Answer:
y = -6x^2 + 15x -5
Step-by-step explanation:
equation step 1 for parabola
y2-y1 /x2-x1
= 1 - 4 / 0 - - 1
= -3 / 1
y = -3
We try again different points
y2-y1 / x2-x1
= 7 - 1 / 2 - 0
= 6 / 2
y = 3
we can see that one side is descending and 1 side is ascending
The start of the parabola is 0,1 as x = 0 and crosses the line.
we try again
y2-y1 /x2-x1
7-1 / 2-0
= 6 / 2
y = 3
You should know that a parabola is determined by 3 points, so unless your points happen to be collinear, they will determine a parabola. A straight forward, if not always the easiest way would be to take the general equation
y = ax^2 + bx + c
plug in each point, eg.y = y1 and x = x1 eg) y = y2 and x = y2 eg) y = y3 x=x3
Top equation re-used last see at end.
4 = a(-1)^2 + b(-1 ) + c = a+b+c=4
1 = a(0)^2 +b(0) + c = c =1
7 = a(2)^2 + b(2) + c = 4a+2b=7
a= -1-0 = -1 b = -1-0 = -1 and 4-1 = 3
-a +-b = 3
2nd set of equations
4a-0a = 4a
2b-0b = 2b
7-1 = 6
4a +2b=6 and previous
-a +-b = 3 here we can multiply by -2 to get 2b equality to 1st equation
2a + 2b = -6
4a + 2b = 6
2a = -12
2a = -12 / 2
a = -6
plug a
4(-6) + 2b = 6
-24 + 2b = 6
2b = 6 +24
2b = 30
b = 15
then put a + b+ c into top equation
(-6) + (15) + c = 4
9 + 0 = 4
9 -9 = 4 -9 cancel
c = -5
Then put into first equation as c and complete equation
To find that;
y = -6x^2 + 15x -5 = is our equation of the parabola.
This is how to solve your two linear equations in three unknowns.
The equation of parabola passing through (-1, 4), (0, 1), and (2, 7) is y = 2x² - x + 1.
To find equation of parabola that passes through the given points, we use the general-form of quadratic equation: y = ax² + bx + c.
Since we have three points, we substitute the coordinates of each point into the equation to create a system of equations. Solve for a, b, and c:
Substitute (-1, 4), We get,
4 = a(-1)² + b(-1) + c,
4 = a - b + c,
Next, Substitute (0, 1):
1 = a(0)² + b(0) + c
1 = c
Next, Substitute (2, 7):
7 = a(2)² + b(2) + c
7 = 4a + 2b + c
Now, we have a system of equations:
a - b + c = 4 ...equation(1)
c = 1 ...equation(2)
4a + 2b + c = 7 ...equation(3)
From equation(2), we know that c = 1. Substituting this into equation(1) and 3, we get,
a - b + 1 = 4
4a + 2b + 1 = 7
Solve equation(1) for a - b:
We get, a - b = 3,
Solve equation(3) for 4a + 2b:
4a + 2b = 6
Now we have a system-of-equations as :
a - b = 3
4a + 2b = 6
Solving the system for "a" and "b", We get,
a = 2; b = -1
Now we can write the equation of the parabola:
y = ax² + bx + c ⇒ y = 2x² - x + 1,
Therefore, the required equation of parabola is y = 2x² - x + 1.
Learn more about Parabola here
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Which expression can be simplified to find the inverse of y=2x^2
Answer:
easy
Step-by-step explanation:
its B
Two line segments intersect as shown.
Given that point is the midpoint of CD what additional information will allow for the conclusion that AB is a perpendicular
bisector of CD?
1. CE congruent ED
2. AE congruent EB
3. m
4. m
(< mean angle)
Answer:
CE congruent ED
Step-by-step explanation:
A perpendicular bisector is a line segment which perpendicularly intersects another line, thereby dividing it into two equal parts. In fact, the Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints.
The perpendicular bisector, AB, bisects CD at a point E, that is, the length CE is equal to ED. And the angle formed between the two lines is 90 degrees.Therefore, the additional pertinent information that allows for the conclusion that AB is a perpendicular bisector of CD is that "CE congruent ED".
1.If P ={ a, b, c, d, e,f g}
Q = { a, c, d, f} and R = { d, e ,f, g, h, i,j}
Then ( P Q) =
2.T ={p,q,r,s,t} . The number of subsets of T is?
