Step-by-step explanation:
Explanation:
An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what we call an intercepted arc on the circle. The intercepted arc might be thought of as the part of the circle which is "inside" the inscribed angle. (See the pink part of the circle in the picture above.)
A central angle is any angle whose vertex is located at the center of a circle. A central angle necessarily passes through two points on the circle, which in turn divide the circle into two arcs: a major arc and a minor arc. The minor arc is the smaller of the two arcs, while the major arc is the bigger. We define the arc angle to be the measure of the central angle which intercepts it.
The Inscribed Angle Conjecture I gives the relationship between the measures of an inscribed angle and the intercepted arc angle. It says that the measure of the intercepted arc is twice that of the inscribed angle.
The precise statements of the conjectures are given below. Each conjecture has a linked Sketch Pad demonstration to illustrate its truth (proof by Geometer's Sketch Pad!). The linked activities sheet also include directions for further "hands on" investigations involving these conjectures, as well as geometric problems which utilize their results.
The precise statement of the conjectures:
Conjecture (Inscribed Angles Conjecture I ): In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc..

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent.

Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.
Corollary (Inscribed Angles Conjecture III ): Any angle inscribed in a semi-circle is a right angle.

Proof: The intercepted arc for an angle inscribed in a semi-circle is 180 degrees. Therefore the measure of the angle must be half of 180, or 90 degrees. In other words, the angle is a right angle.
Can someone help me out, I'm having trouble on these two questions.
Answer:
Step-by-step explanation:
7,A=9*6sin30°
=54*0.5
A= 27
8,A=6*10sin60°
A= 60*0.86
A=52....... approximately
9, A=1/2bh
A=0.5*x*xroot 3
A=root3/2 x^2
You can find x using trigonometric values
Hank’s age is 15 years less than twice his sister’ s age. If Hank’s sister is 22 years old, how old is Hank?
Answer:
29
Step-by-step explanation:
2s-15=h
2(22)-15=h
44-15=h
29=h
Answer:
29
Step-by-step explanation:
22 multiplied by 2 is equal to 44. Subtract 15 from 44 and you get 29.
What is the distance from
23, 5) to (33, -12)
Answer: 19.723083
Step-by-step explanation:
question in attachment
Answer:
[tex]cos(x)=-\frac{\sqrt{3} }{2}[/tex]
[tex]sin(x)=\frac{1}{2}[/tex]
[tex]tan(x)=-\frac{1}{\sqrt{3} }[/tex]
[tex]csc(x)=2[/tex]
[tex]sec(x)=-\frac{2}{\sqrt{3}}[/tex]
[tex]cot(x)=-\sqrt{3}[/tex]
Step-by-step explanation:
(I'll just use x for ease of writing)
We have the trig equation [tex]cos(x)=-\frac{\sqrt{3} }{2}[/tex], and we know that its terminal side is in the 2nd quadrant. By using a unit circle, we can determine that the angle is [tex]\frac{5\pi}{6}[/tex] which has an ordered pair of [tex](-\frac{\sqrt{3} }{2},\frac{1}{2} )[/tex]
[tex]sin(x)=y[/tex], so [tex]sin(x)=\frac{1}{2}[/tex]
[tex]tan(x)=\frac{y}{x}[/tex], so [tex]tan(x)=\frac{\frac{1}{2} }{-\frac{\sqrt{3} }{2} }=-\frac{1}{\sqrt{3} }[/tex]
Now that we have sin, cos, and tan, we can just take the reciprocal of each of these to get our answers for csc, sec, and cot.
[tex]csc(x)=\frac{1}{sin(x)}[/tex], so [tex]csc(x)=2[/tex]
[tex]sec(x)=\frac{1}{cos(x)}[/tex], so [tex]sec(x)=-\frac{2}{\sqrt{3}}[/tex]
[tex]cot(x)=\frac{1}{tan(x)}[/tex], so [tex]cot(x)=-\sqrt{3}[/tex]
Step-by-step explanation:
NEED HELP :(
Use the commutative or associative property to simplify the expression.
1/4(4y)
Answer:
y
Step-by-step explanation:
Associative Property a(bc)=(ab)c
1/4(4y)=(1/4(4))y
y
If a ball is dropped, how long does it take to fall 60.0 m?
Answer:
the ball takes 3.1944 sec
Step-by-step explanation:
Answer:
It takes 3.498 seconds.
Step-by-step explanation:
To calculate free fall you must use the formula: h=1/2gt^2
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) =
O A. g(x) = (x+4)2 - 3
O B. g(x) = (x - 42 - 3
O C. g(x) = (x – 4)2 + 3
O D. g(x) = (x+4)2 + 3
Answer:
A
Step-by-step explanation:
Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the right of a units
Given f(x) then the graph of f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here f(x) has been shifted 4 units left and 3 units down, thus
g(x) = (x + 4)² - 3 → A
PLEASE HELP THIS IS URGENT I AM BEING TIMED!!
