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:
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Related Questions
PLEASE HELP SOMEONE. ILL GIVE BRAINIEST.
Caitlyn and Daniela are going out for pizza to their local gourmet pizza shop. They order a pizza with a total of 5 toppings. The restaurant charges 8 dollars for a pizza, plus $1 per basic topping and $2 per premium topping. The girls spend a total of $15 on their pizza. Let x = the number of basic toppings and y = the number of premium toppings. What equation accurately represent this situation? Like as a systems of equations where the two points intersect. The point where they intersect will be the answer.
Answers
25
8×1=8
8 +2=10
10+15=25
The answer is the 1st image, and the explanation is the 2nd image.
The answer in text if seeing the image is not possible; x + y = 5 and x + 2y + 8 = 15
Find the output, y, when the input,x, is 6.
y =?
Answers
Answer:
Y= 0
Step-by-step explanation:
Write the equation for 5x+ 2 y= 3 in slope-intercept form PLEASE HELP ME
y= -5/2x+ 3x
y=5/3x -3/5
y= -2/5x + 3/5
Answers
Answer:
y=-5/2x+3/2
Step-by-step explanation:
5x+2y=3
2y=3-5x
2y=-5x+3
y=-5/2x+3/2
Which of the following ordered pairs is the solution to the following system of equations?
X + y = 11
x - 4y = -14
(5,6)
(5-6)
(6,5)
(6,-5)
Answers
To cancel a term from both equations you have to multiple the top one by 4 so
4x + 4y = 44
x - 4y = -14
cancel out the y’s from both equations and add the terms from both so you’ll have
5x = 30
divide by 5
x = 6
substitute 6 for x in the first equation
6+y=11
subtract 6 from both sides
y = 5
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answers
Answer:
y = 5/6 x
Step-by-step explanation:
rise/run = slope
rise = 5
run = 6
so, 5/6 = slope
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.
Can someone please help me with this
Answers
Answer:
Ted's Organic Market
Step-by-step explanation:
Calculate the unit cost ( price per pound )
From the table using $16.50 for 6 lbs , then
unit cost = $16.50 ÷ 6 = $2.75
From the graph using $8.40 for 3 lbs , then
unit cost = $8.40 ÷ 3 = $2.80
Ted's Organic Market has the better price
Do now: Balance the following equation.
1.
C₂H₂ + O₂--
+
--->
- CO2 + H2O
Answers
Answer:
C2H2 + 3O2 ---> 2CO2 + 2H2O
Step-by-step explanation:
The shortest route from London to Swansea is 180 miles. A lorry is expected to take 4.5 hours to travel this route. The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 4.5 hours. By how many more mph than the expected speed does the lorry travel?
Answers
Answer:
6mph
Step-by-step explanation:
180/4.5=40
180 × (1+15%)=207
207/4.5=46
46-40=6
PLEASE NO LINKS AND NO NEGATIVITY
Answers
Explanation: The order of operations is distributive property so think of it as
(1/2 • 8) - (1/2 • 4g) Also just think of dodging 8 and 4 by two since 1/2 in a number format is .5 and 8 mutuales by .5 is 4 and 4 is 2.
Hope this helps!
Multiply the following expression: 12 x (- 6 1/2 )
Answers
Answer:
-78
Step-by-step explanation:
Simplify -6 1/2 to -13/2
Then multiply by 12
-13/2 x 12/1= -156/2
Simplify -156/2 to -78
Hopes This Helps :)
28. Which category is zero NOT a part of?
NY
A. Whole
B. Integers
C. Rational
D. Natural
Answers
Answer:
Zero is not a natural number
Step-by-step explanation:
Hope this helps!
Rewrite
28/9 as a mixed number.
Answers
Answer: 28/9 as a mixed number is 3 1/9
Step-by-step explanation:
Answer:
3 1/9
Step-by-step explanation:
3 times 9 is 27
27 plus 1 is 28
Is (6,7) the same point as (7,6)? Explain
Answers
Answer:
no
Step-by-step explanation:
no
Answer:
NO
Step-by-step explanation:
6,7 is a totally different point from 7,6 if you where to graph it 7,6 would be above 6,7 not on the same point.
The chess clubs at school decides to give $400 to a charity at Christmas time. If the chess club raised $1,000 fund raising. What percent of the fund raiser did they donate to charity
Answers
Answer: 40%
Step-by-step explanation:
To find the percent, divide the amount donated by the full amount of money raised. 400/1000 = 0.4.
Now to make this into a percentage, multiply the answer by 100. 0.4 * 100 = 40.
Percent of the fund raiser did they donate to charity 40%
What is percentage ?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.
To find the percent,
divide the amount donated by the full amount of money raised. 400/1000 = 0.4.
Now to make this into a percentage,
multiply the answer by 100. 0.4 * 100 = 40.
To learn more about the percentage here:
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Pleaseeee help meenpleaseeee!!!!!!!!
Answers
Answer:
-5/4
Step-by-step explanation:
4x-5y=10
-5y=-4x-10
-5y/-5=-4/-5-10/-5
y=4/5+2
perpendicular slope is -5/4
If 10 plus 2 equals 12 the what does 10 times 8 times 12 times 1 mean
Answers
Answer:
960
Step-by-step explanation:
(10 + 2) = 12
"10 times 8 times 12 times 1"
what does 10 times 8 times 12 times 1 mean
10 * 8 * 12 * 1 = (10)(8)(12)(1)
= (80) * 12
= 960
A scale drawing of a rectangular park had a scale of 1 cm = 100 m. What is the actual perimeter of the park in meters?
