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:
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)²Take square root both sides:
⇒ √189 = √(x)²⇒ x = √189 ≈ 13.747... meters
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 = ladderPythagoras' 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 ftSubstitute 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
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
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:
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:
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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]
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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.
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!
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.
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 + 21Which 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
Find the area (no explanation needed)
Answers
Area of bottom rectangle:-
2(8)16cm²Area of rectangle above it:-
6(2)12cm²Area of rectangle above it
11(2)22cm²Area of triangle:-
1/2(11)(6)11(3)33cm²Total:-
12+16+22+3383cm²Can 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 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
Based only on the information given in the diagram, it is guaranteed that ABC ~ XYZ.
Answers
Check the picture below.
please help me i need help
Answers
Answer:
Step-by-step explanation:
a c d are the answer
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
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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
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
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
!!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 36To 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:
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
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
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:
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
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
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
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 :)
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
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
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
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