Four children have the following weights: 45.5 pounds, 61 pounds, 37.2 pounds, and 16.34 pounds. What is the average weight of the children?
Answer:
40.01 lb
Step-by-step explanation:
mean:
(45.5+61+37.2+16.34)/4
160.04/4
40.01
Answer:
40.01
Step-by-step explanation:
First add all of the weights together and it should give you 160.04 divide that by 4 children and there is your answer
Terrell wrote that 5-4.2=8. Which statement about this answer is true?
Answer:
No.
Step-by-step explanation:
No. 5 - 4.2 = 0.8
Answer: 8 is wrong because a number gets smaller, not larger, when you take 4.2 from it.
Step-by-step explanation: I had this on my Imagine Math. The reason why this is wrong is because 5 – 4.2 doesn't not equal 8!Estimation might help. 5 doesn't need to be rounded. 4.2 is rounded to 4...5-4 = 1The Actual answer is actually 0.8.I hope this helps :)
Which is greater 15/27 or 16/24
Answer:
16/24
Step-by-step explanation:
let’s use the GCF of both which is 3 for 15/27
15/27 divided by 3 is 5/9
for 16/24 the gcf is 8
16/24 / 8 is 2/3
now we have to multiply 2/3 times 3
2/3 times 3 6/3 which is 2
so 16/24 is greater.
Calculate the mean given the frequency table
Class
Frequency
0-9
24
10-19
20
20-29
32
Answer:
So the mean of the given data set is approximately 15.55.
Step-by-step explanation:
The mean is calculated by taking the sum of the product of each class midpoint and its corresponding frequency and dividing by the total frequency.
The midpoint of each class can be calculated as the average of the lower and upper class boundaries:
Class 0-9: Midpoint = (0 + 9) / 2 = 4.5
Class 10-19: Midpoint = (10 + 19) / 2 = 14.5
Class 20-29: Midpoint = (20 + 29) / 2 = 24.5
Now we can find the sum of the product of each midpoint and its frequency:
(4.5 * 24) + (14.5 * 20) + (24.5 * 32) = 108 + 290 + 784 = 1182
Finally, we divide this sum by the total frequency (76) to find the mean:
1182 / 76 = 15.552632
So the mean of the given data set is approximately 15.55.
A man divided some apples among his two children and himself. If the man took 3 apples for
himself and divided the remaining apples evenly between each of his children and each child had
fewer than 5 apples. How many apples were there originally?
Answer:
15
Step-by-step explanation:
What is the equation of the line that is perpendicular to the linear
graph of y= -2/3x+5 and passes through the point (0, -2)?
Answer:
y=3/2x-2
Step-by-step explanation:
gradient line 1= -2/3
perpendicular meaning gradients when multiplied should be -1
gradient line 2=3/2
y+2=3/2
x-0
y+2=3/2(x-0)
y+2=3/2x-0
y=3/2x-2
The equation of the line perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2) is y = 3x/2-2 (1st option is correct)
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 is perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2)
The standard equation of a line is y = mx+c, where m is the slope of the line.
We know that, the slopes of the lines which are perpendicular to each other are negative reciprocal of each other,
Therefore, the slope of the asked line is 3/2.
Finding the c,
-2 = 3/2X0 + c
c = -2
Therefore, the equation will be,
y = 3x/2-2
Hence, The equation of the line perpendicular to the linear graph of y= -2/3x+5 and passes through the point (0, -2) is y = 3x/2-2
For more references on slope, click;
https://brainly.com/question/3605446
#SPJ2
Does the equation represent a direct variation? If so, find the constant of variation.
4x -5y = 0
a. yes; k = -5 b. no c. yes; k = 4/5 d. yes; k = - 4
Answer:
4/5
Step-by-step explanation:
4x-5y=0
subtract 4x on both the sides
4x-4x-5y = 0-4x
-5y = -4x
divide by -5 on both the sides
-5y/-5 = -4x/-5
y =( 4/5 )x
what is the vertex of y=1/2(x+4)^2+1
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The
number b varies directly with the number a. For example b = 2 when a = -2. Which equation represents this direct
variation between a and b?
b = -a
-b= -a
b - a = 0
b(-a)=0
Answer:
b=-a
Step-by-step explanation:
we know that b is located the same distance from 0 as another number, a, but in the opposite direction.
so the sum of the two numbers equal zero
a+b=0
a=-b or b=-a
11) Omar is flying a kite on a 50-foot string at a diagonal distance. The kite gets stuck at the top
of a 40-foot tree. How far is Omar from the tree?
