Identify the parametric equations that represent the same graph as the following parametric equations. Select all that apply.x=4ty=t^2-1
Answers
Given the equations:
\(\begin{gathered} x=4t \\ \\ y=t^2-1 \end{gathered}\)Let's identify the parametric equations which represent the same graph as the given equations.
Here, we have:
Rewrite the first equation for t
\(t=\frac{x}{4}\)Now, plug in x/4 for t in the second equation:
\(\begin{gathered} y=(\frac{x}{4})^2-1 \\ \\ y=\frac{x^2}{4^2}-1 \\ \\ y=\frac{x^2}{16}-1 \end{gathered}\)Also we have:
\(t^2=\frac{x^2}{16}\)Rewrite equation 2 for t²
\(t^2=y+1\)Hence, we have:
\(\begin{gathered} \frac{x^2}{16}=t^2=y+1 \\ \\ \frac{x^2}{16}=y+1 \\ \\ y=\frac{x^2}{16}-1 \end{gathered}\)Now, let's solve for the following to confirm:
\(\begin{gathered} \text{ When x = 3t} \\ Substitute\text{ 3t for x:} \\ y=\frac{(3t)^2}{16}-1 \\ \\ y=\frac{9t^2}{16}-1 \\ \end{gathered}\)Option B:
\(\begin{gathered} \text{ When x = 2t:} \\ \text{ Substitute 2t for x} \\ y=\frac{(2t)^2}{16}-1 \\ \\ y=\frac{4t^2}{16}-1 \\ \\ y=\frac{t^2}{4}-1 \\ \\ Option\text{ B is correct.} \end{gathered}\)Option C:
\(\begin{gathered} \text{ When x =8t} \\ \text{ Substitute 8t for x:} \\ y=\frac{(8t)^2}{16}-1 \\ \\ y=\frac{64t^2}{16}-1 \\ \\ y=4t^2-1 \\ \\ Option\text{ C is correct.} \end{gathered}\)Therefore, the correct parametric equations are:
\(\begin{gathered} B.\text{ x = 2t} \\ y=\frac{t^2}{4}-1 \\ \\ \\ \\ C.x=8t \\ y=4t^2-1 \end{gathered}\)ANSWER:
• B. x = 2t
y = t²/4 - 1
• C. x = 8t
y = 4t² - 1
Related Questions
Is -3 a real irrational rational integer or a whole number 
Answers
-3 is not an irrational number, but it is a real number, a rational number, an integer, and a whole number.
What are whole numbers and rational numbers?
All numbers, including integers, fractions, decimals, and irrational numbers, that can be represented on a number line are considered real numbers.
In summary, real numbers include rational and irrational numbers, and integers include whole number and their negatives.
When two integers are compared, a number can be stated as a ratio, such as -3/1, 1/2, or 5/7. Writing rational numbers as recurring or ending decimals is an option.
Numbers that can't be stated as a ratio of two integers, like 2 or, are referred to as irrational numbers. It is impossible to write irrational numbers using repeating or ending decimals.
Positive and negative whole numbers, as well as zero, are considered integers. Since whole numbers are non-negative integers, they contain zero and only positive values.
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HELP ME OUT
Using the digits 1 to 9 at most one time each fill in the boxes to make a whole number product
Answers
answer: x^9
x^7 * x^(8/4)= (x^3)(^6/2)
x^7 * x^2= x^3*3
x^9=x^9
exponents are added when there are variables associated with them, and are multiplied directly when like the right side
PLEASE HELP i have been on this question forever
Answers
Answer:
1520.5
Step-by-step explanation:
The area of a circle is pi times r^2. r stands for radius. r, which is 22 squared is 484, Multiply that with pi and you have your answer.
Answer:
The area of circle is 1520.5 in².
