A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole?
Answers
The flagpole is vertical and is at 90° to the ground. This makes a right-angle to the ground, which is flat.
Since we have two sides of the triangle already, and they are in a ratio of ?? : 16 : 20 = ?? : 4 : 5, that means that because the triangle is a right-angled triangle, the third and last side must be 3 to complete the ratio! (This is called 'Pythagoras')
Since the other sides were divided by 4 to get the simple ratio, we must multiply 3 to get the actual ratio! 3 × 4 = 12 ft tall flagpole.
The height of the flagpole is 12 feet.
To determine the height of the flagpole, we can use the Pythagorean theorem.
Given: The length of the cable (hypotenuse) is 20 feet.The distance from the point on the ground to the base of the flagpole (one leg) is 16 feet.Let the height of the flagpole be h (the other leg).Using the Pythagorean theorem:
c² = a² + b²
Here, c = 20 feet (length of cable), a = 16 feet (distance from flagpole base to ground point), and h = b (height of the flagpole).
Therefore, we have:
202 = 162 + h²
400 = 256 + h²
To find h, subtract 256 from 400:
400 - 256 = h²
144 = h²
h = √144 = 12.
Related Questions
To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.
Answers
Answer:0.075
Step-by-step explanation:
round 1,647 to the nearest thousand
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out of a swarm of bees one fifth part settled on a kadamba blossom; one third on a silihindra flower; three times the difference of those numbers flew to the bloom of a kutaja. one bee, which remained, hovered about in the air. tell me, charming woman, the number of bees
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let x be the # of bees in the swarm, then
[tex]\frac{x}{5}+\frac{x}{3}+3(\frac{x}{3}-\frac{x}{5})+1=x[/tex]
multiply across by 15
[tex]3x+5x+3(5x-3x)+15=15x[/tex]
[tex]8x+3(2x)+15=15x[/tex]
[tex]8x+6x+15=15x[/tex]
[tex]14x+15=15x[/tex]
[tex]15=x\leftrightarrow x=15[/tex]
how many solutions are there to this equation?
9x - 16 = 9x - 23
a. infinitely many
b. 0
c. 1
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Answer: the correct option is
(b) 0.
Step-by-step explanation: We are given to find the number of solutions for the following linear equation :
[tex]9x-16=9x-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions of the given equation, we must try to solve the equation and find the value of x.
From equation (i), we have
[tex]9x-16=9x-23\\\\\Rightarrow 9x-9x=-23+16\\\\\Rightarrow 0=-7,[/tex]
which can never be possible.
Thus, the given equation has NO solution.
Option (b) is CORRECT.
Estimate the volume of material in a cylindrical shell with height 30 in., radius 2 in., and shell thickness 0.5 in.
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What is 7.58E8 expressed in standard notation?
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appleseed a tech company spends a fixed cost of $1500 to manufacture the wristbands for their new appleseed watch plus $100 per unit manufactured solution
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The y-intercept is 1500. It represents the fixed cost to manufacture the wristbands.
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
Given that,
The fixed cost of $1,500 for manufacturing the wristbands. And, there is $100 per unit.Based on the above information, we can conclude that
a. The slope is 100. It shows the cost per wristband.
b. The y-intercept is 1500. It shows the fixed cost for manufacturing the wristbands.
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To solve a three-variable system of equations, you can use a combination of the elimination and substitution mehtods.
True or False ...?
Answers
This is the best way to solve these kinds of equations, as you get rid of the unnecessary variables.
Final answer:
True, a combination of the elimination and substitution methods can solve a three-variable system of equations.
Explanation:
The statement is True. We can use a combination of the elimination and substitution methods to solve a three-variable system of equations. In the elimination method, we aim to eliminate one variable by adding or subtracting the equations, allowing us to solve for the remaining variables. This method works well when the coefficients of one variable are opposites in two equations.
In the substitution method, we solve one equation for one variable and substitute this expression into the other equations. This allows us to solve for the remaining variables. This method is more straightforward when one equation can be easily solved for one variable.
Write an equation of the direct variation that includes the point (9, –12).
(A.) y = 1 1/3x (B.) y = - 1/12x (C.) y = 1 1/3x (D.) -3/4x ...?
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The equation of direct variation for the point (9, -12) would be y = -1 1/3x. The constant of variation, 'k', is found by dividing 'y' by 'x'. Therefore, 'k' is -12/9, which simplifies to -1 1/3.
Explanation:In a direct variation, the equation can be represented in the form y = kx, where 'k' is the constant of variation. Here, 'k' can be found by dividing 'y' by 'x'. So, in the given point (9, -12), 'k' would be -12/9, which simplifies to -4/3 or -1 1/3. Therefore, the equation of the direct variation that includes the point (9, -12) would be y = -1 1/3x. The provided options don't include this equation, so it might be a mistake in the question options. Remember, the correct equation should always have 'y' and 'x' directly vary, and 'k' have the same sign as the given 'y' value.
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In the Math Club, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors. What is the probability of randomly selecting a boy or a senior to represent the Math Club at a statewide math contest?
Answers
34 In All. 14 boys (14/34) 11 Seniors, - 4 so we don't double count. (14/34) + (7/34)
There are in total 34 children: 20 girls + 14 boys = 34 children
There are in total 11 seniors: 7 senior girls + 4 senior boys = 11 senior children
When we have two events that do not occur together, so only one of the events can happen (there is OR in a sentence), then we use the addition rule and add up probabilities of the events. We have two events not occurring together:
1. The probability of selecting a boy is 14/34 (because there are 14 boys among 34 children).
2. The probability of selecting a senior is 11/34 (because there are 11 seniors among 34 children).
Now, we just need to add them up. However, we have already counted 4 senior boys in the probability of the first event and thus, must subtract the probability of selecting a senior boys (4/34):
14/34 + 11/34 - 4/34 = (14+11-4)/34 = 21/34
Kayla notices that she can buy snacks and candy in bulk at the grocery store. The snacks she wants to buy cost $1.29 per kilogram.
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Leslie can determine which option will give her more yogurt by comparing the weights of the two options.
Explanation:To determine which option will give Leslie more yogurt, she needs to compare the weights of the two options. First, she needs to convert the weight of the first option from pounds to ounces. Since 1 pound is equal to 16 ounces, the 2 pound container is equal to 32 ounces. Next, she can compare the weights of the two options. The first option is 32 ounces and the second option is 5 containers of 6 ounces each, which is a total of 30 ounces. Therefore, the first option will give Leslie more yogurt.
At a gas station, the price of a regular gas was $3.80 per gallon on monday. the price increased to $3.85 per gallon on tuesday. round the price per gallon for each day to the nearest tenth of a dollar.
Answers
Tuesday' gas, $3.85 rounded to the nearest tenth of a dollar would be $3.90
Hope this helps!! and if you ever need anything else just ask! :)
Answer:
A round number is less accurate, but easier to use, because you get rid of certain decimals.
There are some rules to do this:
If we want to round a number to the nearest tenth, we have to look what's the unit after it, if that unit is more than 5, we round the tenth to the upper number. For example, 10.66 would be rounded to 10.7.If we want to round a number, and the next digit is lower that 5, we just maintain the same digit. For example, 10.44 would be rounded to 10.4However, there's a specific case, if we want to round a number to the tenth, and the following digit is 5, we could round up or round down the tenth digit. If the digit we want to round is pair, then we maintain the same digit, if it's odd, we can round to the upper digit. For example, 10.65 would be rounded to 10.6, and 10.75 would be rounded to 10.8Therefore, according to these rules, the round number would be $3.8 and $3.8
If xy^2 = 20, and x is decreasing at the rate of 3 units per second, the rate at which y is changing when y = 2 is nearest to?
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[y^2]' = [20/x]'
2y [dy/dt] = [-20/x^2] [dx/dt]
dy/dt = [-10/yx^2] [dx/dt]
[dx/dt] = - 3 u/s ....(the negative sign was included to account for decreasing)
y = 2 => x(2)^2 = 20 => x = 20/4 = 5
dy/dt = [-10/(2*5^2)] [- 3]
dy/dt = [-1/5][- 3] = 3/5
Answer: dy/dt = 3/5 units/s
When sam breathes in, his chest expands, causing air to fill his lungs. which structure causes his chest to expand?
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If Harrisen makes $10 an hour, how much will he make in a 40 hour work week?
$30
$50
$40
$400
Answers
For 40 hour, it would be: $10 * 40 = $400
So, option D is your answer.
Hope this helps!
What is 0.98 rounded to the nearest thousandth?
Answers
it may also be asking for 0.980, which is equal but shows the thousandth place
The number 0.98 already has a zero in the thousandths place and no further digits; hence it remains as 0.980 when rounded to the nearest thousandth.
The given number, 0.98, when rounded to the nearest thousandth, does not change because it has a zero in the thousandths place. To round a number to the nearest thousandth, you look at the digit in the ten-thousandths place. If this digit is 5 or greater, you round up.
If it is less than 5, you keep the digit in the thousandths place as it is. Since 0.98 has a zero in the thousandths place already and there are no further digits, it remains as 0.980 when rounded to the nearest thousandth.
Help me please !
Scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95. Certificates are given to students whose scores are in the top 2% of those who took the test. This means that they scored better than 98% of the other test takers. Marcus received his score of 13.7 on the exam and is wondering why he didn’t receive a certificate. Show all work to determine whether Marcus’ score was high enough to earn a certificate. Write a letter to Marcus explaining whether or not he will be receiving a certificate. Include a brief summary of your statistical analysis in your letter.
Answers
Expression as a decimal number 6x0.1 6x0.01 1x0.001
Answers
Final answer:
To express the given multiplications as decimal numbers: 6 times 0.1 equals 0.6, 6 times 0.01 equals 0.06, and 1 times 0.001 equals 0.001. Moving the decimal point due to multiplication by powers of 10 is the underlying concept.
Explanation:
The student's question involves expressing multiplications involving decimals in decimal form. To convert each term:
6 x 0.1 is moving the decimal point one place to the left in the number 6, which results in 0.6.6 x 0.01 is moving the decimal point two places to the left in the number 6, giving 0.06.1 x 0.001 is moving the decimal point three places to the left in the number 1, resulting in 0.001.When numbers are multiplied by powers of 10, the decimal point is shifted to the right for positive exponents and to the left for negative exponents. Scientific notation is often used for this purpose.
Here are examples demonstrating the use of scientific notation:
0.006 can be expressed as 6 x 10-3 (moving the decimal point three places to the left).0.0000045 becomes 4.5 x 10-6 (the decimal point moves six places to the left).Negative exponents indicate the decimal point moves to the left, whereas positive exponents indicate it moves to the right. For instance, 2.4 x 10-2 is equivalent to 0.024 as the decimal has moved two places to the left.
Solve the system by the elimination method. Check your work. 2a + 3b = 6 5a + 2b - 4 = 0
Answers
2a + 3b = 6
5a + 2b - 4 = 0
multiply thru the top equation by 2
Multiply thru the bottom equation by 3
4a + 6b = 12
15a+ 6b = 12
Subtract and solve for "a":
11a = 0
a = 0
Solve for "b" using 2a + 3b = 6
2*0 + 3b = 6
b = 2
Answer:
Step-by-step explanation:
a=0
b=2
answer (0,2)
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answers
Answer:
I believe the answer is (C.2)
Step-by-step explanation:
The answer isn’t 1. I took the test and ‘B’ is incorrect
Final answer:
C: 2
To find the average rate of change of the function f(x) from x = 0 to x = 1, we compute (f(1) - f(0)) / (1 - 0), which results in (3 - 1) / 1 = 2. The average rate of change is therefore 2.
Explanation:
To calculate the average rate of change for the function f(x) = −x⁴ + 4x³ − 2x² + x + 1 from x = 0 to x = 1, we use the formula:
Average rate of change = ∆f/∆x = (f(x_2) - f(x_1)) / (x_2 - x_1)
First, we need to find the values of f(x) at x = 0 and x = 1:
f(0) = −(0)⁴ + 4(0)³ − 2(0)² + (0) + 1 = 1f(1) = −(1)⁴ + 4(1)³ − 2(1)² + (1) + 1 = 3Using these values, we calculate the average rate of change:
Average rate of change = (3 - 1) / (1 - 0) = 2 / 1 = 2
Therefore, the average rate of change of the function from x = 0 to x = 1 is 2.
three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sampls
1,1 1,3 1,8 3,1 3,3 3,8 8,1 8,3 8,8
find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values
s^2 Probability
3.3
1
6.3
49
Answers
The variances for the samples were calculated, and then the probability of each distinct variance value was found. The results were summarized in a table showing the probability distribution of the variances.
Explanation:The variance of a sample is calculated using the formula:
s^2 = Σ ( xi - X_bar )^2 / (n - 1).
Where 'xi' represents each value in the sample, 'X_bar' is the mean of the sample and 'n' is the number of values in the sample. Let's calculate the variance for each of these samples:
Next, find the probability of each distinct variance value by counting the number of times it occurs and dividing by the total number of samples (9 in this case). The sampling distribution of the variances with probabilities looks something like this:
Variance = 0 : Probability = 3/9 = 0.33Variance = 2 : Probability = 2/9 = 0.22Variance = 25 : Probability = 2/9 = 0.22Variance = 49 : Probability = 2/9 = 0.22Learn more about Variance and Probability here:https://brainly.com/question/31698743
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(1) Which fraction is a multiple of 1/6
A) 7/16
B) 11/12
C) 4/6
D) 6/9
(2) which fraction is a multiple of 1/8
A) 14/18
B) 7/16
C) 8/9
D) 5/8
(3) which fraction is NOT a multiple of 1/10
A) 10/3
B) 8/10
C) 3/10
D) 10/10
(4) which fraction is NOT a multiple of 1/12
A) 5/12
B) 11/12
C) 2/10
D) 3/13
Answers
___________
1) [C]: 4/6 ;
___________
2) [D]: 5/8 ;
___________
3) [A]: 10/3 ;
___________
4) Both: [C]: 2/10; and: [D]: 3/13; are NOT multiples of 1/12
_______________________
Helpppppppp I'm really bad in math
Answers
What you could do is multiply each side by 12.
Then it will become 6x + 2x = 24
Combine like terms: 8x = 24
Now divide each side by 8
The answer is x = 3
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
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Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece m = 90 - 6d
Answer:
m=90-6 days or b
Step-by-step explanation:
i got a hundred on the quiz...
A number decreased by 10 is greater than -5.
How can I write this in an inequality?
Answers
simplified:
x>5
What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?
Answers
f(x) = 5(2)^x
f(1) = 5(2)^1
f(1) = 10
So the point (1,10) is on this curve
Do the same for x = 5
f(x) = 5(2)^x
f(5) = 5(2)^5
f(5) = 160
The point (5,160) is also on the curve
Use the slope formula now
m = (y2-y1)/(x2-x1)
m = (160-10)/(5-1)
m = 150/4
m = 37.5
The average rate of change is 37.5
original price $18 markup 15%
Answers
6 sweets cost 24p altogether how much do 5 sweets cost
Answers
To calculate the cost of 5 sweets when 6 sweets cost 24p, divide the total cost by the number of sweets to determine the cost of one sweet, then multiply by 5. The cost for 5 sweets is 20p.
To find out how much 5 sweets cost when 6 sweets cost 24p altogether, we first need to calculate the cost of one sweet. We divide the total cost by the number of sweets to get the cost per sweet. Here's how it's done:
Find the cost of one sweet by dividing the total cost of 6 sweets (24p) by 6: Cost per sweet = 24p / 6 = 4p.Now, multiply the cost per sweet by the number of sweets you want to find the cost for, which in this case is 5: Cost for 5 sweets = 4p / sweet × 5 sweets = 20p.Therefore, 5 sweets would cost 20p.
carla looks from the top of a diving board, and lines up a ball floating on the surface of the water with the bottom of the opposite corner of the pool. calculate the total distance across the surface of the pool. explain your reasoning
Answers
Below is the solution:
12/x = 10/9
10x/ 20 = 108/10
x = 10.8
9 + 10.8 = 19.8 ft
What is the sum of square root -2 and squareroot -18
Answers
1.414i + 4.234i = 5.657i
The 'i' is included because the sqrt of a negative number is imaginary.
The sum of the square roots of -2 and -18 is [tex]\( 4\sqrt{2}i \)[/tex], where i is the imaginary unit.
The sum of the square roots of -2 and -18 involves complex numbers because both -2 and -18 are negative.
The square root of a negative number is not a real number, but it can be expressed using imaginary units.
The square root of -2 can be represented as [tex]\( \sqrt{-2} = \sqrt{2}i \),[/tex] where i is the imaginary unit, defined as [tex]\( i = \sqrt{-1} \).[/tex]
Similarly, the square root of -18 can be written as [tex]\( \sqrt{-18} = \sqrt{18}i \).[/tex]
Now, to find the sum of these square roots:
[tex]\[ \sqrt{-2} + \sqrt{-18} = \sqrt{2}i + \sqrt{18}i \][/tex]
[tex]\[ = \sqrt{2}i + \sqrt{2 \times 9}i \][/tex]
[tex]\[ = \sqrt{2}i + 3\sqrt{2}i \]\\\\ = (\sqrt{2} + 3\sqrt{2})i \][/tex]
[tex]\[ = 4\sqrt{2}i \][/tex]
So, the sum of[tex]\( \sqrt{-2} \) and \( \sqrt{-18} \)[/tex] is [tex]\( 4\sqrt{2}i \).[/tex]