Answer:
30 ft
Step-by-step explanation:
We have a right triangle.
Hypotenuse = c = 50 ft
Leg #1 = a = 40 ft
Leg#2 = b = ?
We need to use Pythagorean Theorem
c² = a² + b²
50² = 40² + b²
b² = 2500 -1600 = 900
b = 30
Newton currently has an account balance of $6,225.18. He opened the account 15 years ago
with a deposit of $4,543.11. If the interest compounds daily, what is the interest rate on the
account?
30.3%
7.7%
58.3%
2.1%
Answer: 2.1%
Step-by-step explanation:
r = n [(A/P)^1/nt - 1
What is the solution to the equation 1/4x +2= -5/8x - 5
Answer:
x = -8
Step-by-step explanation:
1/4x +2= -5/8x - 5
Add 5/8x to each side
1/4x +5/8x +2= -5/8x+5/8x - 5
1/4x+5/8x +2= - 5
Subtract 2 from each side
1/4x+5/8x +2-2= - 5-2
1/4x+5/8x = - 7
Get a common denominator
1/4 *2/2 x + 5/8x = -7
2/8x + 5/8x = -7
7/8x = -7
Multiply each side by 8/7
8/7x * 7/8x = -7 *8/7
x = -8
Answer:
x=-8
Step-by-step explanation:
1/4x+2=-5/8x-5
find l.c.m=8
multiply through by l.c.m which is 8
x/4×8+2×8=-5x/8×8-5×8
2x+16=-5x-40
2x+5x=-40-16
7x=-56
divide both sides by 7
7x/7=-56/7
x=-8
How many one-half cubes with dimensions of 1\2x1x1 fit in a unit cube?
0 1
O 2
Answer:
2 half cubes
Step-by-step explanation:
this has only half the width, you just need 1 more to make a whole, therefore 2
The function ƒ(x) = 4x + 1 is transformed to g(x) = 2x + 1. What type of transformation has occurred? A) Reflection and Vertical Translation B) Rotation C) Reflection D) Rotation and Vertical Translation
Answer:
B) Rotation
Step-by-step explanation:
The only difference between functions f(x) and g(x) is the slope. To get from f(x)=4x+1 to g(x)=2x+1, you would need to rotate slightly clockwise about point (0,1) - the y-intercept. This would make the graph less steep (2x is less steep than 4x) while still retaining the (0,1) y intercept.
Answer:
Rotation
Step-by-step explanation:
I have finished the table but stuck in the question after...
Answer:
7/48
Step-by-step explanation:
there are 48 in total
there are 7 white females
7/48
Use the elimination method to solve the system of equations
Answer:
D
Step-by-step explanation:
2x + 3y = 18
3x - 3y = 12
the 3y and -3y cancel and you add the other like terms
5x = 30
x = 6
plug x back into any of the equations
2(6) + 3y = 18
12 + 3y = 18
3y = 6
y = 2
answer is (6,2)
What is the shape of the cross section of the figure that is parallel to the triangular bases? A triangular prism.
a parallelogram that is not a rectangle
a rectangle
a triangle that must have the same dimensions as the bases
a triangle that may not have the same dimensions as the bases
Answer:
AStep-by-step explanation:
a parallelogram that is not a rectangle
Hope this helpsAnswer:
A
Step-by-step explanation:
I did it on the quiz
Which values of x make the inequality below true?
5 - 3 + 3x < 13
Convert 7/15 to a decimal.
SHOW WORK
Answer:
.4666...
Step-by-step explanation:
What you do:
Too convert 7/15 to a decimal you need too divide it.
7/15 = 0.466666667 So its a repeating decimal.
There are two things you can do, either add a bar to the decimal to show its repeating or round it up like this: 0.467 or 0.47
^ that is more accurate.
Have a good day! :)
Jasmine draws a circle with a radius of 9x². What is the area of her circle?
Answer:
Look at the attachment
plz help asap im timed just this and ill give u 5 stars brainliest and a thank u no cap
no its not a
Answer:
D
Step-by-step explanation:
2 x 4 = 8
8 x 2 = 16
4 x 9 = 36
36 x 2 = 72
9 x 2 = 18
18 x 2 = 36
16 + 72 + 36 = 124
124 = D
pls i need the help.
Answer:
3. 16a+24b
Step-by-step explanation:
I know this because I grouped the eqatiobs together
Answer:
#3. 16a + 24b
Step-by-step explanation:
P= 2( length plus width).
x+y= 2
y=-12? + 3
\right.V)
1. In two or more complete sentences, explain how to solve the system of equations algebraically.
2. Solve the system of equations. In your final answer, include all of your work.
Answer:
11
Step-by-step explanation:
11