Answer:
I think it would be ( a , b , c , d , e , f , g , )
Step-by-step explanation: It is combining both P and Q together in one set but don't add the same member if they are in both set
Josh mixes blue and white paint to make a lighter shade of white. He needs the ratio of blue to white paint to be 3:2 to get the desired color. If he uses 15 drops of blue paint, how many drops of white paint does he need to use
Answer:
15 drops of blue to 10 drops of white paint.
Step-by-step explanation:
multiply 3 by 5 to get 15
multiply 2 by 5 to get 10
so 10 drops of white paint.
In a class full of men and women,4/9 of the class are women.What is the ratio of men to women in its simplest form.
Answer:
4/9 is already in its simplest form.
Step-by-step explanation:
There is no number besides 1 that can go into both numbers therefore it is in its simplest form already.
Brainliest if you liked the answer
At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $44.00. Tori bought two pairs of gloves and two hats for $28.00. Solve the system to determine the prices of the hats and gloves.
Answer:
$6.00 for pair of gloves and $8.00 for a hat
Step-by-step explanation:
the difference between Tori and Cody is $16.00 its two hats. Then one hat is $8.00
If two hats are $16, two pair of gloves must be $12.00
Then one pair of gloves is $6.00
2t/t-5 + 1/t-3 = 3
Help..
Answer:
1/9
Step-by-step explanation:
1) simplify the expression
Group like terms: (2-5-3) + 1/t = 3
Simplify the arithmetic: -6+1/t=3
2) Isolate the t
Multiply to both sides by t: -6+1/t=3t
Expand the parentheses: -6t+1t/t=3t
Simplify the left side: -6t + 1 = 3t
3) Group all t terms on the left side of the equation
Subtract 3t from both sides: -6t+1-3t=3t-3t
Group like terms: -6t-3t+1=3t-3t
Simplify the arithmetic: -9t+1=3t-3t
Simplify the arithmetic: -9t+1=0t
Simplify the right side: -9t+1=0
4. Group all constants on the right side of the equation
Subtract 1 from both sides: -9t+1-1=0-1
Simplify the arithmetic: -9t=0-1
Simplify the arithmetic: -9t=-1
5. Isolate the t
Divide both sides by-9: -9t/-9=-1/-9
Cancel out the negatives: 9t/9=-1/-9
Simplify the fraction:t=-1/-9
Cancel out the negatives: t=1/9
I'm struggling a bit would someone mind helping?
Answer:
-1/2
Step-by-step explanation:
RATE AS BRAINLIEST
(-3,6), (3,-6)
3-(-3)/-6-6
=6/-12
=-1/2
The ratio of Jay age to Hena's age to Sally age is 4:3:6.Jay is 24 years old
(a)Find Sally's age.
(b)What is their total age?
Answer:
1. Write It Out:
Jay 4: Hena 3 : Sally 6
Jay is 24 years old.
2. Solve
So first you find 24/4 to get 6. This means Jays age was divided by 6 to get his ratio number. Showing that Hena's and Sally's is divided by 6 as well to get there ratios. Now what you need to do is mulitipy Hena and Sallys ratio by six to find there age's.
Hena: 3x6= 18 years old
Sally: 6x6= 36 years old
(Jay: 4x6= 24 years old)
Now to find there total age add them up...
18+36+24= 78
A. Sally is 36
B. 78
Answer:
Sally is 36 years old.
their total age is 78 years.
Step-by-step explanation:
[tex]4 + 3 + 6 = 13[/tex]
that's the total ratio
Jay is 24 years old and his ratio is 4
so assume the total age to be
[tex]x[/tex]
[tex]4 \div 13 \times x = 24[/tex]
[tex]4x \div 13 = 24[/tex]
[tex]4x = 24 \times 13 \div 4[/tex]
[tex]x = 78 \: total \: age[/tex]
t
[tex]sally \: age = 6 \div 13 \times 78[/tex]
[tex]sally \: is \: 36years \: old[/tex]
use the intercepts and graph the equation
x+5y=10
Answer:
5+what gives u 10 5+5=10
Olivia bought t boxes of tissues at$2.50 each and used a coupon. The amount of money (A) she spent is represented by this equation:
A=2.50t - 1.25
If Olivia spent $13.75, how many boxes of tissues did she buy?
