A 52 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jevonte grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 45 ft.) Round to the nearest tenth of a foot

Answers

Answer 1

The ladder will reach up the side of the house to a height of approximately 47.1 feet.

We can use the Pythagorean theorem to solve this problem. Let x be the distance between the base of the ladder and the house after Jevonte pulls the ladder 3 feet farther from the house. Then, we have a right triangle with legs x and 48 feet, and hypotenuse 52 feet (the length of the ladder).

Using the Pythagorean theorem, we have:

x² + 48² = 52²

Simplifying, we get:

x² + 2304 = 2704

x² = 400

x = 20

Therefore, Jevonte pulls the ladder 3 feet farther from the house, so the ladder is now 23 feet away from the house. The ladder will reach up the side of the house to a height of:

√(52² - 23²) = 47.1 feet (rounded to the nearest tenth)

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Related Questions

Select all the correct answers.
If the measure of angle is which statements are true?
sin (0) = -
The measure of the reference angle is 30°.
cos (0) = √3
The measure of the reference angle is 45°.
tan (0) = -√3
The measure of the reference angle is 60°.

Answers

The measures of the trigonometric relations and reference angles are solved

Given data ,

Let the measure of the angle be θ = 2π/3

Now , from the trigonometric relation ,

The tangent of the function tan ( 2π/3 ) = -√3

And , the reference angle of the θ = 2π/3  is given by A = π/3

So , A = 60°

Hence , the reference angle is 60°

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Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

Answers

Answer:

x=9km

Step-by-step explanation:

Pythagorean Theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

The hypotenuse is [tex]c^{2}[/tex], so the equation will be

[tex]12^{2}[/tex] + [tex]b^{2}[/tex] = [tex]15^{2}[/tex]

Evaluating the equation gives us

144 + [tex]b^\\{2}[/tex] = 225

Subtract 144 from each side to have [tex]b^{2}[/tex] alone

[tex]b^{2}[/tex] = 81
square root on each side to get rid of the exponent

[tex]\sqrt{b^2[/tex] = [tex]\sqrt{81}\\[/tex]

[tex]\sqrt{b^2[/tex]'s square root is b and          [tex]\sqrt{81[/tex]'s is 9,-9, giving us b=±9

As distance cannot be negative, x = 9km

find the standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5)

Answers

Answer:

Step-by-step explanation:

To find the equation of a circle given three non-collinear points, we can use the following steps:

Find the equations of the perpendicular bisectors of the line segments connecting the pairs of points.

Find the intersection point of the two perpendicular bisectors. This point is the center of the circle.

Find the distance between the center and any one of the three points. This distance is the radius of the circle.

Let's apply these steps to the given points:

Find the midpoint and slope of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18+(-7))/2, (-5+(-16))/2) = (-12.5, -10.5)

Slope of (-18, -5) and (-7, -16): (-16 - (-5))/(-7 - (-18)) = -11/11 = -1

Midpoint of (-18, -5) and (4, -5): ((-18+4)/2, (-5+(-5))/2) = (-7, -5)

Slope of (-18, -5) and (4, -5): (-5 - (-5))/(4 - (-18)) = 0

Midpoint of (-7, -16) and (4, -5): ((-7+4)/2, (-16+(-5))/2) = (-1.5, -10.5)

Slope of (-7, -16) and (4, -5): (-5 - (-16))/(4 - (-7)) = 11/11 = 1

The equations of the perpendicular bisectors passing through the midpoints are:

x + 12.5 = -1(y + 10.5) or x + y + 23 = 0

y + 5 = 0

Find the intersection point of the two perpendicular bisectors:

Solving the system of equations:

x + y + 23 = 0

y + 5 = 0

yields: x = -18, y = -5

So, the center of the circle is (-18, -5).