Step-by-step explanation:
DIAGRAM :
\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large{22\ in}}\end{picture}\)
\(\begin{gathered}\end{gathered}\)
SOLUTION :
Here's the required formula to find the area of circle :
\(\longrightarrow{\sf{A_{(Circle)} = \pi{r}^{2}}}\)
A = Area π = 3.14 r = radiusSubstituting all the given values in the formula to find the area of circle :
\({:\implies{\tt{A_{(Circle)} = \pi{r}^{2}}}}\)
\({:\implies{\tt{A_{(Circle)} = 3.14{(22)}^{2}}}}\)
\({:\implies{\tt{A_{(Circle)} = 3.14{(22 \times 22)}}}}\)
\({:\implies{\tt{A_{(Circle)} = 3.14{(484)}}}}\)
\({:\implies{\tt{A_{(Circle)} = 3.14 \times 484}}}\)
\({:\implies{\tt{A_{(Circle)} = 1520.53}}}\)
\({:\implies{\tt{A_{(Circle)} \approx 1520.5}}}\)
\({\star{\boxed{\tt{A_{(Circle)} \approx 1520.5 \: {in}^{2}}}}}\)
Hence, the area of circle is 1520.5 in².
\(\rule{300}{2.5}\)
A man deposited GH¢14100.00 at 8% per annum compound interest. If at the end of 4
years he transfers the total amount to another bank offering 12% compound interest per
annum.
a. How much interest did he get at the end of 7 years?
b. Calculate the total amount he received at the end of seven years.
Answers
26950 is the total amount he received at the end of seven years.
What is your interest in simple words?
Interest is the price you pay to borrow money or the cost of borrowing money. Interest is usually given as an annual percentage of the loan amount. This percentage is called the interest rate on the loan.
given,
pv= 14100
r1-4= 8%
n = 7
r5-7= 12%
A) interest = FV - PV
= PV * ( 1 + r )ⁿ - pv
= 14100 * ( 1 + 0.08)⁴ * ( 1 + 0.12)³ - 14100
= 26,950.59 - 14100
= $12850.59
b) fv= pv * (1 + r)ⁿ
= 14100 * ( 1 + 0.08)⁴ * ( 1 +0.12 )³
= 26950
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A person decides to build a horse corral using a barn for one side. Has has 30m of fencing materials and wants the corral to have an area of 100m ^ 2 . What are the dimensions of the corral?
Answers
Two possible answers:
A 10 m by 10 m corralA 5 m by 20 m corralSee the diagrams below.
============================================================
Explanation:
x = length
y = width
Let side x be parallel to the barn wall. This means we have 1 copy of x and 2 copies of y to form this partial rectangle. The fourth side is the barn itself, so we don't need this as the fencing.
The perimeter of the fencing is x+y+y = x+2y
Set this equal to the 30 meters of fencing and solve for x.
x+2y = 30
x = -2y+30
----------------
area = length*width
area = x*y
area = (-2y+30)*y
area = -2y^2+30y
Set this equal to the given area of 100 m^2 and solve for y
-2y^2+30y = 100
-2y^2+30y-100 = 0
-2(y^2-15y+50) = 0
y^2-15y+50 = 0
(y-10)(y-5) = 0
y-10 = 0 or y-5 = 0
y = 10 or y = 5
Side note: The quadratic formula is an alternative path you can take.
----------------
If y = 10, then x would be...
x = -2y+30
x = -2*10+30
x = -20+30
x = 10
This produces a 10 meter by 10 meter enclosure.
Or, if y = 5, then,
x = -2y+30
x = -2*5+30
x = -10+30
x = 20
The corral is 5 by 20 in this case.
Unfortunately there are two possible answers. Without more info, we cannot nail down which one to go with.
The diagram of each is shown below.
Ingrid spent $36 and had $12 left. What percent of her money did she spend?
Answers
36+12=48
36÷48×100=75
answer=75%
can you please help i need it today
Answers
She should use the $10 off coupon because she saves more money.
