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Of segments CFD and CED, which of the segments has a greater area based on the given information?
Circle A: radius = 10m, m∠CAD = 90°
Circle B: radius = 12m, m∠CBD = 60°
Answers
If I am understanding you correctly, first solve for the whole sector, which you can use this formula.
[tex] \frac{\Theta}{360} \pi r^2[/tex]
Once you find the area of the sector, all you have to do is get the area of the triangle and then subtract the area of the triangle from the sector and that will tell you the area of CFD and CED and let you know which one is greater.
For instance, Lets find A
sector area = [tex] \frac{90}{360} \pi 10^2 = 25\pi [/tex]
Now lets get the area of the triangle, which is
area triangle = [tex] \frac{1}{2} bh\sin C[/tex]
area triangle = [tex] \frac{1}{2} \times 10 \times 10 \times sin 90 = 50m^2[/tex]
CED = sector area - area of triangle = [tex] 25\pi - 50 = 28.53m^2[/tex]
Now lets find B
sector area = [tex] \frac{60}{360} \pi 12^2 = 24\pi [/tex]
Now lets get the area of the triangle, which is
area triangle = [tex] \frac{1}{2} bh\sin C[/tex]
area triangle = [tex] \frac{1}{2} \times 12 \times 12 \times \sin 60 = 36\sqrt(3)[/tex]
CFD = sector area - area of triangle = [tex] 24\pi - 36\sqrt(3) = 13.04m^2[/tex]
So A has the greater area base.
Related Questions
The diagonals of rhombus FGHJ intersect at point K. If side GH is equal to x + 9 and side JH is equal to 5x – 2, find x.
Answers
Answer: Rhombus
I have all of the properties of the parallelogram PLUS
- 4 congruent sides
- diagonals bisect angles
- diagonals perpendicular
3x - 10 = 6x - 19
3x - 6x = -19 + 10
-3x = -9
x = -9/-3
x = 3
Answer:
x = 2.75
Step-by-step explanation:
5x - 2 = x + 9
5x = x + 11
4x = 11
Which expression is equivalent to radical of 10 over ^4 and the radical of 8.
Answers
------ = ------
4√8 8
The game stop is having a sale and all games are reduced by 55%. If a game is now $29.99, what was the original price? Round your answer to the nearest cent
Answers
Please help
Thanks in advance
Answers
\frac{20}{-20}-2(5-10) \\ \\
-1-2(5-10)\\ \\
-1-2(-5)
\\ \\-1+10
\\ \\9
[/tex]
Final answer: 9
A quadratic equation is shown below: 9x2 − 16x + 60 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
Find the discriminant, b^2 - 4ac, which is the same as the value of the radicand.
(-16)^2 - 4 * 9 * 60 = -1904
Since the discriminant is negative, there will be NO real solutions, and 2 complex solutions.
Part B.
4x^2 + 8x - 5 = 0
You can tell if a quadratic is factorable if you find the discriminant and it is a perfect square. The discriminant for this quadratic is 144 so it is factorable.
(2x + 5)(2x - 1) = 0
Set each factor equal to zero.
2x + 5 = 0 2x - 1 = 0
subt 5 from both sides add 1 to both sides
2x = -5 2x = 1
divide both sides by 2 divide both sides by 2
x = -5/2 x = 1/2
A graph is shown below:
A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line
What is the equation of the line in slope-intercept form?
y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3
Answers
b = 36
m = (y2 - y1) / (x2 - x1)
m = (27 - 36) / (3 -0) = -3
So, the equation of the line would be y = -3x + 36.
The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function mc002-1.jpg. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?
Answers
The average rate is the change in h divided by the change in t, mathematically:
r=(h(3)-h(0))/(t2-t1), in this case:
r=(-16*9+300-0-300)/(3-0)
r=-144/3
r= -48 ft/s
Answer:
the answer on edge is D) h(3)-h (0)/3
And, the answer to the equation is 156.
Gideon made two errors in the proof. Identify and correct the errors
Answers
Answer:
Identify: Step 6 and step 7
Correction:
I think step 6 is just not necessary and should be removed.
