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
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 :)
uually Cxpressions
Which expressions are equal to 0 when x=-1? Check all that apply.
(4x + 5)
4(x - 1)
(5 - 4x)
40% - (-1))
(4 7 + 5)
(4x + 5)
4(x + 1)
(5 - 4x)
Intro
Answer:
Which expressions are equal to 0 when x = –1? Check all that apply.
StartFraction 4 (x plus 1) Over (4 x plus 5) EndFraction
StartFraction 4 (x minus 1) Over (5 minus 4 x) EndFraction
StartFraction 4 (x minus (minus 1)) Over (4 x plus 5) EndFraction
StartFraction 4 (x plus (minus 1)) Over (4 x plus 5) EndFraction
StartFraction 4 (x plus 1) Over (5 minus 4 x) EndFraction
Step-by-step explanation:
i need help with this question( just a simple equation):
3. Greta has two part-time jobs. She earns $14/h at her first job and earns $12.50/h at the second job. In one week, she earned $500.
a) Write an equation that models this information. (hint: define your variables first – what do you not know?)
Answer:
I'm pretty sure it's
14x + 12.50y = 500
The question is above please help
Answer:
i believe it's C i may be wrong
Step-by-step explanation:
PLEASE ANSWER How do you think industries vary according to the wealth of a country? Justify your answer.
Answer:
They very according to the wealth of a country because the wealth of the country also reflects on how much supply there is, and if for example, there is a shampoo factory they will use less quality items because they don't have enough money or supplies to make good quality shampoo. The wealth of the country also affects how many sales are made from those lower quality items. Since the country is so poor, they don't have enough money to buy expensive products from overseas so they will buy the lower quality items, even if they know that they aren't the best quality. This might result to diseases in some serious cases, like in food industries of poor countries.
Step-by-step explanation:
it vary because if the country in which the company is being operated is a wealthy country it means that the company or industry will gain more customers than a country that is poor. Because if the country is wealthy people will come to that country because of it's rich economy but it also differs if the country in which the company is operating and does not offer quality service that industry will not be successful
Joy made a deposit of $1600 into an account with a rate of 5%. How long should she leave the money into the account if she wants to earn $240 in interest
Answer: 3 years
Step-by-step explanation:
The following can be gotten from the question:
Principal = $1600
Rate = 5%
Simple interest = $240
Time = Unknown
Interest = Principal × Rate × Time /100
240 = (1600 × 5 × Time)/100
240 = (8000 × Time)/100
240 × 100 = 8000 × Time
24000 = 8000 × Time
Time = 24000/8000
Time = 3 years
I NEED HELP ITS ON FUNCTIONS! HELPPPPPPPPPPP
Explanation needed
Answer:
D
Step-by-step explanation:
A function of x means that there can only be one value of y per x value. Therefore, D does not match this because there are 4 values of y per x value (3).
Answer:
D
Step-by-step explanation:
Each x value can have only ONE y value
this means that there cannot be more than one of the same x value:
think of the x values as an input, each input has one output right?
ex:
input: 7
output:8
input:3
output:2
how is it possible that the same input has different outputs?
input: 5
output: 6,7
this does not make any sense, one input should only have one output hence, one value of x(input) should have only one value of y(output)
Hope this helps!
Find the diameter, area and circumference.
11
0
Answer:
diameter = two times the radius
2r
the area = πr²
the circumference= 2πr
hope it helps
What is the x-intercept of the line whose equation is x/3 + y/2 = 1
Answer:
y- intercept = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
[tex]\frac{x}{3}[/tex] + [tex]\frac{y}{2}[/tex] = 1
Multiply through by 6 to clear the fractions
2x + 3y = 6 ( subtract 2x from both sides )
3y = - 2x + 6 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + 2 ← in slope- intercept form
with y- intercept c = 2
Please I need help ASAP
Answer:
Step-by-step explanation:
V= π(8)^2(12/3)
V= 64(4)π
V= 256π
V= 804.3 cm^3
The graph below represents the system of equations 3x+4y=12 and 2x-y=8. A coordinate grid with 2 lines. One line passes through (0, 3) and (4, 0). The other line passes through (2, negative 4) and (4, 0). Which ordered pair is a solution to the system of equations? (0, 3) (3, 0) (4, 0) (0, 4)
Answer:
C. (4,0)
Step-by-step explanation:
Given a graph of the system of equations
3x+4y=12; and
2x-y=8.
Line 1 passes through (0, 3) and (4, 0).Line 2 passes through (2, -4) and (4, 0).We can see that both lines pass through (4,0). Therefore, (4,0) is a point of intersection of the two lines.
It is therefore a solution to the system of equations.
Can someone please explain to me what quadrants on a coordinate plane means, for brainliest and some points.
What is (7x − 9) + (3x + 14)?
Answer:
[tex](7x - 9) + (3x + 14) = 10x + 5[/tex]
Step-by-step explanation:
[tex]\left(7x-9\right)+\left(3x+14\right)[/tex]
Remove parentheses: [tex]\left(a\right)=a[/tex]
[tex]=7x-9+3x+14[/tex]
Group like terms:
[tex]=7x+3x-9+14[/tex]
Add similar elements: [tex]7x+3x=10x[/tex]
[tex]=10x-9+14[/tex]
Add/Subtract the numbers: [tex]-9+14=5[/tex]
[tex]=10x+5[/tex]
Hope I helped. If so, may I get brainliest and a thanks?
Thank you. Have a good day! =)
Answer:
pls refer to the pic
Step-by-step explanation:
PLS MARK ME AS BRAINLIAST PLS MARK ME AS BRAINLIAST AND DON'T FORGET TO FOLLOW AND THANKS MY ANSWER PLS MARK ME AS BRAINLIAST AND DON'T FORGET TO FOLLOW AND THANKS MY ANSWER HOPE IT HELPS.....Given a right triangle with b=3 and c=5 find leg a? Show your work
Find attached to this question, the diagram of the right angle triangle
Answer:
Leg a = 4
Step-by-step explanation:
A right angle triangle has 3 sides : side a, b and c
The formula to solved for a right angle triangle =
a² + b² = c²
In that above question,
a = unknown
b = 3
c = 5
Therefore,
a² + 3² = 5²
a² = 5² - 3²
a² = 25 - 9
a² = 16
a = √16
a = 4
Therefore, leg a = 4
i need help with this and how you got it please! 10 points
Answer:
B, x=40 is the right answer
Step-by-step explanation:
DAC is one half of the right angle and CAB is another half. So, you know that since a right angle is 90 degrees, DAC + CAB must equal 90.
They have given you equations for both angles, so now its just a matter of rearranging and solving for x.
DAC = x
CAB = 2x - 30
DAC + CAB = 90
Using the equations above, we can come up with this final equation:
x + 2x - 30 = 90
If we add the x together:
3x - 30 = 90
If we move the 30 to the other side by adding it to 90
3x = 90 + 30
3x = 120
If we divide 120 by 3:
x= 40
Therefore, the answer is B
Hope this helped : )
Temperatures in °F can be converted in °C
Answer:
[tex] \frac{9c + 160}{5} [/tex]
Step-by-step explanation:
C = 5(F - 32)/9
so we do a little algebra here
9C = 5F - 160
we move both side
5F - 160 = 9C
5F = 9C + 160
so in the end
F =
[tex] \frac{9c + 160}{5} [/tex]
a = 9
b = 160
c = 5
Answer:
[tex]F=\frac{9C+160}{5}[/tex]
Step-by-step explanation:
[tex]C=\frac{5(F-32)}{9}[/tex]
Multiply both sides with 9.
[tex]9C=5(F-32)[/tex]
Use distributive property.
[tex]9C=5F-160[/tex]
Add 160 to both sides.
[tex]9C+160=5F[/tex]
Divide 5 to both sides.
[tex]\frac{9C+160}{5}=F[/tex]
A car has a full tank of gas, holding
15 gallons
. It drives
300 miles
, and then stops for gas. After
10 gallons
of gas are added, the tank is full again. What is the gas mileage of the car?
Answer:
The mileage of the car is 30 miles per gallon
Step-by-step explanation:
Here, we are interested in calculating the gas mileage of the car.
The gas mileage refers to the number of kilometers the car can travel on a particular amount of fuel.
The full capacity of the car tank is 15 gallon
Now after traveling 300 miles, it stops for gas and 10 gallons of fuel are added to make the car full again.
What this means is that the car used up a total of 10 gallons of fuel for the 300 miles
Thus, the gas mileage of the car is that it used 10 gallons to travel a total of 300 miles
Expressing this as a ratio, we have 300 miles/10 gallons = 30 miles/ gallon
This means that on a gallon of fuel, the car can travel 30 miles
Need some help with number word problems, tysm if you do :)
Answer:
Read below
Step-by-step explanation:
x is always the smaller number
y is always the larger number
underlined means it's the question
bolded means it's the answer
1.
One number is 6 times as large as another. Their sum is 42. Find the numbers.
The numbers need to fit the criteria:
6x=yx+y=42A. 6+36=42 (correct)
B. 7+42=49 (incorrect)
C. 7+35=42 (incorrect because it doesn't follow the 1st rule)
D. 6+42=48 (incorrect)
Only A. 6, 36 fits the criteria.
2.
One number is 3 less than another. Four times the smaller is 4 more than 3 times the larger. Find the numbers.
The numbers need to fit the criteria:
x+3=y4x-4=3yA.
4+3=7
12-6≠21 (incorrect)
B.
7+3=10
28-3≠30 (incorrect)
C.
13+3=16
52-4=48 (correct)
D.
9+3≠13 (incorrect)
Only C. 13, 16 fits the criteria.
3.
One number is 4 less than another. Five times the smaller is 3 less than 4 times the larger. Find the numbers.
The numbers need to fit the criteria:
x+4=y5x+3=4yA.
13+4=17
65+3=68 (correct)
B.
-23+4= -19
-115+3≠ -76 (incorrect)
C.
17+4=21
85+3≠84 (incorrect)
D.
-11+4+ -7
-35+3≠ -33 (incorrect)
Only A. 13, 17 fits the criteria.
4.
The sum of two numbers is 23. When three times the smaller is subtracted from the larger, the result is 3. Find the numbers.
The numbers need to fit the criteria:
x+y=23y-3x=3A.
5+18=23
18-15=3 (correct)
B.
8+15=23
15-24≠3 (incorrect)
C.
-13+36=23
36+39≠3 (incorrect)
D.
-5+28=23
28+15≠3 (incorrect)
Only A. 5, 18 fits the criteria.
5.
The sum of two numbers is 26. When twice the smaller is subtracted from the larger, the result is 2. Find the numbers.
The numbers need to fit the criteria:
x+y=26y-2x=2A.
8+18=26
18-16=2 (correct)
B.
9+17=26
17-18≠2 (incorrect)
C.
7+19=26
19-14≠2 (incorrect)
D.
6+20=26
20-12≠2 (incorrect)
Only A. 8, 18 fits the criteria.
240 people are going to a charity event 3/5 of the guests have ordered chicken for their meals of the remaining guests 12.5% have ordered gluten free meals how many people haven't ordered their meals yet?
Answer: 84 people
Step-by-step explanation:
From the question, 240 people are going to a charity event and 3/5 of the guests have ordered chicken for their meals. This means (3/5 × 240) = 144 people ordered chicken. Since 144 people have ordered, the number of remain people left will be:
= 240 - 144
= 96 people.
Out of the remaining guests which is 96, 12.5% have ordered gluten free meals. This means (12.5% × 96) = 12 ordered gluten free meals.
The people who haven't ordered their meals yet will be:
= 96 - 12
= 84 people.
Using the appropriate arithmetic operations, the number of guests who haven't made an order yet is 126
Total number of guests = 240Chicken orders = 3/5 × 240 = 144
Number left = 240 - 144 = 96
Gluten free meat = 12.5% × 144 = 18
Not yet ordered = 144 - 18 = 126
Therefore, the Number of guests who haven't made an order yet is 126
Learn more : https://brainly.com/question/18581754
The table shows the number of championsthips won by the baseball and softball leagues of three youth baseball
divisions organized by age groups.
Baseball League (B) Softball League (5)
Ages 7-9 C93
Ages 10-12M 2
Ages 13-15 (
2
if the winning team plays in the Ages 10-12 division, find the probability that the team is in the Basebal League. Answer
in terms of a reduced fraction.
a0
R(BIY)
Answer:
7/10
Step-by-step explanation:
Finding the totals of each column and row, we find:
There are 3+2+1 = 6 children in the baseball league.
There are 7+2+1 = 10 children in the softball league.
There are 3+7 = 10 children in the 7-9 division.
There are 2+2 = 4 children in the 10-12 division.
There are 1+1 = 2 children in the 13-15 division.
There are a total of 10+6 = 16 children.
We start with the information that the team is a member of the softball league. There are 10 children in this league; this is the denominator of the probability.
There are 7 children in the 7-9 division that are in the softball league. This gives us the probability 7/10.
correct me if this is wrong
Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!
Answer:
x5
Step-by-step explanation:
Answer:
(x - 1) (x + 4)
Step-by-step explanation:
Find the volume of a cylinder 10mi and 22mi
Answer:
If the radius is 10mi, height is 22mi, the answer is V≈6911.5
If the radius is 22mi, height is 10mi, the answer is V≈15205.31
What is the measure of A?
ΔABC is an equilateral triangle.
All 3 angles must be equal in an equilateral triangle.
[tex]180/3[/tex]
[tex]=60[/tex] °
3 + 2(2x + 8) = 1 is equivalent to:
Answer:
x = [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
=> 3+2(2x+8) = 1
=> 3+4x+16 = 1
=> 4x+19 = 1
=> 4x = 1-19
=> 4x = -18
Dividing both sides by 4
=> x = [tex]-\frac{18}{4}[/tex]
=> x = [tex]-\frac{9}{2}[/tex]
Answer: -9/2
Step-by-step explanation:
3 + 2(2x + 8) = 1
3 + 4x + 16 = 1
19 + 4x = 1
4x = -18
x = -18/4 = -9/2
Please answer correctly !!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
49
Step-by-step explanation:
y = 7^2
= 49
If y = 1 and y = cos x , list the values of x where 0 degrees <= x <= 360 degrees to make these statements true.
Answer:
90°
Step-by-step explanation:
cosx = y=1
Therefore cosx =1
For cosx= 1
x= 90°, 450°, 810° ... etc.
Now 0° ≤ x ≤ 360°
The only value that satisfies both relations is 90°
Therefore, x= 90°
16 points!
What is the length of line AB?
√17
√35
6
4
Answer:
i think its 6
Step-by-step explanation:
The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The dimension of the rectangular prism will be 3 units long, 5 units wide, and 1 unit high. Then the diagonal of the prism is given as,
D² = 3² + 5² + 1²
Simplify the equation, then we have
D² = 3² + 5² + 1²
D² = 9 + 25 + 1
D² = 35
D = √35 units
The length of the diagonal of the rectangular prism will be √35 units. Then the correct option is B.
More about the rectangular prism link is given below.
https://brainly.com/question/12649592
#SPJ2
Suppose students are independent from one another. 63% of students are using Mr. Martin's new social media app, Mar-tin-stagram. 2 students are randomly selected. What is the probability that both of them use it? (Write answer as a decimal. Do not round)
Answer:
[tex]P(X=2) =0.3906[/tex]
Step-by-step explanation:
Proportion of students using the app, p = 63/100 = 0.63
Proportion of students not using the app, q = 1 - 0.63 = 0.37
Sample size, n = 2
Probability that the two students are using the app.
[tex]P(X = r) = nCr p^{n} q^{n-r} \\P(X = 2) = 2C2 *0.63^{2} *0.37^{2-2}\\P(X = 2) = 2C2 *0.63^{2} *0.37^{0}\\P(X=2) = 0.63^{2} \\P(X=2) =0.3906[/tex]
Fred is planning a fundraiser where he will collect $4.50 fir every mile he runs.
Graph f(x) = -1/2x click on the graph till f(x) =-1/2x appears
Answer:
Step-by-step explanation:
