A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With the level ground for a secure footing. Find, to the nearest inch, how far the base of the latter should be from the side of the building and how far up the side of the building the latter will reach.

Answers

Answer 1

Answer:

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

Step-by-step explanation:

Please refer to the figure attached in the answer area.

A right angled triangle [tex]\triangle ABC[/tex] is formed by the ladder with the building where hypotenuse is the length of ladder.

Hypotenuse, AC = 10 foot

Also, we are given that angle made by the base of ladder with the ground is [tex]72^\circ[/tex].

We have to find AB and BC.

[tex]\angle BAC = 72^\circ[/tex]

Using trigonometric functions:

[tex]cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\$\approx$ 3.1 foot\\$\approx$ 37.2 inches[/tex]

[tex]sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\$\approx$ 9.5 foot\\$\approx$ 114 inches[/tex]

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

A 10-foot Ladder Is To Be Placed Against The Side Of The Building. The Base Of The Latter Must Be Placed

Related Questions

Use the distance formula to write an equation of the parabola with focus F(0, -13) and directrix y=13

y=?

(FINALEXAM)

Answers

Answer:

-1/52 x^2

Step-by-step explanation:

4p(y-k)=(x-h)^2

4(-13)y=x^2

-52y=x^2

y=-1/52 x^2

The area of a square is 196 square meters. What is
the length (in meters) of one side of the square?

Answers

Answer:

14 meters

Step-by-step explanation:

A square must have all equal sides, meaning the square root of 196 would be the length and width of the square, the square root of 196 is 14.

Which number is equal to 10 Superscript 4?
40
1,000
10,000
40,000

Answers

Answer: The answer is 10,000

Step-by-step explanation:

10^4 is equal to 10,000

10^4 to the second power means that you have too add 4 zeros to the end of the number.

Since 10 already has a 0, you would add 3 more.

Therefore, the answer would be 10,000.

(Your Welcome)

Answer:

10^4 is equal to 10,000

10^4 to the second power means that you have too add 4 zeros to the end of the number.

Since 10 already has a 0, you would add 3 more.

Therefore, the answer would be 10,000.

Determine the value of
X in the diagram below. Justify your reasoning.

Answers

Answer:

x = 70°

Step-by-step explanation:

Sum of external angles of polygon = 360

x + 150 + 140 = 360

x + 290 = 360

x = 360 - 290

x = 70°

Please help! I will give you brainliest !

Answers

Answer:

70 and 21

Step-by-step explanation:

6parts of the ratio represents 84 students

Divide 84 by 6 to find the value of one part of the ratio

84 ÷ 6 = 14 ← value of 1 part of the ratio, thus

5 parts = 5 × 14 = 70 ← number of Michigan students

Indiana students = 175 - (84 + 70 ) = 175 - 154 = 21

If the probability of a chance event is 0.67, it is less likely to happen
than which of the following probabilities of another chance event?
Select one:

0.76

0.61

0.65

0

Answers

Answer:

.76

Step-by-step explanation:

Solve.
-6x^2 - 2 - 3x=-8
a)x=5+√57÷16
b)x=-4+√34÷3
c)x=-7+3√41÷16
d)x=1+√17÷-4​

Answers

Answer:

So the d) is right.

Step-by-step explanation:

we have:

-6x^2 - 2 - 3x=-8

6x^2 + 3x - 6 =0

The delta = 3^2 -4*6*(-6) = 9 + 144 = 153= 9*17

These 2 solutions are:

[tex]x_{1} =\frac{-3+3\sqrt{17} }{2*6} = \frac{-3+3\sqrt{17} }{12} =\frac{-1+\sqrt{17} }{4} \\x_{2} =\frac{-3-3\sqrt{17} }{2*6} = \frac{-3-3\sqrt{17} }{12} =\frac{-1-\sqrt{17} }{4}[/tex]

So the d) is right.

Find the radius of the sphere with the given volume 36πin^3

Answers

The answer is 3 inches

Answer:

3 in.

