Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot units and the hypotenuse measures 2x units. (150StartRoot 3 EndRoot – 75π) ft2 (300 – 75π) ft2 (150StartRoot 3 EndRoot – 25π) ft2 (300 – 25π) ft2.
Answers
The area of the shaded region is [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex] option first is correct.
It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.
It is required to find the shaded area (missing data is attached shown in the picture).
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a hexagon with a side length of 10 feet.
We know the area of the hexagon is given by:
[tex]\rm A = \frac{3\sqrt{3} }{2} a^2[/tex] where a is the side length.
[tex]\rm A = \frac{3\sqrt{3} }{2} 10^2[/tex] ⇒ [tex]150\sqrt{3}[/tex] [tex]\rm feet^2[/tex]
We have the shortest length = x feet and from the figure:
2x = 10
x = 5 feet
The radius of the circle r = longer leg
[tex]\rm r = x\sqrt{3} \Rightarrow 5\sqrt{3}[/tex] feet
The area of the circle a = [tex]\pi r^2[/tex] ⇒ [tex]\pi (5\sqrt{3} )^2 \Rightarrow 75\pi \ \rm feet^2[/tex]
The area of the shaded region = A - a
[tex]\rm =(150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]
Thus, the area of the shaded region is [tex]\rm (150\sqrt{3} \ - 75\pi ) \ feet^2[/tex]
Learn more about circle here:
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Answer:
option A
Step-by-step explanation:
Related Questions
Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 4)(0,4) and (2, 256)(2,256).
Answers
Answer:
Step-by-step explanation:
[tex]y=ab^x\\x=0,y=4\\4=ab^0\\4=a(1)\\a=4\\y=4b^x\\x=2,y=256\\256=4b^2\\b^2=\frac{256}{4} =64\\b=\pm8\\y=4(8)^x\\or\\y=4(-8)^x[/tex]
Find 3 irrational numbers between 1/3 and 3/8
Answers
Answer:
4/24,,,5/24,,7/24
hope it helps u
To determine the age of fossils, scientists use radiometric dating. This involves measuring quantities of certain radioactive isotopes and using mathematical equations to compare the amounts of each isotope present.
Suppose a scientist dates a piece of petrified wood and calculates that it is approximately 23,881,392.3102 years old. The petrified wood is later displayed in a museum.
What is the most reasonable way for the museum tour guide to describe the age of the wood to museum visitors?
(A): 2.3881×107 years old
(B): 24 million years old
(C): 23.8813923102 mega years old
(D): 23 billion years old
Answers
Answer:
B 24 million years old
Step-by-step explanation:
i did this quiz a long time ago tho so it might be B or D
An angle measuring (870n)° is in standard position. for which value of n will the terminal side fall on the y-axis? n = 3 n = 4 n = 5 n = 6
Answers
The value of n will the terminal side fall on the y-axis at n=3
The terminal side of an angle fall along the positive portion of the y-axis,
If it can written in the form of [tex](90^0)a[/tex]
Where a = positive odd integer,
We hyave given the given angle is,
[tex](870n)^0,[/tex]
What is terminal side?The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side
Now for n=3
[tex](870(3))^0=2610^0[/tex]
The angle will be 2610°
Its terminal side fall along the positive portion of the y-axis,
[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )
Therefore for n = 3, the terminal side of the angle (870n)° falls along the positive portion of the y-axis,
For n = 4,
Our angle will be 3480°
Its terminal side fall along the positive portion of the y-axis,
[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]
Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis
Next is for n = 5,
Our angle will be 4350°
Its terminal side fall along the positive portion of the y-axis,
[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]
Thus, for n = 5, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,
For n = 6,
Our angle will be 5220°
Its terminal side fall along the positive portion of the y-axis,
[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]
Thus, for n = 6, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.
Therefore,the value of n will the terminal side fall on the y-axis at n=3.
To learn more about the terminal side visit:
https://brainly.com/question/24680641
Answer:
a
Step-by-step explanation:
x=3 on edge
a
April has a sheet of paper that is 3 feet long. She cuts the length of paper into halves and then cuts the
1
length of each of these pieces into sixths.
2
How many pieces does she have?
How many inches long is each piece?
April has
pieces.
Each piece is
inches long.