Find the distance between the center and any one of the three points:

Using the distance formula:

Distance between (-18, -5) and (-18, -5): sqrt(((-18)-(-18))^2 + ((-5)-(-5))^2) = 0

Distance between (-18, -5) and (-7, -16): sqrt(((-18)-(-7))^2 + ((-5)-(-16))^2) = sqrt(221)

Distance between (-18, -5) and (4, -5): sqrt(((-18)-4)^2 + ((-5)-(-5))^2) = 22

The radius of the circle is sqrt(221).

Therefore, the equation of the circle in standard form is:

(x + 18)^2 + (y + 5)^2 = 221

The standard equation of a circle with the points (-18;-5), (-7;-16) and (4;-5) is:

(x + 13)² + (y + 1)² = 41

Standard equation of a circle

From the question, we are to determine the standard equation of a circle with the given points

The given points are:

(-18;-5), (-7;-16) and (4;-5)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle

and r is the radius.

Using the given points (-18, -5), (-7, -16), and (4, -5), we can find the equation of the circle as follows:

Find the midpoint of the line segments connecting the pairs of points:

Midpoint of (-18, -5) and (-7, -16): ((-18 + -7)/2, (-5 + -16)/2) = (-12.5, -10.5)

Midpoint of (-7, -16) and (4, -5): ((-7 + 4)/2, (-16 + -5)/2) = (-1.5, -10.5)

Midpoint of (-18, -5) and (4, -5): ((-18 + 4)/2, (-5 + -5)/2) = (-7, -5)

Find the equations of the perpendicular bisectors of the line segments:

Perpendicular bisector of the line connecting (-18, -5) and (-7, -16):

Slope of the line: (−16 + 5)/(-7 + 18) = -11/5

Slope of the perpendicular bisector: 5/11

Midpoint: (-12.5, -10.5)

Equation: y + 10.5 = (5/11)(x + 12.5)

Perpendicular bisector of the line connecting (-7, -16) and (4, -5):

Slope of the line: (-5 + 16)/(4 + 7) = 11/7

Slope of the perpendicular bisector: -7/11

Midpoint: (-1.5, -10.5)

Equation: y + 10.5 = (-7/11)(x + 1.5)

Perpendicular bisector of the line connecting (-18, -5) and (4, -5):

Slope of the line: 0

Slope of the perpendicular bisector: undefined (perpendicular bisector is a vertical line)

Midpoint: (-7, -5)

Equation: x + 7 = 0

Find the point of intersection of any two perpendicular bisectors:

Intersection of perpendicular bisectors 1 and 2:

y + 10.5 = (5/11)(x + 12.5)

y + 10.5 = (-7/11)(x + 1.5)

Solving for x and y, we get:

x = -13

y = -1

Thus,

The center of the circle is (-13, -1).

Find the radius of the circle:

Using the center (-13, -1) and one of the given points, say (-18, -5):

r² = (-18 - (-13))² + (-5 - (-1))²

r² = 25 + 16

r² = 41

Hence, the equation of the circle is:

(x + 13)² + (y + 1)² = 41.

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Find the missing side lengths. Leave your answers as radicals in simplest form. I need help quickly!

Answers

Answer:

[tex]m = \dfrac{4}{\sqrt{3}} \text{ or, in rational form: } m = \dfrac{4\sqrt{3}}{3}[/tex]

[tex]n = \dfrac{2}{\sqrt{3}} \text{ or, in rational form: } n = \dfrac{2\sqrt{3}}{3}[/tex]

Not sure which form your teacher wants the answers, would suggest putting in both

Step-by-step explanation:

The missing angle of the triangle = 180 - (60 + 90) = 30°

We will use the law of sines to find m and n

The law of sines states that the ratio of each side to the sine of the opposite angle is the same for all sides and angles

Therefore since m is the side opposite 90° and 2 is the side opposite 60°,

[tex]\dfrac{m}{\sin 90} = \dfrac{2}{\sin 60}}\\\\[/tex]

sin 90 = 1

sin 60 = √3/2

So
[tex]\dfrac{m}{1} = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2}{\sqrt{3}/2} \\\\m = \dfrac{2 \cdot 2}{\sqrt{3}} \\\\m = \dfrac{4}{\sqrt{3}}\\\\[/tex]

