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
hlep me plsssssssssssssssssssssssss
Answers
{(-1, -3),(0,-1),(1,1),(2,3),(3,5)}
Answer:
B.
Step-by-step explanation:
It is not A because it does not make sense and does not match up.
It Is not C because that is just points and it is asking for a function.
D is wrong.
So It is B.
Here is the graph for B. It matches up.
[tex]\mathrm{Axis\:interception\:points\:of}\:2x-1:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{2},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:-1\right)[/tex]
[tex]\mathrm{Slope\:of\:}2x-1:\quad m=2[/tex]
Let f(x) = x+2/x+6
f^-1(-6) =
Answers
We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then
[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]
Solve for the inverse :
[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]
[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]
[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]
[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]
[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]
[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]
Then when x = -6, we have
[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]
Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)
We have
[tex]\dfrac{x+2}{x+6} = -6[/tex]
[tex]x + 2 = -6 (x + 6)[/tex]
[tex]x + 2 = -6x - 36[/tex]
[tex]7x = -38[/tex]
[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]
Answer asap! Need help before I go to sleep.
Answers
Answer:
Step-by-step explanation:
Parallel lines have identical slopes
4x - 7y = 9
7y = 4x - 9
y = (4/7)x - 9/7
so the parallel line has form
y = (4/7)x + b
plug in the point on the line
3 = (4/7)7 + b
b = -1
y = (4/7)x - 1
As you did not tell us where you live and what time you intend to go to bed, we have NO way of knowing your actual deadline
i'd appreciate someones help !!!
Solve for angles x, y, and z. In the answer choices, the first number is for angle x. The second number is for angle y.
The third number is for angle z.
A)
65, 65, 65
B)
65, 115,65
C)
115, 65, 115
D)
115, 115, 115
Answers
I think its C sorry if its wrong
I NEED HELP WITH THESE
I am pretty sure of my answers, so I just need someone to double check. Explanation is not needed because I know how to solve it, just needs to be checked. You can put one it you want.
Answers
Answer:
(b) 500 km (b) 6 secondsStep-by-step explanation:
1.The semi-major axis length is √47196900 = 6870 km. That distance from the center of the Earth means the satellite is ...
6780 -6370 = 500 . . . km
from the surface of the Earth.
The satellite is a maximum of 500 km from the Earth.
(It is a minimum of 250 km from Earth.)
__
2.The equation has a zero at t=6. When the car's velocity is zero, it is at a complete stop.
The car comes to a complete stop when time is 6 seconds.
(The car is still being accelerated, so it doesn't stay stopped.)
__
I prefer a graphing calculator for a quick solution. You can also solve this equation algebraically.
0 = 0.5t^2 -10.5t +45 . . . . t when v(t) = 0
t^2 -21t +90 = 0 . . . . . . . multiply by 2
(t -6)(t -15) = 0 . . . . . . . . factor
t = 6 or t = 15 . . . . . . . only t=6 is in the domain of the function
Salaar, Waleed and Muazzam share $ 256. Waleed;s share is four times as much as Salaar. And Salaar's share is one-third of muazzam's. How much is each of their share?
Answers
Answer:
S 32, W 128, M 96
Step-by-step explanation:
W = 4S
S = 1/3M, or 3S = M
S + W + M = 256
Substitute
S + 4S + 3S = 256
8S = 256, S = 32
S = 32
W = 4S = 128
M = 3S = 96
Sammy's Chipmunk & Squirrel Observations
For a science project, Sammy observed a chipmunk and a squirrel stashing
acorns in holes. The chipmunk hid 3 acorns in each of the holes it dug. The
squirrel hid 4 acorns in each of the holes it dug. They each hid the same number
of acorns, although the squirrel needed 4 fewer holes. How many acorns did the
chipmunk hide?
Answers
Answer:12 accorns
Step-by-step explanation:
If they each hid the same number of acorns, although the squirrel needed 4 fewer holes, the chipmunk hid 3 acorns in each hole
Let's assume the number of holes the chipmunk dug is 'c', and the number of acorns it hid in each hole is 'x'. Similarly, let's assume the number of holes the squirrel dug is 's', and the number of acorns it hid in each hole is 'y'.
According to the information provided, the chipmunk hid 3 acorns in each of the holes it dug, so x = 3. The squirrel hid 4 acorns in each of the holes it dug, so y = 4.
Both the chipmunk and squirrel hid the same number of acorns, so cx = sy.
Also, the squirrel needed 4 fewer holes, so s = c - 4.