Step-by-step explanation:

Complete section for 18 points.

Answers

Answer:

2,3,4,6, and 8

Step-by-step explanation:

2 is divisible by 24 because it is a multiple of 24

3 is divisible by 24 because it is a multiple of 24

4 is divisible by 24 because it is a multiple of 24

6 is divisible by 24 because it is a multiple of 24

8 is divisible by 24 because it is a multiple of 24

i am not sure about the explain.

i suck at explaining things

Test each of the following to see if it is divisible by 2,3,4,5,6,8,9,10, or 25 and say why.

1)24

Answers:

Divisible by 2: yes, because it is an even number. The even numbers are those which end in 0, 2, 4, 6, or 8. Result: 24/2 = 12

Divisible by 3: yes, because the sum of its digits is a multiple of 3: 2 + 4 = 6 is a multiple of 3. Result: 24/3 = 8

Divisible by 4: yes, result: 24/4 = 6

Divisible by 5: no, because a number is divisible by 5 if it ends in 0 or 5.

Divisible by 6: yes, because it is divisible by 2 and by 3, then it is divisible by 6. Result: 24/6 = 4.

Divisible by 8: yes, result: 24/8 = 3

Divisible by 9: no, because the sum of its digits is not a multiple of 9.

Divisible by 10: no, because a number is divisible by 10 if it ends in 0.

Divisible by 25: no, because 25 is a number greater than 24.

Spymore

what is the equation of the line passing through ( -5, -3 ) and perpendicular
to the line representing the equation y = - 5/7x + 2?

Answers

Answer:

y = 7/5x + 4

Step-by-step explanation:

use the slope from the equation -5/7 and take the negative reciprocal to get the perpendicular slope = 7/5. Then use the equation y=mx+b. Plug in x and y from the point given and the new slope and solve for b.

(-3) = (7/5)(-5) + b, (-3) = -7 + b, add 7 to both sides. b = 4. Rewrite the equation now to be y = 7/5x + 4

In a Normal Distribution. What percentage of the values lie below the Mean?
100%
75%
25%
50%

Answers

Answer:

50%

Step-by-step explanation:

The mean ideally should be in the exact middle

Which of the following shows the correct simplification assuming the denominator is not equal to zero?

Answers

Answer:

[tex]=\frac{3x+2}{x\left(x+1\right)}[/tex]

or

[tex]\frac{(3x+2)}{x^2+x}[/tex]

Step-by-step explanation:

[tex]\frac{2}{x}+\frac{1}{x+1}\\\mathrm{Least\:Common\:Multiplier\:of\:}x,\:x+1:\quad x\left(x+1\right)\\Adjust\:Fractions\:based\:on\:the\:LCM\\Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:x\left(x+1\right)\\\mathrm{For}\:\frac{2}{x}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x+1\\\frac{2}{x}=\frac{2\left(x+1\right)}{x\left(x+1\right)}\\[/tex]

[tex]\mathrm{For}\:\frac{1}{x+1}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:x\\\frac{1}{x+1}=\frac{1\cdot \:x}{\left(x+1\right)x}=\frac{x}{x\left(x+1\right)}\\=\frac{2\left(x+1\right)}{x\left(x+1\right)}+\frac{x}{x\left(x+1\right)}\\\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2\left(x+1\right)+x}{x\left(x+1\right)}\\[/tex]

[tex]\mathrm{Expand}\:2\left(x+1\right)+x:\quad 3x+2\\2\left(x+1\right)+x\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=2,\:b=x,\:c=1\\=2x+2\cdot \:1\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:1=2\\=2x+2\\\mathrm{Simplify}\:2x+2+x:\quad 3x+2\\2x+2+x\\\mathrm{Group\:like\:terms}\\=2x+x+2\\\\mathrm{Add\:similar\:elements:}\:2x+x=3x\\=3x+2\\=\frac{3x+2}{x\left(x+1\right)}[/tex]

Will mark brainliest!