We can rationalize the denominator by multiplying numerator and denominator by √3 to get
[tex]m = \dfrac{4\sqrt{3}}{3}[/tex]
(I am not sure what your teacher wants, you can put both expressions, they are the same)

To find n
Using the law of sines we get
[tex]\dfrac{n}{\sin 30} = \dfrac{m}{\sin 90}\\\\\dfrac{n}{\sin 30} = m\\\\\dfrac{n}{\sin 30} = \dfrac{4}{\sqrt{3}}\\\\[/tex]

sin 30 = 1/2 giving

[tex]\dfrac{n}{1/2} = \dfrac{4}{\sqrt{3}}\\\\n = \dfrac{1/2 \cdot 4}{\sqrt{3}} \\\\n = \dfrac{2}{\sqrt{3}}[/tex]

In rationalized form
[tex]n = \dfrac{2\sqrt{3}}{3}}[/tex]

Help me with this question please

Answers

Answer:

A line that is perpendicular to another is one that has a slope that is the multiplicative reciprocal of the original funtion's slope and it also has the opposite sign in front. Considering a slope with a value of [tex]\dfrac{1}{7}[/tex], the reciprocal multiplicative is 7, because is a number that equals 1 if multiplied by the original value. Then, we change the sign for it, making it -7.

Thus, correct answer is a. -7.

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State the dimensions of each matrix.
[3 -4 -9]
[2 -7 0]

Answers

Answer:

2 x 3 matrix

Step-by-step explanation:

Helppppppp pleaseee





The loudness of sound in decibels perceived by the human ear depends on the intensity levels according to


D=10log(I/lo)


Find the decibel level when I is 63, 096 times Io.


The decibel is -------------- dB when I is 63, 096 times Io.


Round your answer to the nearest whole number.

Answers

Answer:

We can use the given formula to calculate the decibel level D when the intensity level I is 63,096 times Io:

D = 10log(I/lo)

Where Io is the reference intensity level and is typically taken to be the threshold of hearing, which is 10^−12 watts/m^2.

So, substituting the values, we get:

D = 10log(63,096*Io/Io) = 10log(63,096)

Using a calculator, we find:

D ≈ 47.1 dB

Rounding this to the nearest whole number, we get:

The decibel level is 47 dB when I is 63,096 times Io.

I hope this helps mate.

what is equilivent to 28/2

Answers

Answer:

14

Step-by-step explanation:

28/2 is equivalent to 14. This is because when you divide a number by 2, you are essentially cutting it in half. So, 28/2 is the same as cutting 28 into two equal parts, which is 14.

Answer:

28

2

looks like a fraction but it is actually the whole number 14.

There is an infinity number of equivalent fractions to 28

2

.

To find an equivalent fraction to 28

2

, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By dividing the original fraction by 2, we get:

28 ÷ 2

2 ÷ 2

= 14

1

By multiplying the original fraction by 2, we get:

28 × 2

2 × 2

= 56

4

Here is the full list of equivalent fractions to 28

2

.

14

1

, 28

2

, 42

3

, 56

4

, 70

5

, 84

6

, 98

7

, 112

8

, 126

9

, 140

10

, 154

11

, 168

12

, 182

13

, 196

14

, 210

15

, 224

16

, 238

17

, 252

18

, 266

19

, 280

20

...

4cos45°-2sin45°. Please let me know the answer with thorough steps.

Answers

We know that cos(45) = sin(45) = √2/2.

Substituting these values, we can simplify the expression as follows:

4cos(45) - 2sin(45)

= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)

= 2√2 - √2

= √2

Therefore, the answer is √2.

Las ecuaciones de la demanda y la oferta de cierto producto están dadas por espacio 4 q al cuadrado más p al cuadrado igual 1405 y p igual q más 10 donde p está en dólares por unidad y q está en unidades. Para un precio de 27 dólares por unidad, determine el gasto real del consumidor.

