The figure shows a person estimating the height of a tree by looking at the
top of the tree with a mirror. Assuming that both the person and the tree form
right angles with the ground, which of the following proportions can be used
to estimate the height of the tree?
Answer:
The proportion that can be used to estimate the height of the tree is option;
A. [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]
Step-by-step explanation:
The given parameters in the question are;
The medium through which the person looks at the top of the tree = A mirror
The angle formed by the person and the tree with the ground = Right angles = 90°
The distance of the person from the mirror, d₁ = 5 ft.
The height of the person, h₁ = 6 ft.
The distance of the tree from the mirror, d₂ = 12 ft.
The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂
Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;
TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar
The corresponding legs are;
The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively
The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively
∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR
The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB
Given that θ₁ = θ₂, we have;
tan(θ₁) = tan(θ₂)
∴ tan(∠TMR) = tan(∠AMB)
[tex]tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}[/tex]
[tex]tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}[/tex]
[tex]tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}[/tex]
From tan(∠TMR) = tan(∠AMB), we have;
[tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex]
[tex]\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.[/tex]
The height of the tree, h = 14.4 ft.
Therefore, from the proportion [tex]\dfrac{h}{12} = \dfrac{6}{5}[/tex] the height of the tree can be estimated.
The price of a sweater was reduced from $20.00 to $12.00. By what percentage was the price of the sweater reduced?
Answer:
%40 Off
Step-by-step explanation:
A mortgage has the terms shown below:
Balloon mortgage
$300,000
25/5 balloon
6% annual rate
Initial Monthly Payment: $1932.90
What is the amount of the balloon payment rounded to the nearest dollar?
How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used to calculate your answer. Please don't link me any answers, I am unable to open them.
There's a slight problem with your question, but we'll get to that...
Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by
• a (1) = 1
• a (n) = a (n - 1) + 21 … … … for n > 1
We can find the explicit rule for the sequence by iterative substitution:
a (2) = a (1) + 21
a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21
a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21
and so on, with the general pattern
a (n) = a (1) + 21 (n - 1) = 21n - 20
Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is
a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332
or more compactly,
[tex]\displaystyle\sum_{n=1}^N a(n) = 2332[/tex]
It's important to note that N must be some positive integer.
Replace a (n) by the explicit rule:
[tex]\displaystyle\sum_{n=1}^N (21n-20) = 2332[/tex]
Expand the sum on the left as
[tex]\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332[/tex]
and recall the formulas,
[tex]\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n[/tex]
[tex]\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2[/tex]
So the sum of the first N terms of a (n) is such that
21 × N (N + 1)/2 - 20N = 2332
Solve for N :
21 (N ² + N) - 40N = 4664
21 N ² - 19 N - 4664 = 0
Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead
N = (19 ± √392,137)/42 ≈ -14.45 or 15.36
so there is no positive integer N for which the first N terms of the sum add up to 2332.
Plz help this is due by tomorrow
Answer:
3.4
Step-by-step explanation:
just divide 8.16 by 2.4
:)
If you place a 29-foot ladder against the top of a building and the bottom of the ladder is 24 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.
Answer:
16.3
Step-by-step explanation:
The height of the building to the nearest tenth is 16. 3 ft
The situation forms a right triangle.
Properties of a right triangle:One of its angles is 90 degreesThe sides can can be found using Pythagoras theorem.The length of the ladder is the hypotenuse of the triangle formed.
The distance from the foot of the ladder to the bottom of the building is the adjacent sides.
Therefore,
c² = a² + b²
where
c = hypotenuse
a and b are the other two legs.
b² = 29² - 24²
b² = 841 - 576
b = √265
b = 16.2788205961
b = 16.3 ft
learn more on right angle here: https://brainly.com/question/23919428?referrer=searchResults
if f (12) =4(12)-20 which function represents f(x)?
Answer:F(x)=4x-20
Step-by-step explanation:
The X on both sides is 12.
Answer:
The graph of f (x)=[x+2] after it is translated 4 units to the right
Nathan and Noah each bought a video game. Nathan spent $62.40 on his game. Noah spent 3/4 as much as Nathan. How much did Noah spend on his video game?
Answer:Noah spent $46.80 on video game.
Step-by-step explanation:
Amount spent on game by Nathan =$62.40
Amount spent on game by Noah =3/4 as much as Nathan.
