An architect is designing a hexagonal gazebo. The floor is a hexagon made up of six isosceles triangles. The function y=4 tan θ models the height of one triangle, where θ is the measure of one of the base angles and the base of the triangle is 8 ft long.
b. Find the area of one triangle in square feet when θ=60°.
Answers
The area of one triangle is 48 square feet when θ = 60°
The area of one triangle is 27.7 square feet when θ = 60°.
To find the area of the triangle, we can use the formula for the area of an isosceles triangle: A = (1/2) * base * height. In this case, the base of the triangle is given as 8 ft.
Given that the height is represented by y = 4 tan θ, we need to find the value of y when θ = 60°. Substituting θ = 60° into the equation, we have y = 4 tan 60°. Using the tangent of 60°, which is √3, the height is y = 4 * √3.
Now we can calculate the area of the triangle. Plugging in the values into the formula, we get A = (1/2) * 8 ft * (4 * √3) ft = 16√3 ft².
Rationalizing the denominator (√3) by multiplying both the numerator and denominator by √3, we have A = 16 * √3 * √3 ft² = 16 * 3 ft² = 48 ft².
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Related Questions
what is 5(5+5+5+10+200+50 divided by 10 times 400) to the power of 2 will give brainliest and 50 points
Answers
Answer:
24,753,125
Step-by-step explanation:
done
Answer: 24,753,125
Step-by-step explanation:
First solve the division in the parenthesis
5(5+5+5+10+200+50/10*400)^2
5(5+5+5+10+200+5*400)^2
Then solve the multiplication in the parenthesis
5(5+5+5+10+200+2000)^2
Then solve the addition in the parenthesis
5(2225)^2
Then solve the exponent
5(4950625)
Then solve the multiplication
24,753,125
Hope it helps <3
What is the prime factorzation of 54
Answers
Answer:
2*3*3*3
Step-by-step explanation:
Answer:
54 = 2×3^3
Step-by-step explanation:
Factor the following integer:
54
Hint: | Is 54 divisible by 2?
The last digit of 54 is 4, which means it is even. Therefore 54 is divisible by 2:
54 = 2 27:
54 = 2×27
Hint: | Now try to factor 27. Is 27 divisible by 2?
27 is not divisible by 2 since 27 is odd and 2 is even:
54 = 2×27 (27 is not divisible by 2)
Hint: | Is 27 divisible by 3?
The sum of the digits of 27 is 2 + 7 = 9, which is divisible by 3. This means 27 is divisible by 3:
27 = 3 9:
54 = 2×3×9 (9 is not divisible by 2 since 27 is not)
Hint: | Now try to factor 9. Is 9 divisible by 3?
9 = 3 3, which means 9 is divisible by 3:
9 = 3 3:
54 = 2×3×3×3 (3 is not divisible by 2 since 9 is not)
Hint: | Now try to factor 3. Is 3 prime?
No primes less than 3 divide into it. Therefore 3 is prime:
54 = 2×3×3×3
Hint: | Express 54 as a product of prime powers.
There is 1 copy of 2 and 3 copies of 3 in the product:
Answer: 54 = 2×3^3
Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. *
o 11
o 7.8
o 61
o 14.9
Answers
if a television screen with a length-to-height ratio of 16:9 has an area of 576 square inches, what is its perimeter?
Answers
The perimeter of television is = 100 inches
What is mensuration ?The study of measuring geometric shapes and their qualities such as length, volume, shape, surface area, lateral surface area, and so on is known as mensuration. Mensuration will be covered in fundamental mathematics.
Calculationlet the length be 16x and width be 9x
area given = 576 sq. inches
16x * 9 x = 576
144 \(x^{2}\) = 576
x = 24/12
x = 2
length = 32
width = 18
perimeter = (32 + 18)*2 =100 inches
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reggiethenerd10 what is (8.7 + 3.3) x (1/2) 2 to the second power
Answers
Answer:
3
Step-by-step explanation:
The value of the operation is 3.
The first step is to solve for the terms in the brackets.
The decimals would be added first 8.7 + 3.3 = 12
The second step is to determine the square of one-half² = x = 1/4
The third step is to multiply, 1/4 by 12 1/4 x 12 = 3
If the
average (arithmetic
mean) of 2, 7, and x is 12,
what is the value of x?
Answers
Answer:
x = 27
Step-by-step explanation:
mean is calculated as
mean = \(\frac{sum}{count}\)
sum = 2 + 7 + x = 9 + x and count = 3 , then
\(\frac{9+x}{3}\) = 12 ( multiply both sides by 3 to clear the fraction )
9 + x = 36 ( subtract 9 from both sides )
x = 27
20 +? =100 ÷ 4
Help
Answers
Answer:
5
Step-by-step explanation:
Both answers equal 25.
Dr. Fahrrad has been riding his bike to his job and is curious how many ATP his body is breaking apart in order to do the work required to get to his job.
Dr. Fahrrad rides 4.6 kilometers to his job, has a mass of 74.9 kilograms and has an average acceleration of 1.4 kilometers per second squared.
The molecule ATP is able to do work, measured in kilojoules per mole of ATP broken into ADP. The SI unit for work is a joule. Using the information given we can calculate work and then convert to moles of ATP.
The first step is to take stock of what we are given in the word problem and what we are trying to find. We have mass, distance, and average acceleration. We are trying to find how many ATP are required to power the bike ride to work.
The equation for work, is force times distance and will tell us how many joules Dr. Farrhad is using on his bike ride. It also incorporates one of our given variables, distance. However, the distance was reported in kilometers and the SI unit of distance is the meter. It is necessary to convert to meters before using this equation.
The equation for Force is mass times acceleration. This will incorporate our remaining two variables, mass and acceleration. Again, the information given to us was in km·s-2 but the SI unit for acceleration is m·s-2. It is necessary to convert to m·s-2 before substituting into the equation.
By substituting the equation for F into the equation for W, we can figure out how many joules Dr. Fahrrad is burning on his ride to his job.
In order to use these equations, we are assuming quite a few things. Below are some of the assumptions.
no friction
no mass of the bike
a flat ride with no change in altitude
This equation above will calculate work in joules. The conversion factor for switching between ATP and work is given in kilojoules. The units must match to correctly perform the conversion.
The last step is to convert work, calculated in joules, into moles of ATP being broken required to do the work. If we assume standard temperature and pressure, the breakdown of a mole of ATP releases 29 kilojoules available to do work.
How many moles of ATP is Dr. Farrhad breakdown to get to work? Report your answer to one decimal place.
Answers
Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.
The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:
W = F * d
where:
W is the work done in joules
F is the force in newtons
d is the distance in meters
The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.
The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.
Plugging these values into the equation for work, we get:
W = 102.8 N * 4600 m = 472320 J
The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:
472320 J / 29 kJ/mol = 162.6 mol
To one decimal place, this is 0.23 moles of ATP.
Here are the assumptions that we made in this calculation:
No friction
No mass of the bike
A flat ride with no change in altitude
These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.
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David earns $11 an hour. He was scheduled to work 35 hours. However, he picked up an additional 7 hour shift. He is paid double time for anything over 40 hours. How much did he get paid?
Answers
David earned $484 in total.
Given that, David earns $11 an hour. He was scheduled to work 35 hours. However, he picked up an additional 7 hour shift. He is paid double time for anything over 40 hours.
We need to find how much did he get paid in total.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, total number of hours David worked=35+7=42
Upto 40 hour he get paid $11 per hour.
So, the total money = 40×11=$440
He gets paid $22 for each extra hour.
That is 2×22=$44
Total money earned=440+44=$484
Therefore, David earned $484 in total.
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Combine like terms to answer the question.
Answers
Answer:
3r + 5
Step-by-step explanation:
by "combining like terms", this means that if we have, for example,
1 * x + 5 * x, we can factor this out to be x*(1+5) = 6 * x and the like terms (1x and 5x) are combined
thus, we have
-5r + 8r + 5
the "like terms" here are -5r and 8r because they both have an r attached to it. thus, we can set out to only factor the r in these two numbers, resulting in
-5 * r + 8 * r + 5 = r * (-5 + 8) + 5 = r * 3 + 5 = 3r + 5
ASAP HELpppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
5
This is essentially the third identical question that you posted with the same
type of solution ... if you look at the previous question you asked and the explanation.. you will see that the red line crosses a corner of a box at (4,20)
4 cups = 20 pralines thus the number you are looking for is 20/4 = 5
Step-by-step explanation:
lets try this "story" to explain...
assume that you can walk 3 miles in 1 hour
this means that at 0 hr you go 0 miles , 1 hr you go 3 miles etc
0,0
1,3
2,6
3,9
etc.
if you graph that you will have the red line in you graph, and the x values would be 0,1,2,3 with the y values being 0,3,6,9....
if you DIVIDE any of those points
3/1 ,6/2, 9,3 the result is always a "3" that is the speed that you are walking at
it is a CONSTANT (in this problem) ... note: if the speed is NOT constant then this basically becomes a calculus problem, ant an algebra one.
Harry and Selma start driving from the same location. Harry drives 65 mi north while Selma drives 72 mi east. How far apart are Harry and Selma when they stop? (Assume Harry and Selma are driving at the same speed.)
Answers
Answer:
97 miles apart
Step-by-step explanation:
We can use the Pythagorean Theorem to find the distance between Harry and Selma, which their respective distances from the same starting location become the legs of a right triangle. We find the distance between Harry and Selma by solving for the hypotenuse:
\(a^2+b^2=c^2\)
\(65^2+72^2=c^2\)
\(4225+5184=c^2\)
\(9409=c^2\)
\(\pm97=c\)
\(c=\pm97\)
Because distance is always positive, then the distance between Harry and Selma when they stop is 97 miles.
What is the quotient of 388.25 : 6.25?
Answers
Answer:
62.12
Step-by-step explanation:
write the following number words in symbols. 1.one hundred twenty-seven thousand, four hundred fifty-nine 2.Two hundred six million, three hundred twenty thousand, ninety-six 3.Three hundred twenty-two and 38 hundredths
Ty<33
Answers
2) 206,320,096
3) 322.38
What is the volume of this rectangular prism below?
The volume of this rectangular prism is [a] cubic centimeters.
______________
![What is the volume of this rectangular prism below?The volume of this rectangular prism is [a] cubic](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/5sdHDK97412Dmu4ZGj0ijM7XZ5LlH4n1.png)
Answers
Answer:
225 cm³
Step-by-step explanation:
Volume of a prism = base area × height
The volume of this prism
\( = 5 \times 5 \times 9\)
\( = 225\)
Answer:
225 cu cm ^3
Step-by-step explanation:
can i be brainliest?
Put these numbers in order from least to greatest.
Answers
Answer:
-21/35 is least
12/40 is semi-least
8 is semi-greatest
8-14/35 is greatest
Adam reads 1/8 of a book in 1/6 of an hour. How much time does it take for him to read the whole book?
Answers
Let the time taken to read the whole be y
If he reads 1/8 of the whole book (x), it can be expressed as,
\(\frac{1}{8}\text{ of x =}\frac{1}{8}\times x=\frac{x}{8}\)If it takes Adam to read x/8 of a book in 1/6 hours,
To read the whole book, it will take Adam,
\(\begin{gathered} Adam\text{ read }\frac{x}{8}\text{ in }\frac{1}{6} \\ To\text{ read the whole book (x) in y time} \\ y\times\frac{x}{8}=x\times\frac{1}{6} \\ \frac{xy}{8}-\frac{x}{6} \\ \text{Crossmultiply} \\ 6\times xy=8x \\ \text{Divide both sides by }6x \\ \frac{6xy}{6x}=\frac{8x}{6x} \\ y=\frac{4}{3}=1\frac{1}{3}hours \end{gathered}\)Hence, it will take 1 1/3 hours for Adam to read the whole book.
the mean number of words per minute (wpm) typed by a speed typist is 124 with a standard deviation of 15 wpm. what is the probability that the sample mean would be less than 127 wpm if 84 speed typists are randomly selected? round your answer to four decimal places.
Answers
The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625
What is Mean?
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally. The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organized in ascending order, the Median is the median value of the provided data. While the number in the list that is repeated a maximum of times is the mode.
We have
\(\mu=124\)
\(\sigma=15\)
n=84
We want to find the probability that the sample mean would be greater than 127 WPM is
\(\begin{aligned}P(\bar{X} > 127) &=P\left(\frac{\bar{X}-\mu}{\sigma / \sqrt{n}} > \frac{127-124}{15 / \sqrt{84}}\right) \\&=P(Z > 1.83)\end{aligned}\)
\(=0.033625\)
The required probability is 0.0336.
Hence, The probability that the sample mean would be less than 127 wpm if 84-speed typists are randomly selected is: 0.033625
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17. If x = -2, which inequality is true?
A. -3-5x > 1
B.-5+x>-3
C. 5-3x-1
D. -1+5x > 3
Answers
Answer:
To solve the problem, we substitute x=-2 into each of the inequalities and see which one is true:
A. -3-5x > 1
A. -3-5x > 1 -3 - 5(-2) > 1
A. -3-5x > 1 -3 - 5(-2) > 1-3 + 10 > 1
A. -3-5x > 1 -3 - 5(-2) > 1-3 + 10 > 17 > 1
This inequality is true.
B. -5+x>-3
-5 + (-2) > -3
-7 > -3
This inequality is false.
C. 5-3x-1
5 - 3(-2) - 1
5 + 6 - 1
10 > 1
This inequality is true.
D. -1+5x > 3
-1 + 5(-2) > 3
-11 > 3
This inequality is false.
Therefore, the only true inequality is A. -3-5x > 1.
how do u convert a percentages into fractions ??
Answers
Answer:
Step-by-step explanation:
To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100
ex: 11% = 11/100
7th grade math
Look at photo.
Answers
Answer:
10/z = 15/6
Step-by-step explanation:
Two shapes are similar so their side lengths are proportional, and the correct proportion to find the missing measurements is 10/z = 15/6
What is the inequality shown?
Answers
It shows the interval
[-2,8) or -2≤x<8
Please help me with this math question
Answers
Answer:
5.25 min
Step-by-step explanation:
8.4/1.6 = 5.25
Find the measure of each acute angle. Thank you!
Answers
Answer:
55 for the top left and 35 for the top right
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
7x+6 + 6x -7 + 90 = 180
Combine like terms
13x+89 = 90
Subtract 89 from each side
13x+89-89 = 180-89
13x = 91
Divide by 13
13x/13 = 91/13
x =7
The top left angle is
7x+6
7*7+6 = 49+6 = 55
The top right angle is
6x-7
6*7-7 = 42-7 = 35
A force of newtons is applied to a 20cm^2 surface. The force applied is then increased by f Newtons and the surface area is increased by 5cm^2. Complete the following sentence describing the outcome of the increases.
Answers
Answer:
The pressure decreased by 18%
Step-by-step explanation:
Given two scenarios:
Step 1: Find the initial pressure
Initial force = 90 Newtons
Initial surface force is applied on = 20 cm²
Initial pressure = initial force/initial surface
*Note: the SI unit for pressure is N/m²
We need to convert cm² to m²
1 cm² = 0.0001 m²
20 cm² = 0.002 m²
Initial pressure = 90/0.002 m²
Initial pressure = 45,000 N/m²
Step 2: find new pressure
New force = 90+5 = 95N
New area = 20+5 = 25 m² = 0.0025m²
New pressure = 95/0.0025 = 38,000
Step 3: find the outcome of the increases by calculating the % change in pressure
% change in pressure = (new pressure - initial pressure)/initial pressure × 100
Thus,
% change in pressure = (38,000 - 45,000)/38,000 × 100
= -7,000/38,000 × 100
= -18.42 ≈ -18%
The outcome of the increase resulted in a decrease in pressure. Thus,
The pressure decreased by 18%
Answer:
The pressure is decreased by 15.56%
One bag of rice that weighs 5.25 pounds will have enough rice if a recipe calls for 88 ounces of rice. (1 pound = 16 ounces) (3 points)
True
False
Answers
Answer:
False
Step-by-step explanation:
5x16=80
16x0.25=16÷4=4
80+4=84
PLEASE HURRY, LIMITED TIME EARLY!!!
Question-The center of circle A with equation (x – 7)2 + (y – 1)2 = 16 is mapped to the center of circle B with equation (x + 8)2 + (y – 2)2 = 16. Determine the translation needed for this mapping.
Answers-
A. (x, y) ⟶ (x - 15, y + 1)
B. (x, y) ⟶ (x - 12, y + 9)
C. (x, y) ⟶ (x - 8, y + 2)
D. (x, y) ⟶ (x + 15, y - 1)
Answers
The solution is Option A.
The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the equation for the circle A be represented as
( x - 7 )² + ( y - 1 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )
Let the equation for the circle A be represented as
( x + 8 )² + ( y - 2 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )
So , the translation of circle A to B is given by
( 7 , 1 ) to ( -8 , 2 )
So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up
Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
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How do I explain my knuckle being bruised to the office because they made me mad and I punched a Locker about 10 times? Without them thinking i'm crazy.
Answers
Answer: Tell them you've recently joined boxing and didn't have proper hand protection.
A company has to buy computers and printers. Each computer costs $550 and each printer costs $390. If
the company spends $8160 and buys a total of 16 machines, how many of each did it buy?
a. Let Statements:
b. Write the system:
Answers
Answer:
Answer:the company bought 12 computers and 4 printers.
Step-by-step explanation:
Step-by-step explanation:
Let x represent the number of computers that the company bought.
Let y represent the number of printers that the company bought.
The company buys a total of 16 machines. It means that
x + y = 16
Each computer costs $550 and each printer costs $390. If the company spends $8160 for all the computers and printers that was bought, it means that
550x + 390y = 8160 - - - - - - - - - - 1
Substituting x = 16 - y into equation 1, it becomes
550(16 - y) + 390y = 8160
8800 - 550y + 390y = 8160
- 550y + 390y = 8160 - 8800
- 160y = - 640
y = - 640/ - 160
y = 4
Substituting y = 4 into x = 16 - y, it becomes
x = 16 - 4
x = 12
Answer:
The company bought 12 computers and 4 printers.
Step-by-step explanation:
Let x represent the number of computers that the company bought.
Let y represent the number of printers that the company bought.
The company buys a total of 16 machines. It means that
x + y = 16
Each computer costs $550 and each printer costs $390. If the company spends $8160 for all the computers and printers that was bought, it means that
550x + 390y = 8160 - - - - - - - - - - 1
Substituting x = 16 - y into equation 1, it becomes
550(16 - y) + 390y = 8160
8800 - 550y + 390y = 8160
- 550y + 390y = 8160 - 8800
- 160y = - 640
y = - 640/ - 160
y = 4
Substituting y = 4 into x = 16 - y, it becomes
x = 16 - 4
x = 12
Use the explicit formula to find the 7th term of the Geometric sequence.
A(1) = 5 r = 4
Answers
Answer:
a
Step-by-step explanation:
a