Answers
Answer:
6x3=18 pieces
6/18 = 1/3
=
18 pieces
72 inches
A man invests a sum of money ($8,000) in a bank that offers a rate of 5%. He invests the money for 2 years. Calculate the amount of money in the bank at the end of the 2-year period if invested at:
(a) simple interest
(b) compound interest.
Question 6 (6 marks)
The diameter of a circle is 10 cm (as shown in the diagram). Use π = 3.14 Calculate to 2 decimal places, the:
(a) circumference
(b) area
Answers
Answer:
(a) 8000 times 5 times 2 = 800
a fast food chain surveyed a random sample of students to determine what pizza they prefer.cheese pizza was preferred by 40 students.pepperoni pizza was preferred by 28 students.based on the results,how many of 340 student can be expected to prefer cheese pizza
Answers
Answer:
12%, 0.12, 5/17, or as a ratio: 5:17
Step-by-step explanation:
To find the percentage:
Take the 40 students who prefer cheese and divide it by 340:
0.11764705882 rounded would be 0.12.
Convert 0.12 into 12% of students prefer cheese pizza.
To find the decimal, to the same exact thing I did up there, but, don't turn it into a percent, just leave it as 0.12.
To find the fraction, turn it into:
40/340
Then simplify it:
5/17 prefer cheese pizza.
For ratio, do the same as fraction, but, instead of the slash mark, turn it into a colon like this: 5:17.
:)
What is the area of a circle with a diameter of 12 inches?
Answers
Step-by-step explanation:
[tex]radius = \frac{12}{2} \\ = 6 \\ area \: of \: circle =\pi \: {r }^{2} \\ = \pi \times {6}^{2} \\ \pi \times 36 \\ = 113.14[/tex]
anss....wer....
Answer:
can be solved in two ways here you go
one is by either by finding r and using the formula
Area = πr²
Or by directly using the formula
Area = 1/4 πd²
) There are 8 children in Sophie's preschool class. During free time yesterday, 1 of them
chose to read books. What is the experimental probability that a randomly selected
preschooler would choose to read books today?
Answers
Using it's concept, it is found that there is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these numbers of outcomes are taken from previous trials.
In this problem, in the previous trial, one out of eight students read a book, hence:
p = 1/8 = 0.125 = 12.5%.
There is a 0.125 = 12.5% experimental probability that a randomly selected preschooler would choose to read books today.
More can be learned about probabilities at https://brainly.com/question/14398287
Use the equation machine to help you solve the addition equation.
k=8
k=9
k=17
k=26
Answers
Answer below
due today at noon
Answers
Answer:
x = -3
Step-by-step explanation:
A vertical line has an equation of the form
x = a
where a is the x-coordinate of every point on the line.
Every point on the line has x-coordinate -3, so the equation is
x = -3
I just need help on this one :) could u please try quickly
-3 x 2-1
Answers
I got -7. I tried probably wrong
NEED ASAP!!!!!
The graph shows a school's profit for selling lunches
on pizza day. What is the cost for selling 100
lunches? You must show your work.
Answers
Answer:
The cost for selling 100 lunches is 150 dollars.
Step-by-step explanation:
First, consider the equation: y = mx + b
y in this case is the profit in dollars (what' on the y axis) x in this case is the number of lunches sold (x- axis), m is the slope.
How do we calculate the slope of a graph? we take two points from the graph, let's say, (65,45) and (20,-90)
the formula for finding the slope is:
[tex]\frac{rise}{run} = \frac{y2 - y1}{x2-x1} \\\\[/tex]
where (x1, y1) is coordinates of first point in the line
where (x2, y2) is coordinates of second point in the line
[tex]\frac{45-(-90)}{65-20} = 3[/tex]
m = 3
y = 3x + b
now we need to find b. We just insert one point of your choice from the grpah, let's choose (50,0) now plug them in out newfound equation (y = 3x + b)
0 = 3(50) + b
find b using algebra:
0 = 150 + b
b = -150
Yay! we found b, now we have the equation y = 3x - 150
(by the way I just noticed you can find b from the graph, the point that touches the y-axis is b)
now we are told to find the cost for selling 100, we need to plug in 100 instead of x in our equation.
y = 3(100) - 150 = 150
therefore the cost is 150 dollars.
hope this helps, tell me if you misunderstood something.
