Question 4.
The angle of elevation of the top of a tree from a point on the ground 22 m away is 24⁰°.
Calculate the height of the tree (in metres) correct to 2 decimal places.
22 m
tree
Answers
Answer:
9.80 m
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.
__
setupThe geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...
Tan = Opposite/Adjacent
Using the given values, we have ...
tan(24°) = AC/AB = (tree height)/(distance from tree)
tan(24°) = AC/(22 m)
solutionMultiplying by 22 m gives ...
tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m
The height of the tree is about 9.80 meters.
Related Questions
what type of parent function is f(x) = |x|
Answers
Answer: Absolute value function
The type of parent function is f(x)= |x| is Absolute valued function
What is Absolute valued function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
Given function:
f(x)= |x|
As, we know the modulus generally give the absolute value of any function and also the modulus always give the positive value.
The above property perfectly resemble the absolute valued function.
Learn more about absolute valued function here:
brainly.com/question/18405415
#SPJ1
A square has a perimeter of 64 yd. What is the length of each side?
Answers
[tex]\huge\sf\color{red}{Answer:}[/tex]
Formula:
To get the length of each side just divide it by 4.Lets solve : )
64 ÷ 4 = 16.So the answer would be [tex]\large\sf\color{red}{16}[/tex]
What is the mean, median, and mode for this set of data:24, 20, 26, 24, 21?
Answers
Answer:
Mean = 23
Median = 24
Mode = 24
Step-by-step explanation:
Mean: The sum of all data values divided by the total number of data values.
⇒ Mean = (24 + 20 + 26 + 24 + 21) ÷ 5 = 23
Median: The middle value when all data values are placed in order of size.
Ordered data values: 20, 21, 24, 24, 26
⇒ Median = 24
Mode: The most frequently occurring data value.
20, 21, 24, 24, 26
⇒ Mode = 24
If Q, DE=FG. Which must be true? Select all that apply.
Answers
Answer:
A and E
Step-by-step explanation:
A is already given by the basic fact that DE = FG. this makes the 2 lines automatically also congruent.
but this does not tell us anything about EF.
E and F could be very close together or far apart, and still DE = FG can be true in either case.
and that is why B, C and D could be true, but they are not in all cases true, and therefore these statements are in general false.
brainiestI WILL GIVE BRAINLIEST look at the right angled triangle abc
the square fits exactly inside the triangle
work out the sizes of angles x y and z
Answers
Answer:
x = 90°
y = 40°
z = 40°
Explanation (Concepts) :
A straight line has total 180° angle. A square has 4 sides of each 90° angle. A triangle is build up of 180° interior angle.
Workouts:
z + 90° + 50° = 180°
z = 180° - 90° - 50°
z = 40°
=================
x + 90° = 180°
x = 180° - 90°
x = 90°
==================
50° + 90° + y = 180°
y = 180° - 90° - 50°
y = 40°
Answer:
x = 90°y = 40°z = 40°Step-by-step explanation:
x = 90°
…………………
y = 90 - 50
= 40°
……………………………
z = 180 - (50 + 90)
= 180 - 140
= 40°
Can someone help with number 4. I will reward brainliest.
Answers
Answer:
theta = pi/6 and
theta = 5pi/6
Step-by-step explanation:
see image. Factor the expression. Solve for sin theta. Then use a calculator or unit circle to solve for theta. See image.
Let's simplify the problem down a little:
⇒ set 'sin(θ)' as x
⇒ the new equation looks like: [tex]2x^2+5x-3=0[/tex]
Now let's solve this equation as a quadratic:
[tex]2x^2+5x-3=0\\(2x-1)(x+3)=0\\\\2x-1=0\\x = \frac{1}{2} \\\\x+3 = 0\\x=-3[/tex]
Now set the x value of '1/2', to sin(θ)
it can't be -3, because trig functions can't equal a negative numbersin(θ) = 1/2
θ = π/6, which is between the range given
Answer: π/6
Hope that helps!
These box plots show the basketball scores for two teams.
Which statement is the most appropriate comparison of the spreads?
Answers
The most appropriate statement is the interquartile range for the Wolverines, 30 is less than the IQR for the panthers, 40.
What is the correct statement?
The box plot is used to show the distribution of data. The box plot can be used to determine the range, interquartile range and median of the data set.
The range is the difference between the two ends of the whiskers.
