How to get the equation of a parabola with 3 pointsy- intercept : (0, -1.4)x-intercept : (0.905,0)3rd point: (2,0.6)
Answers
he standard form of a quadratic efunctionis:
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{Where } \\ a,b,\text{ and }c\text{ are real constants such that }a\ne0. \end{gathered}[/tex]Since the y-intercept is (0, -1.4), it follows that:
[tex]\begin{gathered} -1.4=a(0)^2+b(0)+c \\ \text{ Therefore,} \\ c=-1.4 \end{gathered}[/tex]Substitute c = -1.4 into the equation:
[tex]y=ax^2+bx-1.4[/tex]Since the x-intercept is (0.905, 0), it follows that:
[tex]\begin{gathered} a(0.905)^2+b(0.905)-1.4=0 \\ \text{Therefore,} \\ 0.819025a+0.905b=1.4-------(1) \end{gathered}[/tex]Since the graph passes through the third point (2, 0.6), it follows that:
[tex]\begin{gathered} 0.6=a(2)^2+b(2)-1.4 \\ \text{Therefore} \\ 4a+2b-1.4=0.6 \\ 4a+2b=0.6+1.4_{} \\ 4a+2b=2 \\ \text{Divide both sides by }2 \\ 2a+b=1 \\ \text{Hence} \\ b=1-2a---------(2) \end{gathered}[/tex]Substitute equation (2) into equation (1):
[tex]\begin{gathered} 0.819025a+0.905(1-2a)=1.4 \\ 0.819025a+0.905-1.81a=1.4 \\ \text{ Collect like terms:} \\ 0.819025a-1.81a=1.4-0.905 \\ -0.990975a=0.495 \\ \text{ Therefore,} \\ a=\frac{0.495}{-0.990975} \\ a\approx-0.5 \end{gathered}[/tex]Substitute a = -0.5 into equation (2), therefore,
[tex]b=1-2(-0.5)=1+1=2[/tex]Therfore the function is given by:
[tex]y=-0.5x^2+2x-1.4[/tex]The equation of the parabola is y = -0.5x² + 2x - 1.4
.
Related Questions
The cost of 8 shirts is $72 find the cost of 12 shirts
Answers
Answer: $108
Step-by-step explation:
It takes 4 cups of sugar to make 6 batches of cookies. How many cups of sugar is needed for 15 batches of cookies?
Answers
Answer:
10 cups
Step-by-step explanation:
6 divided by 4 is 1.5 and if you take 15 divided by 1.5 it'd be 10
Answer:
10 cups of sugar
Step-by-step explanation:
you can easily make it into a ratio.... ( the amountof sugar needed to make 15 batches of cookies is x)
x/15 = 4/6
when you multiply you get 6x = 4 × 15
6x = 60, then you divide by 6
giving you x=10
Please help with number 8 step by step
Answers
Answer:
It is a function because circles are functions
Step-by-step explanation:
the formula for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h,k) = center
r=radius
radius is 4 because diameter is 8
Center is (2,1)
plug it into the equation:
[tex](x-2)^2+(y-1)^2=16[/tex]
Which of the following are the coordinates of point F' , the image of point F, after a rotation of 90° about (1 point)
the origin?
Answers
Answer:
(3, 0)
Step-by-step explanation:
I assume this means a clockwise rotation.
let's think this through logically :
the last option (0, 3) cannot be right, because that is F before the rotation. to go back to the original position requires a full rotation of 360° (remember, a circle has 360°, and that means to travel one complete time around the circle).
(0, -3) cannot be right, because this is just mirrored down, and would represent a turn of 180° (a half-circle).
for the other options imagine you use a math compass, put the pin on the origin, and the writing arm on F. and the you draw a circle through F.
(3, 0) is the result of the clockwise (right) turn of 90°, (-3, 0) would be the result of a counterclockwise (left) turn of 90°.
so, if my assumption above is incorrect, please pick (-3, 0) for the counterclockwise solution.
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)[tex]z = x^{7}y^{7}, x = s cos(t), y = s sin(t)[/tex]
Answers
Applying the Chain Rule, the derivatives are given as follows:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex][tex]\frac{\partial z}{\partial t} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]What is the derivative of Z as a function of s?
The function Z is defined as follows:
z = x^7y^7.
The variables x and y are functions of variables s and t, as follows:
x = s cos(t).y = s sin(t).Hence the derivative of z as a function of s is given as follows:
∂z/∂s = (dz/dx)(dx/ds) + (dz/dy)(dy/ds).