Will give brainliest to correct answer
Question 1 Which statement about convergent infinite geometric series is true? O The graph of a convergent infinite geometric series goes to infinity. O A finite geometric sequence will have an infinite geometric series. O An infinite geometric series converges if -1 < r 1 is true. The graph of an infinite geometric series curves away from its sum. Question 2
Answers
Answer:
Third option: An infinite geometric series converges if −1<r<1 is true.
Step-by-step explanation:
An infinite geometric series contains an infinite number of terms. A convergent infinite geometric series can go to infinity on a graph. An infinite geometric series can converge if the ratio "r" is true in the equation " –1 < r < 1".
A four sided sandbox has exactly 2 right angles to side lengths 5 feet what geometric shape as described shape of the sandbox
Answers
Answer:
The sandbox is most likely in the shape of a kite. As it has only two right angles, it cannot be a square or other form of rectangle. It also cannot be a parallelogram, which has no right angles, nor is it a rhombus- all four sides are not of the same length.
A kite, however, has two pairs of equal-length sides that are adjacent to each other. It also has two sets of equal-measure angles, one of which can be 90° if it is a cyclic kite.
solve for x use the trig to find angle
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]
Let's solve, using Trigonometry ~
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{54}{72} [/tex]
[tex]\qquad \sf \dashrightarrow \: \tan(x) = \frac{3}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 37 \degree[/tex]
Answer:
[tex]\displaystyle 36,9[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
OR
[tex]\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
Don recently received his first credit card, a MasterCard with a credit line of $500. In the first month he had it, he ran up charges of $425. How much of that must he pay if he wants to charge a discount airline ticket, which costs $200, on his card without going over his credit limit
Answers
The amount Don must pay on his card without going over the credit limit is $125.
How much must Don pay?
Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.
Amount to be paid = (425 + 200) - 500 = $125
To learn more about addition, please check: https://brainly.com/question/19628082
What is 60% markup on $18.25?
Compute the total cost of an item you purchased for $18.25, but you now want to resell it for 60% more than what you've paid for it. What is the new cost?
Answers
Answer:29.2
Step-by-step explanation:The equation used to add a markup percent to a product is the cost plus the markup percentage multiplied by the cost.
Answer:
$29.20
Step-by-step explanation:
The original price of an item is 100%, so a 60% mark up means that the price will now be 160% of the original price.
160% = 160/100 = 1.6
⇒ 160% of $18.25 = 1.6 × 18.25 = $29.20
I have to finish this before next week because of grades please thanks
Answers
Answer:
D
Step-by-step explanation:
Help me answer this question about congruent triangles. 50 points available.
Answers
Answer:
B
Step-by-step explanation:
No these triangles are not congruent.
Left triangle
Shortest side = 6 cm
Longest side = 13 cm
3rd side = unknown but < 13
Right triangle
Shortest side = 6 cm
Longest side = unknown but > 13
3rd side = 13 cm
Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.
We do not know if any of the angles are congruent. If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.
Which of the following best explains why one graph appears skewed and one graph appears symmetric? the intervals on the x-axis of the histogram are too large. the interval on the y-axis of the histogram is too small. the interval on the x-axis of the histogram is inconsistent. the interval on the box-and-whisker plot is too small.
Answers
The reason for one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.
What is histogram?A histogram is the way of representation of data which is used to show the frequency distribution using the rectangle similar to a bar graph.
In the problem, the data given as,
In the attached image below, the histogram and box plot is shown for the ages of Elizabeth's Grandchildren and their frequency.In the 3rd and 4the bar of histogram, the data is jumped from 14 to 20 instead of 15.The frequency distribution in histogram for this data is inconsistent.This inconsistency brought the between the two graphs.Thus, the reason of one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.
Learn more about the histogram here;
https://brainly.com/question/2962546
Tom earns $3200 a month. He pays $950 to rent an apartment. What percent of Tom’s income does he pay
Answers
Hey there!
Answer:
336.84%
3200 out of 950 is 336.84%
Solution:
3200 out of 950 is what %?
