A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
What is the height of the pole? Round to the nearest hundredth.
12.00 feet
19.60 feet
24.17 feet
38.40 feet
Answers
Solution:
Length of wire = 22 feet =AB
Distance between the point where wire is attached to the ground from the point on the ground where pole is fixed= 10 feet=OB
In Right Δ O A B
By Using pythagoras theorem
O A² + OB² = AB²
O A² +10²= 22²
O A²= 484 - 100
O A²= 384
O A= √384= 19.60 (Approximately)
So, the height of pole to nearest hundredth = 19.60 feet
The height of the pole is 19.60 ft
The situation forms a right angle triangle.
Right angle triangleRight angle triangle have one of its sides as 90 degree.
The length of the wire is the hypotenuse of the triangle formed.
The distance of the wire attached to the ground to the base of the pole is the adjacent side of the triangle.
The height of the pole can be found using Pythagoras theorem.
c² = a² + b²
22² - 10² = b²
b² = 484 - 100
b = √384
b = 19.5959179423
b = 19.60 ft
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Related Questions
someone help me plz.
Answers
The solution generated by the calculator is 5.779E–8. Describe how to interpret the solution.
Answers
the E-8 at the end means the number is multiplied by 10^-8
so 5.779E-8=
5.779 x 10^-8 =
a negative power means move the decimal place that many places to the left
so 5.779 x 10^-8 =
0.00000005779
Answer:
the E-8 at the end means the number is multiplied by 10^-8
so 5.779E-8=
5.779 x 10^-8 =
a negative power means move the decimal place that many places to the left
so 5.779 x 10^-8 =
0.00000005779
Step-by-step explanation:
Describe how you can tell that a fraction corresponds to a repeating decimal and not a terminating decimal
Answers
For example, 4/11 = 36/99 = 0.36 with bar notation over 36.
Example #2: 2/3 = 6/9 = 0.666....
or also written as 0.6 with bar notation over 6.
You know a fraction responds to a terminating decimal because it can be simplified to a terminating decimal.
Example: 2/4 = 0.5
At 10 am, a building casts a shadow that is 98 feet long. At the same time, a 5 feet tall man casts a shadow that is 4 feet long. Find the height of the building.
Answers
height:shadow=5:4
so
given that the shadow is 98 ft
the height of the building is?
?:98=5:4
?/98=5/4
times both sides by 98
?=490/4
?=122.5ft
te height of the building is 122.5ft
A social networking site recorded that 80% of the people who became members of the site one month were between 30 and 40 years old. The equation below represents this information, where x represents the total number of people who became members of the site that month: x = 0.8x + 72 How many people who became members of the site that month were between 30 and 40 years of age?
Answers
x = 0.8x + 72
when x is alone you can say it is 1x
Subtract 0.8x from both sides:
0.2x = 72
x = 72/0.2
x = 360
To solve the equation x = 0.8x + 72, subtract 0.8x from both sides and then divide by 0.2 to solve for x. The result is 360.
Explanation:To solve the equation x = 0.8x + 72, we need to isolate the variable x on one side of the equation. First, subtract 0.8x from both sides: x - 0.8x = 0.8x + 72 - 0.8x. Simplifying this gives 0.2x = 72. Then, divide both sides by 0.2 to solve for x: x = 72 ÷ 0.2 = 360. Therefore, 360 people who became members of the site that month were between 30 and 40 years of age.
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Jose and a group of friends bought concert tickets for $257. The booking agency also charged a fee, bringing the total cost to $274.99. The amount of change is $17.99. What is the percent increase in the cost due to the fee?
A.6%
B.7%
C.8%
D.9%
Answers
Answer:
A.6%
B.7%
C.8%
D.9%
Charlott is running at a rate of 9 km/h. What is charlotte's speed in m/s?
Answers
1h = 60min = 3600s
9000m/3600s plug it into calculator
Answer:
The Charlott's speed in m/s is 2.5 m/sec
Step-by-step explanation:
Given : Charlott is running at a rate of 9 km/h.
We have to find the Charlott's speed in m/s.
Consider the given speed of Charlott is 9 km/h.
Since, 1 km = 1000 m
and 1 hour = 3600 sec
Therefore, [tex]9\frac{km}{hr}[/tex] becomes,
[tex]9\frac{km}{hr}=9\times\frac{1000\ m}{3600 \ sec}=2.5[/tex]
Thus, The Charlott's speed in m/s is 2.5 m/sec
What is the constant of variation for the quadratic variation? 6y = 4x2
Answers
x/10+5/12= 3x-1 what is x
Answers
Which statement best compares the rate of change of the two functions?
Answers
The rate of change of a function is reflected in the steepness of its graph. A function with a higher rate of change will have a steeper line. The correct comparison statement will depend on the specific slopes of Line A and Line B.
Explanation:In the context of this question, the rate of change refers to the steepness of the lines or the slopes of the functions represented by the lines. When comparing the rates of change of two functions, you look at how steep or flat each line is.
