A painter leans a 30 foot ladder against one wall of a house. At what height
does the ladder touch the wall if the foot of the ladder is 10 feet from the base
of the wall?
Answers
Answer:
20ft
Step-by-step explanation:
The height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Consider the diagram below.
We've got:
Length of the ladder = |AC| = 30 ftDistance between ladder's bottom and base of wall = |BC| = 10 ftHeight of wall from base to the point where ladder touches = |AB| is to be known.The wall is usually perpendicular to ground, therefore making 90° angle with it. Thus, ABC is a right angled triangle.
Using Pythagoras theorem in it, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\30^2 = |AB|^2 + 10^2\\|AB|^2 = 900 - 100\\\\|AB|^2 = 800\\\\\text{Taking sq. root of both the sides}\\\\|AB| = \sqrt{800} = \sqrt{ (\pm 20\sqrt{2})^2}\\\\|AB| = \pm 20\sqrt{2} \: \rm ft[/tex]
But as length cannot be a negative quantity, so we get:
[tex]|AB| = 20\sqrt{2} \: \rm ft[/tex]
Thus, the height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
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Related Questions
What is the slope of the line through (0,5) and (-2, -1)?
(0.5)
3
2
X
2
4
-4 -3
+(-2,-1)
-1
-2
-3
A. -3
O
B. -
o
C. 3
O
D.
10
PREVIOUS
Answers
Answer: 3
Step-by-step explanation:
*Slope formula*
Y2 - Y1 / X2 - X1
-1 - (5) / -2 - (0) = -6/-2 = 3
PLEASE HELPP!! I’ll mark brainliest!!!!
Answers
Julio considers the reduction of the triangle. What is the correct cross product that he should use to solve for the missing dimension? (8)(12) = 21x (8)(21) = 12x (12)(8) = 12x (12)(21) = 8x
Answers
Answer:
(8)(21) = 12x
Step-by-step explanation:
(8)(12) = 21x
(8)(21) = 12x
(12)(8) = 12x
(12)(21) = 8x
Opposite : Adjacent
12 in : 21 in
Opposite : Adjacent
8 in : x in
Equate both ratios to solve for x
12 : 21 = 8 : x
12 / 21 = 8 / x
Cross product
(12)(x) = (21)(8)
12x = 168
x = 168 / 12
= 14
x = 14
Answer:
B
Step-by-step explanation:
What percent of offspring will be blue eyed?
0%
25%
50%
100%
Please I need help
Answers
Answer:
I believe the answer is 0% because the blue eye trait is recessive.
Step-by-step explanation:
Hope this helps!
✧◝(⁰▿⁰)◜✧
Answer:
25%
Step-by-step explanation:
blue eyes are the resesive gene but there is still a 25% chance.
2 Name the diameter of the circle shown.
A co
B ec
C eo
D rc
Answers
Answer: a
Step-by-step explanation:
A bowl contains 61 red and yellow Skittles. The number of red Skittles is 10 more than twice the number of
yellow Skittles. How many of each color are in the bowl?
Define your variables and write a system of equations that could be used to determine the number of red
Skittles and yellow Skittles in the bowl. (DO NOT SOLVE THE SYSTEM)
Let
Equation 1:
Let
Equation 2:
Answers
Answer:
the red skittles be 44 and yellow skittles be 17
Step-by-step explanation:
The computation of the number of each color are in the bowl is as follows;
Let us assume the red skittles be y
And, the yellow skittles be x
The first equation is
x + y = 61
And, the second equation is
y = 2x + 10
Now put the second equation in the first equation
x + 2x + 10 = 61
3x = 51
x = 51 ÷ 3
= 17
And, y = 2 (17) + 10
= 34 + 10
= 44
Hence, the red skittles be 44 and yellow skittles be 17
Need help plz help plz
Answers
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find x
The theorem that applies to this question is the theorem of external angles. And it translates to:
[tex]11x +2 = 58 + 5x + 10[/tex]
Collect Like Terms
[tex]11x -5x = 58 + 10-2[/tex]
[tex]11x -5x = 66[/tex]
[tex]6x = 66[/tex]
Divide through by 6
[tex]\frac{6x}{6} = \frac{66}{6}[/tex]
[tex]x = \frac{66}{6}[/tex]
[tex]x = 11[/tex]
Please help down below
Answers
Answer:
The answer is B
Hope this helps
Answer:
The first answer
Explanation:
Ok I added an explanation lol-
So B is incorrect. It gets confused. 332/4 simplified isn't 1/83, but it's 83/1 (aka 83)
C doesn't even make sense 6-6
And D isn't 5 2/5 it's 7 2/5
Which expression is not equivalent to 3x-2
Answers
Answer: Let's simplify step-by-step.
3x−2
There are no like terms.
So it going to be the same, =3x-2
Step-by-step explanation: hope you understand
Answer:
2x + 2 + x
Step-by-step explanation:
simplify the expression
-2 - 3n =
Answers
Answer:
-3n-2
-3 -3
n=2/3
you would be dividing
it would be N=2/3
Answer:
brainliest plsssss
Step-by-step explanation:
−2−3n
= −2 + −3n
What is the total price of 2.6 pounds of pears at 90 cent per pound?
