a 12-ft ladder leans against a building so that the angle between the ground and the ladder is 74°. how high does the ladder reach on the building? (round your answer to the nearest foot.)
Answers
Answer:
12 feet
Step-by-step explanation:
Sometimes, a simple drawing is a great way to start! In the attached drawing, the red line represents the ladder, the brown represents the ground, and the black represents the building!
We want to find the side of the triangle from where the ladder meets the building to where the building meets the ground. This can be found using trigonometric identities, namely sine:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
Plug in known values:
[tex]sin(74^o)=\frac{x}{12}[/tex]
Rearrange to isolate the variable:
[tex]x=12sin(74^o)[/tex]
Simplify!
[tex]x=11.535140... ft[/tex]
Round to the nearest foot:
[tex]x=12ft[/tex]
Related Questions
A student's grade in a Psychology course is comprised of tests (40%), quizzes
(20%), papers (20%), and a final project (20%). His scores for each of the
categories are 85 (tests), 100 (quizzes), 92 (papers) and 84 (final project).
Calculate his overall grade.
Answers
which statements describe transformations performed in f (x) = x^2 to create g (x) = 2x^2 + 5? select all that apply.
a. a vertical stretch with a scale factor of .5
b. a translation of 5 units to the right.
c. a translation of 5 units up.
d. a vertical stretch with a scale factor of 2.
Answers
Answer:
The statements describe transformations performed in f(x) to create g(x) are:
a translation of 5 units up ⇒ c
a vertical stretch with a scale factor of 2 ⇒ d
Step-by-step explanation:
If f(x) stretched vertically by a scale factor m, then its image g(x) = m·f(x)If f(x) translated vertically k units, then its image h(x) = f(x) + kLet us use these rule to solve the question
∵ f(x) = x²
∵ g(x) is created from f(x) by some transformation
∵ g(x) = 2x² + 5
→ Substitute x² by f(x) in g(x)
∴ g(x) = 2f(x) + 5
→ Compare it with the rules above
∴ m = 2 and k = 5
→ That means f(x) is stretched vertically and translated up
∴ f(x) is stretched vertically by scal factor 2
∴ f(x) is translated 5 uints up
The statements describe transformations performed in f(x) to create g(x) are:
a translation of 5 units upa vertical stretch with a scale factor of 2QUIC what is the LCM of 6 and 8
Answers
Answer:
24
Step-by-step explanation:
The price of a sofa was £880. It was reduced in a sale by 35%. What is the cost of the sofa in the sale?
Answers
Answer: 308
Step-by-step explanation:
SOLUTION STEPS
880×35%
Reduce the fraction
[tex]\frac{35}{100}[/tex]
to lowest terms by extracting and canceling out 5.
[tex]880*(\frac{7}{20} )[/tex]
Express [tex]880*(\frac{7}{20} )[/tex]
as a single fraction.
[tex]\frac{880*7}{20}[/tex]
Multiply 880 and 7 to get 6160.
[tex]\frac{6160}{20}[/tex]
Divide 6160 by 20 to get 308.
308
Someone please help pleaseeee
Answers
Ralph went for a drive in his new car he drove at a speed of 62.5 miles per hour for 5 hours how many miles did he drive
Answers
Answer:
in step by step
Step-by-step explanation:
Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.
The formula for distance problems is: distance = rate × time or d = r × t.
Things to watch out for:
Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.
It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.
Distance Problems: Given Total Time
Example:
John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?
Solution:
Step 1: Set up a rtd table.
r
t
d
Case 1
Case 2
Step 2: Fill in the table with information given in the question.
John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?
Let t = time to travel to town.
7 – t = time to return from town.
r
t
d
Case 1
40
t
Case 2
30
7 – t
Step 3: Fill in the values for d using the formula d = rt
r
t
d
Case 1
40
t
40t
Case 2
30
7 – t
30(7 – t)
Step 4: Since the distances traveled in both cases are the same, we get the equation:
40t = 30(7 – t)
Use distributive property
40t = 210 – 30t
Isolate variable t
40t + 30t = 210
70t = 210
210/70
Step 5: The distance traveled by John to town is
40t = 120
The distance traveled by John to go back is also 120
So, the total distance traveled by John is 240
Answer: The distance traveled by John is 240 miles.
