A 30 -foot ladder is leaning against a building. The base of the ladder is 18 feet from the side of the building. How high does the ladder reach along the side of the building?
Answers
========================================================
Explanation:
Refer to the diagram below. We have a right triangle with known horizontal leg 18, and unknown vertical leg x. The hypotenuse is 30.
Let a = x, b = 18, c = 30.
Apply the Pythagorean theorem to solve for x
a^2 + b^2 = c^2
x^2 + 18^2 = 30^2
x^2 + 324 = 900
x^2 = 900-324
x^2 = 576
x = sqrt(576)
x = 24
The top of the ladder reaches 24 feet high.
Related Questions
If Maggie rides for 2 hours on a bicycle, what is her rate if she rides for 8 miles?
__________________ mph
Answers
Answer:
4 mph
Explanation:
8 miles / 2 hours = 4 miles each hour
Using a computer or calculator that provides proportions falling below a specified z-score, determine the approximate proportion for each of the following situations. In each case, assume the values are approximately bell-shaped. (Round your proportions to four decimal places.) A button hyperlink to the SALT program that reads: Use SALT. (a) The proportion of SAT scores falling below 420 for a group with a mean of 500 and a standard deviation of 100. -0.8 Correct: Your answer is correct. (z-score) (approximate proportion)
Answers
Answer: uhhhh what
Step-by-step explanation:
Nathan buys coffee and hot chocolate for his co-workers. Each cup of coffee costs $1.55 and each cup of hot chocolate costs $1.05. If he pays a total of $9.35 for 7 cups, how many of each does he buy?
Answers
Answer:
he buys 6.78
Step-by-step explanation:
write the expression as a product of the to factors: 6m+ 8n+ 4
Answers
Answer:
No answer do u today
Step-by-step explanation:
Lol
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prove that (n+5)^2-(n+3)^2 is a multiple of 4 for all positive integer values of n
Answers
Answer:
Proved
Step-by-step explanation:
Given
[tex](n+5)^2-(n+3)^2[/tex]
Required
Show that [tex](n+5)^2-(n+3)^2[/tex] is a multiple of 4
Expand each bracket
[tex](n+5)(n+5)-(n+3)(n+3)[/tex]
Open brackets
[tex]n^2 + 5x + 5x + 25 - (n^2 + 3x + 3x + 9)[/tex]
[tex]n^2 + 10x + 25 - (n^2 + 6x + 9)[/tex]
Open bracket
[tex]n^2 + 10x + 25 - n^2 - 6x - 9[/tex]
Collect Like Terms
[tex]- n^2 + n^2 - 6n + 10n + 25 - 9[/tex]
[tex]- 6n + 10n + 25 - 9[/tex]
[tex]4n + 25 - 9[/tex]
[tex]4n + 16[/tex]
Factorize
[tex]4(n + 4)[/tex]
Hence, the multiples of [tex](n+5)^2-(n+3)^2[/tex] are [tex]4[/tex] and [tex](n + 4)[/tex]
Helppppppppppppppppppppppp please
Answers
Answer:
A
Step-by-step explanation:
Two Squares
There are 2 squares at the top and bottom. All sides = 3
2* s^2
2 * 3^2
2 * 9
18
Middle Figure.
Triangles
There are many ways to solve this. I think the most easily understood is to break it into 2 triangles and a rectangle.
Base of both triangles = 5 + 5 = 10
The height of each triangle = (7 - 3)/2 = 4/2 = 2. You divide by 2 because there are 2 bases -- one in each triangle.
Area = 1/2 * 2 * 10 = 10
But there are 2 of them so the total area is 20
Rectangle
The length of the rectangle = 5 + 5 = 10
The width = 3
Area = 30
Total
Total Area = 2 squares + 2 triangles + 1 rectangle
Total Area = 18 + 20 + 30 = 68
six less than six times a number is 12
Answers
Answer:
x = 3
equation: 6x - 6 = 12
Step-by-step explanation:
6x - 6 = 12
aka:
6x + -6 = 12
+6. +6
6x = 18
/6. /6
x = 3
check: 6(3) - 6 = 12
18 - 6 = 12
12 = 12
6(3)-6= 12
18-6=12
12=12
The number is 3
In the diagram, ABC ~ DEF. The area of ABC is 72 square cm. Find the area of DEF.
