Urgent and pls explain thoroughly. O is the centre of the circle. OA, OB and OC are radii. Angle AOB = 72°.
Work out
a) angle OAB b) angle OCB c) angle ABC
Answers
Answer:
<ABC=90° <OCB=36° <OAB=54°
Step-by-step explanation:
<ABC=90°
<ocb= half of aob
<oab + <abc+<ocb=180°(triangle abc)
Answer:
a) ∠OAB = 54°
b) ∠OCB = 36°
c) ∠ABC = 90°
Step-by-step explanation:
a)
If O is the center of the circle, then OA and OB are both the radius. Therefore, OA = OB
This means that ΔAOB is an isosceles triangle, as is has two sides of equal length (OA and OB).
The angle between the equal sides (∠AOB) is called the vertex angle. The side opposite the vertex angle (AB) is called the base and base angles are equal. Therefore, ∠OAB = ∠OBA
Given:
The sum of the interior angles of a triangle is 180°∠AOB = 72°∠OAB = ∠OBA⇒ ∠OAB + ∠OBA + ∠AOB = 180
⇒ ∠OAB + ∠OBA + 72 = 180
⇒ ∠OAB + ∠OBA = 108
⇒ ∠OAB = 108 ÷ 2 = 54°
b)
Again, we can see that OB and OC are both the radius, so OB = OC. This means that ΔBOC is also an isosceles triangle, with ∠BOC as the vertex and BC as the base.
Calculate ∠BOC:
Given:
Angles on a straight line add up to 180°∠AOB = 72°⇒ ∠AOB + ∠BOC = 180
⇒ 72 + ∠BOC = 180
⇒ ∠BOC = 108°
Calculate ∠OCB:
Given:
The sum of the interior angles of a triangle is 180°∠BOC = 108°∠OBC = ∠OCB⇒ ∠OBC + ∠OCB + ∠BOC = 180
⇒ ∠OBC + ∠OCB + 108 = 180
⇒ ∠OBC + ∠OCB = 72
⇒ ∠OCB = 72 ÷ 2 = 36°
c)
Thales's theorem is a special case of the inscribed angle theorem and states that:
If A, B, and C are distinct points on a circle where the line AC is a diameter, then ∠ABC is a right angle.Given that AC is the diameter of this circle, and points A, B and C are on the circle, then ∠ABC = 90°
Related Questions
1. What is the measure of
Answers
So since one is 70 and the other is a right angle which is equal to 90 that means
180-70=110 110-90=20
Answer=20degrees
Find the product. -2x(x2 - 3) -2 x3 - 6 x -2 x2 6 x 6 x3 -2 x3 6 x.
Answers
Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex]-2x(x^2 - 3)[/tex] is [tex]-2x^3 + 6x[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is
[tex]-2x(x^2 - 3) = -2x^{1 + 2} + 6x = -2x^3 + 6x[/tex]
It is because when bases are same and there is multiplication, then powers add up, so we have: [tex]a^b \times a^c = a^{b+c}[/tex]
Thus,
The product of [tex]-2x(x^2 - 3)[/tex] is [tex]-2x^3 + 6x[/tex]
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Amanda is looking out her window and spots a wild turkey in the yard. The turkey is 43 feet from the house at an angle of depression of 72 degrees. How high up is Amanda's window? show proof of it by making a drawing related to angle of elevation
Answers
Answer:
29 if I’m Wrong I’m sorry
Step-by-step explanation:
Need help with math! Margin of error
Answers
Answer:
See below
Step-by-step explanation:
Problem 4
[tex]H_0:p=0.40\\H_a:p>0.40[/tex]
Problem 5
[tex]H_0:p=0.42\\H_a:p<0.42[/tex]
Make sure to read the problems and translate it into math
If angle 4 has a measure of 42° in the given diagram, what is the measure of angle 6?
Answers
Answer:
138 degrees
Step-by-step explanation:
its a cointerior angle so the angles add up to 180
so 180 - 42 = 138
Answer:
138°Step-by-step explanation:
If angle 4 has a measure of 42° in the given diagram, what is the measure of angle 6?