6. Sheila simplified an expression using the following steps. Which property justifies Step 3?
Step 1: 5x + 4(3 + 2x)
Step 2: 5x + 12 + 8x
Step 3: 5x + 8x + 12
Step 4: 13x + 12
O A. Identity Property
O B. Associative Property
O C. Distributive Property
D. Commutative Property
Answers
Answer:
answer is Commutative Property
Step-by-step explanation:
Answer:D
Step-by-step explanation:Don't have one
The temperature is 21' C below zero
which interger repersents this temperature k12 6th grade Quiz 4.03 integers and rational numbers
pls quik answer no long one seriously pls no long
Answers
-21 since its below zero
The product of two numbers is 155952. If one number is 342, find the other
number.
Answers
Answer:
456
Step-by-step explanation:
Product means an answer derived from multiplication. Therefore, if the product is 155952, and one value is 342, then the following equation is true:
342x = 155952, or 342 * x = 155952
Divide 155952 by 342 to get: 456.
Check the work in the equation:
342(456) = 155952
155952 = 155952, which is true, so the answer is 456.
If I helped, please make this answer brainliest! ;)
2. What is the place value of the 5 in 3562?
Answers
Answer:
Hundreds Place
Step-by-step explanation:
The 5 is in the hundreds place.
Hope this helps :D
3 is the thousands place
5 is the hundreds place
6 is the tens place
2 is the ones place
You tell me the answer.
Mrs. Banks made cookies. 2/3 FRACTION BTW
of them are chocolate chip cookies and 1/5 ALSO FRACTION BTW
of them are sugar cookies. The rest are oatmeal.
What fraction of the cookies are chocolate chip or sugar?
Answers
Answer:
13/15
Step-by-step explanation:
We Know
2/3 of them are chocolate chip cookies.
1/5 of them are sugar cookies.
What fraction of the cookies are chocolate chip or sugar?
2/3 + 1/5 = 10/15 + 3/15 = 13/15
So, 13/15 of the cookies are chocolate chip or sugar.
Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
Answers
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
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What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
Answers
An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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Need helppppppppppppppppp
Answers
Answer:
45.95% is the correct answer
Answer:
free freeee3eeeeeuuuuuu
what number represents the same amount as 2 hundreds + 12 tens + 6 ones ?
Answers
Answer:
326
Step-by-step explanation:
The value of the given expression is 326.
Given:
The given expression 2 hundreds + 12 tens + 6 ones.
To find:
The value of the given expression.
Explanation:
The numeric form of given expression is:
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
Therefore, the value of the given expression is 326.
PLEASE HELP!!! DSFVAGETRYHUJ
Answers
Answer: Remeber 2+2=5 and
Step-by-step explanation: if yur on fire stop drop and roll do it and your awesome. Another thing is if someones taking forever drinking water when your behind them sing 123 can you hurry up please 456 imma hit you with a brick 789 imma spit this sick ryme
For each value of x, determine whether it is a solution to 3x + 5 = 8.
Is it a solution?:
-6: yes or no
-2: yes or no
7: yes or no
8: yes or no
Answers
Answer:
-6:No
-2:No
7:No
8:No
The only number to make this equation true is 1
Step-by-step explanation:
I will substitute each value in place of the variable. Hopefully you understand PEMDAS
3(-6)+5=8
-18+5=8
-13=8
-13 does not equal 8 so false.
3(-2)+5=8
-6+5=8
-1=8
-1 doe not equal 8 so false
3(7)+5=8
21+5=8
26=8
26 does not equal 8 so false
3(8)+5=8
24+5=8
29=8
29 does not equal 8 so false
Let's see what would make this true:
3x+5=8
3x=3
×=1
The solution is: :
-6:No
-2:No
7:No
8:No
The only number to make this equation true is 1
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
We will substitute each value in place of the variable.
we know PEMDAS
3(-6)+5=8
-18+5=8
-13=8
-13 does not equal 8 so false.
