In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?
a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees
Answers
Answer:
(D) 120 degrees
Step-by-step explanation:
From the figure drawn, we have
∠ABC=60°
And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)
Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)
[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]
[tex]x+240^{\circ}=360^{\circ}[/tex]
[tex]x=120^{\circ}[/tex]
Therefore, the value of x is [tex]120^{\circ}[/tex]
Hence, option D is correct.
Answer: d. 120 degrees
Step-by-step explanation:
From the given figure drawn, we can see that
∠ABC=60°
Also we know that tangents are radius are perpendicular at the point of tangency
And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)
Therefore, we have
[tex]\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^{\circ}\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^{\circ}+60^{\circ}+90^{\circ}=360^{\circ}\\\\\Rightarrow\ x=360^{\circ}-240^{\circ}\\\\\Rightarrow\ x=120^{\circ} [/tex]
Related Questions
What does the underlined conjunction connect in the sentence? The family enjoyed fishing, but they loved hiking during their trip. A. sentences B. predicates C. subjects D. direct objects
Answers
Will give brainliest! pts to the correct answer! Are quadratic equations already in rectangular form? I'm asked to eliminate the parameter t from these two questions to get it into the rectangular equation with x and y. Is it possible?
x(t) = 0.5t^2+0.4t-87.30
y(t)= 0.4t^2+0.1t +29.44
Answers
so, as you already know, we'll borrow from our good friend Mr Zero, 0, to get that missing value for the perfect square trinomial,
[tex]\bf x=\cfrac{1}{2}\left[ t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2-\left( \cfrac{2}{5} \right)^2 \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\cfrac{4}{25}-\cfrac{4}{25} \right]-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{2}{25}-\cfrac{873}{10} \\\\\\ x=\cfrac{1}{2}\left[t^2+\cfrac{4}{5}t+\left( \cfrac{2}{5} \right)^2\right]-\cfrac{4369}{50}[/tex]
[tex]\bf x=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2-\cfrac{4369}{50}\implies x+\cfrac{4369}{50}=\cfrac{1}{2}\left( t+\frac{2}{5} \right)^2 \\\\\\ 2x+\cfrac{4369}{25}=\left( t+\frac{2}{5} \right)^2\implies \sqrt{2x+\cfrac{4369}{25}}=t+\cfrac{2}{5} \\\\\\ \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5}=t[/tex]
[tex]\bf -------------------------------\\\\ y(t)=0.4t^2+0.1t+29.44\implies y=\cfrac{2}{5}t^2+\cfrac{1}{10}t+\cfrac{736}{25} \\\\\\ y=\cfrac{2}{5}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)^2+\cfrac{1}{10}\left( \sqrt{2x+\cfrac{4369}{25}}-\cfrac{2}{5} \right)+\cfrac{736}{25}[/tex]
Which graph shows the same end behavior as the graph of f(x) = 2x6 – 2x2 – 5?
Answers
[tex]Given \ function : \ f(x) = 2x^6-2x^2-5[/tex]
In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.
Degree of the given function is the highest power of the variable.
We have variable x there.
Highest power of x is 6.
So, we can say:
Degree = 6 ( an even degree)
And leading coefficent is the coefficent of highest power term.
We have highest power term is 2x^6.