T is a flat angle (180°)
angle 4 = angle 8
angle 2 = angle 6
180 - 42 = 138°
Researchers estimate that 21.5% of men and 17% of women smoke cigarettes.1
The rate of new cases in 2008 showed that men develop lung cancer more often than women (70.2 and 50.5 cases per 100,000 persons, respectively).2
Smoking, a main cause of small cell and non-small cell lung cancer, correlates to 90% and 80% of lung cancer deaths in men and women, respectively.3 That is, 90% of men who are diagnosed with lung cancer are active smokers, and 80% of women who are diagnosed with lung cancer are active smokers.
1. What answer do you predict? Why? (2 points)
2. Given what you know about probability, how can you determine if smoking and lung cancer are related? (2 points)
Analyze the Data:
3. What is the probability that a randomly chosen man is a smoker? (1 point)
4. What is the probability that a randomly chosen man will be diagnosed with lung cancer? (1 point)
5. Given that a man has lung cancer, what is the probability that he is a smoker? Write this event with the correct conditional notation. (2 points)
6. What is the probability that a randomly selected man will be a smoker and be diagnosed with lung cancer? (2 points)
7. For a randomly selected man, are the events diagnosed with lung cancer and smoker independent events? Support your answer with probabilities. (2 points)
Consider the Case for Women:
8. For a randomly selected woman, are the events diagnosed with lung cancer and smoker independent or conditional? Support your answer with probabilities. (4 points)
Making a Decision:
9. What can you conclude about smoking and lung cancer? Are they conditional or independent events? (2 point)
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence? (1 point)
Answers
Answer: Given what i know about probability, you can determine if smoking and lung cancer are related by testing a group of smokers and non smokers and finding out the percent of each that develope lung cancer and the percent that dont for both
Step-by-step explanation:
Lily threw a ball. The balls equation that demonstrated its height and velocity is:
h(x) = -16x2 + 3x + 35
What was the initial height that she threw the ball from?
Answers
The initial height of the ball is the y-intercept of the function
The initial height she threw the ball from is 35
How to determine the initial heightThe function is given as:
[tex]h(x) = -16x^2 + 3x +35[/tex]
Set x = 0.
So, we have:
[tex]h(0) = -16 * 0^2 + 3*0 +35[/tex]
Evaluate the exponent
[tex]h(0) = -16 * 0 + 3 * 0 + 35[/tex]
Evaluate the products
[tex]h(0) = 0 + 0 + 35[/tex]
Evaluate the sum
[tex]h(0)= 35[/tex]
Hence, the initial height she threw the ball from is 35
Read more about quadratic functions at:
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Factorise fully 7y+84
Answers
Answer:
7 (y + 12)
Step-by-step explanation:
7 times y = 7y
7 times 12 = 84
7 (y + 12)
Answer:
y+12
Step-by-step explanation:
Divide 7y and 84 by 7
There are 10 teachers and 5 school guards in the school. The principal wants to form a 4-member safety committee for the upcoming Grade 10 night. In how many ways can the committee be formed if there are 3 teachers and 1 guard?
a. 35
b. 50
c. 125
d. 600
Answers
10 x 5=50
50 combinations
the radius of a circle is 7 cm .the circle is divided into two equal parts .what is the perimeter of the semi circular part
Answers
Answer:
P = 35.98 cm
Step-by-step explanation:
The Perimeter of a shape is the distance around the outside of it. This semi-circle (half circle) has a straight part and the curved part. See image. The straight part is the diameter (distance through the center) it is double the radius that was given, 7 cm.
The circumference of a circle is the perimeter of the whole circle.
C = 2pi•r or pi•d
C = 2pi•7 = 14pi
But you only need half, so 14pi/2 is 7pi.
ADD the straight part and the curved part to get the whole distance around the shape
P = 14 + 7pi
P ~= 35.98 cm
See image
An object with a mass of 4.0 kg accelerates 2.0 m/s² when an unknown force is applied to it. What is the
amount of the force
Answers
Answer:
F=ma
Mass is in kg, so we have mass= 4.0kg
since we have a= 2.0 m/s² and m= 4.0kg
F=ma
F= 4.0 x 2.0
F= 8.0N
what is 8 ÷ 3/4 ? and 11 ÷ 2/5?
Answers
Answer:
10 2/3 = 10.6667
27 1/2 = 27.5
Step-by-step explanation:
8 ÷ 3/4
Convert any mixed numbers to fractions.
