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]
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Answer:
option A
Step-by-step explanation:
Related Questions
Sonia earned $2,100 at her uncle's orchard. if she worked for 70 weeks and earned the same amount of money each week, how much did she earn per week?
Answers
Answer:
30 dollars a week
Step-by-step explanation:
2100/70 is 30
What is the pattern;
1=4
2=4
3=64
4= ?
Answers
Answer:
64
Step-by-step explanation:
because the next number is equal to the same
Answer:
256
Step-by-step explanation:
Look closely at the stated list in the question:
1=4
2=16
3=64
Notice that the second number is reached by taking the first number and placing it as an exponent to 4.
4^1=4
4^2=16
4^3=64
So the missing number must be 4^4 which is equal to 256
5 and 1/3 divied by 2 and 2/9
Answers
Answer:
Step-by-step explanation:
16/3 / 20/9 = 16/3 x 9/20= 12/5 which is 2 2/5e
Sunny made a deposit into an account that
earns 6% simple interest. After 7 years, Sunny
had earned $420. How much was his initial
deposit?
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$420\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &7 \end{cases} \\\\\\ 420 = (P)(0.06)(7)\implies \cfrac{420}{(0.06)(7)}=P\implies 1000=P[/tex]
Find the equation of the line shown.
Answers
Answer:
(0,6) to (4,10) it might be the answer..........
The equation of the line passing through the points (0, 6) and (4, 10) is y = x + 6.
Here, we have,
To find the equation of the line passing through the points (0, 6) and (4, 10), we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b,
where m is the slope of the line, and b is the y-intercept.
First, let's calculate the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁),
where (x₁, y₁) = (0, 6) and (x₂, y₂) = (4, 10).
m = (10 - 6) / (4 - 0) = 4 / 4 = 1.
Now that we have the slope (m = 1), we can substitute it into the slope-intercept form along with one of the given points to find the y-intercept (b).
Using the point (0, 6), we have:
6 = 1(0) + b,
b = 6.
Therefore, the y-intercept (b) is 6.
Now we can write the equation of the line using the slope-intercept form:
y = mx + b,
y = 1x + 6,
y = x + 6.
Hence, the equation of the line passing through the points (0, 6) and (4, 10) is y = x + 6.
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it takes 120 unit cubes to completely fill a rectangular prism. the prism is 10 units cubes high
how would i answer this ?
Answers
Answer:
12
Step-by-step explanation:
Well, I am pretty sure you are looking for the length.
Since area = length x width, I would say that you could divide as well.
120 = 10 x 12
I am pretty sure the length is 12.
:)
These two figures have the same perimeter. Solve for x and find the perimeter.
(Please say the actual number and not a link please!)
Answers
Answer:
x=4, perimeter is 30.
Step-by-step explanation:
Let's calcualte the perimeter of the two figures. I'm assuming the pentagon is regular else the problem lacks information.
[tex]5(x+2) = 3x+(2x-1)+(x+7)\\5x+10=6x+6\\4=x[/tex]
At this point the easiest to compute is the pentagon, one side is 6, the whole perimeter is 30.
The equation 2x² + 2y2 – 8x - 12y + 16 = 0 defines a circle.
which of these shows a correct step for determining the center and radius of this circle? choose all that are correct.
(2x2 – 8x + 16) + (2y2 – 12y + 36) = -16 + 36
(x - 4)2 + (y - 9)2 = 5
(x2 - 4x + 4) + (y2 – 6y + 9) = -8 +13
ox? + y2 - 4x - 6y = -16
(x - 2)2 + (y - 3)2 = 5
Answers
Answer:
C, E
Step-by-step explanation:
Here, we want to change the equation of a circle from general form to standard form. This is done by making the leading coefficients 1, completing the squares, and then rewriting the equation in standard form.
The leading coefficients of the given equation are 2, so we first want to divide by 2. This gives ...
x² +y² -4x -6y +8 = 0
Subtracting 8 puts us in better position to complete the squares.
x² +y² -4x -6y = -8
Now, we can add the squares of half the coefficients of the linear terms.
(x² -4x +4) +(y² -6x +9) = -8 +13 . . . . . . matches C
And we can simplify this to the standard form equation:
(x -2)² +(y -3)² = 5 . . . . . matches E
What quadrilaterals can you draw that have two sides with length 8 cm and two sides with length
5 cm?
Which of these quadrilaterals can have two sides with length
8 cm and two sides with length 5 cm?
Select all that apply.
OA. Trapezoid
OB. Square
OC. Parallelogram
OD. Rectangle
E. Kite
Answers
Answer:
C. parallelogram
D. rectangle
E. kite
Step-by-step explanation:
Cannot be the square because all sides are the same. A trapezoid can have two sides the same, but not two pairs of equal sides. The remaining shapes can have two pairs of equal length sides. see image.
will give brainliest!!!
Answers
P.E.M.D.A.S
P.arenthesis
E.xponents
M.ultiplication
D.ivide
A.dd
S.ubtract
[(40+5)-3^2]/9*2
[45-3^2]/9*2
[45-9]/9*2
36/9*2
36/18
2
The last selection 2 is your answer.