So, the leading coefficent is : 2 (Positive number)
For even degree and positive leading coefficent, end behaviour is
x --> ∞ f(x) = +∞
x-->-∞ f(x) = +∞
Answer:
The answer is A on edg
Step-by-step explanation:
just took the test
Aubrey has a new art box in the shape of a rectangular prism. The box is 5 inches, by 8 inches, by 2 inches. How much volume is not take-up by the eraser if the dimension of the eraser is 5.5 inches^3
Answers
volume of the rectangular prism = base area * height
base area = length * breadth
volume of the rectangular prism = length * breadth * height
volume of the rectangular prism = 5*8*2 = 80 inches ^3
volume of taken up by the eraser = 5.5 inches^3
volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3
HELP PLEASE Simplify the rational expression. State any excluded values. x^2-12x+35/x^2-3x-10
Answers
[tex]\frac{{x}^{2} - 12x + 35 }{ {x}^{2} - 3x - 10 } [/tex]
Factorise both the term by splitting the mid term and you'll get
[tex] \frac{ {x}^{2} - 5x - 7x + 35}{ {x}^{2} - 5x + 2x - 10 } \\ = \frac{x(x - 5) - 7(x - 5)}{x(x - 5) + 2(x - 5)} \\ = \frac{(x - 7)(x - 5)}{(x + 2)(x - 5)} \\ = \frac{x - 7}{x + 2} [/tex]
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
Answers
x ^ 2 - 5x + _____ = 7
To complete the square, we must add to both sides of the equation a constant of the form:
(b / 2) ^ 2
We have then:
x ^ 2 - 5x + (-5/2) ^ 2 = 7 + (-5/2) ^ 2
Rewriting we have:
x ^ 2 - 5x + 6.25 = 7 + 6.25
x ^ 2 - 5x + 6.25 = 13.25
Answer:
The constant term that should be used to complete the square is:
6.25
Brian wants to build a ramp that leads to a storeroom 5 meters above the ground. He wants the ramp to be 10 meters long. What should the angle of elevation of the ramp be?
15°
30°
45°
60°
Answers
Answer:
It would be 30
Step-by-step explanation:
I did it on plato
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
Answers
the z-score is given by:
z=(x-μ)/σ
where:
μ-mean
σ-standard deviation
P(x>X)=1-P(z<Z)=0.01
⇒P(z<Z)=1-0.01=0.99
thus:
the value of z that corresponds to 0.99 is 2.33
thus:
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8
thus the cutoff was 739.8
You flipped a coin 70 times and recorded 23 heads. What is the experimental probability of flipping tails?
ANY HELP IS APPRECIATED!
Please show work
Answers
thus:
experimental probability of our case will be:
P(H)=(# of times of occurrence of the event)/(# of trials)
=23/70
So the probability of getting a head in the experiment is 23/70=0.33
What do the graphs of sine and cosine have in common with the swinging you see?
Which reasons did you think of?
Answer:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.
Answers
The graphs of sine and cosine functions have similarities with the swinging motion such as repeating patterns at equal time intervals and smoothness.
Explanation:The graphs of sine and cosine functions have several similarities with the swinging motion you observe:
Both the high and low points in the graphs of sine and cosine functions repeat in a pattern, just like the motion of a swing repeating from its highest to lowest points.The cycle of both graphs repeats at equal time intervals, just like the swinging motion of a swing that takes the same amount of time to swing back and forth.The swinging motion of a swing is smooth and uninterrupted, just like the graphs of sine and cosine functions.These similarities are because simple harmonic motion, which includes swinging, is closely related to sine and cosine waves.
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Simplify: x+2/x2-6x-16 ÷ 1/9x
Answers
Identify the values that create ordered pairs that are solutions to the equation 3x - 5y = 20.
(5,y) (x,2)
Answers
thats your answer hope it helps ;P
(5; y) - put x = 5 to the equation
3 · 5 - 5y = 20
15 - 5y = 20 |-15
-5y = 5 |:(-5)
y = -1
Answer: (5; -1)
(x; 2) - put y = 2 to the equation
3x - 5 · 2 = 20
3x - 10 = 20 |+10
3x = 30 |:3
x = 10
Answer: (10; 2)
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
What is the vertical clearance 7 m from the edge of the tunnel?
Answers
Explanation:
1) Since the vertex is at the origin, i.e point (0,0), and the simmetry axis is paralell to the vertical axis, you know that the canonical equation of the parabola is:
y = -4px², where p is the focal distance.
You can also use y = ax², where a = -4p.
2) Using y = ax², you can find a from the fact that at x = 8 (one edge of the tunnel), y = - 16 ( negative value of the height).
Substitute those values (8,16) in the equation y = ax², and you get:
- 16 = a (8²) ⇒ a = - 16 / 64 = - 1/4
Therefore, the equation of the parabola is: y = (-1/4)x².
3) To find the vertical clearance at 7 m from the edge of the tunnel, you must realize that the x-coordinate is x = 8 - 7 = 1.
Then, find y for x = 1:
y = (-1/4)(1²) = - 1/4 = - 0.25
That is the y-coordinate; the clearance is the 16m - 0.25m = 15.75m
Which kind of function best models the data in the table? Use differences or ratios.
A. linear
B. quadratic
C. exponential
D. none of the above
Answers
I would appreciate it if someone could please check my work on this calculus problem! My steps/answers are in green.
Answers
B. Some error in evaluation. The result should be near 2.10592505299.
C. Your final answer should have ln(2) in the denominator. The evaluation should be near 1.354326176.
D. Need ln(4) in the denominator everywhere. The evaluation should be near 79.408765453.
Need help please asap.
Answers
trapezoid
isosceles trapezoid
parallelogram
Anyone know the answer?
Answers
When i am divided into 22, the remained is one. when i am added to 5, the answer is an even number. what number am i? * 5 7 9 10 4 2/5?
Answers
Answer:
Number is 23.
Step-by-step explanation:
We have been given the information when a number is divided by 22 the remainder is 1.
And when it is added to 5 it will give us an even number.
So, the number 23 if we take when divided by 22 it will give the remainder 1.
And when added to 5 it will give 23+5=28 which is an even number.
So, the number is 23.
Find the slope of the line graphed below
Answers
The slope of the line is 2/3
To find the slope of the line, first choose two points that are on the line. For this example we'll use (0, -4) and (6, 0). Now use the slope formula with these two points to find the slope.
m(slope) = (y2 - y1)/(x2 - x1)
m = (0 - -4)/(6 - 0)
m = (0 + 4)/(6 - 0)
m = 4/6
m = 2/3
What is the place value of the digit 4 in 6,296.04
Answers
The digit 4 is in the hundredths place, since it's behind a decimal.
Place value in front of a decimal goes as:
Ones, tens, hundreds, thousands, etc
Place value behind a decimal goes as:
Tenths, Hundredths, Thousandths, etc
The digit 4 in 6,296.04 is in the hundredths place, representing four hundredths or 4/100. This can also be expressed in scientific notation as 4 x 10⁻².
The place value of the digit 4 in 6,296.04 is in the hundredths position. This is because the digit 4 is two places to the right of the decimal point. In a decimal number, the first place to the right of the decimal point is the tenths place, the second is the hundredths place, and it continues with thousandths, ten-thousandths, and so on. Therefore, in the number 6,296.04, the 4 represents four hundredths, or 4/100, which can also be written in scientific notation as 4 × 10⁻².
Algebra question ( Matrices and Determinants ) 20 points
Answers
The answer is as following
The new matrix is 2 rows and 2 columns . i.e. it is 2*2 matrix
The element a₁₁ =5*2 + 0*2 = 10
The element a₁₂ = 5*-1 + 0*-2 = -5
The element a₂₁ = 3*2 +-5*2 = -4
The element a₂₂ = 3*-1 + -5*-2 = 7
The new matrix will be [tex] \left[\begin{array}{ccc}10&-5\\-4&7\end{array}\right] [/tex]
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!! ALL PARTS A, B, C, D, E
Answers
y = - x^(2/5)(x(5/5) + 7).
y = - x^(2/5)(x + 7)
So one of the x intercepts is 0 and the other one is -7.
The reasons are known because the factors can be equated to 0. It does not look to me like there is exact symmetry. There is a local minimum however at what the graph says is (-2,-6.5 or so)
You could differentiate that to find the exact point, but you are not asked for that.
So the domain is from -∞ to zero and 0 to plus ∞ I think you have to exclude 0 even though it is an x intercept.
The graph decreases from -∞ < x < -2
It increases from -2 < x < 0
It decreases form 0< x < ∞
Write the expression in complete factored form 5(y-7)+b(y-7)
Answers
What is EC if AC = 12, BC = 5, and DC = 4?
A. 30
B. 9
C. 15
D. 7
Answers
the formula for this would be (AB +BC)*BC = (ED+DC)*DC
lets replace the letters with the given numbers:
If AC = 12 and BC = 5 then AB = 12-5 = 7
so we get:
(7+5) *5 = (ED+4)*4
12*5 = (ED+4)*4
60 = (ED+4)*4
60/4 = (ED+4)
15 = ED +4
ED = 15-4 = 11
now add ED + DC to get EC
11+4 = 15
The answer is C. 15
A number cube is rolled 120 times. The number 4 comes up 47 times. What is the experimental probability of rolling a 4? What is the theoretical probability of rolling a 4?
A. 47/120; 1/30
B. 47/120; 1/6 ******
C. 4/47; 1/6
D. 1/6; 47/120
Am I Correct?
Answers
(Your answer is B, right?)
A number cube is rolled 120 times. The number 4 comes up 47 times.
We have to determine the experimental probability of rolling a 4.
The formula to evaluate probability of an event is given by:
Probability = [tex] \frac{Favourable outcomes}{Total outcomes} [/tex]
So, Probability of rolling a 4 = [tex] \frac{ Total number of times when 4 appears}{Total number of times number cube rolled} [/tex]
= [tex] \frac{47}{120} [/tex]
Now, we have to find the theoretical probability of rolling a 4.
Total number of outcomes of number cube = {1,2,3,4,5,6}
Probability of rolling a 4 = [tex] \frac{1}{6} [/tex]
So, Option B is the correct answer.
Madeline is financing $321,800 to purchase a house. How much money will she save over the life of a 20 year fixed rate loan by buying five points with the rate of 4.23% instead of not buying points with the rate of 5.18%? Round to the nearest dollar. (show work)
A= $39,984
B= $23,894
C= $36,697
D= $36,766
Answers
The window is 60 inches wide. What is the width of the window in feet.
Answers
60 Divided By 12 = 5
Answer: 5 Feet
A toy company produces two kites whose shapes are geomaetrically similar. Find the length of the missing size of similar kite.
Answers
Isabel is purshing a 5 pound bag of dog food.how many 8- ounce servings can she feed her dog (1lb=16oz
Answers
16 ounces / 8 ounces = 2 servings per pound
5 pound bag x 2 servings per pound = 10 total servings
There are 5 cars to be displayed in 5 parking spaces, with all the cars facing the same direction. of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. if the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
Answers
For example :
[tex]1 \times 2 \times 3 \times 4 \times 5 = 120[/tex]
There you go :)
The question relates to combinatorial mathematics and asks for possible arrangements of 5 cars of three different colors. Treating identical colors as one entity, we find that there are 6 ways to arrange the color groups and another 6 ways to arrange the red cars among themselves, resulting in 36 possible arrangements.
Explanation:The subject of this question is combinatorial mathematics. We're asked how many different arrangements there are if we have 5 cars to be displayed in 5 parking spaces, with the condition that the cars are identical besides their color; 3 of them are red, 1 is blue, and 1 is yellow.
Since three cars are identical (red ones), we treat them as one. So initially, we have three 'entities' to arrange: the red group (of 3 cars), the blue car, and the yellow car. These can be arranged in 3! (which means 3 factorial, or 3 * 2 * 1) = 6 ways.
However, within the red group, those 3 red cars can be arranged amongst themselves in 3! = 6 ways.
Therefore, to get the total number of arrangements, we multiply these results together, giving us: 6 * 6 = 36 different arrangements.
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