And step 7 should be the transitive property of equality not the Substitution Property of Equality
You are selling items from a catalog for a school fundraiser.Write and solve two inequalities to find the range of sales that will earn you between $40 and $50. Earn $5 for every $50 in sales!
Answers
You want between 40 and 50, so you want $45
45/5=9
You will need to sell $50 worth of stuff 9 times
9*50=450
you need to sell $50 worth of catalog items
To find the range of sales that will earn you between $40 and $50, you can set up two inequalities and solve them to find the minimum and maximum sales required.
Explanation:To find the range of sales that will earn you between $40 and $50, we can set up two inequalities.
First, let's find the minimum sales required to earn $40. We can use the inequality 5x >= 40, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be greater than or equal to $40.
Next, let's find the maximum sales required to earn $50. We can use the inequality 5x <= 50, where x represents the sales. This inequality represents the condition that earning $5 for every $50 in sales should be less than or equal to $50.
To solve these inequalities:
For the first inequality, divide both sides by 5, giving us x >= 8. This means the minimum sales required to earn $40 is $8.
For the second inequality, divide both sides by 5, giving us x <= 10. This means the maximum sales required to earn $50 is $10.
Therefore, the range of sales that will earn you between $40 and $50 is $8 to $10.
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An item is regularly priced at $75. It is on sale for 40% off the regular price. How much (in dollars) is discounted from the regular price?
Answers
answer
it is discounted $30 from the regular price
what would be the value of 150 after eight years if you earn 12 percent interest per year
Answers
So.....
Simple Interest:
0.12 * 150 = 18
18 * 8 = 144
144 + 150 = $294
Compound Interest:
150(1 + 0.12)^8
150 * 1.12^8
150 * 2.475 = $371
Answer:
$371.3944
Step-by-step explanation:
Principal = 150
Time = 8 years
Rate of interest = 12% = 0.12
No. of compounds per year = n = 1
Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is the rate of interest in decimals
t = time in years
n = no. of compounds per year
Substitute the values in the formula :
[tex]A=150(1+\frac{0.12}{1})^{8}[/tex]
[tex]A=371.3944[/tex]
Hence the value of 150 after eight years if you earn 12 percent interest per year is $371.3944
228% of what number is 33.06
Answers
Jean has 1/3 cup of walnuts for each serving of salad she makes. She has 2 cups of walnuts. How many serving can she make?
Answers
3 servings x 2 cups= 6 servings total
Find the volume of a cylinder with a diameter of 10 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest tenth. (Hint: You may only enter numerals, decimal points, and negative signs in the answer blank)
Answers
V=(hπd^2)/4, and we are told that the height is 3r, r=d/2, so 3r=3d/2=h
V=(3d/2)(πd^2)/4
V=(3πd^3)/8, we know d=10 so
V=3000π/8
V=375π in^3, lastly we are told to approximate π≈3.14 so
V≈375(3.14) in^3
V≈1177.5 in^3
The volume of the cylinder is 1177.5 cubic inches.
Given that the diameter of the cylinder is 10 inches, the radius r is half of that, so [tex]\( r = \frac{10}{2} = 5 \)[/tex] inches.
The height h is three times the radius, so [tex]\( h = 3r = 3 \times 5 = 15 \)[/tex] inches.
Now, we can substitute these values into the formula for the volume of a cylinder:
[tex]\( V = \pi r^2 h \)\\ \( V = 3.14 \times (5)^2 \times 15 \)\\ \( V = 3.14 \times 25 \times 15 \)\\ \( V = 3.14 \times 375 \)\\ \( V = 1177.5 \) cubic inches.[/tex]
Rounded to the nearest tenth.
Ron is half as old as Sam, who is three times as old as Ted. The sum of their ages is 55. How old is Ron?
Answers
To find Ron's age, we set up equations based on their age relations and the total sum of their ages. After solving the system of equations, we determine that Ron is 15 years old.
The question deals with a basic age-related algebra problem. To solve for how old Ron is, we can set up a system of equations based on the information provided:
Let R represent Ron's age.
Let S represent Sam's age.
