A 17-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 10 feet from the base of the building. How high up the wall does the ladder reach?

Answers

Answer 1

Answer:

13.747... meters

Step-by-step explanation:

Refer to image attached~

Let AC represent the length of the ladder.Let BC represent the distance from the base of the ladder from the base of the building.Let AB (x) represent the height of the building.

In this case, the longest side of the triangle formed is AC. Thus, our hypotenuse is AC (17 m).

To determine the height of the building, we need to use pythogoras theorem.

Pythogoras theorem: (Hypotenuse)² = (Side)² + (Side)²

⇒ (17)² = (10)² + (x)²⇒ 289 = 100 + (x)²⇒ 289 - 100 = (x)²⇒ 189 = (x)²

Take square root both sides:

⇒ √189 = √(x)²⇒ x = √189 ≈ 13.747... meters
A 17-foot Ladder Is Placed Against A Vertical Wall Of A Building, With The Bottom Of The Ladder Standing
Answer 2

Answer:

13.75 ft (nearest hundredth)

Step-by-step explanation:

The ladder creates a right triangle with the wall and ground, where:

leg (base) = groundleg (height) = wallhypotenuse = ladder

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

a = 10 ftc = 17 ft

Substitute the given values into the formula and solve for b:

⇒ 10² + b² = 17²

⇒ b² = 17² - 10²

⇒ b² = 289 - 100

⇒ b² = 189

⇒ b = ±√(189)

As distance is positive, b = √(189) ft only

Therefore, the ladder reaches 13.75 ft (nearest hundredth) up the wall.


Related Questions

A small bar of gold measures 20 mm by 250 mm by 2 mm. One cubic millimeter of gold weighs about 0.0005 ounces. Find the volume in cubic millimeters and the weight in ounces of this small bar of gold.

Answers

Answer: v = 40mm * 25mm * 2mm = 2000 mm^3 so, the weight is 2000 mm^3 * .0005oz/1mm^3 = 1oz

Step-by-step explanation:

Based only on the information given in the diagram, it is guaranteed that ABC ~ XYZ.

Answers

Check the picture below.

the club sells 144 cans of lemonade what is the least number of bottles of water that must be sold to cover the cost of rending costumes

Answers

Answer:

A total of 142 units of water bottles must be sold to recover the costs of renting costumes.


Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Find the surface area of the cylinder. Round your answer to the nearest tenth.
6 ft
7 ft

Answers

Answer:

490.1 (If the radius is 6ft and height is 7ft)

571.8 (If the radius is 7ft and height is 6ft)

Step-by-step explanation:

A=2πrh+2πr2

Plug in the value for the radius and height. Then solve.

Jacks bedroom is 14 feet long and 11 feet wide. Annies bedroom is square, with each side measuring 12 feet. Which statement is true?

A. Annie's bedroom is 10 square feet longer than Jack's bedroom
B. Jack's bedroom is 2 square feet longer than Annie's bedroom
C. Annie's bedroom is 2 square feet longer than Jacks bedroom
D. Jack's bedroom is 10 square feet longer than Annie's bedroom

Answers

Answer:

i guess its A.

Step-by-step explanation:

I dont really know

13. If ZA and ZB are supplementary angles and ZA
is three times as large as ZB, find the measures
of ZA and ZB.

Answers

Answer:

A. ZA+ZB =180

B. ZA is 135 and ZB is 45

Step-by-step explanation:

Step-by-step explanation:since ZA and ZB are supplementary

ZA+Zb =180°

But ZA=3ZB

∴ 3ZB+ZB=180° ⇒4ZB=180°

∴ZB =45

What is the area of the composite figure? 262 cm2 264 cm2 266 cm2 268 cm2

Answers

The Area is a two-dimensional scalar quantity. The area of the composite figure is 264 cm².

What is the area?

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that represents its extent. On the two-dimensional surface of a three-dimensional object, the surface area is its counterpart.

The composite figure can be broken down into four parts a square(A), a triangle(B) and two rectangles(C and D).

Now, if the area of the composite figure is taken out it will be,

[tex]\text{Area of composite}=\text{Area of Square A} + \text{Area of triangle B} + \text{Area of Rectangle C} + \text{Area of Rectangle D}\\[/tex]

[tex]\text{Area of Composte}=(10^2)+(\dfrac12 \times 6 \times 4)+(8 \times 4)+(20 \times 6)\\\\\text{Area of Composte}= 100+ 12 + 32 + 120 =264\rm\ cm^2[/tex]

Thus, the area of the composite figure is 264 cm².

