oac is a sector of a circle of radius 8cm, centre O ba and bc are tangents to the circle angle aoc = 120 degrees calculate the area of the shaded region give your answer to 3 significant figures
Answers
Answer:
The area of the shaded region is [tex]49.5 cm^{2}[/tex] to 3. significant figures
Step-by-step explanation:
Step one: find the two diagonals of the kite.
The Horizontal diagonal can be obtained using the cosine rule:
[tex]AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)[/tex]
[tex]AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm[/tex]
The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:
Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.
This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.
[tex]cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm[/tex]
Step two: Use the dimensions of the two diagonals of the Kite to find the area:
The area of a Kite is obtained using this formula:
[tex]Area = \frac{pq}{2}[/tex], where p and q are the two diagonals.
hence,
[tex]Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}[/tex]
Step three: Calculate the area of the sector of the circle.
Area of the sector is obtained using this formula
[tex]Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}[/tex]
Step Four: Subtract the area of the sector from the area of the kite:
Area of the shaded region will be [tex]116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}[/tex]
This will be[tex]49.5 cm^{2}[/tex] to 3. significant figures
Answer:
43.8 cm²
Step-by-step explanation:
1. Split the kite in two and find the length of OB
When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.
Then, use the sine rule we can find out the length of OB. It goes like this:
[tex]\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm[/tex]
2. Calculate the area of the kite
Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of [tex]area of triangle=\frac{1}{2}absinc[/tex].
[tex]\frac{1}{2}[/tex]×8×16×sin60 = [tex]32\sqrt{3}[/tex]
But as there are two triangles, we duplicate the answer.
2×[tex]32\sqrt{2}[/tex] = [tex]64\sqrt{3}[/tex]
2. Calculate the area of the sector
area of sector =[tex]\frac{angle of sector}{360} \\[/tex]×πr²
[tex]\frac{120}{360}[/tex]×8²π = [tex]\frac{64}{3}[/tex]π
3. Subtract the area of the sector from the area of the kite
[tex]64\sqrt{3}[/tex] - [tex]\frac{64}{3}[/tex]π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)
HOPE THIS WILL HELP YOU :)
Related Questions
Please answer correctly !!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!
Answers
Answer:
Step 3 they took the square root incorrectly
Step-by-step explanation:
5 ( x-2)^2 +6 = 86
Subtract 6 from each side
5 ( x-2)^2 +6 -6= 86-6
5 ( x-2)^2 = 80
Divide each side by 5
5 ( x-2)^2 /5 = 80/5
(x-2)^2 = 16
Take the square root of each side
sqrt((x-2)^2) = ±sqrt(16)
x-2 = ±4
Lliana started to evaluate the function f(x)=2x^2-3x+7 for the input value 2. What is the value of the function when x=2?
Answers
Answer:it is 9 because you subtract 6 from the 8 and then you add 2 and 7 to get 9
Step-by-step explanation:
R_T
Choose the relationship symbol that makes the statement true.
Answers
Answer:
R=T
Step-by-step explanation:
We could say that the same symbol = makes it look like a true statement.
We could say that the same symbol makes us see a true statement.
In this case we are showing that R corresponds to T therefore it is true or confirmed, regardless of the value that R has.
2/5 y + 1/5 x -0.2y - 6 + (-2)
Answers
Answer:
[tex]0.2y+0.2x-8[/tex]
Step-by-step explanation:
[tex]\frac{2}{5}y+\frac{1}{5}x-0.2y-6+\left(-2\right)[/tex]
[tex]=\frac{2}{5}y+\frac{1}{5}x-0.2y-6-2[/tex]
[tex]=\frac{2}{5}y-0.2y+\frac{1}{5}x-6-2[/tex]
[tex]\frac{2}{5}y-0.2y[/tex]
[tex]=y\left(\frac{2}{5}-0.2\right)[/tex]
[tex]\frac{2}{5}-0.2=0.2[/tex]
[tex]=0.2y[/tex]
[tex]=0.2y+\frac{1}{5}x-6-2[/tex]
[tex]\frac{1}{5}x[/tex]
[tex]=\frac{1\cdot \:x}{5}[/tex]
[tex]=\frac{x}{5}[/tex]
[tex]=0.2y+\frac{x}{5}-6-2[/tex]
[tex]=0.2y+0.2x-8[/tex]
Solve for j.
j + 42
---------- =2
-7
what does j eqaul
Answers
Answer:
The value of [tex]j[/tex]:
[tex]j = -56[/tex]
Step-by-step explanation:
Solve for [tex]j[/tex]:
[tex]\frac{j + 42}{-7} = 2[/tex]
-Multiply both sides by -7:
[tex]j + 42 = 2 ( -7)[/tex]
[tex]j + 42 = -14[/tex]
-Subtract both sides by 42:
[tex]j + 42 - 42 = -14 - 42[/tex]
[tex]j = -56[/tex]
So, therefore, [tex]x = -56[/tex] would be the final answer.
Answer:
j = -47
Step-by-step explanation:
I think you meant j + 42 - 2 = -7
So what I would do is first find the two number we know which would be
42 - 2 = 40
So, then the equation comes down to j + 40 = -7
So,
j = -47
Because = -47 + 40 = -7
Have a good day. :)
Hope this helps!
(brainliest would be appreciated)
The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 3. Calculate the volume of the box.
Answers
Answer:
The volume of the box would be 6x³+33x²+54x+27.
Step-by-step explanation:
The new dimensions of the box would be (x+3), (2x+3), and (3x+3). Since the volume of a rectangular prism are calculated by multiplying the length, width, and depth, we can just multiply all three of these dimensions together to come up with the answer.
Using foil on the first two terms originally you get (x+3)×(2x+3)= 2x²+3x+6x+9 which can be simplified to 2x²+9x+9.
Then you multiply this equation by (3x+3). (2x²+9x+9)×(3x+3)= 6x³+6x²+27x²+27x+27x+27 which can be simplified to 6x³+33x²+54x+27.
Answer:
6x³+33x²+54x+27
Step-by-step explanation:
dimensions are now:
x+3, 2x+3, 3x+3
Volume
V=lwhV= (x+3)(2x+3)(3x+3)= 3(x+1)(x+3)(2x+3)= 3( x² + 4x+3)(2x+3)= 3(2x³+11x²+18x+9)=6x³+33x²+54x+27Which is a simplified form of the expression 2(2j + 3) – 3j? A. -j + 3 B. 2j + 3 C. j + 6 D. -j + 6
Answers
Answer:
C. j + 6
Step-by-step explanation:
2(2j + 3) - 3j
multiply each term in the parentheses by 2
2 x 2j + 2 x 3
calculate the product
4j + 6 -3j
collect like terms by subtracting their coefficients
(4 - 3)j
then subtract the numbers
1j
when the term has a coefficient of 1, it doesn't have to be written
j
then plug in the other number and that's your answer
j + 6
Answer:
The answer is C).Step-by-step explanation:
C. j + 6
Hope this helps!! :)
opposite quantity of. (i) 28 m South (ii)70 km above sea level.
7
Answers
Answer:
1) 28m West 2)70km below sea level
B
7
25
C
24
A
Find sin(cx) in the triangle.
Answers
Answer:
The sine of cx in the triangle is the opposite side/the hypotenuse
sin(cx) = 7/25
sin(cx) = 0.28
cx = sin^-1 (0.28)
cx = 16.26 degrees
Evaluate the expression for p = 4.
p^2=
Answers
4^2 = 4 * 4.
4 * 4 = 16.
Therefore, p ^2 = 16.
Answer:
16
Step-by-step explanation:
i showed the work in the picture above
Please answer correctly !!!! Will mark brainliest !!!!!!!!!
Answers
Answer:
Area = l x w
Area = (x + 1)(x + 7)
Area = x² + 7x + x + 7
Area = x² + 8x + 7
Step-by-step explanation:
plslslslsl help ASAP you win win brainlist
Answers
Answer:
78 dollars
Step-by-step explanation:
Take the prices and multiply by the percent commission
778 * 10 %
Change to decimal form
778 * .10
77.80
Round to the nearest dollar
78
Answer:77.80
Step-by-step explanation:
Which of these choices are quadratic equations? Check all that apply.