Range for the Wolverines = 96 - 35 = 61
Range for the Panthers = 107 - 33 = 74
The interquartile range is the difference between the first and third lines on the box
IQR for the Wolverines = 85 - 55 = 30
Range for the Panthers = 90 - 50 = 40
To learn more about box plots, please check: https://brainly.com/question/1523909
#SPJ1
x² + 8x = 10 solve this quadratic equation by completing the square
Answers
Joshua has a ladder that is 15 feet long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 14.2 feet above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78 degrees. Will the ladder be safe at this height? Show your work and label the diagram
Answers
Answer:
Step-by-step explanation:
I need help with area
The question 5 and 6
Answers
hb/2 where h is height and b is base so
5: (5.4)(8.5)/2=22.95 yds
6: (5.1)(8.6)/2=21.93 ft
f(-2)for the function f(x)=3x-1
Answers
Step-by-step explanation:
From what I know
3x-1=0
3*(-2)-1=0
-6-1=0
=-7.
I'm not sure but u can try it.
The value of f(-2) in this function is f(-2) = -7
To solve this expression, just replace 'x' with -2. When the expression is ready, let's calculate it.
First we multiply or divide, then add or subtract.
Resolutionf( x ) = 3x - 1
f(-2) = 3 · (-2) - 1
f(-2) = -6 - 1
f(-2) = -7
So, the alternative value is f(-2) = -7
I will give brainliest! 40 points!
ling wants to determine the average distance she travels each day in her car. she records the odometer reading, which measures the distance the car has traveled, each morning for a week.
day 1 2 3 4 5 6 7
odometer (mi) 10,150 10,211 10,424 10,769 10,884 11,155 11,477
what is the mean distance ling travels each day? show your work.
Answers
Answer:
221.16
Step-by-step explanation:
Find the difference between each day. Add all the differences together, then divide that number by 6 (the number of differences) to find the mean.
Answer:
189.57 miles per day.
Step-by-step explanation:
I took the test
Please help
Which equation represents a line with an undefined slope?
Answers
Answer:
x = 0
Step-by-step explanation:
The slope relation is given as :
y = mx + b
Now, if we take x = 0, there is no way of finding out the value of m as the product of mx will be equal to 0.
Hence, x = 0 represents a line with undefined slope.
Find the length of the segment AB.
Answers
We can first draw two more lines to complete the triangle.
We then have two more lines, one with a length of 5, and another with a length of 7.
The Pythagorean theorem states that a^2 + b^2 = c^2.
7^2 is 49, and 5^2 is 25.
Add those together and you get 74.
We then square 74, and get 8.602, which we can round to 8.6.
The length of segment AB is 8.6.
Hope this helps!
Find the LCM of 3, 7, 10
Answers
Explanation=
3|3,7,10
7|1,7,10
2 |1, 1,10
5|1, 1, 5
| 1, 1, 1
LCM of 3,7,10= 3x7x2x5
=21x10
=210 ans
Two socks are selected at random from a draw of loose socks- there are 4 green socks and 6 yellow socks
What is the probability that two of the socks will both be green if the socks are drawn without replacement
Answers
Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, we have that the values of the parameters are:
N = 10, k = 4, n = 2.
The probability that both are green is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333[/tex]
0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
More can be learned about the hypergeometric distribution at https://brainly.com/question/24826394
#SPJ1
A. The graph is translated 2units down.
B. The graph is translated 2 units left.
C. The graph is translated 2 units right.
D. The graph is translated 2 units up.
Answers
Answer:
c
Step-by-step explanation:
the -2 causes a shift 2 units right
The measure of angle Q is 70 degrees. Find the measure of angle p
Please answer quick please! 30 points
Answers
answer the question below, will give brainliest to first answer
Answers
Answer:
deductive reasoning
Step-by-step explanation:
it is based on what is true based on what happened before
Answer:
2 option, deductive reasoning
Step-by-step explanation:
based on true events
Factorize -3x^3 + 12x^2 - 15x + 6
With the steps please
Answers
[tex]-3x^3 +12x^2 -15x +6\\\\=-3(x^3 -4x^2 +5x-2)\\\\=-3(x^3 -2x^2-2x^2 +4x+x-2)\\\\=-3\textbf{[} x^2(x-2) -2x(x-2)+ (x-2)\textbf{]}\\\\=-3(x-2)(x^2 -2x +1)\\\\=-3(x-2)(x-1)^2[/tex]
The number of guppies in an aquarium is doubling every day. there are 4 guppies initially in the aquarium. a) write an exponential function for the guppy population in the aquarium. b) how many guppies are in the aquarium after 4 days
Answers
if the guppies are doubling, that means whatever they were yesterday, today is 100% more, so the rate of growth is 100%.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=4(1 + 1.)^{t}\implies A=4(2)^t~\hfill \stackrel{\textit{after 4 days, t = 4}}{A=4(2)^4}\implies A=64[/tex]
What is the sign of m/n X (-m X n squared )
positive
Negative
zero
Answers
Step-by-step explanation:
mx=n
⟹x=mn
Since m and n are both negative, x=mn will be positive.
Hence, the solution of mx=n will be a positive number.
other sulotion :-
A stack of 30 science flashcards includes a review card for each of the following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting a tree or a flower?