Therefore Noah spent 3/4 x $62.40= $46.80 on video game.
Jenny went on a walk everyday for 4 weeks with her dog. She got paid $30 dollars everyday. How much money does she have?
Answer:
$840
Step-by-step explanation:
4 weeks = 28 days
28 x 30 = 840
I need help I don't know how to do this
Answer:
Step-by-step explanation:
Your construction company needs to pay a large bill for materials. You decide to pay the bill over the next few months. The bill is $8,970. The first month, you paid $1,250. How much do you still owe for the materials?
$5,970
$6,720
$7,720
$10,120
$10,220
Answer: 7,720
The answer is 7,720! got the question correct with it
Is -5, 12, 29, 46 an arthmetic sequence
Answer:
Yes
Step-by-step explanation:
PLEASE HELP ANS HURRY!
Abigail and her children went into a bakery and she bought $11.25 worth of cupcakes and cookies. Each cupcake costs $3.75 and each cookie costs $0.75. She bought a total of 7 cupcakes and cookies altogether. Graphically solve a system of equations in order to determine the number of cupcakes, x,x, and the number of cookies, y,y, that Abigail bought.
Number of cupcakes 2
number od cookies 5
7. A boy on ice skates has a momentum of 200 kg m/s to the left at a velocity of 20
m/s. How fast is the boy going?
Answer: 10 m/s
Step-by-step explanation:
Given
Momentum of boy [tex]P=200\ kg.m/s[/tex]
Mass of boy is [tex]m=20\ kg[/tex]
Momentum is the product of mass and velocity
[tex]P=mv[/tex]
Substitute value
[tex]\Rightarrow 200=20\times v\\\Rightarrow v=10\ m/s[/tex]
Thus, the boy is moving with a velocity of 10 m/s
Can someone plz help me
Answer:
A = 28.27
Step-by-step explanation:
Answer:
9pi meters^2
Step-by-step explanation:
The area of a circle is pi * r^2. Basically, pi is simplified to 3.14 but for an exact answer, you'd leave it as a symbol. the "r" stands for the radius which is given(3). we square 3 to get 9. so the answer should be 9 pi or about 28.26.
A child's ticket to a concert costs x and an adult ticket cost four times as much as a child's ticket The difference between Mrs. Royal ticket and her
child's tickets is $600.
(a) Write an equation to show this information.
(b) Solve your equation and write down the cost of an adult ticket.
Answer:
Mrs.Royal's ticket costs $800.
Step-by-step explanation:
Child's Ticket= x
Adult's Ticket= 4x
4x-x=600
3x=600
x=200
200*4=800
Find the values of x and y . Write your answer in simplest form.
Answer:
y = 4 root 3, x = 8
Step-by-step explanation:
If 1llm, find the value of x
Answer:
D
Step-by-step explanation:
HAHAHA
Answer:
E) 22
Step-by-step explanation:
[tex] l || m\: \&\:line\: j\: is \: their \: transversal [/tex]..... (given)
[tex]\therefore(5x - 16)\degree = (2x)\degree + 50\degree [/tex]
(Corresponding angles)
[tex]\therefore(5x - 16)\degree = (2x+50)\degree [/tex]
[tex]\therefore 5x - 16 = 2x+50 [/tex]
[tex]\therefore 5x - 2x = 16+50 [/tex]
[tex]\therefore 3x = 66 [/tex]
[tex]\therefore x =\frac {66}{3} [/tex]
[tex]\therefore x =22 [/tex]
Find the value of x.
X =
Tell whether the side lengths form a Pythagorean triple.
o yes
no
Answer:
x = √72 and yes, it forms a Pythagorean triple
Step-by-step explanation:
a^2 + b^2 = c^2,
3 is a, x is b, anf 9 is c
3^2 + x^2 = 9^2
9 + x^2 = 81
Subtract 9 from both sides
x^2 = 72
x = √72
a Pythagorean triple is a^2 + b^2 = c^2, and this has it
Answer:
X = 9.4
Step-by-step explanation:
Pythagorean Theorem:
Formula: a² + b² = c²
9 x 9 = 81 3 x 3 = 9 81 + 9 = 90 √90 = 9.48 (Rounded 9.5)- A Pythagorean triple consists of any three positive integers.
