What is the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches?
A. 45 inches
B. 9 inches
C. 15 inches
D. 14 inches
Answers
We have to determine the length of segment CE if AE = 15 inches and ED = 5 inches and EB = 3 inches.
Since ,we can observe that AB and CD are chords intersecting at point E.
Therefore, by intersecting chord theorem which states:
" When two chords intersect each other inside a circle, the products of their segments are equal"
So, [tex] AE \times EB= CE \times ED [/tex]
[tex] 15 \times 3= CE \times 5 [/tex]
[tex] 45= CE \times 5 [/tex]
[tex] CE = \frac{45}{5} [/tex]
CE = 9 inches.
So, the measure of segment CE is 9 inches.
So, Option B is the correct answer.
Related Questions
Consider a single spin on the spinner shown below. Which events are mutually exclusive? Check all that apply.
landing on an unshaded portion and landing on 2
landing on a shaded portion and landing on 3
landing on a shaded portion and landing on an even number
landing on an unshaded portion and landing on a number greater than 3
landing on a shaded portion and landing on an unshaded portion
Answers
Answer:
Options A, B and E represent mutually exclusive events.
Step-by-step explanation:
Two events are mutually exclusive that can not happen at a same time.
Now let us look at our options and find which statements represent mutually exclusive events.
A. We can see that landing on an unshaded portion and landing on 2 are mutually exclusive events as unshaded portion contains 3 and 4 and 2 lies on shaded portion.
B. Landing on a shaded portion and landing on 3 is also mutually exclusive as 3 lies on unshaded portion.
C. Landing on a shaded portion and landing on an even number can happen at the same time as 2 is an even number and it lies on shaded portion.
D. Landing on an unshaded portion and landing on a number greater than 3 can happen at the same time as 4 in greater than 3 and it lies on unshaded portion.
E. Landing on a shaded portion and landing on an unshaded portion are mutually exclusive events as spinner can be either in shaded portion or in unshaded portion.
Therefore, Options A, B and E are our correct choices.
Answer:
A, B, E
Step-by-step explanation:
I just did it on edge and got it right
If the area is 72 and the perimeter is 34, what are it's dimensions
Answers
2x + 2y = 34 (Im assuming uts a rectangle or square)
2 (72/y) + 2y = 34
144 + 2y^2 = 34y
2y^2 - 34y + 144 = 0
y = 9 or 8
So the length is 9 and width = 8
El área de un rectángulo es 675cm2, si el largo es 3 veces. ¿Cuáles son las dimensiones del rectángulo?
Answers
1.)Simplify the expression: 4 times Start Root 18 End Root plus 5 times Start Root 32 End Root
2.)Simplify the expression: 7 times Start Root 5 End Root minus 3 times Start Root 80 End Root
3.)Simplify the expression: Start Root 21 End Root times Left Parenthesis Start Root 3 End Root plus Start Root 14 End Root Right Parenthesis.
4.)Simplify by rationalizing the denominator: Start Fraction 4 over Start Root 10 End Root minus Start Root 6 End Root End Fraction
I WILL MAKE YOU THE BRAINIEST! PLEASE HELP
Answers
2.) -5 start root 5 end root
3.) 3 start root 7 end root + 7 start root 6 end root
4.) start root 10 end root + start root 6 end root
hope this helped :)
Answer:
I agree with Sydneyjones :D i very much agree
1.) 32 start root 2 end root
2.) -5 start root 5 end root
3.) 3 start root 7 end root + 7 start root 6 end root
4.) start root 10 end root + start root 6 end root
The cost function for kara's new clothing store where she sells t-shirts is c = $9.90n + 1060. what is the slope of the cost function for kara's new store?
Answers
In our cost function [tex]c=9.90n+1060[/tex], [tex]y=c[/tex] and [tex]x=n[/tex], so we can infer that the independent variable is [tex]n[/tex]. Since the coefficient of [tex]n[/tex] is 9.90, the slope of the cost function is 9.90.
We can conclude that the slope of Kara's new store cost function is $9.90
Answer:
The slope of the function is 9.90
Step-by-step explanation:
You can find the slope by looking at the coefficient of the independent variable in the equation. In this case, we would be looking for the coefficient of n.
Add. Express your answer in lowest terms. 8 3/10 + 7 2/15
Answers
[tex]= 8 \dfrac{9}{30} + 7 \dfrac{4}{30} [/tex]
[tex]=15 \dfrac{13}{30} [/tex]
To add 8 3/10 and 7 2/15, we need to find a common denominator. The sum is 15 1/15.
Explanation:To add 8 3/10 and 7 2/15, we need to find a common denominator. The least common multiple of 10 and 15 is 30. So we convert both fractions to have a denominator of 30: 8 3/10 = 8 9/30 and 7 2/15 = 7 4/30. Now we can add the whole numbers and the fractions separately:
8 + 7 = 159/30 + 4/30 = 13/30Combining the results, the sum is 15 13/30. To express the answer in lowest terms, we can simplify the fraction: 13 and 30 are both divisible by 13, so dividing both by 13 gives us 1 and 2/30. Therefore, the final answer is 15 2/30, which can be further simplified to 15 1/15.
HELP, MARKING BRAINLIEST
How many compass settings are required to complete the construction?
Answers
Hint: if you don't know the answer you can count the number of arcs
A string of christmas tree lights has 15 lights what is the probability that the defective light is the 3rd from the plug
Answers
A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.
Answers
Begin by using the cosine rule to find the unknown side.
Where a- unknown side, b is 12, c is 16 and angle in between is 108°
The cosine rule...
a² = b² + c² - 2bc cosA
= 12² + 16² - (2×12×16 cos108°)
= 518.655076
Taking the positive square root...
a = 22.774
a = 22.8 cm nearest tenth
The question involves finding the length of the third side of a triangle using the Law of Cosines. The known parameters are two sides and the included angle. The formula c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees) can be used to calculate the length of third side.
Explanation:In this problem, you're dealing with a triangle and need to find the length of the third side. This is a classic case of using the Law of Cosines - a geometric rule that helps you find the length of a side of a triangle when you know the lengths of the other two sides and the angle in between (or in this case, SAS information).
The Law of Cosines formula is: c² = a² + b² - 2ab*cos(C), in which 'a' and 'b' represent the sides of the triangle adjacent to angle 'C', and 'c' is the other side. In your case, 'a' is 12.0 cm, 'b' is 16.0 cm and angle 'C' is 108.0 degrees. The third side 'c' can be calculated accordingly.
So, in this scenario, c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees). With some basic arithmetic and the use of a calculator to compute the cosine, you can determine the length of the third side, 'c', to the nearest tenth of a cm.
Learn more about Law of Cosines here:https://brainly.com/question/21634338
#SPJ3
Does anyone know anything about The Distributive property? Please help!
Answers
What is the exact value of cos 30° ?
Answers
Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.
Side AB will be the hypotenuse.
cos 60° = AC / AB -------[ cos 60° = 1/2]
So, AB = 2 AC -------------------------------(1)
Apply Pythagorean Theorem to find BC
AB² = BC² + AC²
4 AC² = BC² + AC²
So, BC = √3 AC ------------------------(2)
Now, we shall find the value of cos 30°
cos 30° = CB / AB
or, = √3 AC / 2 AC -------using equations (1) and (2)
So, cos 30° = √3 / 2
Hence, the exact value of
Since ∠A = 2∠B. So, cos 30° will be √3 / 2
The answer is √3 / 2
What is the total number of miles Akim runs over the course of 18 days?
Answers
First you have to list the miles he ran
He started with 1.75 and increases it by 0.25 miles every day
He ran 1.75, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5.75 and 6 miles
Now we add all these numbers
1.75 + 2 + 2.25 + 2.5 + 2.75 + 3 + 3.25 + 3.5 + 3.75 + 4 + 4.25 + 4.5 + 4.75 + 5 + 5.25 + 5.5 + 5.75 + 6 = 69.75
The answer is B) 69.75 mi
Hope this helps!
Akim's total mileage is 18×3.875 = 69.75 miles. . . . . . . matches the 2nd choice
the amount that results when $4000 is compounded at 6% annually over seven years
Answers
what is the quotient of 15p^-4q^-6/-20^12q^-3 in simplified form
Answers
[tex] \frac{15p^{-4} }{-20^{12} q^{3} } [/tex]
Determine the sign of the fraction.
[tex] -\frac{15p^{-4} }{20^{12} q^{3} } [/tex]
Now if a negative exponent is in the numerator,, then you must move the expression to the denominator and then make the exponent positive. This will change the expression to the following:
[tex]- \frac{15}{ 20^{12} q^{3} p^{4} } [/tex]
Lastly,, use the commutative property to reorder the terms on the bottom of the fraction.
[tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex]
Since we cannot simplify this expression any further,, the correct answer to this question is [tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex].
Let me know if you have any further questions.
:)
The simplified form of the expression: [tex]\( -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \)[/tex]
To simplify the expression [tex]\( \frac{15p^{-4}q^{-6}}{-20^{12}q^{-3}} \)[/tex], we can apply the rules of exponents and simplify each part of the expression separately.
First, let's rewrite [tex]\( -20^{12} \) as \( -(20^{12}) \)[/tex] to make it clear that the exponent applies to the entire term:
[tex]\[ \frac{15p^{-4}q^{-6}}{-(20^{12}q^{-3})} \][/tex]
Now, let's simplify each part:
1. \( p^{-4} \) can be rewritten as [tex]\( \frac{1}{p^4} \).[/tex]
2. \( q^{-6} \) can be rewritten as [tex]\( \frac{1}{q^6} \).[/tex]
3. [tex]\( 20^{12} \)[/tex] can be calculated.