3(-2)+5=8
-6+5=8
-1=8
-1 doe not equal 8 so false
3(7)+5=8
21+5=8
26=8
26 does not equal 8 so false
3(8)+5=8
24+5=8
29=8
29 does not equal 8 so false
Let's see what would make this true:
3x+5=8
3x=3
x=1
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What is the solution set of the equation 2z+6z+2=3−1z
Note: z≠0,−2
Answers
Answer:
z = 1/9
Step-by-step explanation:
2z + 6z + 2 = 3 - 1z
2z + 6z + 1z = 3 - 2 (on rearranging)
9z = 1 (on solving)
z = 1/9
HOPE IT HELPS (✿^‿^)
Which set shows an average of 3?
A) A
B) B
C) A and B
D) none of the above
Answers
Answer:
B
Step-by-step explanation:
bbbbbb brainless me
helpppppppppppppppppppppppppppppppppppppp
Answers
Answer:
the last one
Step-by-step explanation:
there is no rhythm
Please help urgent thank you
Answers
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Find the range of the data. 8, 13, 5, 11, 3, 10 Range = [?] Enter
Answers
From the given question
There are given that data: 8, 13, 5, 11, 3, 10.
Now,
For the range, subtract the minimum data value from the maximum data value
So,
The maximum data value is 13 and the minimum data value is 3
Then,
13 - 3 = 10
Hence, the range of the data is 10.
Which of these is the correct ratio of strawberries to blueberries for the fruit salad?
A. 8 strawberries: 30 blueberries
B. 8 strawberries: 8 blueberries
C. 4 strawberries: 30 blueberries
D. 32 strawberries: 30 blueberries
Answers
The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.
(8 x 4) : 30
32 : 30
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Answer: A. 8 strawberries: 30 blueberries
Step-by-step explanation:
id : 237 514 2470
pass : frmCV5
Answers
Answer:
which subject ....
anyone wanna bang?
Answers
Answer:
me
Step-by-step explanation:
Answer:
Yes pls
Step-by-step explanation:
im thirsty my guy
I need helpl i dont understand
Answers
Answer:
the answer is 1.3x + 2 ≥ 20
Step-by-step explanation:
the tree is already 2ft which mean it would need to be added to the rate of growth, 1.3 by the amount of year to find out the height. The question is saying however that I can be at least 20ft. so no less than 20 which is why the greater or equal to sign is used (≥)
7 ft equal how many inches
Answers
Answer:
Step-by-step explanation:
There is 12 inches in a foot: therefore, 12inches x 7ft. = 84 ft.
Answer: 84 inches
Step-by-step explanation:
A conversion factor is a number that is used to multiply or divide one set of units into another. For instance, 12 inches equals one foot when converting between inches and feet.
Since 1 foot = 12 inches
And we are trying to figure out how much inches are in 7 ft.
We can create a conversion (or cross multiply)
\(\frac{12}{1} =\frac{x}{7}\)
Where inches are in the numerator and ft are in demoninator.
When cross multiplying (multiplying in a diagonal) you get:
x = 84 inches
So 7 ft equals 84 inches.
---
A quicker method would be to multiply 7 ft by 12 inches/1 ft (foot), and get 84 inches.
--
Answer these two questions correctly and I’ll give brainlist ❤️.
A fall dance sold 18 tickets during the first day of sales. This was 25% of the total sales. How many tickets were sold to the fall dance?
A mix of solid and striped shirts are hanging on a store rack. Sixty percent of the shirts are solid. If there are 45 shirts, how many are striped?
I will be giving out brainlist if the answer you submitted was correct❤️.
Please answer correctly and don’t waste my points these were hard to earn :((
Answers
first question:
72 tickets were sold.
so... if 18 is 25%
18+18=36
then 36 would be 50%
36+36=72
so then 72 would be 100%
72*.25=18
second question:
27 striped shirts
60% of 45 is 27 so that means there are 27 solids, the remaining 18 are striped.