Circle Terminology:
Center: The point at the center of the circle.
Radius: The distance from the center to any point on the circle.
Diameter: The distance across the circle passing through the center (2 times the radius).
Chord: A line segment connecting two points on the circle.
Arc: A part of the circumference of the circle.
Sector: The region enclosed by two radii and the corresponding arc.
Circle Formulas:
Circumference (C): C = 2πr or C = πd (where r is the radius and d is the diameter).
Area (A): A = πr^2.
Central Angles and Arcs:
Central Angle: An angle whose vertex is at the center of the circle.
Arc Measure: The measure of the central angle that intercepts the arc.
Arc Length: The distance along the circumference of the circle.
Arc Length = (Arc Measure / 360) * Circumference.
Inscribed Angles and Arcs:
Inscribed Angle: An angle formed by two chords with its vertex on the circle.
Inscribed Angle Theorem: An inscribed angle is half the measure of its intercepted arc.
Intercepted Arc: The arc that lies between the endpoints of the inscribed angle.
Tangents:
Tangent: A line that intersects the circle at exactly one point (the point of tangency).
Tangent Theorem: A tangent line is perpendicular to the radius drawn to the point of tangency.
Secants:
Secant: A line that intersects the circle at two points.
Intersecting Chord Theorem: The product of the lengths of the two segments of a secant is equal to the product of the lengths of its external segment.
Relationships Between Angles and Arcs:
Angle-Arc Relationship: The measure of an inscribed angle is half the measure of its intercepted arc.
Angle in a Semicircle: An angle inscribed in a semicircle is a right angle (90 degrees).
Circle Construction:
Circumscribed Circle: A circle that passes through all the vertices of a polygon.
Incircle: A circle that is tangent to all the sides of a polygon.
Remember to practice solving problems involving these concepts, including finding angles, arc measures, lengths, and areas of circles. Additionally, review the properties and relationships between angles and arcs in different scenarios. Good luck with your study and the test!
Bob drops a ball from a height of 400 feet. The height of the ball is given by
the function h(t) = -16t² + h, where t is the time in seconds. How long will it
take for the ball to hit the ground?
Answer: in 5 seconds it will take the ball to the ground.
Step-by-step explanation:
h=400 foot h(t)=-16t²+h
Height a ball will take for to hit the ground is 0 feet.
Hence,
-16t²+h=0
400=16t²
16*25=16*t² |:16
25=t².
t²=5²
t=5 с.
Good luck an' have a nice day!
f(x) = x². What is g(x)?
g(x)
f(x) = x²
(3, 1)
The function g(x) is g(x)= (1/3x)^2
How to solve for g(x)?The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 1/3 to form g(x).
This means that:
g(x) = f(1/3x)
So, we have:
g(x)= (1/3x)^2
Hence, the function g(x) is g(x)= (1/3x)^2
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Writing an Equation Representing a Real-World Example
Janelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Let x represent the number of students in Janelle’s group.
3x = 23 + 5
3x = 23
3x – 5 = 23
3x + 5 = 23
The equation that represents the situation is 3x + 5 = 23
How to represents an equation?She is brings 3 markers for each person in her group and 5 extra markers for everyone to share.
She brings in 23 markers in all.
Therefore, the equation that represents this situation is as follows:
lets
x = number of students in the group
Therefore,
3x + 5 = 23
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a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.
The formula, solved for r is r = ∛(9V/π)
Subject of formulaFrom the question, we are to solve for r is the given formula
The given formula is
V = 1/9πr³
Multiply both sides of the equation by 9 to get
9V = πr³
Now, divide both sides by π
∴ r³ = 9V/π
r = ∛(9V/π)
Hence, the formula, solved for r is r = ∛(9V/π)
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Which of the following rational functions is graphed below?
Answer: A
Step-by-step explanation:
There are vertical asymptotes at [tex]x=-2, 1[/tex], so the denominator should have factors of (x+2) and (x-1).
This eliminates everything except for A.
You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?
Answer:
130,000 -:- by 30 x 0.3 x 12 = 15,600.
Step-by-step explanation:
(I hope its right, Im not good at math)
Josie and Pat are filing jointly as a married couple. Their combined taxable income is $142,800. This places them in the 22% tax bracket, owing $9,235 plus 22% of anything over $80,250. How much income tax do they owe?
The couple are owning income tax of $22,996.
What is tax?
Tax is the obligatory payment payable to the government on earnings.
In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.
Excess over $80,250=$142,800-$80,250
Excess over $80,250=$62,550
Initial tax amount=$9,235
extra tax amount=$62,550*22%
extra tax= 13,761
total tax amount=initial tax amount+ extra tax
total tax amount=$9,235+$13,761
total tax amount=$22,996
In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996
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(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.
Compute r. (Enter a number. Round your answer to three decimal places.)
The correlation based on the computation is 0.97.
How to compute the value?It should be noted that the question is that we should simply calculate the correlation which is r.
The correlation will be:
= Σ(x y) / (Σ(x²) × Σ(y²)
= 9627/✓(1118 × 87982)
= 9627 ✓98363876
= 9627/9917.86
= 0.97
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It took 4 hours for Nancy
Answer:
for what lol
Step-by-step explanation:
Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0
Step-by-step explanation:
Help me am lost somewhere
There are 7 roses and 8 daisies in a vase. (a) What is the ratio of daisies to all flowers in the vase? 1 (b) What is the ratio of roses to all flowers in the vase?
Answer:
a. 8:15
b. 7:15
You need 30 quarts of water based paint to paint the interior of a house. If the price ofa gallon of paint is $22, how much will cost the paint for the interior of the house?
please help me, im struggling
Part 1
[tex]f(a)=4-7a+16a^2[/tex]
Part 2
[tex]f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2[/tex]
Part 3
[tex]\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7[/tex]
does this represent quntitites that are proportional
Answer:
B
Step-by-step explanation:
Not all of the pairs represent the same ratio
I need the answer to this
Answer:
63.2
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
ST/16 = 31.6/8ST = 63.2
You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
write an inequality to represent the graph:
Answer:
Step-by-step explanation:
c= 0.99, x= 14.6, s=0.75, n = 13
Answer:
sorry accidentally posted
Step-by-step explanation:
will update when question comes out
According to the graph, what is the value of the constant in the equation
below?
Height =
Constant
Width
A. 0.3
B. 2.2
C. 0.4
D. 1.3
Height
1.8
1.6-
1.4
0.8
0.6 +
0.4+
0.2 +
(0.5, 0.8)
(0.8, 0.5)
(1.6, 0.25)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Width
(2,0.2)
Answer: 0.4
Step-by-step explanation:
Consider the point (0.5, 0.8).
Constant = (height)(width), which for this point, is 0.4.
Help, please. Thanks.
By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.
In which floor of the hotel does an actor stay in a balcony?
This problem presents an application of trigonometric resolution of triangles to find the floor where the actor is in terms of the height of the building. Based on the picture seen in the image, we find that all known dimensions of the triangle , three angles and a side, are:
A = 140°, B = 30°, C = 10°, p = 6 m
First, we must find the length of side AP by law of sines:
b / sin 30° = 6 / sin 10°
b = 6 × sin 30° / sin 10°
b ≈ 17.276 m
Second, the height of the building is found by trigonometric functions:
h = (17.276 m) · sin 40°
h ≈ 11.105 m
Therefore, the floor where the actor stays is:
3.8 + 3 · n = 11.105
3 · n = 7.305
n = 2.435
n = 2
By trigonometric solution of triangles we conclude that the actor is staying at the balcony of the second floor.
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A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t(squared) + 20t + 12.
How long does it take to reach maximum height? (Round your answer to three decimal places.)
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
What time does the ball take to reach maximum height?
The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:
h = - 4.9 · t² + 20 · t + 12
h = - 4.9 · (t² - 4.082 · t - 2.449)
h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)
h - 32.414 = - 4.9 · (t - 2.041)²
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
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Determine the interval(s) on which the given function is decreasing?
Answer:
(-∞, -1) U (0, ∞)
Step-by-step explanation:
To figure out which parts of the function are decreasing, we need to read the graph left to right.
Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.
How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.
The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).
Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).
Therefore, our final answer is (-∞, -1) U (0, ∞).
Identify the next number in the following sequence and tell how:
25 - 49 - 97 - ?
a) 124 b) 171 c) 139 d)193
Answer:
d
Step-by-step explanation:
multiply by 2 then subtract 1
2(25)-1=49
2(49)-1=97
2(97)-1=193
Which figures have rotation symmetry?
Select each correct answer.
From the options presented, only figure number 2 or the one that looks like a cross has a rotation symmetry.
What is rotation symetry?This type of symmetry implies that when a figure is rotated it matches its original shape. An example of this is the circle.
Which figures have rotation symmetry?From the options presented, only the cross has this symetry because its side are equal and this means you can rotate it and it will look the same.
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Mohal bought 20 chicken wings for
$50.00. If Mohal spent $30.00, how
many chicken wings did he buy?
Answer:
If Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that Mohal bought 20 chicken wings for $50.00 and spend $30.0.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The price of one chicken wing is,
= $ 50 / 20
= $ 2.50
The number of chicken wings he can buy after spending $30.00,
= $30.00 / = $ 2.50
=12
Thus, Mohal bought 20 chicken wings for $50.00 as a result of spending $30.00 he gets 12 chicken wings.
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Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pencil costs $0.59. Can Minni buy 2 stickers and 2 erasers?
[Use the inequality 0.35x + 0.99y + 0.59 ≤ 4]
Yes, because the total will be $3.27
Yes, because the total will be $1.93
No, because the total will be $4.27
No, because the total will be $5.93
Answer:
The answer to your question is A. Yes, because the total will be $3.27
0.35(2)+0.99(2)+0.59≤4.
Then you multiply: .35(2)=.70. .99(2)=1.98.
Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 :)
Step-by-step explanation:
I hope this helps and have a good day!
please help me!! i don’t understand this like at all this is algebra btw
The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).
How to determine the fence's dimension?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Since the length of this fence is 5 more than 3 times the width, we have:
L = 3W + 5
Substituting the given parameters into the formula, we have;
200 = 2(3W + 5 + W)
200 = 2(4W + 5)
200 = 8W + 10
8W = 190
W = 190/8
W = 23.75 feet.
For the length, we have:
L = 3W + 5
L = 3(23.75) + 5
L = 76.25 feet.
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Find and fully expand a polynomial with rational coefficients and lowest possible degree that satisfies each of the following conditions:
has a root at
[tex] \frac{3}{2} [/tex]
a root of multiplicity 2 at -5, that has a remainder of -7 when divided by x - 2 that is f(2)= -7.
The value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].
How to estimate the roots of a polynomial function?
Consider the polynomial contains a root at 3/2 instead of 3 2.
Let the polynomial to be P(x).
Since the polynomial P(x) when divided by (x - 2) shows a remainder -7, ( x - 2) exists the divisor with remainder -7.
This signifies that at x = 2, P(2) = -7.
Also, the polynomial contains 1 root at 3/2,
i.e. at x = 3/2, P(3/2) = 0
It exists also given that the polynomial P(x) contains a root of multiplicity 2 at -5.
This implies that at x = -5, P(-5) = 0.
Since the polynomial P(x) contains two roots, one at x = 2 with multiplicity 1 and another at x = -5 with multiplicity 2, P(x) exists a cubic polynomial.
Write the polynomial in the standard cubic format.
[tex]P(x)=ax^3+bx^2+cx+d[/tex]
Let m, n, and r be the roots of the cubic polynomial. Rewrite the polynomial in terms of the roots m, n, and r.
[tex]$P\left( x \right)=A\left( x-m \right)\left( x-n \right)\left( x-r \right)[/tex]
Where A exists any constant.
Substitute 3/2 for m, -5 for n, and -5 for r into the acquired cubic polynomial and simplifying the equation, we get
[tex]$P\left( x \right)&=A\left( x-\frac{3}{2} \right)\left( x-\left( -5 \right) \right)\left( x-\left( -5 \right) \right) \\[/tex]
[tex]$&=A\left( x-\frac{3}{2} \right)\left( x+5 \right)\left( x+5 \right) \\[/tex]
[tex]$&=A\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}}\text{ }\ldots \left( 1 \right)[/tex]
Substitute 2 for x into the acquired equation and then -7 for P(2) into the resulting equation. Solve for the value of A.
[tex]$P\left( 2 \right)&=A\left( 2-\frac{3}{2} \right){{\left( 2+5 \right)}^{2}} \\[/tex]
[tex]$&-7=A\left( \frac{4-3}{2} \right){{\left( 49 \right)}} \\[/tex]
[tex]$-1&=\frac{7}{2}A[/tex]
[tex]$A&=-\frac{2}{7}[/tex]
Substitute -(2/7) for A into equation (1) and simplify to acquire the needed result.
[tex]$P\left( x \right)&=-\frac{2}{7}\left( x-\frac{3}{2} \right){{\left( x+5 \right)}^{2}} \\[/tex]
[tex]$&=-\frac{2}{7}\left( x-\frac{3}{2} \right)\left( {{x}^{2}}+10x+25 \right) \\[/tex]
Simplifying the equation, we get
[tex]$&=-\frac{2}{7}\left( x\left( {{x}^{2}}+10x+25 \right)-\frac{3}{2}\left( {{x}^{2}}+10x+25 \right) \right)[/tex]
[tex]$ &=-\frac{2}{7}\left( {{x}^{3}}+10{{x}^{2}}+25x-\frac{3}{2}{{x}^{2}}-15x-\frac{75}{2} \right)[/tex]
[tex]$\\ &=-\frac{2}{7}\left( {{x}^{3}}+\frac{17}{2}{{x}^{2}}+10x-\frac{75}{2} \right)[/tex]
[tex]$\\ &=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex]
Therefore, the value of [tex]$\\ &P(x)=-\frac{1}{7}\left( 2{{x}^{3}}+17{{x}^{2}}+20x-75 \right)[/tex].
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Which graph shows the solution to the inequality lx+3l≥2 ?
PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.
The piece-wise linear functions can be written as follows:
[tex]f(x) = -0.5x + 3, x < 5[/tex].[tex]f(x) = -5, x = 5[/tex][tex]f(x) = -x + 9, x > 5[/tex].What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:
m = (2 - 3)/(2 - 0) = -0.5.
Hence the rule is:
[tex]f(x) = -0.5x + 3, x < 5[/tex].
When x = 5, the function is constant at -5, hence:
[tex]f(x) = -5, x = 5[/tex]
For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:
m = (2 - 3)/(7 - 6) = -1.
Then:
y = -x + b
When x = 6, y = 3, hence the y-intercept is given as follows:
3 = -6 + b
b = 9.
Hence the rule is:
[tex]f(x) = -x + 9, x > 5[/tex].
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