Then your initial equation becomes:
[tex]\frac{8}{1}[/tex] ÷ [tex]\frac{3}{4}[/tex]
Applying the fractions formula for division,
[tex]=\frac{8*4}{1*3}[/tex]
=[tex]\frac{32}{3}[/tex]
Simplifying 32/3, the answer is
[tex]10 \frac{2}{3}[/tex]
Decimal Form = 10.6667
=================================================================
11 ÷ 2/5
Convert any mixed numbers to fractions.
Then your initial equation becomes:
[tex]\frac{11}{1}[/tex] ÷ [tex]\frac{2}{5}[/tex]
Applying the fractions formula for division,
[tex]=\frac{11*5}{1*2}[/tex]
=[tex]\frac{55}{2}[/tex]
Simplifying 55/2, the answer is
27 1/2
Decimal Form = 27.5
[RevyBreeze]
what is the slope of the line that passes through the points (-9,10) and (-13,13)
Answers
Answer:
-3/4
Step-by-step explanation:
The slope of line passes through the points (-9,10) and (-13,13) is -3/4.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
(-9,10) and (-13,13)
So, slope= (13 - 10)/ ( -13 + 9)
slope= 3 / (-4)
slope= -3/4
Hence, the slope of line is -3/4.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
Write the point slope form of the equation of the line through the given point and slope
Answers
Step-by-step explanation:
the point-slope form in general is
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of a point, and m is the slope.
so, we have
y - -1 = 4/3 × (x - 3)
or simplified
y + 1 = 4/3 × (x - 3)
Answer:
[tex]y + 1 =\frac{4}{3} (x-3)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line contains the point (3, -1), and has a slope of [tex]\frac{4}{3}[/tex].
We want to write the equation of this line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1 ,y_1)[/tex] is a point.
SolvingSince we are already given the slope and the point of the line, we can plug these values into the formula to get the equation.
Let's start with the slope; replace m with [tex]\frac{4}{3}[/tex] in the formula.
[tex]y-y_1=\frac{4}{3}(x-x_1)[/tex]
Now, replace 3 as [tex]x_1[/tex] and -1 as [tex]y_1[/tex]. Remember that the formula has subtraction in it.
[tex]y--1=\frac{4}{3} (x-3)[/tex]
This can be simplified to become:
[tex]y + 1 =\frac{4}{3} (x-3)[/tex]
Topic: writing the equation of the line
See more: https://brainly.com/question/16888568
what is
(588/2)9=n
a)n=294
b)n=2646
c)n=1323
Answers
Answer:
b)
Step-by-step explanation:
9 × (588/2)
= 9 × (294)
= 2646
Find the perimeter of the trapezoid
(5,1)( 5,-4) (1,1) (-2,-4)
Answers
Answer:
i cold not find the answer
Step-by-step explanation:
need this by midnight please show your work :)
Answers
Answer:
See belowStep-by-step explanation:
Part 1P = $800r = 2% (since P > $500)I = $100t = ?Find t:
I = Prt100 = 800*0.02t0.16t = 1t = 1/0.16t = 6.25 yearsPart 2P = $100r = 1.5% (since P < $500)I = $50t = ?Find t:
I = Prt50 = 100*0.015t0.03t = 1t = 1/0.03t = 33.33 yearsPart 3P = $10000r = 3% (since P > $5000)I = $750t = ?Find t:
I = Prt750 = 10000*0.03t300t = 750t = 750/300t = 2.5 yearsMy little brother spent $53 on comic books and magazines. He bought 17 items. If comic books cost $4 and magazines cost $3, how many of each item did my brother buy?
Answers
Answer:
comic books = 2
magazines = 15
Step-by-step explanation:
Let c = number of comic books bought
Let m = number of magazines bought
He bought 17 items, so
c + m = 17
Comic books cost $4 each and magazines cost $3 each.
He spent $53 on comic books and magazines, so
4c + 3m = 53
Rearrange c + m = 17 to make m the subject:
m = 17 - c
Substitute m = 17 - c into 4c + 3m = 53 and solve for c:
4c + 3(17 - c) = 53
⇒ 4c + 51 - 3c = 53
⇒ c = 2
Substitute c = 2 into m = 17 - c to and solve for m:
m = 17 - 2 = 15
3(5+6) distributave property
Answers
Answer:
3(5+6)
3x5 + 3x6
15 + 18
33
after 18 years, Rajesh will be 4 times as old as he is now. His present age is.....