Let T represent Ted's age.
From the information:
Ron is half as old as Sam, so R = 1/2 * S
Sam is three times as old as Ted, so S = 3 * T
The sum of their ages is 55, so R + S + T = 55
Substituting the expressions for R and S in terms of T into the third equation gives:
1/2 * (3 * T) + 3 * T + T = 55
Simplifying and solving for T, we find that:
1.5T + 3T + T = 55
5.5T = 55
T = 10
Now we can find Sam's age:
S = 3 * 10 = 30
And Ron's age:
R = 1/2 * 30 = 15
Therefore, Ron is 15 years old.
Deon rented a truck for one day. there was a base fee of $16.95, and there was an additional charge of 75 cents for each mile driven. Deon had to pay $220.20 when he returned the truck. For how many miles did he drive the truck?
Answers
220.20-16.95=203.25
203.25/.75=271
0.75*271=203.25
203.25+16.95=220.20
How do I solve this problem: -2(7-y)+4=-4?
Answers
-2(7-y) = - 8
7 - y = = 4
y = 7 - 4
y = 3
1. Use the distributive property.
If there is any parentheses in your equations, you can simplify them with the distributive property.
a(b + c) = ab + ac
2. Combine like terms.
Make sure to combine all like terms on both sides of the equation.
3. Use The Addition Principle of Equality if needed.
The Addition Principle of Equality states that if you add an expression to both sides of the equation, you will get a second equation that is equivalent to the original equation. Or in other words, they will both have the same solution set.
4. Use The Multiplication or Division Principle of Equality if needed.
Similar to the above rule. If you multiply or divide both sides of an equation with the same expression, the resulting equation will have the same solution set as the original equation.
Now that I showed you the rules necessary to solve an algebraic equation, let's solve the one you asked us to solve.
-2(7 - y) + 4 = -4
I see parentheses and we can use the distributive property to get rid of them.
-2(7 - y) + 4 = -4
-14 + 2y + 4 = -4
On the left-hand side, we have like terms that we can combine.
-14 + 2y + 4 = -4
-10 + 2y = -4
Now use The Addition Principle of Equality by adding 10 to each side of the equation.
-10 + 2y + 10 = -4 + 10
2y = 6
Awesome! The -10 constant term disappeared on the left-hand side.
Finally, use The Multiplication or Division Principle of Equality.
Divide both sides by the coefficient of the term 2y.
2y / 2 = 6 / 2
y = 3
So, y is equal to 3.
Let set A = {1, 3, 5, 7} and set B = {1, 2, 3, 4, 5, 6, 7, 8}
Which notation shows the relationship between set A and set B?
Answers
All of the items found in set A can be found in set B. The other way is not true (eg: 8 in set B is not found in set A)
If you are drawing a venn diagram, all of circle A is inside circle B
Answer:
A ⊆ B
Step-by-step explanation:
A savings account earns 6% (APR) interest calculated monthly, paid into the account at the end of 6 months. Travis deposits $100 into the account at the beginning of the first month. At the end of each month, he deposits an additional $100 into the account. How much interest will Travis have earned after 6 months?
Answers
End of month 1 = 100×1.06 = 106
Beginning of month 2 = 106+100 = 206
End of month 2 = 206×1.06 = 212
Beginning of month 3 = 212+100 = 312
End of month 3 = 312×1.06 = 330.72
Beginning of month 4 = 330.72+100 = 430.72
End of month 4 = 430.72×1.06 = 455.8
Beginning of month 5 = 555.8
End of month 5 = 555.8×1.06 = 589.148
Beginning of month 6 = 689.148
End of month 6 = 689.148×1.06 = 624.49688
The amount of interest Travis will receive at the end of month 6 is
624.49688 - 600 = 24.49688 ≈ $24.50
Find the value of a and z: (x^8)^3=ax^z
Answers
(x^8)^3=ax^z
x^24 = ax^z
so : z=24 and a= 1
Can you please help me
Answers
HELP PLEASE!!1!
Part A
First, take a look at Preston’s sequence. How does a 180-degree rotation about the origin change the coordinates of a shape?