Hence, applying the derivative rules for the exponents, and for the exponents, we have that:
[tex]\frac{\partial z}{\partial s} = 7x^6y^7\cos{(t)} + 7y^6x^7\sin{(t)} = 7x^6y^6(y\cos{t} + x\sin{t})[/tex]
Replacing the values of x and y, we have that:
[tex]\frac{\partial z}{\partial s} = 7(s\cos{t})^6(s\sin(t))^6(y\cos{t} + x\sin{t})[/tex]
What is the derivative of Z as a function of t?We follow the same logic as above, only that now the inside derivatives, that is, the derivatives of x and y, are as function of t and not of s, hence:
∂z/∂t = (dz/dx)(dx/dt) + (dz/dy)(dy/dt).
Then:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7sx^6y^6(-y\sin{t} + x\cos{t})[/tex]
Then, replacing x and y as functions of s and t, we have that:
[tex]\frac{\partial z}{\partial t} = -7x^6y^7s\sin{(t)} + 7y^6x^7s\cos{(t)} = 7s(s\cos{t})^6(s\sin{t})^6(-y\sin{t} + x\cos{t})[/tex]
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El volumen de un cubo que tiene como arista 14 cm es?
1000 cm3
2.744 cm3
216 cm3
Answers
The volume of the cube is 2744 cm³.
QuadrilateralsThere are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square all angles are 90° and all sides present the same value.
A square is a 2D figure, when the square is associated a 3D figure, the figure is called a cube. The cube presents 6 faces with length (l) , height (h) and width (w) equal. Thus, the cube presents congruent edges.
The volume is given from the formula V=a³, where a is a congruent edge.
The question gives:
edge=14 cmTherefore,
V=a³
V=14³
V=14*14*14
V=2744 cm³
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A hat costs $10.95 and a T-shirt costs $14.20. How much change will you receive if you pay for both items with a $50 bill?
Pls give a good explanation
Answers
Answer: $24.85
Step-by-step explanation:
10.95+14.20= 25.15
25.15+24.85= 50
Answer:
24.35
Step-by-step explanation:
Add 10.95 to 14.20:
10.95+14.20=25.15
Then subtract the answer 25.15 from 50
50-25.15=24.35
The Omicron Model 99 television costs $450. During a special sale, it’s marked 1⁄3 off. How much money will you save buying this TV on sale?
Answers
Answer:
225
Step-by-step explanation:
if it is 1/3 off, then it means it's at 2/3 the price. now, you have to divide 450/2 to get the answer. 2/3 divided by 2=1/3
450/2=225, and thats how much money you will save
Every month, Omar buys baskets of wings to serve at a party for his friends. In May, he bought three more than twice the number of baskets of wings he bought in April. If Omar bought 15 baskets of wings in May, how many did he buy in April?
*Use distributive property*
Answers
Answer:
33
Step-by-step explanation:
If 6times a number is added to -3, then the results is equal to 9 times the number. Find the number
Answers
To determine the missing number:
[tex]\text{Let the missing number = x}[/tex][tex]\begin{gathered} 6\text{ times a number = 6x} \\ 6x+(-3)=9x \\ 6x-3=9x \end{gathered}[/tex]collect like terms
[tex]\begin{gathered} 6x-9x=3 \\ -3x=3 \\ \text{divide both side by -3} \\ -\frac{3x}{-3}=\frac{3}{-3} \\ x=-1 \end{gathered}[/tex]Therefore the missing number = -1
Simplifying a Rational Expression Simplify (a ^ 2 * b ^ 8)/(a ^ 2 * b ^ 3 - a ^ 4 * b ^ 2); (a * b ^ 2)/(1 - a ^ 4 * b ^ 2); (a ^ 3 * b ^ 8)/(a ^ 2 * b ^ 2 * (b - a ^ 2)); b/(1 - a); (a * b ^ 4)/(b - a ^ 2)
Answers
Answer:
ab^4/b-a^2
Step-by-step explanation:
...........
graph AgraphwebImaginary A3222Real342 3 4-123graphAe7in A22Reals+3212343a-44which graph depicts a complex number with as the imaginary partA graphOgraphCCgraph
Answers
Graph (D) shows a complex number with an imaginary component, i.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. Bar graphs, circle graphs, and line graphs are the three most frequently used types of graphs.Different types of data can be displayed using different types of graphs.So, we are aware that a complex number is shown as:
z= x+iyWhere x stands for a number's real value and y for a number's imaginary value.