Now, we can use the information to set up a system of equations:
cx = sy
c - 4 = s
Substitute the value of s from the second equation into the first equation:
c(c - 4) = 3(c - 4)
Expand the equation:
c² - 4c = 3c - 12
Now, bring all terms to one side of the equation:
c² - 4c - 3c + 12 = 0
Combine like terms:
c² - 7c + 12 = 0
Now, factor the quadratic equation:
(c - 3)(c - 4) = 0
Now, set each factor to zero and solve for 'c':
c - 3 = 0 => c = 3
c - 4 = 0 => c = 4
Since the chipmunk hid 3 acorns in each hole, the correct answer is The chipmunk hid 3 acorns.
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What does Point P on the number line represent? (Use the hyphen for negative numbers, such as −9)
Number line from negative 8 to positive 10 in increments of 1 is shown. Only the even numbers are labeled. A point labeled P is placed at the third tick mark to the left of 0.
(5 points)
Answers
Answer:
P = -3, each line in the negative direction is 1 number
so you would have -1, -2, -3 , -4, etc.
P is on the -3 line.
See attached picture.
Step-by-step explanation:
A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 1800 cubic feet.
Find the dimensions of the pool.
Answers
Answer:
19 x 23.5 x 4
Step-by-step explanation:
4 * x * (x + 4.5) =1800
Divide both sides by 4
x * (x + 4.5) = 450
Use distributive property
x^2 + 4.5x = 450
Move all terms to one side
x^2 + 4.5x - 450 = 0
Use quadratic formula to solve a = 1, b = 4.5, c = -450
-4.5 +- [tex]\sqrt{4.5^2 - 4 * 1 * -450}[/tex]/2
=-4.5 + - [tex]\sqrt{1820.25}[/tex] / 2
= -4.5 +- 42.664 / 2
=19.08 and -23.582. You can't have a negative length, so it is 19.08, or 19
19 x 23.5 x 4
Suppose you select 4 skittles at random from the bowl. What is the proba- bility exactly 1 of those skittles is green
Answers
Answer:
1/4
Step-by-step explanation:
4 skittles and one being green
Answer:
4/5
Step-by-step explanation:
According to the Wrigley's Consumer Care Department, the fruit candies are produced in equal proportions— 20% of each of the five colors (green, red, orange, yellow, and purple). However, although these candies are made in equal proportions, the individual Skittles bags are filled by weight and by machines but on average I'd say 4/5 chance its a green.
Which of the following is most likely the next step in the series?
A.
B.
C.
D.
Answers
Each consecutive element of the series has one less blue points than the before element, with that, we conclude that the correct option is D, where there is only one blue point.
Which of the following is most likely the next step in the series?
Here we can see a series of 3 elements.
the first element is a circle with 4 blue points on its circumference, such that the points are connected to form a rectangle.
The next element is a circle with 3 blue points on it, such that when the points are connected a triangle is formed.
The third element is a circle, this time with 2 points, and the connection forms a segment.
So what we can see is that in each consecutive element the number of blue points on the circumference of the circles decreases by one, so the logical conclusion is that the next element will have only one point on its perimeter, then the correct option is D, where we can see only one blue point on the perimeter of the circle.
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Suppose a special discount makes the price of Nike air max shoes 10% lower. As result, there is a 20% increase in the quantity demanded for the shoes, which statement is correct ____?
Answers
It is evident from the problem statement that an overall price reduction of Nike air max shoes will lead to an increase in the demand for the shoe.
In Economics, the relationship between price and demand is stated as follows "If all other factors remain equal, the higher the price of a good, the fewer people will demand that good. In other words, the higher the price, the lower the quantity demanded and vice versa."
In all, the Law of Demand tells us that if more people want to buy something, given a limited supply, the price of that thing will be bid higher, also of the price of something is low the demand will be high.
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Genes are sections of DNA that code for a particular trait. Genes are?
Answers
Answer:
Genes are DNA transferred to off spring by parents
Answer:
Genes are sections of DNA that code for a particular trait. Genes are nucleic acids.
Step-by-step explanation:
help me please please
Answers
Answer:
17/18
Step-by-step explanation:
To add fractions, you need to have common denominators. (4/9)*(2/2)=8/18.
Now that they have common denominators, you can add 8 and 9 to get 17. So, the answer would be the second one, 17/18.