Express the Probability as a reduced fraction
Answers
The probability of randomly selecting a tree or a flower is 8/15.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability of randomly selecting a tree or a flower = (number of trees / total number of flash cards) + (number of flowers / total number of flash cards)
8/30 + 8/30 = 16/30 = 8/15
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
A jar has 10 red marbles, 6 purple marbles, and 4 turquoise marbles. Grace wins if she selects a turquoise marble from the jar. Is this game fair? Why or why not?
Yes, the game is fair because Grace has equal probabilities of winning and losing.
Yes, the game is fair because Grace has equal probabilities of choosing a marble of either color.
No, the game is not fair because Grace has equal probabilities of winning and losing.
No, the game is not fair because Grace has a higher probability of choosing a marble of another color.
Answers
Please Help! The value of x is:
Answers
Answer:
9
Step-by-step explanation:
5*x=15
X=3
3*3=9
[tex]\\ \rm\dashrightarrow \dfrac{5}{3}=\dfrac{15}{x}[/tex]
[tex]\\ \rm\dashrightarrow 5x=45[/tex]
[tex]\\ \rm\dashrightarrow x=\dfrac{45}{5}[/tex]
[tex]\\ \rm\dashrightarrow x=9[/tex}
1 pound is equivalent to ____ grams.
Answers
Answer:
1 pound is equivalent to 453.59237 Grams.
✎let's answer it :3
☟ answer
-> ( 453.59237 grams )
hope it helps
by #galadohannadivine29What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = 2x2 +15?
OA. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units up.
OB. The graph of f(x) is horizontally stretched by a factor of 2 and
shifted 15 units up.
OC. The graph of f(x) is vertically stretched by a factor of 2 and shifted
15 units to the left.
D. The graph of f(x) is horizontally compressed by a factor of 2 and
shifted 15 units to the left.
Answers
Answer:
A
Step-by-step explanation:
h(x) = 2x² + 15 = 2×f(x) + 15
so, every y value of f(x) is multiplied by 2, and that means the whole curve is stretched up and down (vertically).
and then we add constantly 15 to every y value. that moves then the previous stretched result up by 15 units.
no solution, one solution, or infinitely many solutions?
Answers
8v + 3 -4v = 4v + 5 -3 has infinitely many solutions
7v - 11 = 7v + 11 has no solution
3(v-4) = 2(v-6) has one solution
5(2v+3) - 2 = 12v + 12 -2v has no solution
When does an equation have one solution, no solution or infinitely many solutions?A linear equation is said to have infinitely many solution when the variable term and the constant term are the same on both sides of the equation.
A linear equation is said to have no solution, if the coefficient of the variable term is zero and the constant term a non-zero term
A linear equation is said to have one solution if the coefficient of both the constant term and the variable terms are no zero.
Analysis:
8v + 3 -4v = 4v + 5-2
4v +3 = 4v+3
The equation has an infinitely many solutions
7v-11 = 7v+11
7v-7v = 11+11
0v = 22
The equation has no solution since the coefficient of the variable term is 0
3(v-4) = 2(v-6)
3v -12 = 2v - 12
v = 12-12 = 0
The equation has one solution
5(2v+3) -2 = 12v + 12-2v
10v+15-2 = 10v +12
0v = -1
The equation has no solution.
In conclusion,
8v + 3 -4v = 4v + 5 -3 has infinitely many solutions
7v - 11 = 7v + 11 has no solution
3(v-4) = 2(v-6) has one solution
5(2v+3) - 2 = 12v + 12 -2v has no solution
Learn more about equations with infinitely many solutions: brainly.com/question/11695252
#SPJ1
Line segment pr is a directed line segment beginning at p(-10,7) and ending at r(8,-5). find point q on the line segment pr that partitions it into the segments pq and qr in the ratio 4:5.
Answers
[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,7)\qquad R(8,-5)\qquad \qquad \stackrel{\textit{ratio from P to R}}{4:5} \\\\\\ \cfrac{P\underline{Q}}{\underline{Q} R} = \cfrac{4}{5}\implies \cfrac{P}{R} = \cfrac{4}{5}\implies 5P=4R\implies 5(-10,7)=4(8,-5)[/tex]
[tex](\stackrel{x}{-50}~~,~~ \stackrel{y}{35})=(\stackrel{x}{32}~~,~~ \stackrel{y}{-20})\implies Q=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-50 +32}}{4+5}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{35 -20}}{4+5} \right)} \\\\\\ Q=\left( \cfrac{-18}{9}~~,~~\cfrac{15}{9} \right)\implies Q=\left( -2~~,~~\cfrac{5}{3} \right)[/tex]
Find the y-value when x = -5 for the equation y = -3x
Answers
Answer:
y=15 is the answers for the question
Step-by-step explanation:
please mark me as brainlest