[tex]\[ \frac{15}{-(20^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
Now, let's calculate [tex]\( 20^{12} \):[/tex]
[tex]\[ 20^{12} = (2^2 \times 5)^{12} = 2^{24} \times 5^{12} \][/tex]
[tex]\[ = (2^4)^6 \times 5^{12} = 2^{24} \times 5^{12} \][/tex]
Now, we can rewrite the expression:
[tex]\[ \frac{15}{-(2^{24} \times 5^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^6 \times q^{-3}} \][/tex]
[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \][/tex]
This is the simplified form of the expression.
Any help I don’t really understand this
Answers
The point is how to remove the brackets when a minus sign is on the left hand side. A second problem is how to get all the terms on one side over to the other.
Step One
Remove the brackets on the left side. This is an absolutely necessary step in the rest of your mathematical studies. What was done in this step affects all three terms on the inside of the brackets. Minus signs are real bad things to misuse. Study carefully how to change the signs when multiplying by a minus.
Rule a minus sign outside the brackets, when multiplied by anything inside the brackets, change the sign to the opposite of what it was.
-20 + 4x + 5x^2 = 20 - 7x^2
Comment
Before doing the last step, look at the answers. Two of them are 40. That is the answer for 20 and -20 when transferred. It's 40 which is a plus. So you should be transferring from left to right.
Step Two
Transfer from left to right.
-20 + 4x + 5x^2 = 20 - 7x^2 Add 20 to both sides.
4x + 5x^2 = 20 + 20 - 7x^2 Subtract 4x from both sides.
5x^2 = 40 - 7x^2 - 4x Subtract 5x^2 from both sides
0 = 40 - 7x^2 - 5x^2 - 4x
0 = 40 - 12x^2 - 4x Now you have to put them in the right order.
0 = 40 - 4x - 12x^2 <<<<< Answer
How do you solve this problem?
Answers
Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name
c = AB
a = BC
b = AC It just makes the calculations easier.
AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27
So
a = 15.39
b = 13.27
c = 12.58
Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 - 333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 * Cos(A)
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees
Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39
12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42
Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57.
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.
Write the equation of the perpendicular bisector of RS. Point R is located at (–1, 3), and point S is located at (3, 1).
Answers
Point R is located at (–1, 3), and point S is located at (3, 1)
we know that
the perpendicular bisector of RS go through the midpoint of RS
step 1
find the midpoint RS
midpoint M (Mx,My)
Mx=(x1+x2)/2
My=(y1+y2)/2
Mx=(-1+3)/2------> Mx=1
My=(3+1)/2-------> My=2
the midpoint M is (1,2)
step 2
find the slope RS
m=(y2-y1)/(x2-x1)-------> m=(1-3)/(3+1)-----> m=-2/4-----> m=-1/2
we know that two lines are perpendicular if the slopes
m1*m2=-1
step 3
find the slope of the perpendicular bisector of RS
m2=-1/m1------> m2=2
step 4
with m=2 and the midpoint M (1,2) find the equation of a line
y-y1=m*(x-x1)------> y-2=2*(x-1)----> y=2x-2+2-----> y=2x
the answer is
y=2x
see the attached figure
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
A) 3x2 − 11x + 8 may or may not be a polynomial
B) 3x2 − 11x + 8 will be a polynomial
C) 3x2 − x + 4 may or may not be a polynomial
D) 3x2 − x + 4 will be a polynomial
Tip: Every 2 after 3x is an exponent.. so it would be 3x^2
Answers
3x^2 - 6x + 2 will be a polynomial
======================================
Explanation:
Line up the terms and subtract straight down
3x^2 - 6x + 2
5x - 6
-----------------
3x^2 -11x + 8
this is a polynomial as it is a sum of three monomials
Subtraction of any two polynomials will result in another polynomial. This is what closure means. In math terms, closure is the idea of taking two objects and performing some operation on them (eg subtraction). If we get the same type of object back, then the set of considered closed under that operation.
Here's another example of closure. Take two glasses of water and pour them together. The two glasses can be of different shapes and sizes. It doesn't matter. The fact that we have two containers of water is all that matters. In this example,the water is like the polynomial. Combining the two containers of water into one will result in a greater amount of water. Combining water with water leads to more water.
The tree diagram shows Pam’s choices for her appetizer and a meal at a restaurant. How many choices include chicken
Answers
Answer is 8, i just did it
Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?