I hope this helps and is the BRAINLIEST!!
Good luck with your studies!!
Answer:
2 is the answer
i used pemdas/ order of operations
Step-by-step explanation:
PLEASE I NEED HELP WITH THIS!! BRAINLIEST FOR THE FASTEST ANSWER
Answers
Answer:
B - 2093 in cubed
Step-by-step explanation:
Use the formula 4/3 * pi * r^3 to find the volume of one basketball, using 5 as the radius. Next, multiply this number by 4 to find the volume of 4 basketballs. The answer should be option B.
Hopefully this helps- let me know if you have any questions!
Answer:V≈268.08
Step-by-step explanation:Volume of a sphere: V = (4/3)πr. times 4 equals V≈268.08. i think this is it!! i hope it works loe you have an amazing day:) -marina mae
the sum of a minutes and b seconds, expressed in minutes, is:
Answers
Answer:
(1+b/60) minutes
Step-by-step explanation:
A minute = 1minute
b seconds = b/60minutes =b/60 minutes
sum of a minute and b seconds= (1+ b/60) minutes
HELP ASAP
Mr. Rodriguez asked 60 randomly chosen students from each grade level at Willowbrook School about their favorite types of reading materials. Of those 60 students, 12 chose science fiction. Mr. Rodriguez used the data to draw the inference that about 20% of middle school students prefer to read science fiction. If 150 students attend the school, did he make a reasonable inference? Explain
Answers
Answer:
No
Step-by-step explanation:
The sample size wasn't big enough. It could only be a trend in that grade.
Answer:
Mr. Rodriguez made a reasonable assumption. His surveys were random, non-biased, and relatively large in comparison to the school population. 12 out of 60 is 20%.
Step-by-step explanation:
find the median of first 10 prime numbers
Answers
Median=11+13/2 =24/2 =12//
Miranda's heart beats 3 times every 2 secounds. At that rate, how many times does her heart beat in 1 minute?
Answers
30 x 3 = 90
Answer is 90
2. Victor Larson had fixed costs totaling $2,805.60 last year, not
including depreciation. His variable costs totaled $1,870.40. His
3-year-old automobile cost $24,890.00 new and is now worth
$12,290.00. Larson drove his vehicle 16,700 miles last year. What
was his depreciation? What was his cost per mile?
Answers
The depreciation of the car is $12,600.
The cost of the car per mile is $0.28
What is the depreciation of the car?Depreciation is the decline in the value of an asset as a result of wear and tear.
Depreciation = cost of the asset - value of the asset now
$24,890 - $12,290 = $12600
What is the cost per mile?
Cost per mile = total cost / total mile
($2,805.60 + $1,870.40) / 16700 = $0.28
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Point X is located at 11 on the number line. Point Y is 5 less than point X. Where on the number line is point Y?
Answers
Answer:
6
Step-by-step explanation:
If you draw out a number line, and a little tick for each number, X will be on the 11 mark (I'll try to do a little thing here)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
The 11 is where X is
The question says that point Y is 5 LESS than point X, so we want to go down 5 numbers.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16f
(6 is 5 less than 11)
So the point Y will be on the 6
find the simple interest on $6000 invested for 8 years at 4%
Answers
Answer:
$1920.00
Step-by-step explanation:
You want to calculate the interest on $6000 at 4% interest per year after 8
year(s).
The formula we'll use for this is the simple interest formula, or:
I= P * r * t
Where:
• P is the principal amount, $6000.00.
• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.
• t is the time involved, 8.…..year(s) time periods
So, t is 8...year time periods.
To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:
The interest is: $1920.00
A triangle has side lengths of (5h – 4k) centimeters, (10h + 7m) centimeters, and
(5m – 2k) centimeters. which expression represents the perimeter, in centimeters,
of the triangle?
Answers
A mathematical expression which best represents the perimeter of this triangle is (15h - 6k + 12m) centimeters.
Given the following data:
Length A = (5h – 4k) centimeters
Length B = (10h + 7m) centimeters
Length C = (5m – 2k) centimeters.
What is a triangle?A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.
How to calculate the perimeter of a triangle.Mathematically, the perimeter of a triangle is given by this formula:
[tex]P=A+B+C[/tex]
Where:
A, B, and C are length of sides.Substituting the given parameters into the formula, we have;
[tex]P=(5h - 4k) +(10h + 7m) +(5m - 2k)\\\\P=5h+10h-4k-2k+7m+5m\\\\P=(15h-6k+12m)\;centimeters[/tex]
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Factor: 35b + 15c -10
Answers
Answer:
5(7b+3c-2)
Step-by-step explanation:
Common factor of 5
35b/5= 7b
15c/5= 3c
-10/5= -2
Take the common factor and multiply it by the quotients
5(7b+3c-2)
Really need help, I’m trying to catch up in my math and get my marks back up before mid term..
Answers
Answer:
a) 12x + 22 b) 17[tex]x^{2}[/tex] - x
Step-by-step explanation:
Perimeter is the sum of the each side length.
The first example is a rectangle so the (4x+8) and the (2x+3) are doubled.