Which stands for the point (x,y)As a result, the number I is written as:
z=0+1.iThis indicates that the symbol for the number I is a point (0,1).
Therefore, the number I has a value of 1 on the hypothetical axis.So, Graph D is the appropriate selection.Therefore, graph (D) shows a complex number with an imaginary component, i.
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The complete question is given below:
Which graph depicts a complex number with i as the imaginary part?
Please help I’ll mark you as brainliest if correct!
Answers
Answer:
21 Degrees.
Step-by-step explanation:
It was 22 degrees by noon, by then the temperature had already risen by
eight degrees, but since we are going back in time, we would subtract the eight degrees.
22 - 8 = 14.
Now we are at 9 A.M, it is 14 degrees. But, the temperature had doubled from 5-9 A.M, so we would divide our fourteen by two in order to half it.
14 ÷ 2 = 7.
Now we are at 5 A.M.
From midnight to 5 A.M the temperature dropped fourteen degrees so we would add that fourteen back into the equation.
7 + 14 = 21.
Hope this helped!!
Right triangle DEF is shown below.What is DF to the nearest tenth of a meter?
Answers
Answer: 25.1º
Explanation
As the given triangle is a right triangle, we can use trigonometric functions to find DF, specifically:
[tex]\cos x=\frac{adjacent}{hypotenuse}[/tex]where the adjacent is the side adjacent to our angle and the hypotenuse is the longest side (side opposite to the 90º angle).
Based on this, we can replace the values as follows:
[tex]\cos(23\degree)=\frac{DF}{27.3}[/tex]Solving for DF:
[tex]DF=27.3\cdot\cos(23\degree)[/tex][tex]DF=27.3\cdot\cos(23\degree)[/tex][tex]DF\approx25.1[/tex]Help pls!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
it should be 180
9 1/4 to 9
20 stays the same
Clancy has 423 cups of yogurt to share with his friends at a party. Each guest will receive 1 serving of yogurt which is 34 of a cup.
Write a multiplication equation to determine the number of people, p, who can be invited to the party.
Answers
Answer: Around 141 guests can be invited
Explanation: 423 divided by 3/4 is 141, and 141 x 3/4 is 423
2(64x² - 25) (x² + 49) = 0
Answers
Answer:
[tex]x=-7i, 7i, 5/8, -5/8[/tex]
Step-by-step explanation:
[tex](64x^2-25)(x^2+49)=0 \\ \\ (8x-5)(8x+5)(x+7i)(x-7i)=0 \\ \\ x=-7i, 7i, 5/8, -5/8[/tex]
simplify the expression -1.1 + (-3.9). On the test, when tom simplified the expression he got -2.8. What mistake did tom likely make when he simplified the expression?
Answers
Answer:
the answer is -5.0
Step-by-step explanation:
Tom subtracted -1.1 from -3.9 instead of adding them together
What is 581/14 in partial quotients?
Answers
The quotient of 581 and 14 has a value of 40.07
How to evaluate the expression using partial quotients?The quotient expression is given as
581/14
Next, we express 581 as the sum of a multiple of 14 and another number
Say 581 = 280 + 280 + 1
So, we have the following equation
581/14 = (280 + 280 + 1)/14
Expand the bracket
So, we have the following equation
581/14 = 280/14 + 280/14 + 1/14
Evaluate the quotients
581/14 = 20 + 20 + 0.07
Evaluate the sum
581/14 = 40.07
Hence, the value of the quotient expression is 40.07
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what are the domain and range of the function?
Answers
The domain and range are the set of all real numbers, so:
Domain: x ∈ R
Range: x ∈ R
Thus, the correct option is the second one
What are the domain and range of the function?
For any function y = f(x), we define the domain as the set of the possible values of x (the ones on the horizontal axis) and the range is the set of the possible values of y (vertical axis).
In this case, we have a linear equation (you can see that the lines extend to the bottom left and the top right)
So both domain and range are the sets of all real numbers.
Thus, the correct option is the second one.
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RS has endpoints R(-11, 10) and S(-6, -5). Point T divides RS such that ST:TR is 2:3.
What are the coordinates of T?
Write your answers as integers or decimals.
()
Answers
Check the picture below.
[tex]\textit{internal division of a line segment using ratios} \\\\\\ S(-6,-5)\qquad R(-11,10)\qquad \qquad \stackrel{\textit{ratio from S to R}}{2:3} \\\\\\ \cfrac{S\underline{T}}{\underline{T} R} = \cfrac{2}{3}\implies \cfrac{S}{R} = \cfrac{2}{3}\implies 3S=2R\implies 3(-6,-5)=2(-11,10)[/tex]
[tex](\stackrel{x}{-18}~~,~~ \stackrel{y}{-15})=(\stackrel{x}{-22}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-18 -22}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-15 +20}}{2+3} \right)} \\\\\\ T=\left( \cfrac{ -40 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies {\Large \begin{array}{llll} T=(-8~~,~~1) \end{array}}[/tex]
You put some money in a bank account one year ago. You have not done anything with it since. The bank takes out a low balance fee of $0.25 each month. After 8 months, you had $28 in the account. Choose the equation that best shows the money in your bank account over time. CLEAR CHECK Balance=−0.25⋅Months Balance−28=−0.25(Months−8) Balance−8=−0.25(Months−28) Balance−28=−0.25(Months+8)
Answers
Answer:
Step-by-step explanation:
Find the slope from the given table. Simplify your answer. Hint: Make Time (x) and Distance (y). Does it matter which two points you use? Type yes or no.
Answers
m = 15/8 and yes it dep
Here, we want to find the slope from the given table
Mathematically, that could be calculated using the formula;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ we\text{ can select any two points} \\ \\ \text{let us select the first and the last;} \\ \\ m\text{ = }\frac{17-2}{9-1}\text{ = }\frac{15}{8}\text{ } \end{gathered}[/tex]Now, we want to find out if it differs if we use any other random two points
Let us select the 1st and the 3rd point
Mathematically, the slope here would be;
[tex]m\text{ = }\frac{12-2}{6-1}\text{ = }\frac{10}{5}\text{ = 2}[/tex]From these, we can see that the value of the slope obtained depends on the two points that are selected
use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.
Answers
The two approximations of the region's area between the graph of the function and the x-axis over the given interval are 14.31 < AREA < 17.01
We have :
f(x) = 9 -x [ 2, 4 ], 6 rectangles.
Here, a = 2 and b = 4 , n = 6
The width of the rectangles will be
x' = [tex]\frac{b-a}{n}[/tex]
x' = [tex]\frac{4-2}{6} = \frac{2}{6} = \frac{1}{3} = 0.33[/tex]
Now, The given function is f(x) = 9 -x
[tex]f(x_{i}) = x_{i} - 9[/tex]
For [tex]x_{0} = 0[/tex], [tex]f(x_{0} ) = 9[/tex]
For [tex]x_{1} = 0.3[/tex], [tex]f(x_{1} ) = 9 -0.3 = 8.7[/tex]
For [tex]x_{2} = 0.6[/tex], [tex]f(x_{2} ) = 9 -0.6 = 8.4[/tex]
For [tex]x_{3} = 0.9[/tex], [tex]f(x_{3} ) = 9 -0.9 = 8.1[/tex]
For [tex]x_{4} = 1.2[/tex], [tex]f(x_{4} ) = 9 -1.2 = 7.8[/tex]
For [tex]x_{5} = 1.5[/tex], [tex]f(x_{3} ) = 9 -1.5 = 7.5[/tex]
For [tex]x_{6} = 2.1[/tex], [tex]f(x_{3} ) = 9 -2.1 = 7.2[/tex]
Now, The area by using an approximation using 6 approximating rectangles and right endpoints is given by.
A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6})x'\\[/tex]
A = (8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3
A = 47.7*0.3 = 14.31
The area by using an approximation using 6 approximating rectangles and left endpoints is given by:
A = Sum of [tex]f_{i}x'[/tex] = [tex](f_{0} + f_{1} + f_{2} + f_{3} + f_{4} + f_{5} + f_{6} } )x'\\[/tex]
A = (9+8.7 + 8.4 + 8.1 + 7.8 + 7.5 + 7.2)*0.3
A = 17.01
Thus 14.31 < AREA < 17.01
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A train travels along a straight piece of track between 2 stations
A and B. The train starts from rest at A and accelerates at
1.25m/s² until it reaches a speed of 20m/s. Find the distance
from A to B.
Answers
Answer:
v=20m/s ,u= 0m/s( from rest) a=1.25m/s Distance s=?