3200 out of 950 is P%
Equation: Y/X = P%
Solving our equation for P
P% = Y/X
P% = 3200/950
p = 3.3684
Convert decimal to percent:
P% = 3.3684 * 100 = 336.84%
well, if we take 3200 to be the 100%, what is 950 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3200 & 100\\ 950& x \end{array} \implies \cfrac{3200}{950}=\cfrac{100}{x}\implies \cfrac{64}{19}=\cfrac{100}{x} \\\\\\ 64x=1900\implies x=\cfrac{1900}{64}\implies x = 29.6875[/tex]
Keiko drove 225 miles using 10 gallons of gas. At this rate, how many gallons of gas would she need to drive 441 miles?
Answers
Answer:
19.6 gallons
Step-by-step explanation:
divide 225 by 10 and you get 22.5 this means you are getting 22.5 miles per gallon so all you have to do is divide 441 by 22.5 and you get 19.6 so you are going to need 19.6 gallons to drive 441 miles
What is the slope-intercept equation for this line?
Answers
Answer:
y=-2x-1
Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.
(5) to the 7 over 3 power
Answers
[tex]5^{7/3} = 42.75[/tex] (approximately)
using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem
so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75
What is the sum of the two amounts of money shown?
Enter your answer in the box.
$
Answers
first amount:
$10 + $5 + 25 cents + 25 cents + 25 cents + 5 cents + 5 cents $10 + $5 + $0.25 + $0.25 + $0.25 + $0.05 + $0.05$15.85second amount:
$5 + 25 cents + 25 cents + 1 cents + 1 cents + 1 cents + 1 cents$5 + $0.25 + $0.25 + $0.01 + $0.01 + $0.01 + $0.01$5.54total amount:
$5.54 + $15.85 $21.39Hey there!
Guide:
• Penny = 0.01¢ (1 cent)
• Nickel = 0.05¢ (5 cents)
• Dime = 0.10¢ (10 cents)
• Quarter = 0.25¢ (25 cents)
• Half dollar = 0.50¢ (50 cents)
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
EQUATION #1.
$10.00 + $5.00
= $15.00
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.25¢ + 0.25¢ + 0.25¢ + 0.05¢ + 0.05¢
= 0.75¢ + 0.10¢
= 0.85¢
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
$15.00 + 0.85¢
= $15.85
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Total/Answer: $15.85
______________________________
EQUATION #2.
$5.00 + 0.00
= $5.00
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.25¢ + 0.25¢ + 0.01¢ + 0.01¢ + 0.01¢ + 0.01¢
= 0.50¢ + 0.04¢
= 0.54¢
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
$5.00 + 0.54¢
= $5.54
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Total/Answer: $5.54
______________________________
NOW ADD THEM TOGETHER!
$15.85 + $5.54
= $21.39
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
JL and MO are parallellines.
Which angles are alternate exterior angles?
Answers
Answer:
<N and <K
Step-by-step explanation:
Alternate exterior angles are a pair of angles on the outer side of the two parallel lines and are opposite of each other yet their measure is equal to each other.
The pair of angles that meet these requirements mentioned above are angle N and angle K.
pls help. it’s due tomorrow.
Answers
Answer:
the rest aren't wholly visible;like the signs under the letters
Step-by-step explanation:
11, 15, 19, 23, 27intervals of +4
18, 13, 8, 3, -2intervals of -5
Combine like terms:
-4k+15k-30=-78
(must be a decimal)
Answers
Answer:
I don't know sorry, I wish I could help you
Let's combine like terms:-
[tex]\bigstar{\sf{-4k+15k-30=-78}[/tex]
Add the k's:-
[tex]\bigstar{\sf{11k-30=-78}[/tex]
Add 30 to both sides:-
[tex]\bigstar{\sf{11k=-78+30}[/tex]
[tex]\bigstar{\sf{11k=-48}[/tex]
Divide both sides by 11:-
[tex]\bigstar{\boxed{\sf{k=4.36}}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
A survey asked 100 seventh graders if they have either a cell phone or a tablet. Of the 32 students that have a cell phone, 19 do not have a tablet. Of the 70 students that have a tablet, 57 do not have a cell phone. A total of 11 students stated they do not have a cell phone or a tablet. Some of this information is included in the frequency table.
help please
Answers
Answer:
I don't know sir actually I didn't understand your question no need to reply to my answer bye
Answer:
13
Step-by-step explanation:
if you read through the paragraph and pot your data on the table, the answer will show and is 13