Elliot ate 3/8 of a pizza that was cut into 8 slices. How much is left?
Answers
Answer:
5/8
Step-by-step explanation:
Answer:
Convert to a decimal by dividing the numerator by the denominator.
0.046875. Then, change the decimal into a fraction which is 3/64ths
Help ill give brainlist
Answers
A= 2x10=20
20-16=4
Ratio is 1:3
So 12divided by 3 = 4
B
What is the value of x?
10
O 2 units
3 units
А х
D
4x
С
O 5 units
8 units
Answers
Answer:
C. 5units
Step-by-step explanation:
whats the answer 2x+22 do not factor
Answers
Answer:
There are no like terms.
Step-by-step explanation:
Since your not factoring then will simply it
Let's simplify step-by-step.
2x+22
There are no like terms.
whos a bad boy today
Answers
Answer:
lllllllllllllllllllololollllll
Can someone please help me on this?
Jessica is ordering rackets for her school. Racket
World charges $4.75 for each racket and a one-time
shipping fee of $40. Tennis King charges $8.50 for
each trophy and a one-time shipping of $23. What
inequality can be used to find x, the minimum number
of rackets that can be ordered so that the total charge at
Racket World is less than the total charge at Tennis
King?
(I can write and solve an equation from a word problem.
Answers
Answer:
76.25
Step-by-step ex planation:
Sorry if this isn't right, I haven't done inequalities in a while.
Last year, half the graduates from Harold's Clown College became circus clowns. Another 60 graduates became rodeo clowns. The rest of the graduates became mimes. Harold's Clown College has 200 graduates last year. What percentage were mimes?Immersive Reader (3 Points) 20% 40% 60% 100%
Answers
Answer:
20 percent
Step-by-step explanation:
Answer:
20%
Step-by-step explanation:
since 100% is a 200, half of them were circus clowns 200/2 = 100
so 100 persons are 50%
from these 100, only 60 graduated as rodeo clowns and 40 as memes
1 percent of 200 is 2, so 40/2=20%
Mrs. Winship sells chocolate
fudge for $7.50 per pound and peanut butter fudge for $7.00 per pound. The total number of pounds sold on Saturday was 146 and the total amount of money collected was $1065. How many pounds of each type of fudge were sold?
Answers
Answer:
cf chocolate fudge
pbf peanut butter fudge
A) 7.50 cf + 7.00 pbf = $1,065
B) cf + pbf = 146
Multiplying equation B) by -7.50
B) -7.50cf -7.50pbf = -1,095 then adding equation A)
A) 7.50 cf + 7.00 pbf = $1,065
-.50pbf = -30
pbf = 60 pounds of Peanut butter fudge
cf = 146 -pbf = 86 pounds of peanut butter fudge
Double Check
86 + 60 = 146
7.50 * 86 + 7.00 * 60 = 1,065.00
Correct!!!
Step-by-step explanation:
Which of the following is the best description of a person-versus-society conflict?
A.
an argument or a physical fight between two people
B.
a person who is fighting against an idea or a group
C.
a person who is trying to benefit from being part of a group
D.
a person who is helping others who are poor and weak
E.
a person who is trying to make a decision
Answers
Answer:
B
Step-by-step explanation:
Answer:
im pretty sure b
Step-by-step explanation:
Ella had 36 coins in her collection. Justin had 4 times as many coins as Ella
had. Which equation can be used to determine the number of coins Justin
Had? (2 pts)
Answers
Answer:
A. 36 x 4 = ?
Answer:
a. 36 x 4
Step-by-step explanation:
If Justin has 4 times as many coins as Ella, who has 36 coins, he would have 144 coins.
Therefore, 36 x 4 = 144
0.0001982 in scientific notation
Answers
answer : 0.0001982 in scientific notation = see picture
Write log7t using the natural logarithm.
