Answers
Check the picture below.
there are a few angles shaded, I'll call that angle at O ∡O, and that angle at "x" ∡x and the green angle at A, ∡A, and the angle at B, ∡B, just so you know which angle we're referring to.
well, first off let's notice that B and C are points of tangency, meaning we get right-angles as you see in the picture, if we run an angle bisector from ∡x, towards point O, we get two congruent triangles, lemme shorten that up some, 90 + 90 + ∡O +∡x = 360, which means that ∡O + ∡x = 180, meaning that ∡O = 180 - ∡x, if that's so, the angle at point O across the shade, is 360 - ∡O or 360 - (180 - ∡x).
alrighty, by the inscribed angle theorem, ∡A is half of ∡O.
let's now focus on the triangle AOB, we'll be using half of ∡A and half of ∡O and ∡B on that triangle, let's proceed.
[tex]\measuredangle x + \measuredangle O=180\implies \measuredangle O=180-\measuredangle x \\\\\\ \measuredangle A = \cfrac{\measuredangle O}{2}\implies \measuredangle A = \cfrac{180-\measuredangle x}{2} \\\\\\ \stackrel{\textit{the angle across from }\measuredangle O~is}{360-\measuredangle O}\implies 360-(180 - \measuredangle x)\implies 180+\measuredangle x \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\large the sum of all three angles at }\triangle AOB}{\stackrel{\textit{half of }\measuredangle A}{\cfrac{1}{2}\cdot \cfrac{180-\measuredangle x}{2}}~~ + ~~\stackrel{\textit{half the angle across from }\measuredangle O}{\cfrac{180+\measuredangle x}{2}}~~ +~~\measuredangle B~~ =~~180} \\\\\\ \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B = 180[/tex]
now, let's multiply both sides by the LCD of all denominators, hmmmm in this case that'll be 4, so multiplying both sides by the LCD will do away with the denominators, so let's do so.
[tex]4\left( \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B \right) = 4(180) \\\\\\ (180-\measuredangle x)+2(180+\measuredangle x)+4\measuredangle B = 720 \\\\\\ (180-\measuredangle x)+(360+2\measuredangle x)+4\measuredangle B = 720\implies 540+\measuredangle x+4\measuredangle B = 720[/tex]
[tex]\measuredangle x+4\measuredangle B = 180\implies 4\measuredangle B = 180-\measuredangle x\implies \measuredangle B = \cfrac{180-\measuredangle x}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle B = 45 - \cfrac{\measuredangle x}{4}~\hfill[/tex]
Related Questions
Jacob sells lemonade at a park. His cost to sell the lemonade is a one-time fee for the table,
plus a fixed cost to make each cup of lemonade. The line shows the total cost, y, for 3 cups
of lemonade.
v
Cost of Selling Lemonade
Use
y
A
y
60
50
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Cost ($)
30
20
10
→ X
0
10
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20
30
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Answers
The required equation that represents the graph is y = x + 30
The standard linear equation is given as y = mx + b
m is the slope b is the y-interceptUsing the coordinates (20, 50) and (40, 70)
Get the slope of the line:
m = 70-50/40-20
m = 20/20
m = 1
Since the line cuts the y-axis at y = 30, hence the y-intercept is 30.
The required equation that represents the graph is y = x + 30
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Work out m and c for the line: y = 8 − x
Answers
M = -1
C = 8
m=-1 and c=8 for the line y = 8 − x
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation is y = 8 − x
This equation we can write in the form of slope intercept form
y=-x+8
y=(-1)x+8
Now compare the above equation with slope intercept form
m=-1 and c=8
Hence, m=-1 and c=8 for the line y = 8 − x
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A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?
Answers
Answer:
50 miles
Step-by-step explanation:
Take the number of miles and divide by the number of gallons
400 miles / 8 gallons
50 miles per gallon
Answer:
50 miles
Step-by-step explanation:
if for each 8 gallons it can go to 400 miles
so the 8 will be divided to 8 and get 1
and also divide the 400 into 8 you will get 50 miles per 1 gallon
estimate 127600 multipled by 0.93
Answers
Answer : 115,200
Step - by - step explanation :
sorry if this is wrong !
127,600 --> 128,000
0.93 --> 0.90
128,000 x 0.90 = 115,200
Simplify
O A. 6^16
O B. 6
O C. 6^4
O D. 1/6
Answers
To make four cakes, Dena used 6 cups of sugar. Using the same recipe, how much sugar does she need to make one cake?