Explain why the exponents cannot be added in the products 12 to the third power times 11 to the third power
Answer:
Because the exponent rule that let's the base to the sum of the exponents power equal the base too the x power times the base to the y power states that the bases must be the same. And the bases 12 and 11 are not equal.
the ratio of protein to fiber in a granola bar is 9/2
Answer:
Theres not question
Step-by-step explanation:
What is the traslation rule?
Mapping Rule A mapping rule has the following form (x,y) → (x−7,y+5) and tells you that the x and y coordinates are translated to x−7 and y+5. Translation A translation is an example of a transformation that moves each point of a shape the same distance and in the same direction.
Answer:
(X,Y)
Step-by-step explanation:
depends on the number so if it is (x-7) which is left 7 (y+5) up 5
Which describes the difference between the two sequences?
1st sequence: 1/4, 1/2, 3/4, 1
2nd sequence: 13, 39, 117, 351
Answer:
The first sequence is an arithmetic sequence having a constant difference of 1/4 while the second one is a geometric sequence having a common ratio of 3.
Answer: C
Step-by-step explanation:
Janice buys four boxes of paper clips . She pays with a $ 10 bill and receives $ 6.08 in change . What is the price of one box of paper clips ?
Answer:
$0.73 per paper clip
Step-by-step explanation:
So to start off you want to find out how much she paid for the paper clips. We know that she paid with a 10 dollar bill and she got $6.08 in change. Now just subtract to find the amount.
10-6.08 which is 2.92
So she paid $2.92 for 4 boxes of paper clips.
The question asks for 1 box So you divide.
2.92/4 which is 0.73
The answer is $0.73 per box of paper clip.
100 POINTS PLEASE HELP
What are the coordinates of the image of the point (−2, 6) after a clockwise rotation of 90° about the origin?
(−6, −2)
(6, 2)
(2, −6)
The rule is
(x,y)=(y,-x)So
Our coordinate is (-2,6)
Rotated point
(6,-(-2))(6,2)Option B
Answer:
(6, 2)
Step-by-step explanation:
Rotation rules about the origin:
90° clockwise (or 270° counterclockwise): (x, y) → (y, -x)180° clockwise (or 180° counterclockwise): (x, y) → (-x, -y)270° clockwise (or 90° counterclockwise): (x, y) → (-y, x)Therefore, to rotate (-2, 6) clockwise 90° about the origin:
⇒ (-2, 6) → (6, -(-2)) → (6, 2)
Someone help me with this I will make you brain
Answer:
It is A, the first one. Pls mark brain
Step-by-step explanation:
1+1+1+2+4+1+8+8+9+9+9+103+4
Answer:
160 is your answer, have a good day :')
Answer:
160
Step-by-step explanation:
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kkkkkkkkkkkkkk I don't know if y
ou are joking or not but here
Solve 4 x + 7) = 24.
Answer:
x=17/4
Step-by-step explanation:
please answer this question
Answer:
Graph C
Step-by-step explanation:
They are "opposites" for each other, and aside from 0, are functions.
Son "opuestos" entre sí y, a excepción de 0, son funciones.
Angela enjoy swimming and often swims at a city pace to burn calories at this pace Angela can’t swim 1700 m in 40 minutes. A: what is Angela‘s unit rate, this is kind of an answer but I think it is 42.5
B: what is the rate unit
Original price: $60; Markup: 15%; Retail price:
Answer:
Retail Price = $69
Step-by-step explanation:
Original Price = $60
Markup = %15
Retail Price = $60 + (0.15 * $60)
Solve:
We can say that 60 is 100% of 60 or 1 x 60
So the equation is:
1 x 60 + 0.15 x 60 = Retail Price
1.15 x 60 = Retail Price
Retail Price = 69
-Chetan K
Answer:
Original Price is $60
But it is markup 15%
(15x60) / 100 = 9
the 15% of 60 is 9
60 + 9 = 69
Now the retail price is $69
Step-by-step explanation:
Charlie is shopping for a jacket that he likes. The jacket, regularly priced at $200, is on sale at Clothes Are Us for $150. Jacket World is offering a 25% discount on the same jacket that regularly sells for $190 at that store. Which statements are correct for this situation?