Answers
Answer:
It would be $2.34
Step-by-step explanation:
2.6x90=234 but in this case it is money so add a decimal
WILL MARK BRAINLIEST Solve this system of linear equations. Separate
the x- and y-values with a comma.
2x = -24 - 4y
-5x = 36 + 4y
Enter the correct answer.
Answers
Answer:
x=-4 , y=-4
Step-by-step explanation:
see the attached pic
A.it is a function
B.it is not a function
Answers
Whats values x= 2+/- i are the the roots of the quadratic equation?
Answers
Answer:
x^2 - 4x + 5 = 0
Step-by-step explanation:
:)
x = (2 + i) and (2 - i) are the roots of the quadratic equation f(x) = x² - 4x + 5.
What are roots of a quadratic equation?The values of variables satisfying the given quadratic equation are called its roots.
Given (2 + i) and (2 - i) are roots of the quadratic equation.
Let the quadratic equation be f(x).
(x - (2 + i)) and (x - (2 -i)) are the factors of f(x).
Since, f(x) is a quadratic equation, it has only two roots.
f(x) = (x - (2 + i))(x - (2 - i))
f(x) = x² - (2 - i)x - (2 + i)x + (2 - i)(2 + i)
f(x) = x² - 2x + ix - 2x - ix + 4 - i²
f(x) = x² - 4x + 4 + 1
f(x) = x² - 4x + 5
Learn more about roots of quadratic equation here
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What is a formula for the nth term of the given sequence? 48, 72, 108
Answers
Answer:
[tex]a_n=48*1.5^{n-1}[/tex]
Step-by-step explanation:
Geometric Sequence
In geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.
We are given the sequence:
48, 72, 108, ...
The common ratio is found by dividing the second term by the first term:
[tex]r=\frac{72}{48}=1.5[/tex]
To ensure this is a geometric sequence, we use the ratio just calculated to find the third term a3=72*1.5=108.
Now we are sure this is a geometric sequence, we use the general term formula:
[tex]a_n=a_1*r^{n-1}[/tex]
Where a1=48 and r=1.5
[tex]\boxed{a_n=48*1.5^{n-1}}[/tex]
For example, to find the 5th term:
[tex]a_5=48*1.5^{5-1}=48*1.5^{4}=243[/tex]
Given quadrilateral RSTU, what is the measure of angle R? HELPPPPPPP PLEASEEEEE!!!!!!
Answers
Answer: did you ever get the answer?
Step-by-step explanation:
Answer:
Step-by-step explanation:
?
Please help me ^^ This is due tomorrow
Answers
You just plug whatever number is in the f(?) part in for x!
Find the unit rate.
352 miles on 16 gallons of gas
Answers
Answer: 22 mpg (miles per gallon)
Step-by-step explanation: Just divide 352 by 16 to find the unit rate :)
2 + 2 = ______________________________________________
Answers
Answer:4
Step-by-step
what is 9741 divided by 45
Answers
Answer:
216.466666667
Step-by-step explanation:
Which equation best represents the line on
the graph?
3
y
B.
-
A. y--3-4
y
-x-4
C. y ---4
D. y-r+4
Answers
Answer:
B. y=3/2x - 4
Step-by-step explanation:
As you see in the graph the y intercept was lying on -4 and you rise 3 time and run 2 time to get to your next point.
Write an integer (positive or negative whole number) to represent each description.
Integer Vocabulary
The football player had a 5-
yard loss on the play.
17 units to the left of -6 on a number
line.
Answers
Answer:
Football player= -5
Number line= -23
Step-by-step explanation:
Loss means negative
Left on a number line is subtraction
2x - 3y = 3 solve y
Answers
Answer:
Y=-1+2x/3
Step-by-step explanation:
Move all the terms that don't contain y to the right side and solve. Hope this helps!
What is 6/-1 expressed as an integer?
Answers
Answer:
-6
Step-by-step explanation:
Please help me with this ;(
Answers
Brainliest.
Good luck
34. HOME What's the Error? Nathan says
that Madison Square Garden is located
at (0,3) on the map. Is his ordered pair
correct? Explain.
Answers
Violet saw a scarf online for $24. If she has an 18% discount coupon what would be the discount amount?
Answers
10 yd
5 yd
What’s the surface area of the cylinder
Answers
Answer:
471.24 yd²
Step-by-step explanation:
The formula for the surface area of the cylinder
= 2πr(r + h)
Height = 10 yd
Radius = 5 yd
Surface area =
2 × π × 5(5 + 10)
= 471.24 yd²
The surface area of the cylinder = 471.24 yd²
Someone please do this!
Answers
Answer:
£518.42
Step-by-step explanation:
The graph shows the number of miles you and a friend run each week while training for a race.
Answers
Answer: 4 miles
Step-by-step explanation: