Answer:
(a) The unit circle is centered at (0,0) with a radius of 1.
(b) The equation of a circle of radius r, with a center located at (0,0):
x²+ y² = r².
(c) (i) P(1,0)
(ii) P(0,1)
(iii) P(-1,0)
(iv) P(0,-1)
Step-by-step explanation:
Part (a)
The unit circle is centered at (0,0). This point is the origin.
The radius of the unit circle is 1
The term "unit" means "one", which describes the radius length.
=========================================================
Part (b)
The equation of the unit circle is x^2+y^2 = 1
The general equation of any circle is (x-h)^2+(y-k)^2 = r^2
In this case, the unit circle has center (h,k) = (0,0) and radius r = 1.
=========================================================
Part (c)
The following four points are on the unit circle
(1,0)(0,1)(-1,0)(0,-1)As shown below in the diagram. The idea is to plug each given coordinate into the equation from part (b), and solve for the missing variable.
For example, if we know x = 1, then...
x^2+y^2 = 1
1^2+y^2 = 1
1+y^2 = 1
y^2 = 1-1
y^2 = 0
y = sqrt(0)
y = 0
Meaning x = 1 leads to y = 0. So (x,y) = (1,0) is one point on the circle. The other parts are handled in a similar fashion.
Pls help i dont understand :(
7th grade math help me plzzz
Answer:
1. 3>-3
2. 12<24
3. -12>-24
4. 5=-(-5)
5. 7.2>7
6. -7.2<-7
7. -1.5=-3/2
8. -4/5>-5/4
9. -3/5=-6/10
10. -2/3<1/3
Step-by-step explanation:
PLEASE HELP 50 PTS
For a function j(x), the difference quotient is 3x2 + 3xh + h2. What is the average rate of change of j(x) over the interval [–1, 6]?
15
21
25
31
Answer:
31 is correct guys
Step-by-step explanation:
Since the data is incomplete, for the given question the required average rate of change is given by 15 + 3h.
Given that,
For a function j(x), the difference quotient is 3x2 + 3xh + h2.
The average rate of change of j(x) over the interval [–1, 6] is to be determined.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is independent while Y is the dependent variable.
Here, the average rate of change = f(6) - f(-1) / (6 + 1)
So,
f(6) = 108 + 18h + h²
f(-1) = 3 - 3h + h²
Now,
average rate of change = [(108 + 18h + h²) - (3 - 3h + h²)]/(7)
= [105 + 21 h ] / 7
= 15 + 3h
Thus, the required average rate of change is given by 15 + 3h.
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Tyler then takes his remaining paper and does it again. He cuts the paper to create four equal pieces, then hands one piece each to the others and keeps one for himself. What fraction of the original piece of paper does each person have now?
Answer:
Each person has 1/4 of a peice of paper
Step-by-step explanation: Tyler cut the peices of paper in 4 equal pieces and if he gave himself and another person one peice then they would each of 1/4 of a peice of paper
The table below shows a proportional relationship between s and t . Which equation represents the relationship between s and t?
Answer:
[tex] s = 7t [/tex]
Step-by-step explanation:
The table given shows that both variables are directly proportional to each other. That is, as s variable increases, y variable also increases.
Equation to represent this direct proportion would be:
[tex] s = kt [/tex],
where, k = constant of proportionality.
Let's find k from the table given.
Let's use any pair values of of s and t given in the table. Say, s = 21, t = 3
[tex] s = kt [/tex]
[tex] 21 = k3 [/tex]
Divide both sides by 3
[tex] \frac{21}{3} = \frac{k3}{3} [/tex]
[tex] 7 = k [/tex]
[tex] k = 7 [/tex]
Plug in k = 3 into [tex] s = kt [/tex]:
[tex] s = 7t [/tex]
Answer:
B
Step-by-step explanation:
Divide 7
Mary Jo takes her son to get a haircut at the barbershop. The total cost of the haircut is $12.60, including a 20% tip. How much was the haircut before the tip?
Based on the total cost of the haircut with the tip included, the cost of the haircut before the tip was $10.50
How to find the cost of the haircut?The cost of the haircut give of $12.60 is merely the cost of the haircut including the 20% tip.
To find the cost of the haircut before the tip was included, assume that it is x. The relevant expression would then be:
Total cost including tip = x × (1 + tip percentage)
Solving for the haircut cost before the tip gives:
12.60 = x ( 1 + 20%)
12.60 = 1.20x
x = 12.60 / 1.20
x = $10.50
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greatest common factor for 32-4x
Answer:
4
out of
32
−
4
x
.
4
(
8
−
x
)
Step-by-step explanation:
what is the model of 1/4 divided by 3
Answer:
bust a uhhh
Step-by-step explanation:
ya dig
3x square - 6x + 3=0
Answer: 1
Step-by-step explanation:
First you need to multiply 3 x 3 (9), because that's all 3 squared means.