Answers
Answer:
log₇t = ln t / ln 7
Step-by-step explanation:
Given:
log₇t
Computation:
We know that
logₐb = log b / log a
So,
log₇t = log t / log 7
= log₇t = ln t / ln 7
Describe the transformations:
LaTeX: g(x) = f(x +5) + 6g ( x ) = f ( x + 5 ) + 6
Choose all that apply
Answers
(b) Suppose the actual number of pizzas sold today was 65. Describe the number of pizzas sold as a percent increase or decrease, rounded to the nearest hundredth Show your work
Answers
Answer:
65 + 0.20(65) = 65 + 13 = 78..they would have to sell 78 to get the bonus
Step-by-step explanation:
(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday
Solve the following problems. Remember that all reasoning must be explained, and all steps of math work must be shown!
Topic: Perpendicular to Chord Property
Answers
Since the diagram shows a right triangle and gives out some measurements of the sides, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the length of MP.
Given:
hypotenuse = 7 – because the radius is 7 units and it can be used as the hypotenuse
One side of the triangle = 4 – because the length of PO is 4 units and it can be used as one sides of the triangle
To Solve:
Since we know two values of the triangle, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find what the other value is. The variables c and b in the formula are already given, and we need to find what a is to find the length of MP. So, plug the given values of c and b into the formula:
[tex]a^{2}+4^{2}=7^{2}[/tex]
Simplify:
[tex]a^{2}+16=49[/tex]
Subtract 16 from both sides of equation:
[tex]a^{2}=33[/tex]
Do the square root of both sides to isolate the variable a:
[tex]\sqrt{a^{2}}=\sqrt{33}[/tex]
Evaluate:
[tex]a=\sqrt{33}[/tex] Which simplifies to [tex]a= 5.744562646....[/tex] and round it to the nearest tenth to finally get [tex]a=5.7[/tex]
Answer: The length of MP is 5.7 units
How to solve Part AIf you look at the diagram in the question, you can see that the length of MN is twice the length of MP. So multiply the length of MP, which is 5.7, by 2:
5.7 · 2 = 11.4
Answer: The length of MN is 11.4 units
___________________________________________________________
Question 2:How to solve Part ALook at the first image below ↓
Description of the first image:
The first image shows a drawn image of the circle with labeled parts and measurements from the infomation given from the question.
The diameter is 26cm, which means that the radius is 13cm because the radius half of the diameter in a circle. The very top line is the surface of the water where it’s filled and it has a length of 20cm. Side b of the triangle is 10cm becuase it’s half the length of the the surface of the water bowl. The hypotenuse (side c) is 13cm because it’s the length of the radius. And side a is what what we need to find because it’s the distance between the surface of the water and the center of the bowl. But after when you find the length of side a, you need to add the length of the radius (which is 13cm) to the length of side a because that’s the rest of the length/depth of the water that’s filled in the bowl. The length of the radius is included with the depth of the water.
Total information given:
⇒ radius = 13cm – because the radius is half of the diameter, and the diameter has a length of 26cm
⇒ length of the surface where the water’s filled = 20cm
⇒ hypotenuse (side c) = 13cm – because it’s the length of the radius
⇒ side b = 10cm – because it’s half the length of the surface where the water’s filled
To Solve
Since there is a right triangle shown in the image, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the missing length of side a. Plug the given values of c and b into the formula:
[tex]a^{2}+10^{2}=13^{2}[/tex]
Simplify:
[tex]a^{2}+100=169[/tex]
Subtract 100 from both sides of the equation:
[tex]a^{2}=69[/tex]
Do the square root of both sides to isolate the variable a:
[tex]\sqrt{a^{2}}=\sqrt{69}[/tex]
Evaluate:
[tex]a=\sqrt{69}[/tex] Which simplifies to [tex]a= 8.30662386....[/tex] and round it to the nearest tenth to finally get [tex]a[/tex] ≈ [tex]8.3[/tex]
This means that 8.3 is just the length of side a, which is the length between the surface of where the water’s filled and the center of the circle. But, now you need to add 13 to 8.3 to find the total depth of the water because the length of the radius is included with the depth of the water.