Answers
6 cups/ 4 cakes
= 1.5 cups per cake
Answer:
Step-by-step explanation:
So 4 cakes = 6 sugars, right so try taking it slow and think to yourself, 3=? then take it even slower until you go to 1=0.67 repeated
000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ooooooooooooooooooooooooo0oo00o00oo0oo0o0o0o0o0oooooooooooooooooo
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Answer:
wat?
Step-by-step explanation:
merry christmas....yey!!
Pls look at photos I’ll give 30 points
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Need a little help on this
Answers
triangle total angle value = 180°
180° - 56° = 124° : 2 = 62°
Answer:
Step-by-step explanation:
This is an isosceles triangle. You can tell because 2 of the sides are equal and the third is not equal to either of the other two.
x + x + 56 = 180 Combine the left
2x + 56 = 180 Subtract 56 from both sides.
2x = 180 - 56
2x = 124 Divide by 2
x = 124/2
x = 62
Solve using substitution.
y = -9x - 8
y = -6x – 2
Please help
Answers
Answer:
y = 10; x = -2
Step-by-step explanation:
Because both are equal to y, you can set them equal to each other.
-9x - 8 = -6x - 2
- 6 = 3x
x = -2
y = -9(-2) - 8 = 10
Round 479 to the nearest ten. Enter your answer in the box below.
Answer here
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SUBMIT
Answers
Answer:
480
we round up because the last number is bigger than 5
Consider the following conversation.
Paul: Alsafat telling a lie.
Alsafat: I am telling a lie.
Emman: Paul telling a lie.
Suppose that exactly one of them telling a truth. Who is telling a truth?
Answers
Answer: Emman is telling the truth because no one is saying that he is telling a lie.
Step-by-step explanation:
How do I get the answer for exponents? Please explain step by step to get marked!
Answers
Answer:
4900
Step-by-step explanation:
70^2 means 70*70
70*70=4900
Answer:
you will do 70 times 70 because 70^2 is 70 times 70 which is 4,900.
Graph the line that has a slope of 4/3 and contains the point (0,-4)?
Please I need help fast
Answers
Answer:
It's attached
Step-by-step explanation:
y=4/3x-4
is the equation for the line
So you just plot the line.
The equation for the given slope and point is y = 4x/3 - 4
What is slope?The slope of a line is a number that describes both the direction and the steepness of the line.
Given that, a line that has a slope of 4/3 and contains the point (0,-4)
The slope intercept of a line is y = mx+c, where m is slope,
Here, m = 4/3, x = 0 and y = -4
Finding for c,
-4 = 4/3x0+c
c = -4
Establishing the equation,
y = 4x/3-4
Now plotting the graph,
(Attached)
Hence, the graph will pass through the points (3,0) and (0,-4)
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Function h gives the height of a tennis ball, in feet, t seconds after it is tossed straight up in the air. The equation h(t) = -16t2 +12t+10 defines function h
Answers
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The required value of "k" is 8. Option B is correct
Given the polynomial function
[tex]P(x) =2x^3-4x^2+kx-3[/tex]
What is remainder theorem?
The remainder theorem is a formula used to find the remainder when a polynomial is divided by a linear function.
If this polynomial has a factor of x - 1 and remainder of 3, hence x = 1 and P(x) = 3. This means that P(1) = 3
[tex]P(1) =2(1)^3-4(1)^2+k(1)-3\\3 = 2-4+k-3\\6 = -2 + k\\k = 8\\[/tex]
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Answers
Answer:
arrange them: -9x^3+2x^3-4x^2+x^2-6x-5x
the simplified is: -7x^3-3x^2-11x
Find two consecutive whole numbers that 60 lies between.
Answers
Answer: Benchmark numbers can be used to state that the square root of 60 is between 6 and 7.
Answer: 50 and 100
Step-by-step explanation:
( sorry if this is not what you meant ;-; )
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Draw a dilation of the figure using the given scale factor )
Answers
Answer:
A (2,2) B (2,4) C (3,2) D (3,3)
Step-by-step explanation:
K = 1/2
K is the scale factor so the distance between points will be cut in half
A 4,4 new 2,2
B 4,8 new 2,4
C 6,4 new 3,2
D 6,6 new 3,3
Answer:
A = (2,2)
B = (2,4)
C = (3,2)
D = (3,3)
Step-by-step explanation:
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Answers
[tex]\lim \limits_{x \to 0^{+}} \left( \csc x + \dfrac 1x \right)\\=\lim \limits_{x \to 0^{+}} \csc x + \lim \limits_{x \to 0^{+}} \dfrac 1x\\\\=\infty[/tex]
What is the area of a square whose perimeter is 12x cm?