A. 2x – 1 = 0
B. 2x2 - 1 = 0
C. 2x2 - 1
D. 3x2 + 5x - 1 = 0
E. x - x² +5=0
F. - 4x2 + x = 0
Answers
Answer:
Quadratic Equations ⇒ D, E, F
Step-by-step explanation:
Let us say that each of these equations can only be defined as a quadratic equation if it can be factored / solved through completing the square / application of quadratic formula as solve for the value of x;
[tex]A. 2x - 1 = 0, Add + 1 to either side,\\2x = 1, Divide sides by 2,\\x = 1 / 2 ; Not Quadratic Equation[/tex]
[tex]B. 2x^2 - 1 = 0, Add + 1 to either side,\\2x^2 = 1, Divide sides by 2,\\x^2 = 2, Take | | of x, \sqrt{x} - either side \\\| x | = \sqrt{1 / 2},\\x = \sqrt{1 / 2} = - \sqrt{1 / 2} ; NotQuadraticEquation[/tex]
[tex]C. 2x^2 - 1, NotInForm - ax^2 + bx + x = 0 ; NotQuadraticEquation[/tex]
[tex]D. 3x^2 + 5x - 1 = 0, Add 1 to either side,\\3x^2 + 5x = 1, Divide sides by 3,\\x^2 + 5x / 3 = 1 / 3, Solve for a,\\2ax = 5 / 3x, Divide sides by 2x,\\a = 5 / 6, Add a^2 - ( 5 / 6 )^2 to either side,\\x^2 + ( 5x / 3 )^2 + ( 5 / 6 )^2 = 1 / 3 + ( 5 / 6 )^2, simplify,\\( x + 5 / 6 )^2 = 37 / 36, solve for x,\\x = ( \sqrt{37} - 5 ) / 6 = ( - \sqrt{37} - 5 ) / 6 ; QuadraticEquation[/tex]
[tex]E. x - x^2 + 5 = 0, Similar Form ; QuadraticEquation\\[/tex]
[tex]F. - 4x^2 + x = 0, Factor the Expression,\\- x * ( 4x - 1 ) = 0, Apply Zero Product Property,\\x = 0, and, 4x - 1 = 0,\\x = 0 = 1 / 4 ; QuadraticEquation[/tex]
The quadratic equations are:
2x² - 1 = 0
2x² - 1
3x² + 5x - 1 = 0
x - x² +5 = 0
-4x² + x = 0
Options B, C, D, E and F are the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A polynomial with degree 2 is called a quadratic equation.
A.
2x – 1 = 0
This is not a degree 2 equation.
B.
2x² - 1 = 0
This has degree 2.
C.
2x² - 1
This has degree 2.
D.
3x² + 5x - 1 = 0
This has degree 2.
E.
x - x² +5 = 0
-x² + x + 5 = 0
This has degree 2.
F.
- 4x² + x = 0
This has degree 2.
Thus,
B, C, D, E, and F are quadratic equations.
Learn more about polynomials here:
https://brainly.com/question/2284746
#SPJ2
Which function is graphed
Answers
Answer:
Step-by-step explanation:
what kind of graph
Answer:
A) this function has vertical asymptotes at an interval of π.
1/2 cosecx is the answer
Step-by-step explanation:
EDGE2020
Daria sells televisions. She earns a fixed amount for each television and an additional $ 20 if the buyer gets an extended warranty. If Daria sells 15 televisions with extended warranties, she earns $ 1 comma 200. How much is the fixed amount Daria earns for each television?
Answers
Answer:
$60
Step-by-step explanation:
Firstly, you would divide $1,200 by 15, which is 80.
This gives you the cost for each television including the additional $20.
Then, you would do 80-20 = 60 to find the cost of the individual television without the warranty.
A circular rug has a radius of 10 feet. What is the area of the rug? Use 3.14 for π.