Now the equation should be 9x-6x+3=0
Next we need to combine like terms. Do 9x - 6x which should give you 3x
Now your equations should be 3x+3=0
Now for the somewhat harder part...
Under the three (the one without the x) write -3 and under the zero write the same thing. the +3-3 cancels out so just put a line or something across it.
0-3= -3
so now you should have...
3x=-3 ignore the 3x, at this point it's useless in getting the answer because it would cancel out.
-3 divided by -3 is 1 because a negative (-) divided by a negative (-) equals a positive (+).
The answer should be x = 1
Could someone help me with 19 please :)
Answer:
Step-by-step explanation 我认为那是一个美好的一天
Wǒ rènwéi nà shì yīgè měihǎo de yītiān
Answer:
wouldn't that just make it -2 1/4 + 9?
Step-by-step explanation:
because f just means +9
What is 24:30 as a decimal
Answer:
.800
Step-by-step explanation:
Answer:
0.8
Step-by-step explanation:
Let's see 24:30 as a fraction first...
24/30
Now let's simplify it,
(24 ÷ 3) / (30÷3)=
8/10
8/10= 0.8
15 less than a number is equal to 12
Answer:
Step-by-step explanation:
x - 15 = 12
x = 27
A submarine dives below the surface, heading downward in three moves. If each move downward was 25 12 feet, where is the submarine after it is finished diving?
Answer:
why is 25 and 12 nex tto each other explian
Step-by-step explanation:
Answer:
It is about 325x3=975 feet below to surface. Hope this helps!!!
Step-by-step explanation:
Pls help
I have this question and I can’t figure it out
Start by crossing out absurd answers, it helps a lot. Then you're left with two and choose the correct answer by doing the math
Step-by-step explanation:
cross the ones that you think are not right
Simple equation with division that equals 8
Answer:
64 divided by 8
Step-by-step explanation:
Answer:
16 divided by 2 = 8
Step-by-step explanation:
Please answer this correctly without making mistakes
Answer:
50%
Step-by-step explanation:
Answer:
50 present
Step-by-step explanation:
Which equation matches the graph?
Answer:
equation C
Step-by-step explanation:
y-axis = 4
gradient of line is -2/3
I can't find the right answer
Answer:
x^2 ≥ 4
Step-by-step explanation:
[tex]x^2\ge \:4\\\\\mathrm{For\:}u^n\:\ge \:\:a\\\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\:\le \:\:-\sqrt[n]{a}\:or\:u\:\ge \sqrt[n]{a}\\\\x\le \:-\sqrt{4}\quad \mathrm{or}\quad \:x\ge \sqrt{4}\\\\\sqrt{4}=2\\\\x\le \:-2\quad \mathrm{or}\quad \:x\ge \:2[/tex]
Answer:
A
You can take the square root of the inequality x^2<4, which will make it x< plus or minus 2 (x<2, x<-2)
You know it is this answer because, the sign cannot be greater than or equal to since the circles aren't filled, and if you solve the other inequality, the answer you get does not match.
Hope this helps!! :)
Suppose you're given a data set that classifies each sample unit into one of four categories: A, B, C, or D. You plan to create a computer database consisting of these data, and you decide to code the data as A1, B2, C3, and D4. Are the data consisting of the classifications A, B, C, and D qualitiative or quantitative? After the data are input as 1, 2, 3, or 4, are they qualitative or quantitative?
Answer:
The data consisting of the classifications A, B, C, and D are qualitative.
After the data are input as 1, 2, 3, or 4 the data still be qualitative.
Step-by-step explanation:
The data consisting of the classifications A, B, C, and D are qualitative because data is categorized in A B C and D categories.
When the data are input as 1,2,3 or 4 it would be still be qualitative because here 1,2,3 or 4 as used as identifier rather than actual numerical meaningful digits.
Kelsey graphed the equation y = 3x + 1 as shown below.
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Which describes Kelsey’s error?
Kelsey graphed the y-intercept on the x-axis.
Kelsey graphed –3 instead of 3 as the y-intercept.
Kelsey graphed the slope as up 1 right 1 instead of up 1 left 1.
Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.
Answer:
D. Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.
Step-by-step explanation:
The equation to graph was : y= 3x + 1 where the slope is 3 and the y-intercept is 1
However, Kelsey graph line passes through points (-3, 0)and (0, 3).From these points the equation of the line is;
m=Δy/Δx where
m=the slope of the graph
Δy= 3-0 =3
Δx= 0--3 =3
m=3/3 = 1
The equation of the line should be;
m=Δy/Δx
1=y-3/x-0
1x= y-3
3+1x= y
y= 1x + 3 ----------where the slope is 1 and y-intercept is 3
So you can see here that in the original equation, the slope m is 3 and y-intercept is 1 as shown in the first attached graph.
