the figure below shows a 60 foot pole held in place by wires anchored at point B, 40 feet from the base of the pole.
Answers
Answer: A: 21.4
Step-by-step explanation:
For the figure, on the pole where, tower is attached, the measure of side DC is 21.4 feet.
What is right angle triangle property?In a right angle triangle, the ratio of the opposite side to the adjacent side is equal to the tangent angle between them.
[tex]\thn \theta=\dfrac{b}{a}[/tex]
Here, (a) is the adjacent side, (b) is the opposite side and [tex]\theta[/tex] is the angle made between them.
The height of the pole is 60 foot. Therefore,
[tex]AC=60\rm ft[/tex]
The distance of the wire from the base of the pole is 40 feet. Therefore,
[tex]BC=40\rm ft[/tex]
Therefore, the tangent angle can be given as,
[tex]\tan\angle(ABC)=\dfrac{60}{40}\\\angle(ABC)=\tan^{-1}(1.5)\\\angle(ABC)=56.31^o[/tex]
The angle DBC is half of the angle ABC. Thus,
[tex]\angle(DBC)=\dfrac{56.31}{2}\\\angle(DBC)=28.15^o[/tex]
Now, again in the triangle DBC, the tangent angle can be given as,
[tex]\tan(28.15)=\dfrac{DC}{40}\\DC=21.407\rm ft[/tex]
Hence, on the pole where, tower is attached, the measure of side DC is 21.4 feet.
Learn more about the right angle triangle property here;
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Related Questions
(Help please) Find both the perimeter and the area of the following rectangle
2x+3
X+6
Perimeter:_____
Area:____
Answers
Given:
Length of a rectangle = (2x+3) units
Width of the rectangle = (x+6) units
To find:
The perimeter and the area of the rectangle.
Solution:
We know that, the perimeter of the rectangle is
[tex]Perimeter=2(Length+Width)[/tex]
[tex]Perimeter=2((2x+3)+(x+6))[/tex]
[tex]Perimeter=2(3x+9)[/tex]
[tex]Perimeter=6x+18[/tex]
The area of rectangle is
[tex]Area=Length\times width[/tex]
[tex]Area=(2x+3)\times (x+6)[/tex]
[tex]Area=2x^2+12x+3x+18[/tex]
[tex]Area=2x^2+15x+18[/tex]
Therefore, [tex]Perimeter=6x+18[/tex] and [tex]Area=2x^2+15x+18[/tex].
f(x) = (x + 1)2, g(x) = 2x3
One way to find (f º g)(x) when x = −2 is to start by composing f(g(x)).
Find f(g(x)).
4x6 + 1
4x9 + 1
4x6 + 4x3 + 1
4x9 + 4x6 + 1
Answers
The function (f º g)(x) is 4x⁶ + 1. Option A
What is a function?A function can be defined as a law, rule or expression that shows the relationship between two variables in an equation.
These variables are called;
The independent variableThe dependent variableFrom the information given, we have the function;
f(x) = (x + 1)² g(x) = 2x³To determine the composite function, we have to substitute the value of g(x) as x in the function f(x), we have;
(f º g)(x) = (2x³ + 1)²
expand the bracket
(f º g)(x) = 4x⁶ + 1
Hence, the function is (f º g)(x) = 4x⁶ + 1
Learn more about functions here:
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Answer:
The first question is C: 4x^6 + 4x^3 + 1
The second question is: f(g(−2)) = 225
Step-by-step explanation:
Got it right on edg.
A four-digit code can use the numbers 1, 2, 3, 4. Any of the numbers can be repeated.
What is the total number of possible codes?
What is the probability the code will be 3333?
Answers
Answer:
256 codes
Step-by-step explanation:
does anyone know the answer ??
Answers
Answer:
I would assume 13
Step-by-step explanation:
It is an isosceles triangle and all the angles are the same, so I think it should be 13. I may be wrong, it has been a while since I did geometry.
A new gaming system costs $350. A store offers a 20%
discount on the new gaming system. What is the amount of
the discount?
Answers
Answer:
Step-by-step explanation:
350(20/100)
350(0.2)
70 dollar discount
Choose the system of equations to solve the following: Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Determine the total number of adult and student tickets. *
A: 7.25a + 5.50s = 8 and a + s = 52.75
B: 7.25a + 5.50s = 52.75 and a + s = 52.75
C: 7.25a + 5.50s = 52.75 and a + s = 8
Answers
uMMMMMMMM I don't know
help me with this please !
Answers
Find the solution of the system of equations.