А
6 cm
B
20 cm
m
Area of DEF
cm
Answers
Answer:
120
Step-by-step explanation:
just do 20x 6 and you get 120
Similar triangles may or may not be congruent
The area of triangle DEF is 800 square cm
The given parameters is
[tex]\triangle ABC \sim \triangle D EF[/tex]
This means that the triangles are similar.
The corresponding sides of the triangles are:
[tex]AC = 6[/tex]
[tex]DF = 20[/tex]
So, the scale factor (k) from ABC to DEF is:
[tex]k = \frac{D EF}{ABC}[/tex]
[tex]k = \frac{20}{6}[/tex]
Simplify
[tex]k = \frac{10}{3}[/tex]
The area of triangle DEF is then calculated as follows:
Area = Area of triangle ABC * k^2
So, we have:
[tex]A =72 \times \frac{10}{3} \times \frac{10}{3}[/tex]
[tex]A = 800[/tex]
Hence, the area of triangle DEF is 800 square cm
Read more about similar triangles at:
https://brainly.com/question/14285697
Gabrielle is 12 years younger than Mikhail. The sum of their ages is 76 . What is Mikhail's age?
Answers
Answer:
48 years old
Step-by-step explanation:
Let x = Mikhail's age
then x-15 = Gabrielle's age
x + x-15 = 81
2x-15 = 81
2x = 96
x = 48 years old
Answer:
44
Step-by-step explanation:
x+(x-12)=76
2x-12=76
2x=76+12
2x=88
x=88/2
x=44
1 Which fraction is equivalent to 1/6?
3/8
2/8
3/24
4/24
Answers
Answer:
4/24
Step-by-step explanation:
24 divided by 6 equals 4
Answer:
4/24
Step-by-step explanation:
1/6
=1 × 4 = 4
=6 × 4 = 24
=1/6 = 4/24
Move numbers to the blanks to solve the problem.
6 divided by 1/3
Answers
Answer:
its 2
Step-by-step explanation:
Help me with question. Please!
Answers
Answer: The answer is c
Step-by-step explanation: mark me as brainlisti plsssssssssss
Answer:
The answer I believe is B
Step-by-step explanation:
I made a mistake with me math so i went over and found the the statement is still invalid so the answer is b, sorry again.
The line at the bullet roller coaster is moving about 4 feet for every 15 minutes. At this rate, how many hours would it take for a person to travel 24 feet? Set up a proportion and solve.
Answers
Answer:
90
Step-by-step explanation:
4/15 which is our fraction distance/time
our other fraction is 24/x (x is our variable to find our time)
Now we are doing the buultterfly method
set it up
now multiply 4*x= 4x
15*24=360
now divide 4x ÷ 4 to get our variable alone
do the same to the other side
4 ÷ 360= 90
so x= 90 which is our missing number
Find a number, twice of which decreased by 7 gives 65.
Answers
Answer:
Number = 36
Step-by-step explanation:
Given that,
A number twice of which decreased by 7 gives 65.
Let the number be x.
Twice of the number is 2x.
ATQ,
2x - 7 = 65
We can solve the above equation.
Adding 7 both sides.
2x-7+7 = 65 +7
2x = 72
x = 36
So, the required number is 36.
Help plz:)))I’ll mark u Brainliest
Answers
Answer:
Scale factor = 1.5
Step-by-step explanation:
Formula for the scale factor,
Scale factor = [tex]\frac{\text{Measure of one side of the Image}}{\text{Measure of one side of the preimage}}[/tex]
In this question, image is triangle Y and preimage is triangle X.
Scale factor of X to Y = [tex]\frac{15}{10}[/tex]
= 1.5
Therefore, scale factor = 1.5 is the answer.
A dig-your-own potato farm charges $1.27 per pound of potatoes plus $0.20 per pound to clean the potatoes. Kevin digs 30 pounds of potatoes. The farm cleans 8 pounds for him. How much does Kevin pay in all?
Answers
Explanation:
1.27 x 30 = 38.1
0.20 x 8 = 1.6
38.1 + 1.6 = 39.7
-8/5x -6 equals -54. what is x
Answers
Answer:
30
Step-by-step explanation:
......................
Use the following sets to answer the following:
Y: The set of yellow attribute pieces
H: The set of hexagonal attribute pieces
SY: The set of small yellow attribute pieces
SB: The set of small blue attribute pieces
L: The set of large attribute pieces
1. Which pairs of sets, if any, can be put into one-to-one correspondence?
2. Which pairs of sets, if any, are equal?
3. Which pairs of sets, if any, are disjoint?
4. Which set is a proper subset of another?
5. Which attribute pieces are in Y ∩ L?
6. Which attribute pieces are in Y UL?
Answers
Answer:
i have no clue
Step-by-step explanation:
tbh
Estimate the product
A)Close to 40
B)Close to 004
C)Close to 0.4
D)Close to 4
Answers
Answer:
D) Close to 4
Step-by-step explanation:
Round both numbers and multiply them.
