Mr. Santos wanted to know the height of the tree. He observed from a point A that the angle of elevation of the top of the tree is 36 degrees. He then moved backwards 50 ft away from the initial point A, the angle of elevation of the top of the tree was 22 degrees. Find the height of the tree.
Answer:
The height of the tree is approximately 45.51 ft.
Step-by-step explanation:
The given information are;
The angle of elevation of the top of tree is 36 degrees
The distance backwards Mr. Santos moved = 50 ft.
The new angle of elevation of the top of the tree = 22 degrees
Therefore, we have;
The angle opposite to the 50 ft. side = 180 - (180 - 36) - 22° = 14°
Therefore, we have, by sine rule;
50/(sin(14)) = X/(sin(22))
X = (sin(22)) × 50/(sin(14)) ≈ 77.42 ft.
The height of the tree, T = X × sin(36°)
T = 77.42 ft. × sin(36°) ≈ 45.51 ft.
The height of the tree is approximately 45.51 ft
Some $1.50 per oz spice and some $2.50 per oz are mixed to produce 20 oz of a mixture worth 1.90 per oz. How many oz of each should be used
Answer:
3 ounces of the seed and 7 ounces of the dried fruit.
Step-by-step explanation:
10x + 12 = [2+3(2x-4)+1]
Solve for x
Answer:
-21/4
Step-by-step explanation:
Which one is correct?
Answer:
A
Step-by-step explanation:
a polynomial function with leading term 8x ^9 has a degree of what?
Answer:
9
Step-by-step explanation:
hi! if the leading term is 8x^9, this means that this is the term with the highest power. therefore, its degree is 9.
The degree of the given polynomial is 9
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here; a polynomial function with leading term 8x⁹
Now The Degree of a Polynomial is the largest of the degrees of the individual terms. The degree of an individual term of a polynomial is the exponent of its variable and the highest degree of the terms given in the expression is the degree. And thus the expression with leading term 8x⁹ is 9
Hence, The degree of the given polynomial is 9
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The height of each story of an office building is 9 3/4 feet. The height is measured from the ceiling to the floor. The building has three underground levels for parking. A car is parked two levels below ground. At what elevation are the car’s tires relative to the ground level? Assume the ground level is at zero feet.
A) -19 1/2 feet
B) -12 feet
C) 8 feet
D) 19 1/2 feet
please explane how??
Answer:
The correct answer is A) -19 1/2
Step-by-step explanation:
Write an equation for the line that passes through (10, 17) and (20, 37)
A=1/2bh for h
Need help
Answer:
2A/b = h
Step-by-step explanation:
A=1/2bh
Multiply each side by 2
2A = 2 * 1/2 bh
2A = bh
Divide each side by b
2A/b = bh/b
2A/b = h
you have $40 to spend on n gallons of gas that costs $3.25 per gallon.
Answer:
You can buy 12 gallons of gas.
Step-by-step explanation:
I took 40 and 3.25, then divided them.
I got a very large ugly decimal. When simplified it is 12.
Could anyone please help me with this for Calculus AB? I'm not entirely sure if the answer I put down is correct or not; I got some funky graphs for it though.
Hi there! :)
C. has both jump and infinite discontinuity.
Evaluate both piecewise functions at x = 1;
1 / (x + 1) = 1 / ((1) + 1) = 1/2
2x - 1 = 2(1) - 1 = 1
As the piecewise functions contain different y-values when evaluated at
x = 1, there is a jump discontinuity at x = 1.
However, the first function also contains a vertical asymptote or infinite discontinuity where it is undefined, or at x = -1. (1 / 0 = undefined). This means that the function also contains an infinite discontinuity.
Therefore, the correct choice is:
C. has both jump and infinite discontinuity.
Determine an interest rate less than 15%, a period of investment greater than two years, and a regular payment that will result in the total amount of interest you earn being equal to the total amount of money you put in?for example, under what conditions will you have a future value of $1 000 000, having earned $500 000 interest?)
Answer:
It will take 5.29 years to double our money if we invest $500 at 14 percent interest.
Step-by-step explanation:
Let we invest $500 with the interest rate of 14% ,
Now we will find the time it is going to take to double the money
here, we use the formula of compound interest [tex]A= P( 1+\frac{r}{n}) ^{nt}[/tex]
Here, A = the amount yielded,
P = principal,
r = interest rate ,
n = number of times per year,
and t = time invested.
Now, put A= 1000 , P= 500 , R= 0.14 T= x and N= 1
[tex]1000=500(1+ 0.14)^x[/tex]
[tex]1000=500(1.14)^x[/tex]
[tex]2=1.14^x[/tex]
[tex]\log_{1.14} (2)=x[/tex]
[tex]x=5.29[/tex]
so , It will take 5.29 years to double our money if we invest $500 at 14 percent interest.
Hence , the answer is 5.29 years .
if ribbon candy costs 2.50 per foot. How many feet can you buy if u have 11.25
Currently, there are 65 members in the school computer dub. The club is gaining 12 members per year. How long will take for the dub to have at least 113
membrs?
Answer:
4 years
Step-by-step explanation:
65+12x= 113
12x=113-65
x = 48/12=4
slop intercept form of: y-5=2(x+2)
Answer: y= 2x+9
have a good day!
Can y’all help I don’t know how to do these
Answer:
The measure of angle 6 is 62 degrees.
The measure of angle 3 is 64 degrees.
The measure of angle 8 is 54 degrees.
The measure of angle 4 is 64 degrees.
The measure of angle 12 is 32 degrees.
Step-by-step explanation:
(Help please and thank you very much.)
If cat food is sold in 20 lb bags, what is the least number of bags of cat food needed for one year at this shelter, if 10 lbs of cat food is consumed per week?
Answer:
26 weeks!
Step-by-step explanation:
Hello there!
There are 52 weeks in a year, believe it or not! So, if 1 bag of food was 10 lbs, then it would be 1 bag of 10lbs x 52 weeks, so it would be 52 bags. However, we are dealing with 20 lb bags, which will last twice as long as the 10 lb bag! So, if 1 bag will last 2 weeks, and there are 52 weeks in a year, then it is weeks divided by number of weeks it takes to consume 1 bag, 52 divided by 2. 52 divided by 2 is 26.
So in 1 year, the shelter will need 26 bags of 20 lb cat food!
Hope I helped!
If you enjoyed my answer, I'd appreciate a rating and a Thanks!
What is the quotient of 3/4 1/6?
Answer: 9/2
......................
Your generation will likely be most affected by these changes. Active or passive? HELP NEEDED ASAP WILL GIVE BRAINLIEST
Answer:
Passive
Step-by-step explanation:
Active voice means that a sentence has a subject that acts upon its verb. Passive voice means that a subject is a recipient of a verb's action.
Sue is offered a job reshelving books in the University of Montana library from noon until 1 p.M. Each Friday. Her reservation wage for this task is $10 per hour. If the library director offers Sue $100 per hour, how much economic surplus will she enjoy as a result of accepting the job? Now suppose the library director announces that the earnings from the job will be divided equally among the 400 students who live in Sue's dormitory. Will Sue still accept? Explain how your answers to parts a and b illustrate one of the incentive problems inherent in income redistribution programs.
Answer:
Step-by-step explanation:
Sue's initial wage per hour = $10
Sue's wage per hour after the increase = $100
a. Economic surplus to be enjoyed = $100 - $10
= $90
Sue would enjoy an economic surplus of $90.
b. No, because in this case the wage per hour for each 400 student would be;
= [tex]\frac{100}{400}[/tex]
= $0.25
= 25 cents
Redistribution of income is the act of equal sharing of wealth among a certain number of people.
The problem here is that Sue would feel cheated with the division of the earnings among 400 students, but very happy when her wages was increased.
Though the income incentive redistribution programs reduce poverty, but it may be unfair.
Find the missing number 390x__=390,000
Answers
A 10^2
B 10^3
C 10^4
D 10^5
Answer:
B. 10 to the third power
The required missing number in 390 x __ = 390,000 is 10³. option B is correct.
The missing number in the calculation 390x__=390,000 is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the missing number be x,
Now the given expression becomes,
390 * x =390,000
x = 390,000 / 390
x = 1000
x = 10³
Thus, the required missing number in 390x__=390,000 is 10³. option B is correct.