Answers

Answer:

48

Step-by-step explanation:

6*8 = 48

I've seen you so "Will mark brainliest," many times today. Do not export people if that is what you're doing.

Answer:

Your answer is 48 sq. ft.

Step-by-step explanation:

Why? Because A= L(W) Therefore, A= 8(6)=48

Divide and answer in simplest form: 4/5 ÷ 2

Answers

Answer:

2/5

Step-by-step explanation:

4/5*1/2=4/10=2/5

Answer:

0.4 or [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

First convert 4/5 into a decimal of 0.8

Then divide 0.8 by 2 which gives you 0.4 or [tex]\frac{2}{5}[/tex]

Which three-dimensional figures have lateral faces that are polygons? Check all that apply. cones cylinders hemispheres prisms pyramids spheres

Answers

Answer:

Prisms

Pyramids

Step-by-step explanation:

Lateral faces of a pyramid are triangles (3 sided polygon)

Lateral faces of prisms are rectangles (4 sides polygon)

Answer:

Cylinders, Prisms, Pyramids

Step-by-step explanation:

Hope this helps

Brainliest if correct pls

Given the exponential equation y=34(5)x, what is the y-intercept (or starting point) of the graph?

Answers

Answer:

34

Step-by-step explanation:

Given

y = 34[tex](5)^{x}[/tex]

To find the y- intercept let x = 0, that is

y = 34[tex](5)^{0}[/tex] = 34 × 1 = 34 ← y- intercept

Yes the answer is 34 because if you

Which theorem or postulate could be used to prove the congruence of the triangles?

Answers

Answer:

Yes! There's the Side-Angle -Side postulate, or SAS. This states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Step-by-step explanation:

The postulate used to prove the congruence of the triangles is ASA.

Option B is the correct answer.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Two right triangles.

∠90° = ∠90°

side = side (given)

Angle = Angle (given)

By ASA (angle side angle)

The triangles are congruent.

Thus,

The postulate is ASA.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ2

BRAINLIEST!!
3. Describe the shape of the data distribution.

Answers

Answer: postitive skewed

this is correct

Yes it is the third one for This question

W varies inversely as the square of t. If W = 12 when t = 2,

find t when W = 27.

A. 27t = 24

B. 27t2 = 48

C. 108 = 12t

D. 12t = 54

Answers

Answer:

B

Step-by-step explanation:

Given W varies inversely as t² then the equation relating them is

W = [tex]\frac{k}{t^2}[/tex] ← k is the constant of variation

To find k use the condition W = 12 when t = 2, thus

12 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )

k = 48

W = [tex]\frac{48}{t^2}[/tex] ← equation of variation

When W = 27, then

27 = [tex]\frac{48}{t^2}[/tex] ( multiply both sides by t² )

27t² = 48 → B

B)  27 t² = 48 will be the algebraic equation for t if W = 27.

What is proportionality?

In arithmetic, proportional or proportional meaning denotes equivalence between two ratios. In the equation a/b = c/d, a and b have the same percentage as c and d. A percentage is primarily established for solving a word problem using one of its four unknown quantities.

Given W varies inversely proportional to t² then the algebraic equation relating them is

W =  k / t² is the constant of variation

for k we can use the condition W = 12 when t = 2,Hence,

12 =  k / 2²

k = 48

When W = 27, then

27 = 48 / t²  ( multiply by t² )

Therefore, t in the form of algebraic equation is 27 t² = 48 Hence, option B is correct.

Learn more about proportionality here:

https://brainly.com/question/14508634

#SPJ5

three-fourths the square of a number

Answers

Answer:

i think it is D i am sorry if it is wrong

Step-by-step explanation:

Mrs. Smith has $20,000 to invest. She wants to earn $10,000 in interest. She is considering a savingsand loans bank that is offering her 5.6% interest per year. For how long will she have to leave her money in the bank in order to reach her goal of $10,000?

Answers

Answer:

Number of year to get $10,000 as interest = 7.5 year (Approx)

Step-by-step explanation:

Given:

Initial investment = $20,000

Interest on investment = $10,000

Rate of interest = 5.6% = 0.056

Find:

Number of year to get $10,000 as interest:

Computation:

[tex]Interest\ on\ investment = Initial\ investment[(1+r)^n-1]\\\\10,000 = 20,000[(1+0.056)-1]\\\\0.5=(1.056)^n-1\\\\1.5 =(1.056)^n\\\\n=7.44[/tex]

Number of year to get $10,000 as interest = 7.44

Number of year to get $10,000 as interest = 7.5 year (Approx)

At the end of the school year a school system has a table with the total absences and tardies in its 10 schools what is the best way to display these data?

A. Bar Graph
B.Circle Graph
C. Stem and leaf plot
D.Ogive graph

Answers

Answer:

A

Step-by-step explanation:

This graph shows a proportional relationship. (2/3, 3/4)


What is the constant of proportionality?

Answers

Answer: Hi! I'd love to help you but I'd need to see the graph.

Step-by-step explanation: Can you add a picture?

a rectangular field has side lengths that measure 9/10 mile and 1/2 mile what is the area of the field

Answers

Answer:

[tex]\frac{9}{20}miles^2=0.45miles^2[/tex]

Step-by-step explanation:

To find the area of a rectangle:

[tex]a=l*w[/tex]

where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

In this case:

length: [tex]l=\frac{9}{10}miles[/tex]

width: [tex]w=\frac{1}{2} miles[/tex]

thus, we multiply this quantities to find the area:

[tex]a=(\frac{9}{10} miles)(\frac{1}{2}miles )\\\\a=\frac{9*1}{10*2}miles^2\\ \\a=\frac{9}{20}miles^2[/tex]

the area of this rectangle is 9/20 miles squared, or what is the same 0.45 miles squared

Iris had invited 105 people to her party. She needs 7 large tables to have an equal number of people at each table. Which equation shows how many people will sit at each table

Answers

Answer:

105/7= 15 people will seat at each table.

Step-by-step explanation:

It's quadratic, linear or exponential?​

Answers

Looks exponential to me

The probability of not choosing a black shirt is...? please explain!

Answers

Answer:

80% or 8/10.

Step-by-step explanation:

Assuming the shirts in the bottom right are the "black" shirts, there is ten total shirts (1 red, 4 blue, 2 green, 1 white,  2 black.) Out of the ten shirts, 8 are not black. This means that there is an 80% chance that you will select a shirt that is NOT black.

The probability of not choosing a black shirt is 8/10. Because there is 10 shirts and 8 are not black.

Which of these are NOT expressions?
Check all that are true.

123

9 + 3 = 12

3(4x + 5)

6 − 5 − 4 = z

3z + 2x


HELP

Answers

Answer:

6-5-4=z

9+3=12

Step-by-step explanation:

Expressions has no equal sign

“9 + 3 = 12” and “3(4x + 5)”

HELP ME QUICK PLZ WITH THIS MATH PROBLEM!!!!!!!!!!!!!!

Answers

Answer:

I believe it’s 1/2

Step-by-step explanation:

Take a point on the graph and use rise over run method

Answer:

D. 5/8 pounds

Step-by-step explanation:

You can find the slope by picking a point such as (8,5).

Slope = rise over run.

(8,5) is 8 units right and 5 units up, thus the slope is 5/8

Hope this helps.

top side is 6 just couldn’t fit in picture

Answers

Answer: [tex]6<z<18[/tex]

Step-by-step explanation:

Use the pythagorean theorem to find z first.

[tex]c^2=a^2+b^2\\c=\sqrt{a^2+b^2}[/tex]

a = 12

b = 6

c = z

[tex]c=\sqrt{(12)^2+(6)^2}\\ c=\sqrt{144+36}\\ c=\sqrt{180} \\c=13.4[/tex]

z is greater than a and b

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