Enter your answer
Answers
Answer:
A=314 feet
Step-by-step explanation:
[tex]A=\pi r^{2}[/tex]
[tex]A=3.14*10^{2}[/tex]
[tex]A=3.14*100[/tex]
[tex]A=314 feet[/tex]
The integer which lies between -1/4 and 3/2 are:
a)0 and 1 b)0 and -1 c)1 and -1 d)-1 and 2
Which option is right?
Answers
Answer:
The correct answer is a) 0 and 1.
Step-by-step explanation:
By converting the fractions into decimals, we can see that -1/4 is equivalent to -0.25 and 3/2 equals 1.5. Therefore, anything with a value outside of -0.25 < x < 1 should be marked out. So, anything containing anything less than -0.25 cannot be considered (i.e., -1) and anything above one cannot be considered (i.e., 2). Therefore, the only option left is a) 0 and 1.
Answer:
a) 0 and 1
Step-by-step explanation:
the easiest way to think about this problem is using a number line to picture where the numbers are. I cant really do that easily on here but i will try my best to explain it with words.
If you think about where the numbers are on a number line you should see that -1/4 is slightly less than zero, which would put it to the left of zero.
Likewise, if you think about 3/2, which is equal to [tex]1\frac{1}{2}[/tex] it is slightly bigger than 1, which would put it to the right of 1 on a number line.
So if you think about the integers (which are numbers that can be positive or negative but do not involve decimals or fractions ex. -2, -1, 0, 1, 2 etc.) which are between those two numbers on the number line, the only integers are 0 and 1, which gives you your answer.
Which statement best explains why this expression is equal to 9.4? A)Any expression multiplied by 0 equals 0. B)Any number divided by its opposite equals 0. C)The fraction is equal to −9.4. Any number added to its opposite results in the number itself. D)The expression does not have a value of 9.4.
Answers
Answer: A.
Step-by-step explanation:
yeet
Answer:
A.
Step-by-step explanation:
Because if you multiply out the top of the fraction to simplify it, it will equal zero. And zero divided by any number is equal to zero because no number fits into zero. So A. would be the best answer since you are multiplying an expression by zero on the top, and you can't get any number other then zero for the answer of the fraction. And 0 + 9.4 = 9.4.
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
et's solve your equation step-by-step.
(x+3)2−1=35
Step 1: Simplify both sides of the equation.
x2+6x+8=35
Step 2: Subtract 35 from both sides.
x2+6x+8−35=35−35
x2+6x−27=0
Step 3: Factor left side of equation.
(x−3)(x+9)=0
Step 4: Set factors equal to 0.
x−3=0 or x+9=0
x=3 or x=−9
Answer:
x=3 or x=−9
Answer:
Add 1 to each side
Take the square root of each side
Subtract 3 from each side
Step-by-step explanation:
(x+3)^2 -1 = 35
Add 1 to each side
(x+3)^2 -1+1 = 35+1
(x+3)^2 = 36
Take the square root of each side
sqrt ((x+3)^2) =±sqrt (36)
x+3 = ±6
Subtract 3 from each side
x+3-3 = -3±6
x = -3±6
x = -3+6 x = -3-6
x = 3 x = -9
What is the simplified form of StartFractio negative 24 m Superscript 5 Baseline n Superscript 4 Baseline Over 8 m Superscript negative 7 Baseline n Superscript negative 2 Baseline End Fraction? Assume m not-equals 0, n not-equals 0. Start-fraction 3 Over m Superscript 35 Baseline n Superscript 8 Baseline End-fraction Negative Start-fraction 3 n squared Over m squared End-fraction Negative 3 m Superscript 12 Baseline n Superscript 6 Baseline 3 m Superscript 35 Baseline n Superscript 8 Baseline
Answers
Answer:
Option C on E2020
Step-by-step explanation:
just finished the test
Answer:
C
Step-by-step explanation:
Verticle angles must have ?
Answers
Answer: Verticals angles are when 2 line intersect at a point forms 2 pairs of angles. The pairs will be opposite of each other.
The picture I have attached should give a good representation of what I mean.
The A angles are the same and the B angles are the same in the picture.
the side of a triangle are in the ratio of 3:8:7. if the perimeter of the triangle is 63 cm, how long is the shorter side?