Answers
Answer:
his present age is 6??
Step-by-step explanation:
correct me if im wrong^^
please answer these questions my mom is really mad at me because I have a 73 in math and I need to higher my grade pls help
Answers
Answer:
1. D
2.A
Step-by-step explanation:
Hey, with question 1 you add all the numbers and divide them by the number of blue marbles. Then we simply simplify it.
Woth question 2 we divide 20 by 200 and simplify it.
What is the area of this parallelogram?
A=1912 ft²
A = 42 ft²
A=6112 ft²
A=7134 ft²
Answers
Answer:
[tex]A=71\dfrac34 \ \ \textsf{ft}^2[/tex]
Step-by-step explanation:
Area = base x height
⇒ A = 10.25 x 7 = 71.75 = 71 3/4 ft²
Answer:
71 3/4 ft²
Step-by-step explanation:
the area is the product of the base (10 1/4) and height (7)
10.25 x 7 = 71 3/4 ft²
Please help quick !
Answers
Answer:
1. Quadrant 2
2. Quadrant 3
Step-by-step explanation:
The quadrants are ordered in a 'c' pattern. The first quadrant has coordinates (x,y). The second quadrant has coordinates (-x,y). The third quadrant has coordinates (-x,-y). The fourth quadrant has coordinates (x,-y).
Answer:
quadrent 2 for question 1 ( negative x positive y) quadrant 3 for number 2 ( negative x and y)
A clearance rack is marked as 60% off the regular price to be taken at the register. If a jacket on the clearance rack is marked $239. 99, what will it ring up for at the register? a. $14. 40 b. $60. 00 c. $96. 00 d. $143. 99.
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{60\% of 239.99}}{\left( \cfrac{60}{100} \right)239.99}\implies 143.994~\hfill \underset{\textit{sale price}}{\stackrel{239.99-143.994}{\approx 96}}[/tex]
9 X = 36 : i suck at find the missing factor pls HELP
Answers
All you have to do is divide the 9 on both sides.
This will equal x=4
You have to divide 9 by both sides so 36 divided by 9 is 4.
A wooden box has the shape of a rectangular prism. The inside of the box is also a rectangular prism. What is the volume of the solid part of the box?
Answers
Answer:
1560
Step-by-step explanation:
25 x 8 x 10 - 22 x 5 x 4 = 2000 - 440 = 1560
Rob eats a hamburger that has 415 calories for lunch. He also eats French fries that are 10 calories each. If Rob consumed 645 calories, how many French fries did he eat?
Answers
helpppp asap please!!!!
Answers
Answer:
Angle at x is 75°
Step-by-step explanation:
Data :
Angle at A = 65°
Angle at B = 40°
According to the porperty of triangle we know that total interior angle a triangle has is 180° irrespect of type or size
A + B + C = 180
65 + 40 + C = 180
C = 180 - 65 - 40 = 75°
Mark brainliest if you understand
Yesterday, there were q variants of a strain of bacteria. Today there are q^2 variants of the bacteria. There are 900 variants today. How many variants were present yesterday?
Answers
Answer:
30
Step-by-step explanation:
Since there are 900 today, and the variants square each day, we can take the square root of 900.
[tex]\sqrt{900} =30[/tex]
900 = q^2, so q = 30, so yesterday there were 30 variants
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A town is designing a rectangular park that will be 600 feet wide by 1000 feet long. On a scale drawing, the dimensions of the park are 12 inches wide by 20 inches long. A rectangular area of the park for swing sets is 0.5 inches wide by 2 inches long on the scale drawing.
What is the actual length of the swing set area of the park?
Enter your answer in the box.
The actual length of the swing set area of the park is [blank]
feet.
Answers
Answer:
The dimensions of the park on the scale drawing are 12 inches by 20 inches
The actual dimensions are given as:
Park = 600 feet by 1000 feet
Swing set = 25 feet by 100 feet
The dimension of the swing set on the scale drawing is given as: 0.5 inch by 2 inches
The above means that, the scale factor (k) is:
--- i.e. divide the scale measurement by the actual measurement
Evaluate both equations
So, we have:
Multiply the scale factor by the dimensions of the park, to get the scale measurement
Hence, the dimensions of the park on the scale drawing are 12 inches by 20 inches
Read more about scale measurements at:
brainly.com/question/24579126
Step-by-step explanation: