A Christmas tree is supported by a wire that is 9 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 41 meters shorter than the height of the tree. What is the height of the tree
Answers
Answer:
The height of the tree is 80 meters.
Step-by-step explanation:
Let the height of the Christmas tree be x meters.
Then the length of the wire will be, (x + 9) meters.
And the wire will (x - 41) meters away from the base of the tree.
Consider the diagram below.
Use Pythagoras theorem to solve for x as follows:
[tex]AB^{2}=AC^{2}+CB^{2}[/tex]
[tex](x+9)^{2}=x^{2}+(x-41)^{2}\\\\x^{2}+18x+81=x^{2}+x^{2}-82x+1681\\\\x^{2}-100x+1600=0\\\\x^{2} -80x-20x+1600=0\\\\x(x-80)-20(x-80)=0\\\\(x-80)(x-20)=0[/tex]
The value of x is either 80 or 20.
If x = 20, then the base CB will be -21. This is not possible as length is always positive.
Thus, the value of x is 80.
Hence, the height of the tree is 80 meters.
Related Questions
Help pleaseee !!!!!!
Answers
Jerry started doing sit-ups every day. The first day he did 16 sit-ups. Every day after that he did 4 more sit-
ups than he had done the previous day. Today Jerry did 32 sit-ups. Enter an equation that could be solved
to find the number of days Jerry has been doing sit-ups, not counting the first day.
The equation
doing sit-ups.
can help find the number of days Jerry has been
Answers
Answer:
16+(4*x)=32
Step-by-step explanation:
x is equal to the number of days he did sit ups. You can solve this by solving for x.
Find the inverse of the matrix:
A =
4 2
3 2
Step 1: Calculate the determinant:
Answers
Answer:
The answers are correct.
Step-by-step explanation:
Please rate the answer and like it if it helped.
The Lakeside Marina charges a $35 rental fee for a boat in addition to charging $15 per hour. What is the cost of a rental for 3 hours? Show your work.
Answers
Answer:
80
Step-by-step explanation:
35 + 15x
x=3
15. 3 =45
45+35=80
Question 4 If 5 pounds of oranges costs $11.55, how much would it cost for 12 pounds of oranges?
Answers
Answer:
4.8125
Step-by-step explanation:
divide 5 by 12 then multiply 11.55
Decide whether a line with the given slope m=7/6 slants upward or downward from left to right, or whether its horizontal or vertical
Answers
PLEASE HELP! BEST ANSWER MARKED AS BRAINLIEST!!!!!!!!!!!!!!!!!!!
What is the least common multiple of 4, 12, and 15?
Answers
Answer:
60
Step-by-step explanation:
4*15=60=12*5
the prime factor of 4 is 2
the prime factors of 12 are 2 and 3
the prime factors of 15 are 3 and 5
Find the midpoint of the segment with the following endpoints (-3,-3) (1,2)
Answers
What is the complete factorization of the polynomial below?
x3 + 9x2 + 26x + 24
A. (x+3)(x+3)(x + 1)
B. (X + 8)(x+3)(x + 1)
C. (x+6)(x + 2)(x + 2)
D. (x + 4)(x+3)(x + 2)
Answers
Answer:
D) (x + 4)(x+3)(x+2)
Step-by-step explanation:
Used synthetic division to find factors.
Select all tables that represent a proportional relationship between x and y.
x 2 6 7 10
y 8 24 28 40
x 0 5 10 15
y 10 15 20 25
x –2 0 3 5
y –6 0 9 15
x 0 1 2 3
y 4 5 6 7
x –8 –6 –4 –2
y –9 –7 –5 –3
Answers
The answer is B, D , and E
Step-by-step explanation:
You have to look for the same pattern on both rows, wether they come out even or odd.
-6(5r - 6) + 4(6 + 4r)
Answers
Answer: -14r + 60
your welcome.
Greeks bucked a global trend in which people in most countries expect their lives in five years to be better than their current lives. Even among those countries with much lower currrent life ratings, greater optimism was found because people cannot fathom their lives getting worse. But in Greece, only 25% expect their lives to be better in five years. In a simple random sample of 1100 Greek citizens, what is the probability that less than 27 percent of the sample expect their lives to be better in five years?
Answers
Answer:
The value is [tex]P( p < 0.27 ) = 0.67792[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is p= 0.25
The sample size is n = 100
Generally given that the sample size is sufficiently large n > 30 , the mean of this sampling distribution is mathematically represented as
[tex]\mu_{x} = p = 0.25[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \frac{ p(1 - p)}{n} }[/tex]
=> [tex]\sigma = \sqrt{ \frac{ 0.25 (1 - 0.25 )}{100} }[/tex]
=> [tex]\sigma = 0.0433[/tex]
Generally the probability that less than 27 percent (0.27)of the sample expect their lives to be better in five year is mathematically represented as
[tex]P( p < 0.27 ) = P( \frac{ p - \mu_{x}}{\sigma} < \frac{0.27 - 0.25 }{ 0.0433} )[/tex]
[tex]\frac{p -\mu}{\sigma } = Z (The \ standardized \ value\ of \ p )[/tex]
=> [tex]P( p < 0.27 ) = P( Z< 0.4619 )[/tex]
From the z table the area under the normal curve to the left corresponding to 0.4619 is
[tex]P( Z< 0.4619 ) = 0.67792[/tex]
[tex]P( p < 0.27 ) = 0.67792[/tex]
what is the difference of the fractions? Use the number line and equivalent fractions to help find the answer. -2 1/2 - ( -1 3/4)
A: -4 1/4
B: -4
C: -3/4
D: -1/2
ANSWER ASAP PLEASE
Answers
-2 1/2 = -5/2
-1 3/4 = 7/4 positive because of subtract
=-3/4
A major airline knows that about 2 percent of passengers do not manage to show up for their flight. Consider a small aircraft having 50 seats, and suppose that an airline sells precisely 50 tickets for a specific flight. Assuming that all passsengers are independent and have the same probability of not showing up, compute the probability that
Answers
Answer:
a. The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is = 0.6354
Step-by-step explanation:
From the given information:
We are to compute the probability that:
a. The aircraft is fully occupied( i.e. all the passengers show up)
b. Between 1 and 5 (including 1 and 5) passengers do not show up
Given that:
Percentage of passengers that do not show up = 2% = 0.02
And the population of the passengers = 50; since 50 tickets are being sold for a specific flight.
Let assume X be the random variable that follows a binomial distribution, thus, the number of passengers from the aircraft with 50 passengers can be represented as:
[tex]X \sim Bin (n = 50, p =0.02)[/tex]
Thus;
The probability that the aircraft is fully occupied i.e. all the passengers show up is:
[tex]= (1 - 0.02)^{50}[/tex]
= 0.98⁵⁰
= 0.3642
Hence, The probability that the aircraft is fully occupied = 0.3642
b. The probability that between 1 and 5 (including 1 and 5) passengers do not show up is:
= P(X = 1) + P(X =2) + P(X = 3) + P(X = 4) + P(X = 5)
= [tex]=(^{50}_1) 0.02(1-0.02)^{50-1} +(^{50}_2) 0.02(1-0.02)^{50-2} + (^{50}_3) 0.02(1-0.02)^{50-3} + ... + (^{50}_5) 0.02(1-0.02)^{50-5}[/tex]
[tex]=(^{50}_1) 0.02(0.98)^{49} +(^{50}_2) 0.02(0.98)^{48} + (^{50}_3) 0.02(0.98)^{47} + ... + (^{50}_5) 0.02(0.98)^{45}[/tex]
= 0.6354
Hence, The probability that between 1 and 5 (including 1 and 5) passengers do not show up is = 0.6354
What is the slope of the line shown on the graph?
Answers
Answer: 2/4
Step-by-step explanation:
Rise=2
Run=4
Rise/Run(2/4)
Answer:
slope = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
What’s 4/9z - 3/9z + 5 - 5/9z - 8
Answers
Answer:
=−4/9z−3
Step-by-step explanation:
4
9
z−
3
9
z+5−
5
9
z−8
=
4
9
z+
−1
3
z+5+
−5
9
z+−8
Combine Like Terms:
=
4
9
z+
−1/3
z+5+
−5
9
z+−8
=(4/9z+−1/3z+−5/9z)+(5+−8)
80 total students 6/2 are girls how many are girls
Answers
Answer:
60
Step-by-step explanation:
12.5, 25, 37.5, 50 (What is the pattern?)