$1,021.01
$1,188.66
$991.38
$1,192.39
Answers
$991.38 × 0.199/12 = $16.44
The balance subject to the next month's finance charge will be
$991.38 +16.44 -410.00 = $597.82
The finance charge at the end of the second month will be
$597.82 × 0.199/12 = $9.91
The balance remaining after the second payment will be
$597.82 +9.91 -410.00 = $197.73
The finance charge applied at the end of the third month is
$197.73 × .199/12 = $3.28
so Marilyn can make one final payment of
$197.73 +3.28 = $201.01
to pay off the balance.
In all, Marilyn has paid 2×$410.00 +201.01 =
$1021.01 . . . . . . . . corresponds to the first choice
_____
In real life, Marilyn's credit card may not accrue any finance charge until after the first statement on which the charge appears. Thus the total cost of the purchase may be only $1004.02. The attached spreadsheet shows the beginning balance and the finance charges for each month for the two different scenarios.
What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?
Answers
-12 + 20x >= -6x + 9
-12+20x>-6x+9
-12+26x>9
26x>21
Now divide both sides by 26, and the answer is:
Answer: x is greater than or equal to 21/26 (21 over 26)
A spinner is divided into 5 equal sections numbered 1 to 5. The theoretical probability of the spinner stopping on 3 is 20%. Which of the following is most likely the number of 3's spun in 10,000 spins?
A. 3358
B. 1243
C. 2589
D. 2067
Answers
jack paid $2.60 sales tax on a $52 pair of shoes that he purchased. how much sales tax will his friend pay if his friend purhases a $28 shirt?
Answers
5% = 0.05
Find 5% of $28:
0.05 × 28 = 1.4
Answer = His friend will pay $1.40 for sales tax
Hope this helped☺☺
The area of a piece of construction paper is 204 inches. The paper is 17 inches long. What is the width of the paper?
Answers
The width of the construction paper is 12 inches.
The formula for area is length(l)*width(w)=area in units squared(a^2).
To find the width, we divide both sides by length, this gives us the following:
17*w=204in^2 w=204in^2/17
To find the answer, you just perform the operation.
204/17=12
The width is 12 inches.
HELPPPPPPPPPP and explain
Answers
Some say you can if you make it clear that the point causing the trouble is excluded in some way. Others say that you cannot contemplate the idea. You are creating a meaningless situation with no definition. It really depends on what you have been told about division by 0. There are ways of getting around this, but you are not taking a calculus course and therefore you likely don't have the tools to deal with it. In any event, it does not look to me like you know about limits yet.
Your marker or teacher or tutor can go either way on this problem and be justified in marking you wrong no matter what you do. As instructed I will put what I think should be done in the comment section. And remember, I'm counting noses and going with the majority when I answer this. It's not anything I'm 100% certain of, but neither is anyone else.
Share out £80 between Tom and jerry in the ratio 3:2
Answers
3n + 2n = £80
5n = £80
n = 16
3(16):2(16)
48:32
Tom gets £48, and Jerry gets £32
Jerry gets- 32
Hope I helped! tell if I missed something! :)
ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.
Out of 100 students, how many should weigh between 64 and 96 pounds?
Answers
For x = 64: z = (64 - 80) / 8 = -2
For x = 96: z = (96 - 80) / 8 = 2
Therefore we find the probability that -2 < z < 2, which is around 0.95. Therefore, out of 100 students, approximately 100(0.95) = 95 students will weigh between 64 and 96 pounds.
List the following stocks and bonds in order from lowest default risk to highest default risk.
A. foreign government bond, common stock, preferred stock
B. foreign government bond, preferred stock, common stock
C. common stock, preferred stock, foreign government bond
D. preferred stock, common stock, foreign government bond
Answers
Foreign government bond, preferred stock, common stock.
Government bonds are generally referred to as a low risk investment as they have a very low chance of default.
Preferred shared holders are considered first in the disbursement of dividend before common stockholder are considered. Thus, preferred stock is of less risk than common stock.
What is the approximate difference in the growth rate of the two populations? The approximate difference in the growth rate is 10 percent. The approximate difference in the growth rate is 40 percent.
Answers
Answer:
B
Step-by-step explanation:
The approximate difference in the growth rate is 40 percent.
The health care Jimmy’s employer offers is a fee-for-service plan in which Jimmy and his family must pay for $12,500 in health related services in a calendar year before the insurance company begins to pay. Jimmy and his family have several health related issues that demand $685.00 each month. If one of Jimmy’s children were to become seriously injured at the end of the year, how much more would Jimmy and his family need to pay before the insurance company begins to assume responsibility?
a.
$984.58
b.
$4,280.00
c.
$11,815.00
d.
$14,417.92
Answers
Total the amount they could incur because of health issues in a year then deduct it from 12,500.
= 685 x 12 months
= 8,220; they incur $8,220 for their health related issues in a year
= 12,500 - 8,220
= 4,280; amount they need to pay before the insurance company assumes responsibility.