How does a translation 7 units up change the coordinates of a shape?
Now look at Chanel’s sequence. How does a reflection across the x-axis change the coordinates of a shape?
please, help me
Answers
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). In this exercise:
A = (-4, 5) -> (4, -5)
B = (-3, 1) -> (3, -1)
C = (-5, 2) -> (5, -2)
Translation 7 units up change the coordinates from (x, y) to (x, y+7). Continuing with the exercise:
(4, -5) -> (4, 2)
(3, -1) -> (3, 6)
(5, -2) -> (5, 5)
Which are not the coordinates of triangle DEF.
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). In this exercise:
A = (-4, 5) -> (-4, -5)
B = (-3, 1) -> (-3, -1)
C = (-5, 2) -> (-5, -2)
In 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
180° rotation about the origin change the coordinates from (x,y) to (-x,-y). It means if an object having coordinates (3,4) then it will be (-3,-4).
Translation 7 units up change the coordinates from (x, y) to (x, y+7). It means if an object having coordinates (3,4) then it will be (3,4+7).
Reflection across the x-axis change the coordinates from (x, y) to (x, -y). It means if an object having coordinates (3,4) then it will be (3,-4).
Hence we can summarize the above phenomenon as in 180 rotation (x,y) becomes (-x,-y) , In translation 7 units (x, y) becomes (x, y+7) and in reflection across x-axis (x, y) becomes (x, -y).
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Find the area.
Square
A = s^2
s - side.
Answers
area = S^2
side = 12 miles
12^2 = 144
area = 144 miles
Find the balance in the account. $4,100 principal earning 4%, compounded monthly, after 10 years
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A=p (1+r/k)^kt
A future value?
P present value 4100
R interest rate 0.04
K compounded monthly 12
T time 10 years
A=4,100×(1+0.04÷12)^(12×10)
A=6,112.41. ..answer
$4100*(1+0.04/12)^(12*10)
4100*1.490832682=
$6112.41
Jackson's football team lost 6 yards from their starring position and then lost another 5 yards. What number represents a loss of 6 yards? A loss of 5 yards?
On the next play, the team gains 12 yards. Will the team ne at their original starting position? Explain
Answers
A loss of 6 yards is represented by -6, and a loss of 5 yards by -5. After losses of 6 and 5 yards, and a gain of 12 yards, the team will be 1 yard past their original starting position, not exactly back to the original position.
Explanation:A loss of 6 yards can be represented by the number -6, and a loss of 5 yards can be represented by the number -5.
When the football team on the next play gains 12 yards, we add this value to their previous position, which results from adding -6 and -5. To determine if the team returns to their original starting position, we calculate -6 + -5 + 12. The sum of -6 and -5 is -11, then adding 12 gives 1, which means the team advances 1 yard past the original starting position, not just back to it.
Therefore, the team will not be at their original starting position after gaining 12 yards, they will be 1 yard ahead.
Which of these is the algebraic expression for "eight less than some number?"
8 − b
b − 8
Fraction 8 over b
Fraction b over 8
best answer gets brainl;iest
Answers
what is the ratio of x to y (simplest form)
x= 2 y=6
x=5 y=15
x=8 y=24
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The total charge on 6 particles is -48 units. All the particles have the same charge.
What is the charge on each particle?
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6 particles ( n charge) = -48 units
1 particle ( n charge) = ?
6n = -48
n = -8.
Each particle has a charge of -8 units. This is how 6 of them gives a total charge of -48 units.
9 1/4 - 6 2/3
Write answer as mixed number with fractional part in lowest terms.
Answers
To subtract the mixed numbers 9 1/4 and 6 2/3, first convert them to improper fractions, find a common denominator, and then perform the subtraction. The result is expressed as the mixed number 2 7/12 with the fractional part in lowest terms.
Explanation:Subtracting Mixed Numbers
The question involves subtracting mixed numbers, specifically 9 1/4 (nine and one quarter) from 6 2/3 (six and two thirds). First, we need to convert these mixed numbers into improper fractions for easier subtraction.