Please show your work the answer is 80cm^2 I js need the work please will mark brainliest extra points
Answer:
30.1 ft²
Step-by-step explanation:
The area of a triangle with an included angle and two sides cam be found using the formula, A = ½*ab*sin(C)
a = 7 ft
b = 9 ft
C = 73°
Plug in the values
Area = ½*7*9*sin(73)
Area = 30.1235998 ≈ 30.1 ft² (nearest tenth)
what is family ?
saw this is wuestion
MARK ME AS BRAINLIEST OK FRIEND
Family is a group of people who want as well as choose to be together embraced by a bond so powerful and strong that not even the slightest test of trials and troubles can breach.Family means nobody gets left behind or forgotten.
Answer:
Hello There!!
Step-by-step explanation:
Family consists of parents and their children.
hope this helps,have a great day!!
~Pinky~
Find the following measure for this figure.
A
Х
0/60°
6
B
Area of circle =
O 6 square units
O 12 x square units
36 x square units
Answer:
Find the following measure for this figure. Area of circle = 36 I square units. Image: Find the following measure for this figure.
Step-by-step explanation:
23% of a number is 147.2.
What is the original number?
the answer is 640.
if you take 640 and multiply it by .23 (because of 23%), you get 147.2 which is exactly what you are looking for.
Hope this helps! :)
"The frequency of an event uses counting numbers, but the __________________ of an event uses a percent or a number between 0 and 1."
The frequency of an event uses counting numbers, but the ___Relative Frequency__ of an event uses a percent or a number between 0 and 1.
How to find the relative frequency?Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
It ranges from 0 to 1 (since sub group's count ≤ total count. Expressing this decimal form to percent make it range from 0% to 100%
Thus, the frequency of an event uses counting numbers, but the ___Relative Frequency__ of an event uses a percent or a number between 0 and 1.
Learn more about relative frequency here:
https://brainly.com/question/8358304
HELP, MCQ urgent, now
Answer:
angle 13 and 16 is your answer ☺️☺️☺️
Answer:
∠13 and ∠16.
Step-by-step explanation:
The definition of adjacent angles is "two angles that have a common vertex and a common side but do not overlap" (Varsity Tutors). In accordance with the standards, only angles 13 and 16 are adjacent.
Hope this helps!
Which of the graphs represent the equation y=5x-4 and also correctly states whether it is linear or non linear.
Answer:
B
Step-by-step explanation:
Hi! Because the equation is y=5x-4, it tells is that it intersects with the y axis at -4, and that it's slope goes up 5, right 1. Since B is the only graph that shows that, the answer is b.
ASAP WILL MARK BRAINLIEST
Find the volume of the following. Give exact values. I
A sphere with radius 9
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Volume
= 4 / 3 πr ^ 3
= 4 / 3 × π × 93
= 972π
= 3053.6280592893 feet3
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Branilest?
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
ASAP PLS PLS PLS my heart is so brocken if you don't tell me
Answer: meters: 3 6 9 12
Millimeters: 6,000 7,000 9,000
Step-by-step explanation:
Your adding by 3 in meters and then after 7,000 you have 9,000 then 10,000
I hope this helped!
Answer: 1: 6, 2: 7, 3: 9000, 4: 10
im sure thats it
Step-by-step explanation:
Use the first three non-zero terms of a Maclaurin series to estimate the integral from 0 to 1 of the cosine of x squared, dx .
0.905
0.904
0.806
1.016
At last week's track meet, Stacy ran 9/12 of a km, Jules ran 4/5 of a km, and Raul ran 3/4 of a mile. Which two students ran the same distance?
Answer: No two students ran same distance
Step-by-step explanation:
Given
Stacy ran [tex]\frac{9}{12}[/tex] of a km i.e.
[tex]\Rightarrow 1\times \dfrac{9}{12}=\dfrac{3}{4}=0.75\ km[/tex]
Jules ran [tex]\frac{4}{5}[/tex] of a km i.e.
[tex]\Rightarrow 1\times \dfrac{4}{5}=0.8\ km[/tex]
Raul ran [tex]\frac{3}{4}[/tex] of mile i.e.
[tex]\Rightarrow 1\times \dfrac{3}{4}=0.75\ miles\\\\\text{1 mile=1.6 km}\\\\\Rightarrow 0.75\ miles=1.2\ km[/tex]
So, no two students ran the same distance.