−4x+5y= 13
x−5y=-22
Answers
PLS PLS HELP ME IM BEGGING YOU, PLEASE DONT ANSWER IF YOU DONT KNOW. THIS IS IMPORTANT PLEASE
Answers
Answer:
B = 12.8 cm (to 1.d.p)
D = 24.1 cm (to 1.d.p)
Step-by-step explanation:
Using Pythagoras Theorem:
B: 4^2 + 3.5^2 = 28.25
square root 28.25 = 5.3 (to 1 decimal place) so this is the length of the missing side.
To find perimeter add sides a, b and c so...
perimeter of triangle B = 12.8 cm (to 1 decimal place)
D: 10^2 - 6.5^2 = 57.75
square root 57.75 = 7.6 (to 1 decimal place) so this is the length of the missing side.
To find perimeter add sides a, b and c so...
perimeter of triangle D = 24.1 cm (to 1 decimal place)
^2 indicates squared
Sorry but I'm not too sure / confident about A or C
Simplify: 6√x•4√y^3.
Answers
howdy!
the answer is C.
Planet Fitness gym charges $15 per month plus $50 for a membership. Total
Fitness gym charges $25 per month and no membership fee. After how many months
would the total cost be the same for both gyms?
Answers
Answer:
planet fitness will take one month and total fitness will take 3 months
Step-by-step explanation:
planet fitness:
75
total fitness:
25
50
75
Type your response in the box.
Identify the purpose of the video and note the similarities between it and Twain's essay "Taming the Bicycle."
Answers
Answer:
i need the text.
Step-by-step explanation:
The video’s purpose is to instruct the viewer on the steps involved in learning how to ride a bicycle. The video has a few similarities to Twain’s essay. Both describe the process of learning how to ride a bike in a humorous way.
It’s due tonight!! I HAVE TO FIND “r” AS WELL! I NEED HELP
Answers
(12x -2) - (-3x + 4) anyone got the answer?
Answers
Answer:
15x - 6
Step-by-step explanation:
(12x -2) -1 (3x+4)
(12x - 2 + 3x-4
12x-2+3x -4
12x -6 + 3x
15x - 6
Alex only keeps ten pence coins and some twenty pence coins in
his coin box. He has a total of 18 coins which amounts to £2.30.
Work out the number of ten pence coins and twenty pence coins
in Alex's coin box.
Answers
Answer:
In the box. we have 5 20 pence coins and 13 10 pence coins
Step-by-step explanation:
Let the number of 10 pence coins be x and the number of 20 pence coins be y
The sum of these numbers is 18
Thus;
x + y = 18•••••••(i)
Writing the value in pence only
£2.30 * 100 = 230 pence
Now we have that;
total 10 pence coin amount = 10 * x = 10x
Total 20 pence coin amount = 20 * x = 20y
10x + 20y = 230
x + 2y = 23 •••••••(ii)
from ii;
x = 23-2y
Substitute this into i
23-2y + y = 18
23-18 = 2y-y
y = 5
Recall;
x + y = 18
x + 5 = 18
x = 18-5
x = 13
what type of solution is y=12?
Answers
Answer:
ordered pair solution? or the solution to y in an algebra problem? (im not completely sure)
Step-by-step explanation:
Mary rides her horse 30 miles in 2 1/2 hours. What is her average speed in miles per hour?
Answers
Answer:
12 miles per hour
Step-by-step explanation:
John and his 5 friends will share 1 1/2 pizzas if they share the pizzas equally how much pizza will each person get
Answers
Answer:
5/4
Step-by-step explanation:
HELP ME ASAPPP PLZZZZ
The blueprint for an office building uses a scale of 2 cm.:3.5 m. The height of the actual office building is 259 m. What is the height of the office building on the blueprint?
Answers
Answer:
150 cm
Step-by-step explanation:
So the scale is 2 cm on the blueprint = 3.5 meters in real life.
Basically you can just divide the height of the building by 3.5 meters:
259/3.5=75
There are 75, 3.5 meters in 259 meters
Since 3.5 meters on the print is 2 cm
You need to multiply the number of 3.5 meters by 2:
75*2=150
150 cm
Re-write the expression in radical form
Answers
Answer:
[tex]\sqrt[4]{7^3}[/tex]
Step-by-step explanation:
.The measures of the angles of a triangle are in the extended ratio 6: 1: 5. What is the measure of the largest angle?
Answers
Answer:
90
Step-by-step explanation:
Ratio = 6 : 1 : 5
Angles are 6x ,x , 5x
Sum of all the angles of the triangle = 180
6x +x +5x = 180
12x = 180
x = 180/12
x = 15
Largest angle = 6x = 6*15 = 90
SOMEBODY PLEASE HELP ME.Eric and Scott each through a javelin. The height of the javelin that Eric through can be modeled by the function f(x)=-16x^2+64x6 where f(x) represents the height in feet of the javelin after X seconds. The graph represents the height of Scots javelin as a function of time. Which statements are true?THE ANSWER CHOICES ARE IN THE PICTURE PLEASE ANSWER THIS QUESTION RIGHT
Answers
Answer: The maximum height of Scott’s and Eric’s javelins were the same
Step-by-step explanation: bc I put it as my answer and I got it right
What is 70/x = 15/21?
Answers
Answer:
98
Step-by-step explanation:
cross multiply
70×21÷15
1470/15=98
Put the following equation of a line into slope-intercept form, simplifying all fractions. 4y - 4x -32
Answers
Answer:
y=-4x+4x-32
Step-by-step explanation:
Answer:
y=x-8
Step-by-step explanation:
4y-4x=-32
4y=4x+(-32)
4y=4x-32
y=4/4x-32/4
y=x-8
3.7 Questions
You are offered a job in which you can choose any hours you want. You will be paid 13 dollars per hour. 1. Draw a large (half a sheet of lined paper) budget constraint (feasible set) with income on the y-axis and free time per day on the x-axis. Label the x and y intercepts. Draw the optimal point on your budget constraint at 10 hours of work with an indifference curve passing through it. 2. Draw the effect of a wage increase from 13 to 18 dollars per hour. Label the new y intercept. 3. Draw the effect of social security payment of $30 per day with a wage of $13 per hour. 4. What is the equation of your budget constraint in question 3? 5. If your wage doubles from 12 to 24 dollars per hour, what can we can conclude about your opportunity cost of free time? 6. How does the substitution effect change your choice of free time and why? 7. How does the income effect change your choice of free time and why?
pls do this one, I know it might seem long but it will help me out so much.
Answers
Answer:
fjdjdjxjxjdkkekxjdjdkdjdkkxfkfkakaks
A band is playing at an auditorium with floor seats and balcony seats. The band wants to sell the floor tickets for $15 each and balcony tickets for $12 each. They want to make at least $3,000 in ticket sales.
1. How much money will they collect for selling x floor tickets?
Answers
Answer:
Not sure
Step-by-step explanation:
Decrease £843 by 91% rounded to 2 DP
Answers
Answer:
Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
91% = 91/100 = 91 ÷ 100 = 0.91.
100% = 100/100 = 100 ÷ 100 = 1.
Decrease number by 91% of its value.
Percentage decrease = 91% × 843
New value = 843 - Percentage decrease
Calculate the New Value
New value =
843 - Percentage decrease =
843 - (91% × 843) =
843 - 91% × 843 =
(1 - 91%) × 843 =
(100% - 91%) × 843 =
9% × 843 =
9 ÷ 100 × 843 =
9 × 843 ÷ 100 =
7,587 ÷ 100 =
75.87
Calculate absolute change (actual difference)
Absolute change (actual difference) =
New value - 843 =
75.87 - 843 =
- 767.13
Proof.
Calculate percentage decrease:
Percentage decrease =
91% × 843 =
91 ÷ 100 × 843 =
91 × 843 ÷ 100 =
76,713 ÷ 100 =
767.13
Step-by-step explanation:
Hope it is helpful....
I need help with this please, i need it fast
Answers
Answer:
angle equals 15.466 so Answer A, 15.47
Sarah and Nathan each picked a bucket of strawberries. Sarah picked 4 1/4 and Nathan picked 3 3/4. How much more did Sarah pick than Nathan?
Answers
Answer: 1/2 buckets
Step-by-step explanation:
Sarah picked 4¹/₄ buckets of grapes and Nathan picked 3³/₄ buckets.
To find out how much Sarah picked more than Nathan, simply subtract Nathan's buckets from Sarah's.
First convert the fractions to improper fractions:
4¹/₄ = 17/4
3³/₄ = 15/4
As the have the same denominator, you can directly subtract them:
= 17/4 - 15/4
= 2/4
= 1/2 buckets
okay i am gonna beg alot
Answers
Answer:
46
Step-by-step explanation:
110+6x=386
Answer: 46 times
Step-by-step explanation:
Since $110 is the constant and 6 is the coefficient because it is changing with each time he rents a tennis ball. The equation is 110+6t=386 where t in this case can represent (return groundstrokes)
110+6t=386 solve for t
6t=276
t=46
So he can return ground strokes 46 times