9." The objective of equation solution is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more variables. The variable x is elevated to the second degree in the equation "x2 + 2x - 3 = 0." Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

To calculate the sample number required for this poll, use the following formula:

[tex]n=(Z^{2} *P*Q/E^{2}[/tex]

[tex]n=(1.645^{2} *0.5*0.5)/0.015^{2} a578.98[/tex]

We get a sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5 percentage points of the actual population percentage, we would need to poll at least 579 randomly chosen air passengers.

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By looking at the 0 and 1 column, 200 people own less than two smartphones

The coordinate of the figure after translation and reflection is A"(-12, 2), B"(-8, 6) and C'(-7, 13)

To translate the points A(12, -7), B(8, -3), and C(-7, 4) 9 units up, we simply add 9 to the y-coordinate of each point. The new coordinates of the translated points are:

A'(12, 2)

B'(8, 6)

C'(-7, 13)

To reflect the translated points across the y-axis, we simply negate the x-coordinate of each point. The final coordinates of the reflected and translated points are:

A"(-12, 2)

B"(-8, 6)

C'(-7, 13)

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Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots.

A division sentence is a mathematical sentence that expresses the relationships between numbers, when the operation of division is being applied.

The total number of spikes Bella has is 4 packs x 20 spikes per pack = 80 spikes. She wants to put the same number of spikes on each of the 8 Beetlebots. Let's call the number of spikes she puts on each Beetlebot "x".

The division sentence that represents this situation is:

80 spikes ÷ 8 Beetlebots = x spikes per Beetlebot

Simplifying this division sentence, we get:

10 spikes per Beetlebot = x spikes per Beetlebot

Therefore, Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots and wants to distribute the spikes evenly.

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Answer:

68°

Step-by-step explanation:

because the inscribed angle (at B) is half of the arc angle (at A).

angle B = 1/2 × angle A

34 = 1/2 × angle A

angle A = 34×2 = 68°

The value of n = 12, and the area of the trapezium can be written as 12√12.

Let's call the diameter of the circle (and one of the parallel sides of the trapezium) "AB", and let's call the non-parallel sides "CD" and "EF". We know that CD and EF are both equal to the radius of the circle, which is 2 units.

We know that AB is a diameter of the circle, which means that its length is twice the radius, or 4 units.

We also know that CD and EF are each 2 units long.

To find the height of the trapezium, we can draw a perpendicular line from point C to line AB:

We can see that the height of the trapezium is the distance from point H to line AB. Since point H is directly above the center of the circle (point O), we can use the Pythagorean theorem to find its distance from point A (or point B, since AB is a diameter):

The length of the hypotenuse (OB) is 2 units (the radius of the circle), and the length of one of the legs (OA) is 2 units (half of AB). To find the length of the other leg (HB), we can use the Pythagorean theorem:

HB^2 + OA^2 = OB^2

HB^2 + 2^2 = 2^2

HB^2 = 0

This tells us that HB (and therefore the height of the trapezium) is 0 units.

Since the height is 0, the area of the trapezium is simply the average of the two parallel sides (AB and CD) multiplied by the distance between them (which is also AB).

Area = (AB + CD) / 2 * AB

= (4 + 2) / 2 * 4

= 3 * 4

= 12

Therefore, n = 12, and the area of the trapezium can be written as 12√12.

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Answer:

Area = 100 units^2

Step-by-step explanation:

This shape is a trapezoid. The area of a trapezoid is:

A = 1/2(Base+Base)•h

What you do is average the bases and times by the height. The only thing is in your picture the bases are the 12 and 8. And the height is the 10.

Area = 1/2(12+8)•10

= 1/2(20)•10

= 10•10

= 100

The area is 100 square units.

Total weight of piece of leaf which both ant carries can be calculated by summing both the weight of leaf is 1.48×10⁻².

what is weight?

In the context of physics and engineering, weight refers to the force with which an object is attracted towards the Earth or any other celestial body due to gravity. The weight of an object is equal to the product of its mass and the acceleration due to gravity.

In the given question,

we need to just add both weight of leaf to get total weight

total weight= weight₁  of leaf +weight₂ of leaf

=1.25×10⁻² +2.3×10⁻³

=1.25×10⁻² +0.23×10⁻²

=1.48×10⁻²

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Answer:

[tex]x = \frac{18}{ \sqrt{2} } = \frac{18 \sqrt{2} }{2} = 9 \sqrt{2} [/tex]

Each leg is 9√2 cm long.

The limits [tex]\lim_{x \to 0 } f(x)[/tex] exists and the function f(x) is continuous at x = 0

Other solutions are shown below

The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

From the graph, we have the domain and the range to be:

From the graph, we have the values of the function to be

f(-4) = 1 and f(-6) = 2

From the graph, we have the values of the limits to be

[tex]\lim_{x \to 4^{-} } f(x) = -2[/tex]

[tex]\lim_{x \to 4^{+} } f(x) = 2[/tex]

Yes, the limit  [tex]\lim_{x \to 0 } f(x)[/tex]

To check if a function is continuous at x=0, you need to check three conditions:

Hence, the function is continuous at x = 0

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The buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.

The builder's Mortgage offer seems attractive, as it significantly reduces the payments for the first two years. However, it's important to consider the long-term implications of this offer.

While the reduced payments may be helpful for buyers who are facing financial constraints in the short-term, they may end up paying more over the life of the loan.

Let's look at the numbers. With the builder's offer, the payments for the first year would be $377.11 per month, and $565.67 per month for the second year. This means that the total payments for the first two years would be $13,165.52. After that, the regular monthly payments of $754.22 would kick in, and the buyer would need to pay this amount for the remaining 23 years of the loan.

If the buyer were to opt for the fully amortizing loan with monthly payments of $754.22 for the entire 25-year term, the total payments over the life of the loan would be $226,266. This includes interest payments of $143,266.

On the other hand, if the buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.

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