Learn more about the Area:

https://brainly.in/question/14759304

Find the area (no explanation needed)

Answers

Area of bottom rectangle:-

2(8)16cm²

Area of rectangle above it:-

6(2)12cm²

Area of rectangle above it

11(2)22cm²

Area of triangle:-

1/2(11)(6)11(3)33cm²

Total:-

12+16+22+3383cm²

Do number 12 pleasee

Answers

Answer:

114

Step-by-step explanation:

25% = 25/100 = 0.25

152 × 0.25 = 38

152 - 38 = 114

Answer:

$114

Step-by-step explanation:

152x0.75 = 114

please help me i need help

Answers

Answer:

Step-by-step explanation:

a c d are the answer


5x – 5 = 7x + 1 what is this question

Answers

Answer:

x = - 3

Step-by-step explanation:

5x - 5 = 7x + 1 ( subtract 7x from both sides )

- 2x - 5 = 1 ( add 5 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer: x = -3

Step-by-step explanation: Here is my explanation...

Step 1: Take away 5x from both sides 5x - 5x - 5 = 7x - 5x + 1.

Step 2: You should then get -5 = 2x + 1, then take away 1 from both sides -5 - 1 = 2x + 1 - 1

Step 3: -6 = 2x, divide 2x on both sides -6/2 = 2x/2

x = -3

Work Check:

5 (-3) - 5 = 7 (-3) + 1

-15 - 5 = -21 + 1

-20 = -20

If the -20 = -20 then this proves that x = -3. I hope this helped!

Q. Find the area 41.5in2 430in2 215in2 1.5in2​

Answers

Answer:

430 in^2

Step-by-step explanation:

Area of parallelogram =    base * height = 20 * 21.5 = 430 in^2

Can someone please help me? :(

Answers

Answer:

Question 1 is statistical.

Question 2 is not statistical

Statistical means there will most likely be different answers, especially when it is being asked to several people. If it is a certain number for the answer it is considered not statistical.

which of the following expressions is equivalent to 7(x+ 3)?

Answers

Answer:

7x+21

Step-by-step explanation:

Answer:

7x + 21

Step-by-step explanation:

Given

7(x + 3)

Solving

Use the Distributive Property ⇒ x(a + b) = xa + xb7(x) + 7(3)7x + 21

Which sentence is true?
A. 4/5 > 3/4
B. 4/5< 3/4
C. 4/5=3/4
D. 3/4> 4/5​

Answers

Answer:

A.

Step-by-step explanation:

4/5 = 0.8

3/4 = 0.75

0.75 < 0.8

What is the multiplication problem that means the same thing as the division problem 1/9 ÷ 12

Answers

Answer:

12 divided by 1/9 is 1/108. In multiplication, its 1/108 * 12

Step-by-step explanation:

Karina solves the system using linear combination and arrives at the equation 116y = 96.28. she then solves this equation for y. which statement explains karina’s solution? the cost of natural gas is $0.17 per unit. the cost of natural gas is $0.20 per unit. the cost of natural gas is $0.72 per unit. the cost of natural gas is $0.83 per unit.

Answers

The correct option is D. The cost of natural gas is $0.83 per unit.

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation

Consider the provided equation.

116y=96.28

We need to solve the above equation for y.

Divide both sides by 116.

[tex]\dfrac{116y}{116}=\dfrac{96.28}{116}[/tex]

[tex]y=0.83[/tex]

Now consider the provided options.

Hence, the correct option is D. The cost of natural gas is $0.83 per unit.

To know more about Linear equations follow

https://brainly.com/question/14323743

what is the area of the figure​

Answers

Step-by-step explanation:

make the figure into 1 rectangle with dimensions 25 and w,and rite triangle with hypotenuse = 18 and h = 8

applying Pythagoras theorem

18^2 = 8^2 + b^2

b^2 = 260

b = 2√65ft

area of rectangle = 2√65 * 25= 50√65

area of triangle = 1/2 * 2√65*8 = 8√65

total area = 58√65 ft^2

necesito saber el área de un cilindro de 10 cm de ancho y 4 de alto​

Answers

Answer:

40 cm

Step-by-step explanation:

10cm*4cm=40cm

The area of a rectangular field is 4526 m².
If the width of the field is 62 m, what is its length?

Answers

Answer:

73 m

Step-by-step explanation:

The formula for the area of a rectangle is a = w(l). Using this, we can plug in the given values and solve for l, the length.

4526 = 62(l)

[tex]\frac{4526}{62} =\frac{62l}{62}[/tex]

l = 73

hope this helps!

Answer: 73 meters

Step-by-step explanation:

The simple formula to calculate the area of a regular rectangle is (Length x Width)

Given the area is 4526, and the width 62, we can use "y" to represent the unknown length.

So, '

62(y)=4526

Divide both sides by 62

1/2[62(y)]=4526/62

Y= 73 meters.

To check, 73x62= 4526, which follows the formula

What are the sources of a developing country's primary income?
A. Natural resources and primary product export
B. Human resource and primary product export
C. Human resource and manufactured product export

Answers

its lang allam ko. human is rescures till hitman

briwilljohn
16 minutes ago
Mathematics
High School
GIVE A DETAILED AND GOOD ANSWER FOR BRAINLIEST
Question 2(Multiple Choice Worth 5 points)
(06.08A LC)

Look at the triangle ABC.

Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 2, 1, and C at ordered pair 4, 1.

What is the length of the side AB of the triangle?

2
Square root of 20
6
Square root of 38

Answers

Answer:

Square root of 20 :)

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

Now lets solve!!

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

Now lets find the square root if any :)

[tex]\sqrt{20}[/tex] = no square root

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

im answering so you can give other guy brainliest :)

Find x.

Do not round your answer.

8 cm

4 cm

Х

X = [?] cm

Answers

Answer:

2

Step-by-step explanation:

If 8cm divided by 4cm = 2cm

Find the slope of the line represented by the
equation below. Give your answer as a
Fraction in simplest form.
6x - 8y = 2

Answers

answer

7

Step-by-step explanation:

cause I said so

Answer:

m=3/4

Step-by-step explanation:

Explanation:

The slope of a line parallel to a line L has the same slope as line L.

6x−8y=−2

6x+2=8y

y=6/8x+2/8

Simplfied= y=3/4x+1/4

Therefore the answer is 3/4.

Which equation results from taking the square root of both sides of (x 9)2 = 25?

Answers

Answer:

[tex]x^{9}[/tex] = ± 5

Step-by-step explanation:

([tex]x^{9}[/tex] )² = 25 ( take square root of both sides )

[tex]\sqrt{(x^{9})^2 }[/tex] = ± [tex]\sqrt{25}[/tex]

[tex]x^{9}[/tex] = ± 5

The local volleyball team hosts a concession stand to raise money. They spend $120 to purchase popcorn, candy, and drinks. They buy 95 bags of popcorn at $0. 75 each and 35 bags of candy at $1. 20 each. How much money does the volleyball team have left to spend on drinks

Answers

Answer: $6.75

Step-by-step explanation:

Popcorn95 × 0.75 = 71.25

Candy35 × 1.20 =42

Totally 113.25

Deduct from 120

Drinks6.75

Give ten (10) symbols of logic mathematics or logic in computer science.​

Answers

Answer:

Step-by-step explanation:

open the page below

Answer:

please read through the ten symbols of logic mathematics

!!20 points and Brainliest!!!

What should be done to x^2 - 12x to create a perfect square?

A) add 36

B)subtract 6

C)add 6

D)subtract 36

Answers

Answer:

A.) add 36

To find the last term, divide the coefficient of the middle term by 2 then raise to the power of 2,that will be :

[tex]( \frac{ - 12}{2} )^{2} = { - 6}^{2} = 36 [/tex]

Answer:

add 36

Step-by-step explanation:

If x > 0, what is the difference of
[tex]6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]in simplest radical form?​

Answers

Answer:

[tex]\longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

Step-by-step explanation:

[tex] \sf \: if \: x > 0 [/tex]

[tex] \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } [/tex]

[tex] \sf Let's \: solve \: for \sqrt{56 {x}^{3} } \: first, \\\longmapsto \sf \sqrt{56 {x}^{3} } = \sqrt{14 \times 4 {x}^{2} \times x } \\ \sf \longmapsto \sqrt{56 {x}^{3} } = 4x \sqrt{14x} [/tex]

Substituting above value in given equation,

[tex]\longmapsto \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \\ \longmapsto\sf 6x \sqrt{14x} - 5 \times 4x \sqrt{14x} \\ \longmapsto \sf \: 6x \sqrt{14x} - 20x \sqrt{14x} \\\longmapsto \sf \: \sqrt{14x}(6x - 20x) \\ \longmapsto \sf \: \: - 14x \cdot\sqrt{14x}[/tex]

Thanks for joining brainly community!

Which is the completely factored form of 4x2 28x 49? (x 7)(4x 7) 4(x 7)(x 7) (2x 7)(2x 7) 2(x 7)(x 7)

Answers

The completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

How to find the factors of a quadratic expression?

If the given quadratic expression is of the form ax^2 + bx + c, then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]

Then writing b in terms of alpha and beta would help us getting common factors out.

Sometimes, it is not possible to find factors easily, so using the quadratic equation formula can help out without any  trial and error.

For this case, the given quadratic expression is:

[tex]4x^2 + 28x + 49[/tex]

So we've to find two numbers such that:

Their sum = b =  28

Their product = [tex]ac = 4\times 49 = 196[/tex]

We can see that 196 is square of 14, and that 14 added twice forms 28, thus:

14 + 14 = 28

14×14 = 196

Writing b = 28 as sum of 14 twice, we get:

[tex]4x^2 + 28x + 49 = 4x^2 + 14x + 14x +49 \\4x^2 + 28x + 49 = 2x(2x+7) + 7(2x + 7)\\4x^2 + 28x + 49 = (2x+7)(2x+7)[/tex]

Thus, the completely factored form of 4x^2 + 28x + 49 is given by: Option C: (2x+7)(2x+7)

Learn more about factorization of quadratic expression here:

https://brainly.com/question/26675692

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