(4x+8) x 2 = 8x+16
(2x+3) x 2 = 4x + 6
12x+22
(6[tex]x^{2}[/tex] - 12x) + (2[tex]x^{2}[/tex] + x) + (9[tex]x^{2}[/tex] + 10x)
combine like-terms.
17[tex]x^{2}[/tex] - x
Answer:
12x + 22 for the rectangle, 17x^2 - x for the triangle
Step-by-step explanation:
The perimeter of a square/rectangle is equal to 2*width + 2*length
So for the rectangle, it would be 2*(4x + 8) + 2*(2x + 3)
This can be further simplified as 8x + 16 + 4x + 6
Which can be further simplified as 12x + 22
The perimeter of a triangle is equal to length if side one + length of side two + length of base
That would be (6x^2 - 12x) + (2x^2 + x) + (9x^2 + 10x)
Which becomes 8x^2 - 11x + (9x^2 + 10x)
17x^2 - x
These two pentagons are similar.
Answers
If two pentagons are similar, then their sides are proportional. To find PT, we'll need to set up a proportion.
AE / PT = AB / PQ
---There are many ways to set up this proportion, it just depends on what side lengths you have and ensuring that they match up on both shapes.
6 / x = 5 / 12.5
5x = 75
x = 15
Length of PT = 15 cm
Option C
Hope this helps!
Which would be the best trend line for the given data set?
Answers
Anyone know the answer to all of them added together
Answers
Answer:
13x + 14
Step-by-step explanation:
5x + 6 + 3x = 8x + 6.
8x + 6 + x + 1 + x + 1 + 2= 10x + 10
10x + 10 + (2²)(i think) = 10x + 14
10x + 14 + 3x = 13x + 14
final answer
Answer:
[tex]13x+14[/tex]
Step-by-step explanation:
First take all the sides and add:
[tex]5x+6+3x+3x+2+2+2+x+1+x+1[/tex]
Then Combine Like terms:
[tex]5x+3x+3x+x+x+6+2+2+2+1+1[/tex]
There is your answer:
[tex]13x+14[/tex]
(If I misunderstood the handwriting, please tell me, and I will fix my mistakes)
Work out the coordinates of the midpoint of MN.
M (-5, 3) N(7, -8)
Answers
Answer:
(1, - 2.5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = (M (- 5, 3 ) and (x₂, y₂ ) = N (7, - 8 ) , then
midpoint = ( [tex]\frac{-5+7}{2}[/tex] , [tex]\frac{3-8}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{-5}{2}[/tex] ) = ( 1, - 2.5 )
A sum amounts Rs. 720 is divided into two parts in the ratio 3:5. How much will be the amount in second part?) Ans: Rs. 450
Answers
ATQ
[tex]\\ \rm\rightarrowtail 3x+5x=720[/tex]
[tex]\\ \rm\rightarrowtail 8x=720[/tex]
[tex]\\ \rm\rightarrowtail x=90[/tex]
Second part:-
5x=5(90)=450
Find the value of X round your number to the nearest tenths
Explain it please
Answers
In this case, we must use trigonometry to find the value of x:
[tex]tan(\alpha )=\frac{side-opposite-angle}{side-beside-angle} \\tan(70) = \frac{x}{3} \\3*tan(70) = x\\x = 3*tan(70)\\x = 8.24[/tex]
Thus the value of x rounded to the nearest tenth is 8.2
Hope that helps!
Kindly solve this question
Answers
Answer:
x=-1/7
Step-by-step explanation:
[tex]\frac{3x-1}{3} -\frac{2x}{x-1} =x[/tex]
[tex]\frac{(3x-1)(x-1)}{3x-3} -\frac{2x(3)}{3x-3} =x[/tex]
[tex]\frac{3x^2-4x+1}{3x-3} -\frac{6x}{3x-3} =x[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =x[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =\frac{x(3x-3)}{3x-3}[/tex]
[tex]\frac{3x^2-10x+1}{3x-3} =\frac{3x^2-3x}{3x-3}[/tex]
[tex]3x^2-10x+1=3x^2-3x[/tex]
[tex]-10x+1=-3x[/tex]
[tex]-7x=1[/tex]
[tex]x=-1/7[/tex]
7. Assume this policy has a deductible of $1,000 and a coverage limit of
$15,000. If tirere are personal property losses of $7,000 for a covered
event, which best describes how much both parties pay?*
Answers
Answer:
Insured person pays $1,000; insurance company pays $6,000
Step-by-step explanation:
Both parties pay $9000.
What is PEDMAS rule?PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.
Policy has a deductible of $1,000 and a coverage limit of $15,000.
Tirere are personal property losses of $7,000 for a covered event
Based on the given conditions, formulate
= 1000 + 15000 - 7000
= 16000 - 7000
= 9000
Both parties pay $9000.
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Larry earns $5.25 per hour helping his neighbor. Last month he earned $220.50. How many
hours did Larry work?
Answers
Explanation: If he earns $5.25/ hr you would divide the amount of money he earned by 5.25 which equals 42. By doing this you are finding out how many times 5.25 (how much he makes in ONE hour) goes into 220.50 therefore finding out how many hours he worked.