Convert 9 1/4 to an improper fraction: (9 × 4) + 1 = 36 + 1 = 37/4.Convert 6 2/3 to an improper fraction: (6 × 3) + 2 = 18 + 2 = 20/3.To subtract, we need a common denominator. Multiplying the denominators 4 and 3 gives us 12, the LCD.Adjust the fractions: 37/4 becomes 111/12 (since 37 × 3 = 111) and 20/3 becomes 80/12 (since 20 × 4 = 80).Now subtract the numerators: 111 - 80 = 31. So, the difference is 31/12.Finally, convert 31/12 back into a mixed number, which is 2 7/12 (since 31 divided by 12 is 2 with a remainder of 7).The answer is 2 7/12.
To subtract mixed numbers, find a common denominator. Subtract the fractional part by subtracting the numerators. Subtract the whole numbers as usual. The answer is 8 7/12.
Explanation:To subtract mixed numbers, we first need to find a common denominator. In this case, the common denominator is 12. Then, we can subtract the fractions by subtracting the numerators and leaving the denominator the same.
For the whole numbers, we simply subtract them as usual.
So, 9 1/4 - 6 2/3 = 8 7/12.
If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?
Answers
Answer: The values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Step-by-step explanation: For an angle [tex]\theta[/tex],
[tex]\sin \theta=-\dfrac{\sqrt3}{2},~\pi<\theta<\dfrac{3\pi}{2}.[/tex]
We are given to find the values of [tex]\cos\theta[/tex] and [tex]\tan \theta[/tex].
Given that
[tex]\pi<\theta<\dfrac{3\pi}{2}\\\\\\\Rightarrow \theta~\textup{lies in Quadrant III}.[/tex]
We will be using the following trigonometric properties:
[tex](i)~\cos \theta=\pm\sqrt{1-\sin^2\theta},\\\\(ii)~\tan\theta=\dfrac{\sin\theta}{\cos\theta}.[/tex]
The calculations are as follows:
We have
[tex]\cos\theta=\pm\sqrt{1-\sin^2\theta}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(-\dfrac{\sqrt3}{2}\right)^2}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\sqrt{\left(\dfrac{1}{4}\right)}\\\\\\\Rightarrow \cos\theta=\pm\dfrac{1}{2}.[/tex]
Since [tex]\theta[/tex] is in Quadrant III, and the value of cosine is negative in that quadrant, so
[tex]\cos\theta=-\dfrac{1}{2}.[/tex]
Now, we have
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{-\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3.[/tex]
Thus, the values are
[tex]\cos\theta=-\dfrac{1}{2},~~\textup{and}~~\tan\theta=\sqrt3.[/tex]
Since the given theta lies in third quadrant, then you can use the fact that only tangent and cotangent are positive in third quadrant, rest are negative.
The value of cos and tan for given theta is:
[tex]cos(\theta) = -\dfrac{1}{2}\\\\ tan( \theta) = \sqrt{3}[/tex]
How to find if the angle given lies in third quadrant?If angle lies between 0 to half of pi, then it is int first quadrant.
If angle lies between half of pi to a pi, then it is in second quadrant.
When the angle lies between [tex]\pi[/tex] and [tex]\dfrac{3\pi}{2}[/tex], then that angle lies in 3rd quadrant.
And when it lies from [tex]\dfrac{3\pi}{2}[/tex] and 0 degrees, then the angle is in fourth quadrant.
Which trigonometric functions are positive in third quadrant?Only tangent function and cotangent functions.
In first quadrant, all six trigonometric functions are positive.
In second quadrant, only sin and cosec are positive.
In fourth, only cos and sec are positive.
We can continue as follows:
[tex]sin(\theta) = -\dfrac{\sqrt{3}}{2}\\ sin(\theta) = sin(\pi + 60^\circ)\\ \theta = \pi + 60^\circ[/tex]
Thus, evaluating cos and tan at obtained theta:
[tex]cos(\pi + 60^\circ) = -cos(60) = -\dfrac{1}{2}\\ tan( \pi + 60^\circ) = tan(60) = \sqrt{3}[/tex]
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