Answers

The actual consumer spending at a price of $27 per unit is $268.26.

How to calculate the price

Substitute the given price into the supply equation to get the corresponding quantity supplied:

p = q + 10

27 = q + 10

q = 17

Substitute q = 17 into the demand equation to get the corresponding price:

4q² + p² = 1405

4(17)² + p² = 1405

p² = 1405 - 1156

p² = 249

p = 15.78

The actual consumer spending can be calculated by multiplying the quantity demanded by the price:

Actual consumer spending = quantity demanded x price per unit

= 17 x 15.78

= $268.26

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The demand and supply equations for a certain product are given by space 4 q squared plus p squared equals 1405 and p equals q plus 10 where p is in dollars per unit and q is in units. For a price of $27 per unit, determine the actual consumer spending.

find cooordinates of point of interection

11x-6y=2
-8x+5y=3

Answers

Answer:

To find the coordinates of the point of intersection of the given equations, we need to solve the system of equations simultaneously. We can use the elimination method to do this:

11x - 6y = 2 (multiply both sides by 5)

-8x + 5y = 3 (multiply both sides by 11)

55x - 30y = 10

-88x + 55y = 33

Adding the two equations, we get:

-33x + 25y = 43

Solving for y, we get:

y = (33x + 43)/25

Substituting this expression for y into either of the original equations and simplifying, we get:

x = -1/7

Substituting this value of x into the equation for y, we get:

y = 1/35

Therefore, the coordinates of the point of intersection are (-1/7, 1/35).

How many yards are in 150 in.

Answers

The answer

4.16666667 yards

Find an angle in each quadrant with a common reference angle with 285°, from 0°≤θ<360

Answers

The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°

Understanding Quadrant

A common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.

For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.

Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:

First Quadrant: An angle in the first quadrant with a reference angle of 15° is 15° itself.Second Quadrant: An angle in the second quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180°. Therefore, an angle in the second quadrant with a common reference angle with 285° is 180° - 15° = 165°.Third Quadrant: An angle in the third quadrant with a reference angle of 15° can be found by subtracting the reference angle from 180° and then adding 180°. Therefore, an angle in the third quadrant with a common reference angle with 285° is 180° + 15° = 195°.Fourth Quadrant: An angle in the fourth quadrant with a reference angle of 15° can be found by subtracting the reference angle from 360°. Therefore, an angle in the fourth quadrant with a common reference angle with 285° is 360° - 15° = 345°.

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determine whether the sample may be biased. a company randomly selects 500 customers from its computer database and then surveys those customers to find out how they like their service.

Answers

Answer:

Step-by-step explanation:

Based on the information given, it is not possible to determine whether the sample may be biased or not.

However, there is a possibility that the sample may be biased if the company's computer database does not accurately represent its entire customer base. For example, if the database contains only a specific type of customers, such as those who frequently make large purchases, then the sample may not be representative of the company's entire customer base. In this case, the survey results may not accurately reflect the opinions of all the company's customers.

It is also important to consider other factors such as how the survey was conducted and how the questions were framed, as these can also affect the validity of the survey results

Based on the information provided, the sample may be biased. The reason being, the company has selected customers from its computer database which means that only those customers who have interacted with the company and have their data available in the database will be surveyed. This means that the company is not taking into account the customers who may have had a bad experience and did not interact with the company again, or customers who do not use digital platforms to interact with the company. These customers may have different opinions about the company's service and their exclusion from the sample can result in a biased sample.

Find the probability that
event A or B takes place.


Answers

Probability that event A or B takes place is, P(A or B) = 16/21.

Here from the Venn diagram we can obtain that,

Probability of occurring event A = 2/21 + 4/21 = (2 + 4)/21 = 6/21

Probability of occurring event B = 10/21 + 4/21 = (10 + 4)/21 = 14/21

Probability of occurring event A and event B both = 4/21

So, P(A) = 6/21

P(B) = 14/21

P(A and B) = 4/21

We know that the union of events formula,  

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 6/21 + 14/21 - 4/21

P(A or B) = (6 + 14 - 4)/21

P(A or B) = 16/21

Hence the value of P(A or B) = 16/21.