Answer:
r u just cheating ur way through a whole test lol
Step-by-step explanation:
its B or 17/18
factor this polynomial completely x^2-10x+25
Answers
x^2-10x+25
=x^2-5x-5x+25
x(x-5)-5(x-5)
=(x-5)(x-5)
x=5 , x=5
hope it's helpful to you
[tex]x^2 -10x +25\\\\=x^2 -2 \cdot 5 \cdot x +5^2\\\\=(x-5)^2\\\\=(x-5)(x-5)[/tex]
6 divided by x squared
Answers
Answer:
I think x should be equal to 0.
Which inequality matches the graph? A)x >4.B)x < 4.C)x = 4.D)x >_ 4 the line is at bottom of it for d
Answers
Answer: D
Step-by-step explanation: less than or equal to 4. graph leads to negative
how do i do math in division fractions?
Answers
Answer:
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
Answer:
Keep change flip!
Step-by-step explanation:
Example 1/2 divided 3/4
We simply keep 1/2 and then we flip the 3/4 which is now 4/3
now we also flip the division sign which its opposite is multiplying now its simply 1/2 x 4/3 and you get 4/6. Hope this helps please mark brainliest!
Henry's garden which is 1/4 of an acre is to be divided into 12 equal size areas what is the size of each area?
Answers
The size of each area is 3x
Word problems in mathematics involve arithmetic operations and algebraic equations employed to solve real-life cases.
From the given parameters.
Henry's garden is said to be 1/4 of an acre.If an acre = xThen, Henry's garden is (1/4)xSo, Henry's garden is said to be divided into 12 equal size areas.
∴
The size of each area is;
[tex]\mathbf{= \dfrac{\dfrac{1}{4}x}{12}}[/tex]
[tex]\mathbf{= \dfrac{1}{4}(x) \times \dfrac{12}{1}}[/tex]
= 3x
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What is -3/4+2 3/4 O 3 1/2 O 3 3/4 O 2 1/2 O 2
Answers
Answer:
D. 2
Step-by-step explanation:
Common denominator is already presented which is 4.
-3/4 and 3/4 cancel each other out.
you can also convert to decimal form -3/4 + 2 3/4 is the same as:
-0.75 + 2.75 = 2.
Two parallel lines are cut by a transversal, as shown below. Solve for b. Then explain your reasoning.
Answers
Answer:
b = 14
Step-by-step explanation:
Since both angles are diagonal each other, they are equal to each other.
5b = b + 56
-b -b (subtract b from both sides)
4b = 56
4 4 (divide both sides by 4 to solve for b)
b = 14
Help Will give Branliest
Answers
Which of the following cannot be used to prove that two triangles are congruent?
A.AAA
B.ASA
C.SSS
D.HL
Answers
Answer:
A
Step-by-step explanation:
:)
hope it helps
Help me with this question
Answers
Answer:
I don't have any idea of that question
Step-by-step explanation:
I'm sorry
I need help on my homework.
Answers
Answer:
[tex] \frac{3}{4} > \frac{ - 2 + 2x}{4} \\ \\ (4 \times) \frac{3}{4} > \frac{ - 2 + 2x}{4} ( \times 4) \\ \\ 3 > - 2 + 2x \\ \\ 3 + 2 > - 2 + 2 + 2x \\ \\ 5 > 2x \\ \\ 5 \div 2 > 2x \div 2 \\ \\ \frac{5}{2} > x \\ \\ x < \frac{5}{2} [/tex]
I hope I helped you^_^
Solve the inequality below for t.
3 - 13t >/= -9 - 9t
Answers
Answer:
T is =/> 3
Step-by-step explanation:
Add 9t to both sides, 3-4t>/= -9 . Subtract 3 from both sides. -4t>/=-12
divide 12 by 4 for 3. Because 3 results in equality between both sides, it is equal, however if t is greater than 3, the lefthand side becomes greater than the right.
Help help help help
Answers
Answer:
-1
Step-by-step explanation:
Aarón rides his bike away from home at a constant speed he stops at the park for a while before riding back home at a constant speed
Answers
Answer:
Step-by-step explanation: This is the answer
14 divided 4 and 7/8 written in simplest form
Answers
Answer:
7 and that is its simplest form
Step-by-step explanation:
thank me later
Answer:
4
Step-by-step explanation:
14 ÷ 4 = 3.5
3.5 and 7/8 = 4
need help solving this
Answers
Answer:
x ≈ 41.6°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{JK}{KL}[/tex] = [tex]\frac{80}{90}[/tex] = [tex]\frac{8}{9}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{9}[/tex] ) ≈ 41.6° ( to the nearest tenth )