A) Jacket World's price is $150.00
B) Jacket World has the better deal.
C) Clothes Are Us has the better deal.
D) Both stores are offering a 25% discount on the jacket.
E) The difference in the sale prices at the two stores is $7.50.
The correct options are:-
Choice B) Jacket world has the better deal.
Choice D) Both stores are offering a 25% discount on the jacket.
Choice E) The difference in sale prices at the two stores is $7.50
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
25% = 0.25
25% of $190 = 0.25*190 = 47.50
190 - 47.50 = 142.5
This indicates the price at Jacket World is $142.5 instead of $150
Therefore, choice A is false.
Choice B on the other hand is true because $142.50 at Jacket World is a lower price compared to $150 at Clothes Are Us. Jacket World has the better deal.
Because choice B was shown to be true, there's no way choice C can be true as well. Otherwise, we'd have a contradiction. So we can rule out choice C.
Let's find the percentage discount for Clothes Are Us.
The original price is $200 and its sale price is $150. So you save 200-150 = 50 dollars.
Divide that over the original price to find the discount: 50/200 = 0.25 = 25%
Therefore, Clothes Are Us has the same discount percentage as Jacket World. Both have a 25% discount. Choice D is true.
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2. in the expression 9 to the power of -12, what does
the negative exponent mean?
Answer:
Step-by-step explanation:
x^-n = 1/x^n
The negative exponent means means raise the reciprocal to the nth power
Solve the inequality for the smallest integer that would satisfy the given inequality
-x+2<3x-6
Step-by-step explanation:
-x+2<3x-6
-x-3x< -6-2
-4x < -8
-x < -2
When sign changes , inequality sign changes
x > 2
Step-by-step explanation:
-x + 2 < 3x - 6
8 < 4x
2 < x
so, the smallest integer that makes that true is therefore x = 3.
Find the volume of the cylinder. Round your answer to two decimal places
Answer:
565.48
Step-by-step explanation:
Volume for a cylinder equation: V=π(r²)h
π(3²)20 = 565.48cm³
Lesson 14 Introduction
Solutions of Linear Equations
Use What You Know
You've learned how to solve linear equations and how to check your solution. In this
lesson, you'll learn that not every linear equation has just one solution. Take a look
at this problem.
Jason and his friend Amy are arguing. Jason says that a linear equation always has just one
solution. Amy says that some linear equations have more than one solution. Who's right?
Amy asked Jason to explore solutions to the following equation
2x + 1 + x = 3x - 2)+7
Use the math you already know to solve this problem.
Remember that a solution to an equation is a number that makes the equation true.
To check to see if a number is a solution to this equation, replace x with its value.
a. Is 6 a solution to the equation? Show your work
b. Is -2 a solution to the equation? Show your work. 2X
c. Is 0 a solution to the equation? Show your work.
2(-2) + 1 + (-2) = 3(-2 - 2) + 7
-4 + 1 -2 = 3(-4) + 7
-3 - 2 = -12 + 7
-5 = -5
Yes
cual es el numero que aumentado en 16 da 46
Answer:
i think that it is 30 i'm not so sure
Step-by-step explanation:
PLEASE ANSWER THIS QUESTION!!!
The power, P (watts), of a car engine is proportional to the square of its speed, s (m/s).
When s=35, P=2200.
Work out the power (to 1 DP) when the speed is 40 m/s
Answer:
THE ANSWER!!!!!!!!!!
Step-by-step explanation:
The power, P (watts), of a car engine is proportional to the square of its speed, k%28m%2Fs%29; it means if you have two different powers and speeds, you will have a proportion
P%3Ak%5E2=P%5B1%5D%3Ak%5B1%5D%5E2 or
P%2Fk%5E2=P%5B1%5D%2Fk%5B1%5D%5E2
When given:
k=35, P=2200
Work out the power P%5B1%5D (to 1DP) when the speed is k%5B1%5D=40%28m%2Fs%29
so,
P=2200
k=35
k%5B1%5D=40
and you need P%5B1%5D
2200%2F35%5E2=P%5B1%5D%2F40%5E2
2200%2F1225=P%5B1%5D%2F1600
1.79592=P%5B1%5D%2F1600
1.79592%2A1600=P%5B1%5D
P%5B1%5D=2873.5 watts