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The following table shows how far a runner has gone in t minutes. Which of the following equations represents this information?
A. t = 350d
B. t = 300d + 100
C. d = 350t
D. d = 300t + 100 Minutes (t) Meters (d)
2 700
3 1,050
5 1,750
10 3,500
Answer:
d = 350tStep-by-step explanation:
From the information given, we need to get the rate of change of distance which is the velocity (slope.)
velocity = Δd/Δt
v = d2-d1/t2-t1
from the table;
when t = 2, d = 700
when t = 3, d = 1050
v = 1050/750/3-2
v = 350/1
v = 350
Since v = d/t
350 = d/t
cross multiply
350t = d
Rearrange:
d = 350t
Hence the equation that represents the information is d = 350t
Answer:
D
Step-by-step explanation:
Choose the definition of the function
Answer:
answer is A
Step-by-step explanation:
Buzz and Jessie are missing each other and their friend Woody. They want to meet at Woody's house which is halfway between their apartments. The distance from Buzz's apartment to Woody s house is (5x + 4) miles, while Jessie's apartment is (15x + 30) miles. How far apart do Jessie & Buzz live from each other?
Answer:10x + 26
Step-by-step explanation:
solve for w. need help pls
Answer:
w = -8
Step-by-step explanation:
19 = -9w - 5 + 6w
19 = -3w - 5
19 + 5 = -3w
24 = - 3w
w = -8
What is 2/5 of a book to 1/2 of an hour as a unit rate?
Answer: 4/5 book per hour
Step-by-step explanation: in this question, we are to rewrite (2/5)/(1/2) as unit rate.
To write this as a unit rate, what we need to do is to divide 2/5 by 1/2.
That means 2/5 divided by 1/2
Removing the division and replacing with multiplication will give 2/5 * 2/1 = 4/5 books/hour
1. The length of a
rectangle is three inches more than its width. It's area is 130 in^2. Find the width and length of the triangle.
Answer:
Length= 13in
Width= 10 in
Step-by-step explanation:
Let x=length
Let y=width
x=3+y
xy=130in^2
(3+y)y=130in^2
3y+y^2=130in^2
y^2+3y-130=0
y=10
x=3+10
x=13
Please help!!!
3(x – 10) = -9
Answer:
The answer is x = 7
Step-by-step explanation:
Divide each term by 3 and simplify. Move all terms not containing x to the right side of the equation.
Answer:
[tex]\huge\boxed{x=7}[/tex]
Step-by-step explanation:
In order to solve for x, our goal is to isolate it on one side of the equation. We can do this by reversing the equation.
Let's apply the distributive property on the left side:
[tex](3 \cdot x) + (3 \cdot -10) = -9\\\\3x-30=-9[/tex]
Add 30 to both sides:
[tex]3x - 30 + 30 = -9 + 30\\\\3x = 21[/tex]
Divide both sides by 3:
[tex]3x \div 3 = 21 \div 3\\\\x = 7[/tex]
So x = 7.
Hope this helped!
*NOTE YOU WIN 37POINT FOR ANSWERING** Clare mixes 2 1/2 cups of water with 1/3 cup of orange juice concentrate Han mixes 1 2/3 water with 1/4 a cup of orange juice concentrate which one tastes stronger?
Can someone help me?
Answer:
Step-by-step explanation:
Yeah.I would be glad to.
What do you need help with?
15 POINTS!
What is the correct answer for Dean's problem? Explain where he went wrong.
Answer:
The slope is 5/-2.
Step-by-step explanation:
Slope is y1-y2 over m1-m2 (rise over run). The first ordered pair is -2 (m1) and 11 (y1). We then subtract the second ordered pair (4 (m2) and -4 (y2)) from the first.
11 - (-4) = 11 + 4 = 15
-2 - 4 = -6
Remember, slope is rise over run (y over x), so the slope is 15/-6. Now, we must simplify. 15/-6 = 5/-2
Dean went wrong because he thought that slope was run over rise (x over y). If he had switched the two numbers, his answer would have been correct.