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Use words to describe the relationship between the number of miles and each corresponding number of gallons.


10 gallons 300 miles.

Answers

The unit rate that relates the two quantities of distance and volume of gas is:

U = 30 miles per gallon.

How to describe this relation?

To do so, we can find the unit rate.

This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.

Here we have the values:

10 gallons and 300 miles.

Then the unit rate is the quotient between these:

300miles/10 gallons = 30 miles per gallon

This says that with one gallon of gas you can travel 30 miles.

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Find a polynomial f(x) of degree 5 that has the following zeros.
0, 1 (multiplicity 2), -6, -3
Leave your answer in factored form.

Answers

This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

How to solve

A polynomial f(x) of degree 5 with the given zeros can be represented in factored form as:

f(x) = [tex]A(x - 0)(x - 1)^2(x + 6)(x + 3)[/tex]

Since the leading coefficient is not specified, we can leave A as a constant factor. Simplifying the expression, we have:

f(x) = [tex]A(x)(x - 1)^2(x + 6)(x + 3)[/tex]

This polynomial has zeros at 0, 1 (with multiplicity 2), -6, and -3, as required, and is of degree 5.

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A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.

What is the surface area of the prism?

Answers

Answer:

The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width and h is the height.

In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of 2(7) (3.6) + 2(7) (2.4) + 2(3.6) (2.4), which simplifies to 50.4 + 33.6 + 17.28, or 101.28 square centimeters.

So, the surface area of this rectangular prism is 101.28 square centimeters.

Received message. The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is `2lw + 2lh + 2wh`, where `l` is the length, `w` is the width and `h` is the height. In this case, the length is 7 cm, the width is 3 and three-fifths cm (or 3.6 cm), and the height is 2 and two-fifths cm (or 2.4 cm). Plugging these values into the formula gives us a surface area of `2(7)(3.6) + 2(7)(2.4) + 2(3.6)(2.4)`, which simplifies to `50.4 + 33.6 + 17.28`, or **101.28 square centimeters**. So, the surface area of this rectangular prism is **101.28 square centimeters**.

Step-by-step explanation:

e) Write a proof to show AABC ~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.

Answers

Answer:

Step-by-step explanation:

no

Trigonometry homework help

Answers

A. The distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

B. She is walking towards the north, the heading is N 1° 20' W.

C. Acreage = 7.55 acres (rounded to 3 decimal places).

How did we get these values?

A. Convert the angles to decimal degrees:

N. 27° 40′ E. = 27.667°

N. 56° 31′ E. = 56.517°

S. 4° 26′ W. = -4.433°

Now, calculate the distances between the points:

AB = √(696.2917² + 3.5² - 2*696.2917*3.5*cos(27.667°)) = 696.2227 ft

BC = √(487.9792² + 11.75² - 2*487.9792*11.75*cos(56.517°)) = 487.9385 ft

CD = √(1691.125² + 1.5² - 2*1691.125*1.5*cos(-4.433°)) = 1691.1415 ft

B. Finding the distance from D back to A, calculate the distance and angle between AD:

AD = √(AB² + BD² - 2*AB*BD*cos(θ)) where θ = 180° - 4°26' - 27°40' = 147.9°

Substituting AB and BD:

AD = √(696.2227² + 1691.1415² - 2*696.2227*1691.1415*cos(147.9°)) = 1912.3246 ft

Therefore, the distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

C. Finding the heading she walks from D back to A, calculate the angle between AD and the north-south axis:

θ' = atan((AB*sin(27.667°) - BD*sin(θ))/AD) = atan((696.2227*sin(27.667°) - 1691.1415*sin(147.9°))/1912.3246)

θ' = -1.344°

Since she is walking towards the north, the heading is N 1° 20' W.