Answers
Answer:
adding 12.5
Step-by-step explanation:
12.5 --> 25 through +12.5
25 --> 37.5 through +12.5
37.5+12.5 = 50 = 50
Answer:
You are adding 12.5 every time.
Step-by-step explanation:
12.5+12.5=25
25+12.5= 37.5
37.5+12.5=50
Hope this helps!
Difference of 9p3q2 and 13p3q2
Answers
I hope this helps!
Round the weight of one dose to the nearest gram
Answers
Answer:
whats the weights?
Step-by-step explanation:
PLEASE HELP ILL GIVE YOU BRAINLIEST I REALLY NEEW THE ANSWER
Answers
Answer:
i need more info
Step-by-step explanation:
Answer:
exact form is 31/50
decimal form 0.62
Step-by-step explanation:
Find each percent decrease.Round to the nearest percent.
Answers
Answer:
7. 33%
6. 75%
8. 67%
Step-by-step explanation:
5. 80-15=65
65/85=0.8125 => 81%
6. 100-25= 75
75/100= 0.75=> 75%
7. 60-40=20
20/60=0.333333=>33%
8. 39-13=26
26/39=0.666666667=67%
SOMEONE HELP ME LOL
Answers
Answer:
y=3x+1
Step-by-step explanation:
Find the surface area and volume. show your work.
Answers
9514 1404 393
Answer:
area = 211 +7√205 ≈ 311.22 square unitsvolume = 273 cubic unitsStep-by-step explanation:
Surface area
The length of the hypotenuse of the front facing triangle is given by the Pythagorean theorem:
d^2 = 13^2 +6^2 = 169 +36 = 205
d = √205
So, the perimeter of that triangle is ...
P = 13 +6 +√205 = 19 +√205
The total area of the rectangular faces of this triangular prism is then ...
rectangular face area = (base perimeter)·(prism height)
= (19 +√205)(7) = 133 +7√205
The area of the two triangular faces will be ...
triangular face total area = 2·(triangle area) = 2(1/2)(6)(13) = 78
Then the total surface area is ...
total surface area = rectangular face area + triangular face total area
total surface area = (133 +7√205) +78
surface area = 211 +7√205 ≈ 311.22 . . . . square units
__
Volume
The volume is the product of the area of the triangular base and the height of the prism.
V = Bh
V = (39)(7)
volume = 273 . . . . cubic units
what is the quotient 6x^4-8x^2 divided by 2x^2, where x does not equal 0?
Answers
Answer:
3x^2 - 4
Step-by-step explanation:
6x^4 - 8x^2 ÷ 2x^2
= 3x^2 - 4
Use the distributive property to express 24 + 36. *
O. 3 (8 + 13)
O. 6 (4 +5)
O. 12 (1 + 4)
O. 12 (2 + 3)
Answers
Answer:
12(1 + 4) AND 12(2 + 3) are the correct answers.
Step-by-step explanation:
24 + 36 = 60
12(1 + 4)=
12(5) = 60
12(2 + 3)
12(5) = 60
Hope this helps and pls do mark me brainliest if you can:)
Sam will take four science tests this quarter. Her scores on three of the tests are shown below
Test 1: 83%
Test 2: 91%
Test 3: 88%
Test 4: ?
What does Sam need to score on the fourth test to ensure that she will have an average of 90% for all four tests
Answers
please help me with this i don’t know
Answers
Jacob runs total 12 miles run
Answer:
The answer is the first option .
Jacob ran a total of 12 7/10 miles which is equivalent to 12.7 miles
please help 100 points!!!!!!!!!!!!!!!!!!1
Answers
Answer:
2.5
Step-by-step explanation:
Answer:
2 1/2cm is the answer for w
Step-by-step explanation:
the reason for this is because the total area for the triangle is 17 cm
and from whats shown on the rectangle it has only 12 so far so that means the w equals 2 1/2 because 12 + 2 1/2 + 2 1/2 = 17 so therefor the answer is 2 1/2cm
hope this helps :)
- by chance may I get brainliest
Please help with this question
Answers
Answer:
$8.25 is the answer.
Step-by-step explanation:
Answer:
8.25
Good luck!