PLEASE HELP I WILL GIVE BRAINLIST! <3
On a certain hot summer's day, 606 people used the public swimming pool. The daily prices are 1.25 for children and 2.50 for adults. The receipts for admission totaled $1098.75. How many children and how many adults swam at the public pool that day?
Answers
ima cry brainliest giving it out
Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% if Stefanie and john mix the syrups together how many grams of sugar will they have?
Answers
Answer:
23.1%
Step-by-step explanation:
11/48=0.23125
Round up for percent.
0.231x100=23.1
23.1%
Solve for p. U=1/7pd
Answers
Answer:
U =1/7pd
Multiplying through by 7pd, we have U7pd=1
Dividing through by U7d , we have p=U7d*1
Therefore p= U7d
2/3 of a yard = ______ inches
Answers
Answer:
24 inches
Step-by-step explanation:
you're welcome
(4y' - 49 +8) - 092-y+3)
Answers
Answer:
3y-130
Step-by-step explanation:
hope this was helpful! c:
Answer:
3y-130 hope this helps
Step-by-step explanation:
Find the absolute value. |-45 |
Answers
Answer:
45
Step-by-step explanation:
Absolute value is the distance that number is ways from zero
Answer:
45
Step-by-step explanation:
The absolute value of any number is the positive of that number.
Ex:
a) absolute value of |- 23 | is 23.
b) absolute value of 13 is 13 itself.
-Therefore absolute value is always positive.
A square gate has a brace 3.5 feet long.
Approximately how wide is the gate?
F. 2.0 feet
3.5 ft
G. 2.5 feet
H. 4.9 feet
J. 6.1 feet
Answer
Answers
Answer:
h
Step-by-step explanation:
In our amusement park that we built this week, the ride Diablo’s Domain had revenue of $250,000,000 in its first year as expected. The company paid $750,000 for insurance or $3 for every $1,000 in revenue. If the park is wildly successful and revenue increases by 25% in the second year and the rate of $3 for every $1,000 holds true, how much would it pay for insurance? Do you think it’s reasonable for insurance costs to increase proportionally? Why or why not?
Answers
Answer:
The amount to be paid for insurance will be $ 937,500. In this context, it is reasonable that insurance costs increase proportionally, as the ride will have a greater use and, therefore, a greater exposure to risk.
Step-by-step explanation:
Given that the amusement park Diablo's Domain ride generated $ 250,000,000 in revenue, and the company paid $ 750,000 in insurance for that game ($ 3 for every $ 1,000 in profit), to determine the amount of insurance that should be paid if the winnings increase by 25% and the same proportion of 3/1000 to be paid is maintained, the following calculation must be made:
(250,000,000 x 1.25) x (3/1000) = X
312,500,000 x 0.003 = X
937,500 = X
Therefore, the amount to be paid for insurance will be $ 937,500.
Help.
Determine the unknown values, R and W, in the figure below.
Answers
Answer:
W = 28.63
R = 15.59
Step-by-step explanation:
From the right triangle given in the picture,
By applying sine rule in the triangle,
sin(57°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{24}{W}[/tex]
W = [tex]\frac{24}{\text{sin}(57)}[/tex]
W = 28.63
Similarly, by tangent rule,
tan(57)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
1.54 = [tex]\frac{24}{R}[/tex]
R = [tex]\frac{24}{1.54}[/tex]
R = 15.59
Please help I’ll mark you as brainliest if correct!
Answers
Answer:
304
Step-by-step explanation:
The area of the square is 12 x 8 = 96.
There are two triangles with area (11x8)/2=44. 44x2=88.
There are two triangles with area (10x12)/2=60. 60x2=120.
96+88+120=304
Hope I helped!
-3g = 9 what does g =
Answers
Answer:
g=-3
Step-by-step explanation:
-3g=9
divide through by-3
g=9/-3
g=-3
Answer:
Step-by-step explanation:
Here you go mate
Step 1
-3g=9 Equation/Question
Step 2
-3g=9 Simplify
-3g=9
Step 3
-3g =9 Divide by 3
answer
-3
Hope this helps