Lastly, to calculate the acreage of this plot of land, we use Heron's formula to determine the area of triangle ABC:

s = (AB + BC + AC)/2 = (696.2227 + 487.9385 + 1392.625)/2 = 788.8931 ft

A = √(s(s-AB)(s-BC)(s-AC)) = 328756.0207 ft²

Convert to acres:

Acreage = 328756.0207/43560 = 7.55 acres (rounded to 3 decimal places).

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Help please i would appreciated it


here is the picture is about Row Ops

Answers

The matrix operation add -4(row 1) to row 3 is[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

Evaluating the matrix expression

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

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right][/tex]

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

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

[tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

Hence, the result of the matrix expression is [tex]\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right][/tex]

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Can yall help me with this

Answers

Answer:

x = 67

Step-by-step explanation:

The two triangles are identail.

Answer:

x = 67

because 67 and x the same

If the points A,B and C have the coordinates A (5,2), B (2,-3) and C (-8,3) show that the triangle ABC is a right angled triangle.

Answers

Answer:

Step-by-step explanation:

To show that the triangle ABC is a right-angled triangle, we need to prove that one of the angles of the triangle is a right angle, which means it measures 90 degrees.

We can use the Pythagorean theorem to check if the sides of the triangle satisfy the condition for a right-angled triangle. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's find the length of each side of the triangle:

AB = √[(5-2)² + (2-(-3))²] = √(3²+5²) = √34

BC = √[(2-(-8))² + (-3-3)²] = √(10²+6²) = √136

CA = √[(5-(-8))² + (2-3)²] = √(13²+1²) = √170

Now, let's check if the Pythagorean theorem is satisfied:

AC² = AB² + BC²

170 = 34 + 136

Since the Pythagorean theorem is satisfied, we can conclude that the triangle ABC is a right-angled triangle, with the right angle at vertex B.

We know that,

the distance between two points=√(x2-x1)²+(y2-y1)²

∴ The distance between points A and B, AB=√(2-5)²+(-3-2)²

                                                                         =√(9+25)

                                                                         = √(34)

∴ The length of side AB = √(34)

Again,

The distance between points B and C, BC= √[(-8-2)²+{3-(-3)}²]

                                                                      = √(100+36)

                                                                      = √136

∴ The length of side BC =√136

Also,

The distance between points A and D, AC= √(-8-5)²+(3-2)²

                                                                      = √(169+1)

                                                                      = √170

∴ The length of side AC=√170

Now, we get three sides of the triangle as AB = √(34), BC = √136, and AC=√170

Since AC is the longest side, we take it as hypotenuse, and the other sides as base and height in the Pythagoras theorem,

AC²=170

BC²=136

AB²=34

Clearly, 170=136+34

or, AC²=AB²+BC²

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11. The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.

Answers

Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

tan(18°) = h/510

h = 510tan(18°) = 165.7 feet

Answer:

Construction Model Stats

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Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?

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To find the mean, we add up all the values and divide by the number of values:

Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10

Mean = 36.7 / 10

Mean = 3.67

To find the median, we need to put the values in order:

2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4

The middle number is the median, which is 3.35 in this case.

To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.

To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:

2.5, 2.6, 2.8, 3.1, 3.2

The median of this lower half is 2.8, so Q1 = 2.8.

To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:

3.7, 3.8, 4.1, 9.4

The median of this upper half is 3.95, so Q3 = 3.95.

To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1

IQR = 3.95 - 2.8

IQR = 1.15

1.5 times the IQR is 1.5 * 1.15 = 1.725.

The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.

We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:

tan(18 degrees) = h / d

Solving for h, we get:

h = d * tan(18 degrees)

Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:

h = 510 feet * tan(18 degrees)

h ≈ 157.3 feet

Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.

Help with math problems

Answers

Answer:

Step-by-step explanation:

15.) [tex]\sqrt{12}[/tex]

      [tex]\sqrt{4}[/tex] * [tex]\sqrt{3}[/tex]

      Answer: 2[tex]\sqrt{3}[/tex]

17.) Distribute 3[tex]\sqrt{3}[/tex] into both sides of the parentheses

     3[tex]\sqrt{3}[/tex] * 4 = 12[tex]\sqrt{3}[/tex]

     3[tex]\sqrt{3}[/tex] * -3[tex]\sqrt{5}[/tex] = -9[tex]\sqrt{15}[/tex]

     Answer: 12[tex]\sqrt{3}[/tex] - 9[tex]\sqrt{15}[/tex]

19.) Distribute 4[tex]\sqrt{15}[/tex] into both sides of the parentheses

      4[tex]\sqrt{90}[/tex] + 4[tex]\sqrt{75}[/tex]

      4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex] + 4*[tex]\sqrt{25}[/tex]*[tex]\sqrt{3}[/tex]

      4*3*[tex]\sqrt{10}[/tex] + 4*5*[tex]\sqrt{3}[/tex]

      12[tex]\sqrt{10}[/tex] + 20[tex]\sqrt{3}[/tex]

21.) Distribute [tex]\sqrt{15}[/tex] into both sides of the parentheses

      2[tex]\sqrt{150}[/tex] - 4[tex]\sqrt{90}[/tex]

      2*[tex]\sqrt{25}[/tex]*[tex]\sqrt{6}[/tex] - 4*[tex]\sqrt{9}[/tex]*[tex]\sqrt{10}[/tex]

      2*5*[tex]\sqrt{6}[/tex] - 4*3*[tex]\sqrt{10}[/tex]

      10[tex]\sqrt{6}[/tex] - 12[tex]\sqrt{10}[/tex]

What is the surface area of a triangular prism

Answers

Answer:

surface area=bh+2ls+lb

Step-by-step explanation:

If you think it is too long to remember, just find the area of each of the shapes on it and add them together.

Hope this helps :)

Toby throws a coin 2 times.
The outcome of each throw is either Heads (H) or Tails (T).
List all the possible outcomes of the 2 throws.
Use the letters H and T in your listing (eg. HH, ...).

Answers

Answer:

HH

HT

TH

TT

Step-by-step explanation:

Answer:

TT, TH, HT, HH

Step-by-step explanation:

Find F(7)…………………………………………

Answers

Based on the given function conditions of f(x) , the value of f(7) is equal to -6

To find f(7), we need to determine which function definition to use based on the value of x.

Since x = 7 is greater than 5, we know that we'll be using the third definition of the function: f(x) = -x + 1 for 2 < x ≤ 5.

Therefore, we can substitute x = 7 into the third definition of the function:

f(7) = -7 + 1 = -6

So, f(7) = -6.

In summary, to find f(7), we identified which function definition to use based on the value of x. Since x = 7 is greater than 5, we used the third definition of the function, f(x) = -x + 1 for 2 < x ≤ 5, and found that f(7) = -6.

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Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why.

Answers

We can use trigonometric relations or Pythagorean's theorem, we will see that x = 8ft.

How to find the value of x?

We can see that x is the hypotenuse of the triangle, and we know the length of one leg and the angle between them, then we can use the cosine trigonometric relation:

cos(60°) = 4ft/x

solving for x:

x = 4ft/cos(60°) = 8ft

Other way to find x is first find the other side and then use the pyhtagorean theorem, to get the other side y we need:

tan(60°) = y/4ft

y = 4ft*tan(60°)

Then using Pythagorean's theorem we get:

x = √( (4ft)² + (4ft*tan(60°))²)

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Can anyone help with this part of my geometry notes ?

Answers

From the interior angle theorem:

m∠1 = ¹/₂(m∠AD + m∠BC)m∠2 = 180 - m∠1m∠AED = 77°m∠AEB = 103°m∠LK = 50°

What is the interior angle theorem?

The Interior Angle Theorem states that if two secants or chords intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.

Considering the given circles:

m∠AED = ¹/₂(45 + 109)

m∠AED = 77°

m∠AEB = 180 - 77

m∠AEB = 103°

m∠LK = (2 * 62) - 74)

m∠LK = 50°

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