10.1 and 8.8
Answers
Answer:
3780 m
Step-by-step explanation:
First, we find the perimeter of the scale drawing.
perimeter = 2(L + W)
perimeter = 2(10.1 cm + 8.8 cm)
perimeter = 2(18.9 cm)
perimeter = 37.8 cm
Now that we have the perimeter of the drawing, we use the scale to find the real perimeter.
1 cm (drawing) = 100 m (real)
37.8 cm × 100 m/cm = 3780 m
Answer: 3780 m
Please help with math problem! :)
Answers
Answer:
Step-by-step explanation:
y-8=2x-2
y = 2x + 6
y- intersect = 6
x- intersect = -6/2 = -3
Slope: 2
a building 270 feet tall casts a 40 foot long shadow. if a person looks down from the top of the building, what is the measure of the angle between the upper end of the shadow and the vertical side of the building to the nearest degree? (assume the person's eyes are level with the top of the building)
A. 81°
B. 8°
C. 9°
D. 82°
Answers
Answer:
A.
Step-by-step explanation:
Use tangent ratio
Answer:
A.
Step-by-step explanation:
Use tangent ratio
Please help me with this math problem!! :) NO LINKS PLEASE!!
Answers
Answer:
2 more
Step-by-step explanation:
you can only get 1 of everything 2 times
this is - the outfit she already made
3 - 1 = 2 - 1 = 1
7 - 1 = 6 - 1 = 5
4 - 1 = 3 - 1 = 2
2 - 1 = 1 - 1 = 0
SOLVE
x + 3y = -1
y = x - 7
Write the solution below.
Answers
Answer:
x= 5 ........................ .......
Someone help pleaseeeee
Answers
Answer:
[tex]1. \: \: \: a = \frac{5}{7} \\ 2. \: \: \: 4 \\ 3. \: \: \: 15 {x}^{2} + 60x + 135 \\ 4. \: \: \: m = {75}^{o} \\ [/tex]
Step-by-step explanation:
[tex]1. \: \: 7a - 8 = 13 \\ 7a - 8 + 8 = 13 + 8 \\ 7a = 5 \\ \frac{7a}{7} = \frac{5}{7} \\ a = \frac{5}{7} \\ [/tex]
[tex]2. \: \: \: 4 = 2 \times 2 \\ 8 = 2 \times 2 \times 2 \\ 4 \\ [/tex]
[tex]3. \: \: \: 15 {(x + 3)}^{2} \\ 15(x + 3)(x + 3) \\15 (x + 3)(x + 3) \\ 15 |x(x + 3) + 3(x + 3)| \\ 15 ({x}^{2} + 3x + 3x + 9 )\\ 15( {x}^{2} + 6x + 9) \\ {15x}^{2} + 60x + 135 \\ [/tex]
[tex]4. \: \: \: m = {75}^{o} (opposite \: angles)[/tex]
PLZ HELP URGENT GET THE BRAINLIEST AND MORE POINTS
an arithmetic sequence has sixth term 15 and ninth term 16. Find its common difference. determine which term has value 22.
Answers
Answer:
The 27th term is 22Step-by-step explanation:
Let the first term is a and common difference is d.
The nth term is:
aₙ = a + (n - 1)dWe have:
a₆ = 15a₉ = 16The difference of these terms is:
(a + 8d) - (a + 5d) = 16 - 153d = 1d = 1/3Then the first term is:
a + 5*1/3 = 15a = 15 - 5/3 = 13 1/3The nth term equation is:
aₙ = 13 1/3 + 1/3(n - 1) = 1/3n + 13If the nth term is 22, find n:
1/3n + 13 = 221/3n = 22 - 131/3n = 9n = 9*3n = 27I need help on this question it says Find the quotient 60÷5
Answers
What force must be applied to a truck of mass 300kg for it to accelerate at 5m/s2
Answers
Answer:
mass=300kg
acceleration=5m/S2
force=?
Now,
force= m×A
=300kg×5
=1500 Newton answers
Step-by-step explanation:
hop this may help you
What do the following two equations represent?
9-3 = 2(x – 3)
y+5 2(+ 1)
Choose 1 answer:
The same line
ons
Distinct parallel lines
Perpendicular lines
Intersecting, but not perpendicular lines
HELP
Answers
Answer:
Intersecting but not perpendicular
Step-by-step explanation:
Assuming you forgot to add the = between y+5 and 2(1)
Since there is a opposite single variable in either equation the lines will intersect but not be perpendicular
help me pls..........
Answers
Answer:
1000x or 1000 thousand times greater
Step-by-step explanation:
every decimal to the left is 10x greater than the one right of it.
The pric of a new car is $29,990. If the sales tax rate is 6.5%, then how much sales tax is being charged?What is the total cost for the car including tax?
Answers
Solution: ($29990)*(0.065) = $1949.35.
Answer: The sales tax is $1949.35 and the total cost is $29,990.00 + $1949.35 = $31,939.35.
can you help me solve 4^3/4^4?
Answers
Answer:
64/256
Step-by-step explanation:
4*4*4=64/4*4*4*4=256
Answer: 0.25
Let’s break the question down.
4^3 (4 x 4 x 4) = 64.
4^4 (4 x 4 x 4 x 4) = 256.
64/256 = 0.25.