Answers
Answer:
10.5 cm
Step-by-step explanation:
Multiply the ratios by x
3x : 8x: 7x
Add the sides together
3x+8x+7x to get the perimeter
18x = 63
Divide each side by 18
18x/18 = 63/18
x =3.5
The shorter side is 3x
3*3.5=10.5 cm
what does 9n-2<7+20 equal?
Answers
Answer:
[tex]n<\frac{29}{9}\\n<3.222222.....\\[/tex]
n ≈ 3
Step-by-step explanation:
9n-2<7+20
[tex]9n-2<27 \leftarrow \text {Combine Like Terms}\\9n-2+2<27+2 \leftarrow \text {Addition Property of Equality}\\9n<29\\\frac{9n<29}{9} \leftarrow \text {Divsion Property of Equality}\\\boxed{n<\frac{29}{9}}[/tex]
CAN ANYONE HELP ASAP!!!!
Answers
Answer:
C and D
Step-by-step explanation:
since sqrt(4) = 2, we can replace all of the sqrt(4) in D to 2
Once we do that, it becomes
2 1
1 2
2 1
or C
During a promotional weekend, a state fair gives a free admission to every 165th person that enters the fair. On Saturday, there were 7,303 people attending the fair. On Sunday, there were 7,126 people attending the fair. How many people received a free admission over the two days?
Answers
Answer: 87
Step-by-step explanation:
If it is the 165th person each day
7303/165 = 44.26 ( so 44 free admissions on Saturday)
7126/165 = 43.19 (so 43 free admissions on Sunday)
87 free admissions over the two days
If 165th person where it can carry over from day to day
(7303 + 7126)/165 = 87.49
87 free admissions over the two days
Same answer this time, but could be different in a diferent problem.
Which expression can be used to find 38 percent of 22?
Answers
Answer:
[tex]0.38 \times 22[/tex]
Step-by-step explanation:
The correct expression used to find 38 percent of 22 is
[tex]0.38 \times 22[/tex]
????????????????????
Answers
Answer:
A) DEBBIE: 1p+4t=29
B) JOEY: 5p+2t=28
Step-by-step explanation:
Find the value of x in the triangle shown below
Answers
Answer:
28°
Step-by-step explanation:
every Triangle equals to 180°
85+67=152
180-152=28
28°
Solving Solutions:
85° + 67° = 152°
180° - 152° = 28°
A pentagon train is made by attaching regular pentagons with 1" sides so that each pentagon, except the two on the ends, is attached to exactly two other pentagons along sides, as shown. How many inches are in the perimeter of a pentagon train made from 85 pentagons?
Answers
Answer:
There are 341 inches from the perimeter of a pentagon train made from 85 pentagons
Step-by-step explanation:
A pentagon is a polygon with five sides. A regular pentagon have all the five sides equal in length and also all the five interior angles equal.
The perimeter of a pentagon = 5l
Nof for a pentagon train attached to 1 pentagon by its sides;
The perimeter = (5 × 1 - (1-1))
Perimeter = 5
For pentagon train attached to two pentagon
Perimeter = ( 5×2 - (2-1))
Perimeter = (10 1)
Perimeter = 9
For pentagon train with n pentagon
Perimeter = ( 5× n -(n-1))
Perimeter = 5n - n+1
Perimeter = 4n + 1
∴ For pentagon train attached to 85 pentagon; where n=85
Perimeter = 4 n + 1
Perimeter = (4 × 85)+1
Perimeter = 340+1
Perimeter = 341 inches
There are 341 inches from the perimeter of a pentagon train made from 85 pentagons
plz help with slope question fast
Answers
Answer:
The Answer is D. because -4 passes trough the x intercept and -2 passes through the y
Step-by-step explanation:
Answer:
The answers are:
x-intercept = -4
y-intercept = -2
Step-by-step explanation:
According to the following to graph, you need to find the x-intercept and the y-intercept. The x-intercept, is when a line crosses the x-axis of the graph, and the y-intercept, is when a line crosses the y-axis of the graph.
Finding the x-intercept and the y-intercept:
x-intercept = -4
y-intercept = -2