So,
13 + 8.3 = 21.3
Answer: The depth of the water is approximately 21.3 cm
How to solve Part B (is in the image below)Sorry for the very, VERY long explanation and the long solving process, but I really, really hope you understand and that this helps with your question! :)
Amber and Jesse are each given a clue about a mystery number. Amber's clue says the sum of half a number and eighteen. Jesse's clue says the difference of eleven minus three times a number. If Amber and Jesse have the same mystery number, what is the mystery number? **Write the equation and solve for the variable.
Answers
Answer:
1/2x + 18 = 11 - 3x
Step-by-step explanation:
x = -2
sin(73) = cos (x) pls help lol
Answers
-5x + y = -2
- 3x + 6y = -12
Answers
Answer:
1st equation: -5x+y=-2
y= -2+5x
2nd equation: -3x+6y= -12
-3x+6(-2+5x)= -12
-3x-12+30x= -12
-3x+30x=0
27x=0
x=0
The data manager for a state political party gathered data to determine how many citizens would support the party's senate candidate. He polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. Statewide data shows that the population standard deviation is 645.3. What is the approximate 90% confidence interval for this situation?
Answers
Answer:
The approximate 90% confidence interval is;
70,244 to 70,732
Step-by-step explanation:
Here, we want to calculate the approximate 90% C.I for the situation
Mathematically;
CI = mean ± (z * SD)/√n
From the question;
mean = 70,438
SD = 645.3
n = 30
we can get z from the CI table
90% CI is same as; 1.645 z-score
So , substituting these values;
CI = 70,438 ± ( 1.645 * 645.3)/√30
CI = 70,438 ± 194
So the CI = 70,438 -194 to 70,438 + 194
= 70,244 to 70,732
Answer:
B. 70,244 and 70,632
Please give me brainliest, I really need it.
Two brothers, Michael and Alan, were in a bowling league that met once a
week. From past experiences, it is known that both brothers' scores are
approximately normally distributed where Michael has a mean score of 150
with a standard deviation of 30, and Alan has a mean score of 165 with a
standard deviation of 15. Assuming that their scores are independent, which
of the following values is closest to the probability that Michael will have a
greater core than Alan in a single game?
0.16
0.28
0.31
0.33
0.37
Answers
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given parameters are;
The mean score for Michael, [tex]\bar x _1[/tex] = 150
The standard deviation, σ₁ = 30
The mean score for Alan, [tex]\bar x _2[/tex] = 165
The standard deviation, σ₂ = 15
Taking n₁ = n₂ = 1
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Taking μ₁ - μ₂ = 0
[tex]z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577[/tex]
The p-value for a z-score of -0.577 from the z-table is 0.28434
Therefore, the probability that Michael, with mean score, [tex]\bar x _1[/tex] = 150 will have a greater score than Alan, with a mean score of [tex]\bar x _2[/tex] = 165 is 0.28434 ≈ 0.28
Therefore, the correct option is 0.28
Can someone please help me
Answers
Sophie signed up for a streaming music service that costs $6 per month. The service allows Sophie to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Sophie have to pay in a month in which she downloaded 45 songs? How much would she have to pay if she downloaded ss songs?
Answers
Answer:
202.5
Step-by-step explanation:
45x0.75=33.75
then do 6x33.75=202.5
Solve the equation. Explain or show your reasoning.
1/2 x -7 = 1/3 (x-12)
Answers
Answer:
x = 18
Step-by-step explanation:
1: 1/2x - 7 = 1/3x - 4
2: 3/6x - 7 = 2/6x - 4
3: 3/6x = 2/6x + 3
4: 1/6x = 3
5: x = 18
Joey bought a 3-kilogram bag of carrots from the grocery store. He added 0.8 kilograms of carrots to a pot of vegetable soup. Then, he grated 400 grams of carrots for his carrot cake. How many kilograms of carrots does he have left?
Answers
The amount of carrots Joey has left according to the task content is; 1.8kg.
How many kilograms of carrots does he have left?It follows from the task content that the quantity of carrots he has initially is; 3 kg.
On this note, upon adding 0.8 kilograms of carrots to a pot of vegetable soup, and grated 400 grams of carrots = 0.4kg, it follows that the quantity of carrot left is;
= 3 - 0.8 - 0.4 = 1.8kg.
Read more on subtraction;
https://brainly.com/question/220101
#SPJ1