Answers
Answer:
9
Step-by-step explanation:
12/4=3
3*3= 9
Filler and more filler
The area of the square is 9 [tex]cm^{2}[/tex].
What is area?The space occupied by a flat shape or the surface of an object is called area.
Formula for the area of square?[tex]Area = a^{2}[/tex]
Where, a is the length of the side of a square
What is perimeter?Perimeter is the total length of the sides of a two-dimensional shape.
Formula for the perimeter of squarePerimeter of a square = 4a
Where, a is the side of a square
According to the given question
Perimeter of a square is 12cm.
Let a be the length of the side of a square.
Therefore,
Perimeter of the square = 4a
⇒ 12 = 4a
⇒ a = 12/4
⇒ a = 3cm
So, the area of square = 3cm × 3cm = 9 square cm
Hence, the area of the square is 9 [tex]cm^{2}[/tex].
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Zayden has a total of 20 bills in his wallet. Also, his wallet only contains $50 and $100 bills. If the numbers of $50 and $100 bills are interchanged, the total amount of money in Zayden’s wallet would be $500 more than it originally was. Find the original amount of money in his wallet.
$
Answers
Step-by-step explanation:
x = number of $50 bills
y = number of $100 bills
x + y = 20
50x + 100y + 500 = 100x + 50y
50y + 500 = 50x
y + 10 = x
now we use that in the first equation :
y + 10 + y = 20
2y = 10
y = 5
x = y + 10 = 5 + 10 = 15
so, he has 15 $50 bills and 5 $100 bills = $750 + $500 = $1250 in his wallet
ALOT OF POINTS FOR THIS ONE
Admission to the state fair is $12, and each ride ticket costs $3.50. Write an
expression to represent the situation and explain what the variable means.
3.50t + 12 where t represents the number of ride tickets
3.50a + 12 where a represents the cost of admission
12a + 3.50 where a represents the cost of admission
12t + 3.50 where t represents the number of ride tickets
Answers
Answer:
Step-by-step explanation:
12a + 3.50t x 6rides
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Answers
Answer:
10 to 11 would be correct
Answer:
10 to 11
Step-by-step explanation:
Complete the table of values for
1
0
1
1
1
1
1) On the writ, draw the graph of
12
1
0
(0) Use your graph to find
(1)
the value of when x 1.5
(b) the value of x when y6
26
6
Answers
Answer:
can't see the pic properly
flying against the wind, an airplane travels 5220 kilometers in 9 hours. flying with the wind, the same plane travels 6560 kilometers in 8 hours. what is the rate of the plane in still air and what is the rate of the wind?
Answers
a.
The rate of the plane in still air is 700 km/h
Let V = rate of plane in still air and v = rate of wind.
When flying against the wind, an airplane travels 5220 kilometers in 9 hours, we have that since distance = speed × time
(V - v) × 9 = 5220
V - v = 5220/9
V - v = 580 (1)
Also, flying with the wind, the same plane travels 6560 kilometers in 8 hours, we have that since distance = speed × time
(V + v) × 8 = 6560
V + v = 6560/8
V + v = 820 (2)
Adding equations (1) and (2), we have
V - v = 580 (1)
+
V + v = 820 (2)
2V = 1400
V = 1400/2
V = 700 km/h
So, the rate of the plane in still air is 700 km/h.
b.
The rate of the wind is 120 km/h
Substituting V into (1), we have
V - v = 580 (1)
700 - v = 580
v = 700 - 580
v = 120 km/h
So, the rate of the wind is 120 km/h
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If a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answers
Answer:
Step-by-step explanation:
a+√b
a-√b
Company A makes 20 notebooks in 4 hours. Company B make 28 notebooks in
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Given f(x)=1/4(5−x)2 what is the value of f(11)?
Answers
Answer:
-3
Step-by-step explanation:
Substitute the value of 11 into x within the function so it would be f(11) = 1/4(5-11)2 which is - 3.