Answers
The value of the variable x can be determined using the circle theorem to
determine the angle formed by x.
The correct responses are;
(1) x = 30°(2) x = 100°(3) x = 60°Reasons:
(1) From circle theorem, we have;
Equal chords subtends equal arcs and vice versaEqual chords subtend equal angles at the center of a circleTherefore;
Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at center = Angle subtended by [tex]\widehat {BC}[/tex] at the center;
Angle at the center = 2 × Angle at the circumferenceTherefore;
Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at the circumference = Angle subtended by [tex]\mathbf{\widehat {BC}}[/tex] at the circumference
Which gives;
x = 30°(2) [tex]\displaystyle \widehat {AB} = \mathbf{\widehat {CD}}[/tex] given
Angle subtended by arc [tex]\widehat {CD}[/tex] at the center = x
Equal arcs subtend equal angles at the center of a circle.
Therefore;
Angle subtended by arc [tex]\mathbf{\widehat {AB}}[/tex] at the center = x
Angle at center = 2 × angle at circumference
Therefore;
x = 2 × 50° = 100°
x = 100°
(3) [tex]\displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}}[/tex] given
By definition, we have;
Angle subtended by [tex]\widehat {AC}[/tex] at the center = 3 × Angle subtended by [tex]\widehat {AB}[/tex] at the center
According to circle theorem, we have;
Angle at the center = 2 × Angle at the circumference
Let y represent the angle subtended at the circumference by [tex]\widehat {AB}[/tex], we have;
y = 20°
[tex]\widehat {AB}[/tex] = 2·y
[tex]\widehat {AC}[/tex] = 3 × [tex]\widehat {AB}[/tex] = 3 × 2·y = 6·y
Therefore;
[tex]\widehat {AC}[/tex] = 6 × 20° = 120°
[tex]\widehat {AC}[/tex] = 120°
[tex]\widehat {AC}[/tex] = 2·x
Therefore;
2·x = 120°
[tex]\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}[/tex]
x = 60°
Learn more circle theorems here:
https://brainly.com/question/16879446
Related Questions
(I need these answered asap and with work and explanation included)
Answers
Answer:
blue marbles - 2/9. red marbles - 3/9 = 1/3 clear marbles - 4/9. Davis got a 2/9 chance and Tessa got a 2/8 or 1/4 chance. I don't know about the last question. it might be 5/9 but I don't know sorry.
Someone help me with this please
Answers
Answer: x = 43, ABC = 180 degrees, DBC = 48 Degrees
Step-by-step explanation:
(3(x+1))+(x+5)=180 degrees
4x+8=180
4x=172
x=43
using these we plug in.
ABC = is 3(44) + (48) = 180
DBC = 43+5 = 48
Adam has $87.14. He has 10 bills and 19 coins how ? Explain how you solved it .
Answers
Answer: $42
Step-by-step explanation:
PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
Answers
Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
3. You miss a free throw 3/10 of the time
A) likely
B) unlikely
C) certain
D) equally likely
Answers
Converting to a percentage: 3/10 = .3 x 100 = 30%.
Therefore, 3/10=30%. So, you only miss 30% of the time, which means that you make the free throws 7/10 of the time or 70%.
The answer would be that you are likely to make the free throws, so answer A.) is correct.
You miss a free throw 3/10 of the time is unlikely event. Therefore, option B is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, miss a free throw 3/10 of the time.
Here, 3/10 =0.3
The total probability is always equal to unity.
If the event is “certain” to happen, the probability will be 1.
If the event is “likely” to happen, the probability will be between 1/2 and 1.
If the event has an “equal chance” to happen or not, the probability will be 1/2.
If the event is “unlikely” to happen, the probability will be between 0 and 1/2.
You miss a free throw 3/10 of the time is unlikely event.
Therefore, option B is the correct answer.
To learn more about the probability visit:
https://brainly.com/question/11234923.
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Twelve is sixteen less than four times a number. Write it as a mathematical statement.
Answers
Answer:
12=4x-16
x would represent the unknown number.
How many minutes make a hour
Answers
Answer:
60 minutes make an hour
Step-by-step explanation:
Because 1 hour = 60 minutes
3/5 of a number is 30. What’s the number?
Answers
3/5x=30
Multiply each side by 5/3
x=50
Therefore, the number is 50.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two blue marbles if the first one is placed back in
Answers
Answer:
2/9
Step-by-step explanation:
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answers
Answer:
It's the first one. We notice that for every package there are 36/3 = 12 pencils. Therefore for 4 packages there will be 4*12 = 48 pencils.
given that 3^y=243:find the value of y
Answers
Answer:
5
Step-by-step explanation:
So lets do this slowley
3x3=9
9x3=27
27x3=81
81x3=243
It took 5 threes or 3x3x3x3x3 to get 243
Answer:
y=81, try that for answer
Mario and Andrew's hourly charge for mowing lawns is shown.
Mario: $8.25/h
Andrew: $5.85/h
Suppose Mario and Andrew each worked for 20 hours. About how much more money did Mario earn?
Answers
about $40 explanation. in this problem you need to round and multiply so round each number 8.25 rounds to 8 and 5.85 rounds to 6 multiply each by 20 and then subtract the greater number by the less number.
Hurry up some one answer Which statement about the graph of a linear function is true?
A
The graph intersects the x-axis in two unique places.
B
The graph intersects the y-axis in two unique places.
C
The graph is a curved line.
D
The graph is a straight line.
Answers
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
How do I simplify the expression 7^0+7^2 over (7^3)^2
Answers
[tex]\frac{7^0+7^2}{(7^3)^2}=\frac{1+49}{7^6} = \frac{50}{117649}[/tex]
Ok done. Thank to me :>
SOS l don’t understand please help me
Answers
Answer:
that's the answer hope it helps to you
What is the area of a cross section that is parallel to
face ABCD?
Enter your answer in the box.
cm2
Answers
Answer:
1296cm².
Step-by-step explanation:
= 12×36×6÷2 ................
plz check weather correct or notn
Need help SOS l don’t understand
Answers
Answer:
−5<n≤2 I think, I don't really understand the question either I'm sorry!!!!
add (7x^2-3 x)+(5x-6)
Answers
Answer:
Step-by-step explanation:
(
4
x
)<(
15
5(5x−2)−3(7x−3)
)
(
4
x
)<(
15
25x−10−21x+9
)
(
4
x
)<(
15
4x−1
)
15x<16x−4
4<x
∴x∈(4,∞)
what is the ration of 8 lions and 4 tigers
Answers
Answer:
the ration is 2:1 when simplified
explain please i dont get it
Answers
Answer:
.........................
......
please help me, i dont really understand this
Answers
Answer:To convert a mixed fraction to an improper fraction, follow these steps:
Multiply the whole number part by the fraction's denominator.
Add that to the numerator. or this might also help,
Then write the result on top of the denominator. To convert a mixed number to an improper fraction, follow these steps: Multiply the denominator of the fractional part by the whole number, and add the result to the numerator. Use this result as your numerator, and place it over the denominator you already have.
Step-by-step explanation:
Hope this help
What's the area of a triangle and circle?
Answers
Answer:
Formula?
Step-by-step explanation:
Triangle = Area = 1/2bh
circle = Area = pi x r^2
Hope it helps
Determine the two positive integers each square root falls between.
10. ✔️28
11. ✔️3
12. ✔️59
13. ✔️115
14. ✔️772
15. ✔️140
Answers
Answer:
10. (5, 6)
11. (1, 2)
12. (7, 8)
13. (10, 11)
14. (27, 28)
15. (11, 12)
Step-by-step explanation:
If you're not familiar with the squares of small integers, your calculator can help you figure this.
10. √28 ≈ 5.291 . . . . between 5 and 6
11. √3 ≈ 1.732 . . . . between 1 and 2
12. √59 ≈ 7.681 . . . . between 7 and 8
13. √115 ≈ 10.724 . . . between 10 and 11
14. √772 ≈ 27.785 . . . . between 27 and 28
15. √140 ≈ 11.832 . . . . between 11 and 12
On a coordinate grid, point P is at (4, 3) and point R is at (−2, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Q(−4, 3), S(2, −5)
Q(4, −3), S(−2, 5)
Q(−4, −3), S(2, 5)
Q(−4, 3), S(−2, 5)
Answers
Answer:
The answer would be B!
Step-by-step explanation:
How many centimeters are there in 1 yard if there are 2.54 centimeters per inch? Show your work and express your answer without rounding.
Answers
Answer: 91.44
Step-by-step explanation:
There are 3 feet in a yard, 12 inches in a foot. 2.54 x 12= 30.48
30.48 x 3= 91.44
I hope this helps!
It would be appreciated if there could be an explanation along the answer
Answers
Answer:
i think probably 80°
Step-by-step explanation:
PQ = RS
2x+3 = 4x-3
x = 3
PTQ = RTS
9y-3x-1 = 5x+7y-5
2y-8x = -4
y-4x = -2
y-4(3) = -2
y-12 = -2
y = -2+12
y = 10
so PTQ = 9y-3x-1
9(10)-3(3)-1
90-9-1
80°
Find the value of x
First person to answer correctly gets brainliest.
Answers
Answer:
x is 54
Step-by-step explanation:
90-36=54
An item is regularly priced at $55. Miguel bought it on sale for 40% off the regular price. How much did miguel pay?
Answers
Answer: so Miguel payed $33
steps:
1. first find what 40% of $55 which gives us $22
2. Final Price = Original Price - Discount
Final Price = 55 - 22
Final Price = $33.00
what is 80,704 rounded to the nearest 10 thousand
Answers
80,000
Just look at the number in the ten thousand place and check if you have to round up or down.
Select the correct answer.
Write an expression to represent the product of 6 and the square of a number plus 15.
In your expression, what is the value of the coefficient?
A.1
В.15
c. 6
D. 2
Answers
Answer:
15 in the correct answer