V²= UT +2as
make s subject
2as=v²-u²
S= v²-u²/2a
S =20²-0²/2*1.25
S=400/2.5
S= 160m
shade the portion of this figure that represents 14/4
Answers
14/4 = ?
There are 4x5 = 20 squares
Then 14/4 = 3 + 2/4
also 14/4 = 70/20 = 7/2
Take 14 squares, from figure
Now graph portion shade
A cashier has 35 bills, all of which are $10 or $20 bills. The total value of the money is $520. How many of each type of bill does the cashier have?
Answers
After solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
What do we mean by mathematical operations?A mathematical function called an operation, also known as an "operand" or "argument," transforms zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The operations that are most frequently studied are unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, and binary operations (i.e., operations of arity 2), such as addition and multiplication.An operation of arity zero also referred to as a nullary operation, is a constant.The mixed product is an illustration of an operation of arity 3, also referred to as a ternary operation.So, the total value of money by 35 bills is $0, and $20 is $520.
Now, we know that: 20 × 18 = 360Similarly, we know that: 10 × 16 = 160Sum of 360 and 160: 360 + 160 = $520So, 185 bills of $20 and 16 bills of $10.Therefore, after solving some mathematical operations we can conclude that the cashier has 16 bills of $10 and 18 bills of $20.
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Please help I’ll mark you as brainliest if correct!
Answers
The value of a, b, c and d are 25, 3, 14 and 7 such that the sum of all rows, columns and diagonals are 48.
Given to us a magic square in which the sum of all rows, columns and diagonals are same. Then, we have to complete the missing numbers i.e., a, b, c and d respectively.
Let's proceed to solve this magic square accordingly.
First let's calculate that what will be the sum of all rows, columns and diagonals.
From the figure of magic square one diagonal is completely filled from that we can easily calculate the sum of the diagonals.
Sum = 5+16+27 = 48
Then, we can find the value of a, b, c and d easily.
5+a+18 = 48
23+a = 48
a = 48-23
a = 25
Therefore, the value of a is 25.
29+16+b = 48
45+b = 48
b = 48-45
b = 3
Therefore, the value of b is 3.
Now, 5+29+c = 48
34+b = 48
c = 48-34
c = 14
Therefore, the value of c is 14.
Then, we have
c+d+27 = 48
14+d+27 = 48
41+d = 48
d = 48-41
d = 7
Therefore, the value of d is 7.
Hence, we have completed the magic square in which the sum of all rows, columns and diagonals are 48.
Therefore, the value of a, b, c and d are 25, 3, 14 and 7 respectively.
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Write an expression that represents the total owed for 3 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $25?
2(25) + c
25c + 3
3(c) + 25
3(c + 25)
Answers
The final expression that represent the total owed is 3c + 25
How to represent mathematical expression?He owed 3 months cable at a price of c dollars for each month, plus a one-time equipment fee of $25,
Therefore, the situation can be expressed as follows:
For a single month he pays c dollars
Hence, 3 month will be 3 × c.
Recall he also needs to pay a one time fees of 25 dollar.
Therefore, the final expression that represent the total owed is as follows:
total owed = 3c + 25
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Mariam wants to buy strawberries and apples to
make a fruit tart. Strawberries cost $3 per pound
and apples cost $3.25 per pound. How many pounds
of fruit does she buy if she buys 0.5 pounds of
strawberries and 3 pounds of apples? How many
pounds of fruit does she buy if she buys x pounds of
strawberries and y pounds of apples?
Answers
Answer:
Answer bellow with explanations
Step-by-step explanation:
if Miriam buys 0.5 pounds of strawberries and 3 pounds of apples she will in total would have bought 3.5 pounds of fruit.
if you are looking for the price she had to pay for the fruits above the equation to solve that is as following.
0.5 x 3$ = 1.5$
3.0 x 3.25 = 9.75$
total for the fruits needed above would be 1.5$ + 9.75$ = 11.25$
if you are looking for the amount of pounds converted into the amount of fruit
0.5/3$ = 0.16(6) pounds of strawberries
3/3.25$= 0.92307692307 pounds of apples
total of pounds of fruit that have been purchased is equal to 0.16(6) + 0.92307692307 = 1.08974358973 pounds
If Miriam buys x pounds of strawberries and y pounds of apples
it can be shown in an equation using 2 unknown values
X(strawberries)
Y(apples)
x/3$ + y/3.25$
to calculate the amount of pounds that have been purchased