Let's consider the statements given:
Line A is a decreasing line while line B is an increasing line, with line B being much steeper than line A.Line A is a decreasing line while line B is an increasing line, with line A being much steeper than line B.Line B is a decreasing line while line A is an increasing line, with line A being much steeper than line B.Line B is a decreasing line while line A is an increasing line, with line B being much steeper than line A.To determine the best statement, analyze the steepness of the lines. For example, if Line A is decreasing and much steeper than Line B, then it would have a larger (but negative) rate of change.
Remember, the
rate of change
in a function can be understood as the rate at which the y-values are changing for each increment in the x-values. A higher rate of change means the function is increasing or decreasing more quickly.
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8x-2y-5=11 write the equation in function form
Answers
In function form it all has to be on one side
The correct answer to the question *interquartile range
Answers
You find this by subtracting the values of Q3 and Q1
Q3 is the right most edge of the box which is 45
Q1 is the left most edge of the box which is 25
IQR = Q3 - Q1 = 45 - 25 = 20
Side Note: The median is not 45. The median is actually 40 since this is the middle line of the box, which is in between 35 and 45
Plzzzz help me ??!?!?!??
Answers
Pythagorean Theorem is for right triangles
right triangles have a 90 degree angle in them
D is a right triangle
Farmer George is painting 3 chicken coops. He started painting this morning. Now he only has 3/4 of a chicken coop left to paint this afternoon. how many chicken coops did farmer George paint this morning
Answers
Farmer George has painted 2 1/4 chicken coops this morning. This is calculated by subtracting the remaining part of the chicken coop(3/4) from the total chicken coops(3).
Explanation:Farmer George had 3 chicken coops to paint in total. He only has 3/4 of one chicken coop left to paint. We can subtract the amount of work left from the total amount of work to figure out how much work he has done already.
So, if we take the total amount of chicken coops (which is 3) and subtract the remaining part that needs painting (which is 3/4), we will know how many chicken coops Farmer George has painted this morning.
The calculation is as follows: 3 - 3/4 = 2 1/4 coops
So, Farmer George completed painting 2 whole chicken coops and 1/4 of the third chicken coop this morning.
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Farmer George painted 2.25 chicken coops this morning. This is calculated as the total number of chicken coops (3) minus the remaining part of the chicken coop left to paint (3/4).
Explanation:The question is asking us about how many chicken coops Farmer George painted this morning. Farmer George started with 3 chicken coops and now has 3/4 of a chicken coop left to paint. Since he's already started painting the last chicken coop, this means he has painted 2 whole coops and 1/4 of the last coop. Thus, the answer to how many chicken coops Farmer George painted this morning is 2.25 chicken coops. Mathematically, this is calculated as 3 (the total number of chicken coops) minus 3/4 (the remaining part of the chicken coop left to paint).
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Find the equivalent function to f(x) = 3(6)^2x
Answers
f(x)=3(6)^(2x)
f(x)=3(6^2)^x
when we expand the above we get:
f(x)=3(36)^x
the answer is f(x)=3(36)^x
Answer:
f(x) = 3(36)x
f(x) = 182x
f(x) = 108x
f(x) = 9x(36x)
Step-by-step explanation:
A vineyard owner hires 25 people to harvest grapes. The vineyard covers 30 acres. The harvest takes 9 days to complete. A neighbour has a vineyard measuring 20 acres and needs his harvest finished in 5 days. Assuming all people work at the same rate, how many people should he hire?
Please show working out.
Answers
In the first vineyard, it needs 25 people working for 9 days to finish 30 acres of vineyard. Using this information you can determine the worker speed. The number of worker and days were given will increase the speed, but the area of the vineyard will decrease it. The calculation would be:
Worker speed= worker number * times given / vineyard area
Worker speed= 25 people * 9 days / 30 acres = 7.5 people days /acres
Applying the same calculation into the second vineyard would be:
Worker speed= worker number * times given / vineyard area
7.5 people days /acres = worker number * 5 days / 20 acres
Worker number= (7.5 people days /acres ) / 5 days x 20 acres= 30 people
The steps below show the incomplete solution to find the value of x for the equation
7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step?
4x = 24
4x = 16
4x = 5
4x = 80
Answers
therefore, the next step in the process will be to get the term "4" to the right side.
to do this, we add 4 to 20 since it is a negative.
4x=20+4
so the answer is 4x=24
hope this helps! :)
The most likely step after the step3 is 4x = 24.
Linear Equation in one variable:
The linear equation in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question
we have, a linear equation in variable x, 7x - 3x -4 = -1 + 21
For solving the above equation we will do the following steps
7x -3x -4 = -1 +21
Step1: 4x - 4 = 20
Step2: 4x - 4-20= 0
Step3: 4x -24 = 0
Step4: 4x = 24
Step5: x =24/4 =6
Hence, the most likely step after the step3 is 4x = 24.
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write with fractional exponents. (do not use parenthesis) (4)√y^3)
Answers
[tex] x^{ \frac{m}{n} } = \sqrt[n]{x^{m} } = ( \sqrt[n]{x}) ^{m} [/tex]
we have [tex]4 \sqrt{ y^{3} } [/tex]
we write [tex] \sqrt{ y^{3} } = y^{ \frac{3}{2} } [/tex] , note that square root [tex] \sqrt{x} [/tex] equals to [tex] \sqrt[2]{x} [/tex]
hence, the final expression is [tex]4( y^{ \frac{3}{2} } )[/tex]
ONLY THE CORRECT ANSWERS PLEASE!!!!
Which term best represents the intersection of two pages of an open book?
A. line
B. angle
C. plane
D. point
Answers
What is the solution to the following equation?
2(3x − 7) + 18 = 10
1
3
5
6
Answers
Subtract 18 from both sides.
2(3x - 7) = -8
Distribute the side with parenthesis.
2(3x) + 2(-7) = -8
6x -14 = -8
Add 14 to both sides.
6x = 6
Divide both sides by 6.
x = 1
I hope this helps!
Subtract 18 from both sides:
2(3x - 7) = -8
divide both sides by 2
3x - 7 = -4
add 7 to both sides
3x = 3
divide both sides by 3:
x = 1
So your answer is A) 1
Gas station A has posted a chart that shows the price of gasoline in terms of the number of gallons. Gallons Price 3 9.15 5 15.25 7 21.35 Gas station B has an equation that represents the price, p, for gallons, g, of gasoline as p = $3.08g. Which gas station sells gasoline at a lower rate? What price does it charge? Gas station A sells gasoline at a lower rate. Its price is $3.08 per gallon. Gas station B sells gasoline at a lower rate. Its price is $3.05 per gallon. Gas station A sells gasoline at a lower rate. Its price is $3.05 per gallon. Gas station B sells gasoline at a lower rate. Its price is $3.08 per gallon.
Answers
Rate is $3.05
Peter is 2 years older than Winnie. Peter's age is 16 years less than seven times Winnie's age. The equations below model the relationship between Peter's age (p) and Winnie's age (w):
p = w + 2
p = 7w − 16
Which is a possible correct method to find Peter's and Winnie's ages?
Solve w + 2 = 7w − 16 to find the value of w.
Solve p + 2 = 7p − 16 to find the value of p.
Write the points where the graphs of the equations intersect the x axis.
Write the points where the graphs of the equations intersect the y axis.
Answers
w+2 = 7w-16. from there we can see that w = 3
So basically, the first answer.
this,is multiplication variables 2 (5x × 3y)=
Answers
Which set of side lengths forms a right triangle??
Answers
2^2 + 3^2 ??=?? 13^2
4 + 9 ??=?? 169
13 ??=?? 169 FALSE
4^2 + 6^2 ??=??10^2
16 + 36 ??=?? 100
52 ??=?? 100 FALSE
9^2 + 12^2 ??=?? 18^2
81 + 144 ??=?? 324
225 ??=?? 324 FALSE
15^2 + 36^2 ??=?? 39^2
225 + 1296 ??=?? 1521
1521 ??=?? 1521 TRUE 15, 36, 39
25(y+1)-x^2(y+1) i don't know the answer
Answers
Because the inner binomials (the ones in parentheses) are the same, the next step is to rewrite the equation like so:
(25-x^2)(y+1)
From here, we can further factor (25-x^2) since they are both perfect squares.
(5+x)(5-x)(y+1)
No further terms can be factored so that is the final answer. Hope this helps!
Is 2/3 closer to 1 or 1/2
Answers
The 2/3 fraction would be closer to 1/2.
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.
To make them all into decimal points, which allows you to compare them easier than in fraction form. this is done by dividing the denominator by the numerator.
2/3 = 0.66
1/2 = 0.5
1 = 1.00
The answer would be closer to 1/2.
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Final answer:
When comparing 2/3 to 1 and 1/2, 2/3 is closer to 1/2 than 1.
Explanation:
When comparing the fraction 2/3 to 1 and 1/2, we can determine which it is closer to by analyzing the numerical values. To do this, we can convert both 1 and 1/2 to fractions with the same denominator as 2/3, which is 3.
1 as a fraction with a denominator of 3 is 3/3. Comparing 2/3 and 3/3, we can see that 2/3 is closer to 1 than 3/3.
On the other hand, 1/2 as a fraction with a denominator of 3 is 3/6. Comparing 2/3 and 3/6, we can see that 2/3 is closer to 1/2 than 3/6.
Therefore, we can conclude that 2/3 is closer to 1/2 than 1.
Alvin is 12 years older than Elga. The sum of their ages is 112. What is Elga's age?
Answers
12 + x = Alvin
x + 12 + x = 112
2x + 12 = 112
2x = 100
x = 50
Elga's age = 50
Alvin = 50 + 12 = 62
answer
Elga's age = 50
the slopes of two lines are 5/6 and 2/p determine the value of p that will make the lines parallel
Answers
so 5/6 = 2/p
so p =2.4
How does ray ab and ac form both a line and angle
Answers
if the area of a square is 529 in 2 , what is the length of a side of the square