While in the Kelsey's graph, the slope is 1 and the y-intercept is 3 as in the second attached graph.
Thus, the correct answer is D : Kelsey graphed the slope,3 as the y-intercept and the y-intercept,1, as the slope.
Answer choice A is incorrect because Kelsey didnot graph the y-intercept, 1 on the x-axis but graphed point (-3,0) on the x-axis.
Answer choice B is incorrect because on Kelsey's equation the y-intercept is 3 and not -3. i.e. y=1x + 3
Answer choice C is incorrect because Kelsey graphed the slope as up 1 right 1 which is okay per the equation , y=1x+3.However, this incorrect because the correct graph has a slope of 3.
Answer:
the answer is the last option
Step-by-step explanation:
hope this helps
have a good day
did the test on edge
what is 337/25 simplified
Answer: 13.48
Step-By-Step:
Hello there! I will be showing the steps. Let me know if you have any questions or concerns in the comments.
Step 1: For the denominator, recognize that 25 × 4 = 100.
Multiple = 4
Step 2: Multiply both the numerator and denominator by the multiple 4.
[tex]\frac{337 *4 }{25 * 4}[/tex]
Step 3: Simplify.
[tex]\frac{1348}{100}[/tex]
Step 4: Simplify.
13.48
~I hope I helped you! :)~
Jill made 20 muffins.she put them into 3 boxes and has two muffins left . How many are in each box if they contain the same amount of muffin
Answer:
6 muffins
she can fit 6 into each box because 20 divided by 3 is eighteen with a remainder of 3. 18 goes into 3 6 times.
Is the given function exponential function?
3x2 - 4x + 7 = 0 Yes or No? How do you know?
Answer: no
Step-by-step explanation:
because you can do what is known as the vertical line test to determine if it is a function you do that by plotting it and if it goes in a vertical line then it is a function
Which is the most accurate measurement of 1 pound?
Answer:
I would say 15 ounces
you drink a beverage with 120 mg of caffeine. Each hour, the amount m of caffine in a persons system decreases by 12%. About how much caffeine will be in your system after 3 hours? Round your answer to the nearest milligram
Answer:43.2
Step-by-step explanation: multiply 120 x 0.12 and you get 14.4, since it’s 3 hours multiply 14.4 3 times and u get 43.2
Match each part of this algebraic expression with its appropriate description 12.1x - 4.7y + 6x + 1/6
Answer:Terms, like terms, constant(s),Variable (s),Coefficient(s)
Step-by-step explanation: 18.1x,4.7 and 1/6=Terms
The matched part with the respective appropriate description:
1) x and y → Variable(s)
2) 1/6 → Constant(s)
3) 12.1, 4.7, and 6 → Coefficient(s)
4) 12.1x and 6x → Like Terms
5) 12.1x, 4.7y, and 1/6 → Terms
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
We have the algebraic expression,
12.1x - 4.7y + 6x + 1/6.
From the definition,
x and y are the two variables.
And 12.1, 6 and -4.7 are the numbers in front of the variables.
So, 12.1, 6 and -4.7 are the coefficients.
And 1/6 is the constant.
So, 1) x and y → Variable(s)
2) 1/6 → Constant(s)
3) 12.1, 4.7, and 6 → Coefficient(s)
4) 12.1x and 6x → Like Terms
5) 12.1x, 4.7y, and 1/6 → Terms
Therefore, each part of the algebraic expression matched with its appropriate description.
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Jamal wants to subtract 16-7. First he subtract 16-6 then he subtracts 1 why will he get the correct answer
Step-by-step explanation: He will get the answer correct because if you add the 6 & 1 together it equals Seven. Seven was the original number that was supposed to be subtracted from 16.
Sorry if I didnt help
Which equation has exactly one solution?
A. 4x – 4 + 2x = 6x - 4
B. 3x + 5 = 2x - 6
C. 2(4x + 5) = 8x + 10
D. 4x - 8 = 4(x - 4)
Answer:
its B
Step-by-step explanation:
I calaulated all the numbers
Eddie Fantin is paid every two weeks. For the first week of his pay period he worked 42 hours, 4 of which were overtime hours. In the second week he worked 40 regular hours and 7 overtime hours. His regular pay rate is $14.40 an hour with time-and-a-half for overtime. What are his regular, , overtime, and total wages for the two weeks?
what is the nineteenth term in the sequence 7, 10, 13, 16,...? A 64 B 61 C 57 D 19
Answer:
B. 61
Step-by-step explanation:
7, 10, 13, 16...
ok so were starting with 7 and adding 3 every time
im going to do 3 times 19 like as if we started with 3 then im going to add 4
3 x 19 = 57
57 + 4 = 61
the 19th term is 61
Answer:
B: 61
Step-by-step explanation:
Hope this helps :)