Write a quadratic function in standard form whose graph has the given characteristics.
Answers
The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8.
What is a quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.
The standard form of a quadratic equation in vertex form is given as,
y = a(x-h)² + 8
Where (h,k) is the coordinate of the vertex and a is constant.
Given the vertex (h,k) = (-1,8)
Substitute, vertex, and (0,2)
2 = a(0 + 1)² + 8
a = -6
Therefore, the equation converts as,
y = -6(x+1)²+8
Hence "The standard form of the quadratic function with vertex (-1,8) and passing through point (0,2) is y = -6(x+1)²+8".
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Related Questions
Consider the graph of the function f. a) Find the domain, range, and zeros of the function. b) write an equation for the function f. (In vertex form, standard form, or intercept form)c) compare the graph of f to the graph of g(x) = x^2.
Answers
Solution:
Given the graph;
(a) The domain of a function is the set of values for which the function is real and defined. Thus, the domain D is;
[tex]\begin{gathered} (-\infty,\infty) \\ D:All\text{ }real\text{ }numbers \end{gathered}[/tex]The range is;
[tex]y\leq8[/tex]The zeros of the function are the points y=0;
[tex]x=1,x=5[/tex](b) The equation of a parabola in vertex form is;
[tex]\begin{gathered} y=a(x-h)^2+k \\ Where\text{ }(h,k)\text{ is }the\text{ }vertex; \\ and\text{ }given\text{ }(1,0) \\ \\ 0=a(1-3)^2+8 \\ \\ -8=4a \\ \\ a=-2 \\ \\ \end{gathered}[/tex]Thus, the equation is;
[tex]y=-2(x-3)^2+8[/tex](c) Using the graph below;
The graph of g(x) has its intercept at (0,0).
The transformation goes as;
Vertical stretch 2units, reflection over the x-axis, horizontal shift to the the right 3 units, vertical shift up 8 units
Using (5,0);
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 0=a(5-3)^2+8 \\ 4a=-8 \\ \\ a=-2 \end{gathered}[/tex]I'll give brainliest!
Answers
The scientific notation is [tex]5.72 * 10^{6}[/tex]
Factor out 1 of the powers of 10
[tex]= (5.5 * 10^{6}/10^{6} + 2.2 * 10^{5}/10^{6}) * 10^{6}[/tex]
Perform division of exponents:
[tex](5.5 * 10^{0} + 2.2 * 10^{-1}) * 10^{6}[/tex]
Convert Scientific notations to real numbers:
[tex]= (5.5 + 0.22) * 10^{6}[/tex]
Combine real numbers:
[tex]= (5.72) * (10^{6})[/tex]
Convert to proper Scientific notations:
[tex]= 5.72 * 10^{6}[/tex]
Manually check answer
= (5.5 x 1000000) + (2.2 x 100000)
= 5500000 + 220000
= 5720000
[tex]= 5.72 * 10^{6}[/tex]
What are Scientific notations?
Scientific notation is a way to display extremely big or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place following the decimal. This makes it challenging to express a small number of integers in their enlarged form. We thus employ scientific notations. Learn general forms for numbers as well.
Rules for Scientific Notation
We must adhere to the following rule in order to calculate the power or exponent of 10:
The base must always be 10.
Exponents that are non-zero integers must be either positive or negative in order to be used.
The coefficient's absolute value is more than or equal to 1, but it must be less than 10.
Positive and negative numbers, including whole and decimal values, can be coefficients.
The remaining significant digits of the number are represented by the mantissa.
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Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets ofcardboard from which she cuts out 2-in squares from eachPLEASE CHECK PHOTO
Answers
Solution:
Given:
When the cardboard is folded to become a box (cuboid), it will have the following dimensions after the cut of squares from each corner;
[tex]\begin{gathered} l=(x+4)-2-2=x+4-4=x \\ w=x-2-2=x-4 \\ h=2 \\ \\ The\text{ volume }V=792in^3 \end{gathered}[/tex]The volume of a cuboid is given by;
[tex]\begin{gathered} V=lwh \\ 792=(x)(x-4)(2) \\ Dividing\text{ both sides by 2;} \\ \frac{792}{2}=x(x-4) \\ 396=x^2-4x \\ \\ Collecting\text{ all sides to one side to form a quadratic equation;} \\ 0=x^2-4x-396 \\ x^2-4x-396=0 \end{gathered}[/tex]Solve the quadratic equation by factorization;
[tex]\begin{gathered} x^2-4x-396=0 \\ x^2+18x-22x-396=0 \\ x(x+18)-22(x+18)=0 \\ (x-22)(x+18)=0 \\ x=22,x=-18 \\ \\ Since\text{ the dimension of a box can not be negative, then;} \\ x=22in \end{gathered}[/tex]Hence, the dimension of the original piece of cardboard is;
[tex]\begin{gathered} (x+4)\text{ by }x \\ \\ Substitute\text{ the value of x, the dimension of the cardboard is;} \\ (22+4)\text{ by }22 \\ 26in\text{ by }22in \end{gathered}[/tex]Therefore, the dimensions of the original piece of cardboard are 26 in by 22in
The graph of a line passes through the two points (-2, 1) and (2, 1). What is the equation of the line written in general form?answers:•x+y1=0•y-1=0•x-y+1 = 0
Answers
We will have the following:
First, we find the slope:
[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]So, the equation that represents the line is:
[tex]y=1[/tex]So:
[tex]y-1=0[/tex]***Explanation***
We are given the points (-2, 1) & (2. 1).
From this we cans see that the line passes both times through y = 1.
We also know that the slope (m) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So the slope for this line will be:
[tex]m=\frac{1-1}{2-(-2)}\Rightarrow m=0[/tex]Now, we also know that the equation of the line in general form is given by:
[tex]y-y_1=m(x-x_1)[/tex]So, the equation of the line will be given by:
[tex]y-1=(0)(x+2)\Rightarrow y-1=0[/tex]So the function is a constant value, thus a horizontal line.
***Explanation for the general form of a line***
The general form of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]Here "x" & "y" are two variables; "x1" & "y1" are the component of a point that belongs to that lline and "m" is the slope of that line. We remember that (x1, y1) can be any point that belongs to the line.
So, we simply replace the values, in our case I willl solve for (-2, 1), but we could also use (2, 1), the solution at the end will be the same.
So:
[tex]y-(1)=(0)(x-(-2))\Rightarrow y-1=0\cdot x+0\cdot2[/tex][tex]\Rightarrow y-1=0[/tex]How many solutions does the equation 6z − 3z − 7 = −2 + 3 have? (5 points)TwoNoneInfinitely manyOne
Answers
Answer:
One solution.
Explanation:
Let us try to solve the equation and see how many solutions it has.
The first step in solving the equation is to first simplify both the right-hand and the left-hand sides. This means adding all the like terms.
[tex]\begin{gathered} 6z−3z−7=−2+3 \\ \Rightarrow3z-7=1 \end{gathered}[/tex]Next, we add 7 to both sides. This gives
[tex]3x-7+7=1+7[/tex][tex]3x=8[/tex]dividing both sides by 3 gives
[tex]\boxed{z=8/3.}[/tex]which is exactly one solution!
Therefore, our equation had one solution.
Write the equation of the line that passes through the points (4, -1)
and (3,-2).
Ox+y = -5
O y = x-5
O y = -x +3
Oy - 3x + 13
Answers
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Given points:
(x₁, y₁) = (4, -1)(x₂, y₂) = (3, -2)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{-2-(-1)}{3-4}=\dfrac{-1}{-1}=1[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Point-slope Formula}\\\\$y-y_1=m(x-x_1)$\\\\where $m$ is the slope and\\ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and the point (4, -1) into the point-slope formula to create the equation of the line:
[tex]\implies y-(-1)=1(x-4)[/tex]
[tex]\implies y+1=x-4[/tex]
[tex]\implies y+1-1=x-4-1[/tex]
[tex]\implies y=x-5[/tex]
Determine wether y varies directly with x. If so find the constant of variation k and write the equation
Answers
The given data is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
What is defined as the direct variation?A simple connection between two variables is described by direct variation. If y=kx, we say it varies significantly with x (or even as x in some textbooks) for some constant k, known as the constant of variation or the constant of proportionality.Because y varies directly with x, it would fit a equation y=kx for each and every point with in set.We may have 11=7k for the initial point, implying that k=11/7.
Again for second point, we'd have 13=8k, which means k=13/8.
Using proportions, we can see that 11/7 doesn't really equal 13/8: cross multiply and you get 11*8=7*13, or 88=91.
Thus, this is incorrect, k does not constitute a constant, but rather y does not varies directly to x.
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The complete question is-
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
x y
7 11
8 13
9 15
10 17
What is the slope of a line perpendicylar to the line whose equation is 5x - 6y = 30 Fully simplify your answer.
Answers
Answer:
-6/5
Step-by-step explanation:
[tex]5x-6y=30 \\ \\ 6y-5x=-30 \\ \\ 6y=5x-30 \\ \\ y=\frac{5}{6}x-5[/tex]
Perpendicular lines have negative reciprocal slopes, so the answer is -6/5.
find the remainder for the given division. (z^2+3z+1)/(z-2)
Answers
Explanation
Given the expression
[tex]\frac{z^{2}+3z+1}{z-2}[/tex]We are asked to find the remainder. We can use the remainder theorem. This can be seen below.
According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn't essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.
All we need to do is to substitute the value of (a) in the numerator to get the remainder. a is represented in the denominator.
Therefore, we will have;
[tex]\begin{gathered} \text{ Remainder =}2^2+3(2)+1 \\ =4+6+1 \\ =10+1 \\ =11 \end{gathered}[/tex]
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answers
The equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
What exactly are equations?A mathematical formula known as an equation is one in which two expressions with the same value are separated by the "equal to" sign. For instance, 3x plus 5 equals 15.There are numerous kinds of equations, including linear, quadratic, cubic, and others. The slope-intercept form, standard form, and point-slope form are the three main types of linear equations.So, the equation for P will be:
Let, P be the total money earned when Madeline sells the 'x' number of computers.Let, 80 be the constant as that is the basic pay.Let, 'x' be the number of computers Madeline sells.Now, the equation can be:
P = 20x + 80(Refer the table attached below)
Therefore, the equation that calculates the total pay of Madeline when she sells 'x' number of computers is "P = 20x + 80".
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Find Sin A, Cos A, Sin B, and Cos B for the following. Enter answers as fractions in simplest form, not decimals.
Answers
Answer:
[tex]\begin{gathered} \sin A=\frac{\sqrt[]{6}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Explanation:
Let x represent unknown side length
We can go ahead and find x using the Pythagorean Theorem as seen below;
[tex]\begin{gathered} (5\sqrt[]{3})^2=5^2+x^2 \\ (25\times3)=25+x^2 \\ 75-25=x^2 \\ 50=x^2 \\ x=\sqrt[]{50}=\sqrt[]{25\times2}=\sqrt[]{25}\times\sqrt[]{2}=5\sqrt[]{2} \\ x=5\sqrt[]{2} \end{gathered}[/tex]Let's find sin A as seen below;
[tex]\begin{gathered} \sin A=\frac{opposite}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \sin A=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \sin A=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]Let's find cos A as seen below;
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \cos A=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \cos A=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find sin B as seen below;
[tex]\begin{gathered} \sin B=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{5\sqrt[]{3}} \\ \sin B=\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3} \\ \sin B=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]Let's find cos B as seen below;
[tex]\begin{gathered} \cos B=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{5\sqrt[]{2}}{5\sqrt[]{3}} \\ \cos B=\frac{\sqrt[]{2}}{\sqrt[]{3}}=\frac{\sqrt[]{2}\times\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{6}}{3} \\ \cos B=\frac{\sqrt[]{6}}{3} \end{gathered}[/tex]write the equation of the line that passes through the given points.
(4, 0) and (0, 2)
Answers
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First find the gradient. Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).
Gradient = (2-0)÷(0-4) = -1/2
Equation of line is y = -1/2x + c
Substitute either one of the points into the equation to find c.
0 = -1/2(4) + c
c = 2
Hence, the equation of the line is y = -1/2x + 2.
Carly has twice as many sisters as Connor.
Connor has twice as many sisters as Alicia.
Alicia has 3 sisters.
How many sisters does Carly have?
Answers
Answer:
12
Step-by-step explanation:
Alicia has 3 sisters.
Connor has twice as many sisters.
Twice means "two times".
Connor has 2×3, that is 6 sisters.
Carly has twice (two times) as many sisters as Connor.
Carly has 2×6, or 12 sisters.
What is the LCM of 9 and 15?
Answers
What is the LCM of 9 and 15?
we know that
9=(3^2)
15=(3)(5)
so
the LCM=(3^2)(5)=45
the answer is
LCM=453^2=3*3=91. It costs $9.81 for 9 pounds of grapefruit. How much would it cost for 1 pound of grapefruit?
Answers
9.81 / 9 = 1.09
$1.09
Answer:
the anser is 1.09
Step-by-step explanation:
9.81 divided by 9 = 1.09
A 25 ft ladder is leaning against a building.The base of the ladder is 6 ft away from the building.How high up is the ladder?
Answers
Applying the Pythagorean Theorem, the ladder's height from the ground is: 24.3 ft.
How to Apply the Pythagorean Theorem?If we know any two sides of a right triangle, the Pythagorean Theorem can be used to find the length of the third side, c, if c is the longest side, and a and b are the shorter sides of the right triangle, we ill have the equation:
c² = a² + b².
The ladder forms a right triangle with the wall of the building. Therefore:
c = length of the ladder = 25 fta = distance of base of the ladder from the building = 6 ftb = how high the ladder is up on the wall of the buildingSubstitute
25² = 6² + b²
b = √(25² - 6²)
b = 24.3 ft.
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The first term of an Ap is 5 and the common difference is-3/2 Find the term whose value is 201/2
Answers
The term in the AP whose value is 201 / 2 is 71.3.
How to find the term in an arithmetic progression?The first term of an arithmetic progression is 5 and the common difference is - 3/2.
The formula of the arithmetic progression can be described as follows:
nth term = a + (n - 1)d
where
a = first termn = number of termsd = common differenceTherefore, using the arithmetic progression formula,
a = 5
d = 3 / 2
nth term = 201 / 2
let's find the term(n)
Therefore,
- 201 / 2 = 5 + (n - 1) - 3 / 2
- 201 / 2 = 5 - 3 / 2 n + 3 / 2
- 201 / 2 - 3 / 2 - 5 = - 3 / 2 n
- 107 = -3 / 2 n
-3n = - 214
n = 214 / 3
n = 71.3
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is this triangle possible?
Answers
Answer: The triangle is not possible.
Step-by-step explanation:
1) Find the missing angle
62+59+x=180
x=59
2) Use the Law of Sine to check if the triangle sides are the same.
The Law of sine means that Sine the angle and divide with the side across it will equal to same.
[tex]\frac{sin(x)}{x} =\frac{sin(y)}{y}[/tex]
Substitute the numbers.
[tex]\frac{sin(59)}{10} =\frac{sin(62)}{10}[/tex]
0.0636 = -0.0739
3) Solve
Since the decimals aren't the same, the triangle is not possible.
Find the slope of the linear regression line for the given data below. Round your
answer to two decimal places.
x y
2 25
3 19
48
5 11
6 15
7 14
Round your final result to two decimal places.
Answers
Answer:
hey bro listen
Step-by-step explanation:
you can't always
get the answers
here try to
do yourself and
see your potential.
Write the equation of a line in the form y=Mx+b that passes through the point (3,6) and has a slope of -2/3. Sketch this line
Answers
could you please help me out with a question
Answers
of the circumference is 21.2, we get that the diameter is
[tex]d=\frac{21.2}{\pi}\approx6.75[/tex]and therefore the radius is
[tex]r=3.37[/tex]three fifths of thr tshirts in a tshirt shop are on sale. five eighths of those tshirts are on sale. one third of those blue tshirts that are on sale are size medium. what fraction of the shops tshirts are blue tshirts that are on sale and are size medium? explain
Answers
3/5 of the T-shirts of the shop are on sale
5/8 of those on sale are blue
1/3 of the blue shirts on sale are medium size.
First calculate how many of the shirts on sale are blue:
[tex]\frac{5}{8}\frac{\div3}{5}=\frac{5}{8}\cdot\frac{5}{3}=\frac{25}{24}[/tex]25/24 of the shirts on sale are blue
Then divide that number by three to know how many are medium size:
[tex]\frac{25}{24}\div3=\frac{25}{72}[/tex]25/72 are blue and medium size
Find the values of x and y in the following right triangle. Enter square roots not decimals.
Answers
Recall the following trigonometric identities. If the legs of the right triangle have lengths a and b, the hypotenuse has length c, and the side a is adjacent to an angle θ, then:
[tex]\begin{gathered} \sin \theta=\frac{b}{c} \\ \cos \theta=\frac{a}{c} \end{gathered}[/tex]Then, for the given right triangle:
[tex]\begin{gathered} \sin (30º)=\frac{x}{8} \\ \cos (30º)=\frac{y}{8} \end{gathered}[/tex]Then, x and y are given by the expressions:
[tex]\begin{gathered} x=8\cdot\sin (30º)=8\cdot\frac{1}{2}=4 \\ y=8\cdot\cos (30º)=8\cdot\frac{\sqrt[]{3}}{2}=4\cdot\sqrt[]{3} \end{gathered}[/tex]Therefore, the answers are:
[tex]\begin{gathered} x=4\cdot\sqrt[]{3} \\ y=4 \end{gathered}[/tex]Write an equation that says that the length of the green line is equal to the length of theblack line. Combine like terms
Answers
Explanation:
Length of green line = length of black line
Length of green line = 26
Total length of black line = h + h + *
Total length of black line = 2h + 8
Equate the two expressions
26 = 2h + 8
Collect the like terms
26 - 8 = 2h
18 = 2h
Isolate h by dividing both sides by 2
18/2 = 2h/2
h = 18/2
h = 9
The equation is 26 = 2h + 8
In a jar there are 65 red, 154 yellow and 70 green beads. You extract 54 beads at random.
Estimate the number of red beads obtained.
Answers
The number of red beads obtained from the jar is 12 beads.
How many red beads obtained?The number of red beads that can be obtained from the jar is the ratio of red beads to the total number of beads multiplied by the total number of beads picked at random.
Number of red beads obtained = (number of red beads / total number of beads) x number of beads picked
Total number of beads = 65 + 154 + 70 = 289
Number of red beads obtained = (65 / 289) x 54 = 12.14 ≈ 12 beads
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Fill in the blank to make equivalent rational expressions.
2/y^2=_/3y^5
Answers
The expression that can complete the blank is 6y^3
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to complete the blanks?The expression is given as
2/y^2=_/3y^5
Replace the blank with x
So, we have
2/y^2 = x/3y^5
Multiply both sides of the equation by 3y^5
So, we have
x = 3y^5 * 2/y^2
Evaluate the products
x = 6y^3
This means that the blank is 6y^3
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We have to find two partial products to add 513×46
Answers
Answer
Explanations:
The product of two integers using the partial product is expressed using the distributive law as shown:
[tex]513\times46=(500+13)\times(40+6)[/tex]Expanding the result using the distributive law as shown;
[tex]undefined[/tex]Samantha borrowed money to buy lawn equipment to start her new lawn service business. She borrowed $800 for 9 months and paid $70.50 in interest. What was the rate of interest.
Answers
Using simple interest, the rate of interest on the amount that Samantha borrowed to buy the law equipment is 11.75%.
What is the simple interest?A simple interest system does not accumulate (compound) interest on both the principal and interest, unlike compound interest.
The simple interest uses the following formula, Interest = Principal x Rate x Period.
This simple interest formula can be reversed to find either the principal, rate, or period, as the case may be.
The loan amount = $800
Period of loan = 9 months
Total interest paid = $70.50
Rate of interest = (Interest × 100)/(Principal × Time)
= 11.75% ($70.50 x 100)/($800 x 9/12)
Check:
Interest = $70.50 ($800 x 11.75% x 9/12)
Thus, Samantha's interest rate on the loan is 11.75%.
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QUIK ANSWER PLEASE!!! Solve the equationy^3 - 27 = 9y^2 - 27y
Answers
The first step is to simplify both sides of the equation. The equation can be written as
y^3 - 3^3 = 9y(y - 3)
For the left hand side, we would apply the difference of two cubes formula. it is expressed as
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
By comparing with the left hand side of the equation,
x = y and y = 3. It becomes
(y - 3)(y^2 + 3y + 3^2)
= (y - 3)(y^2 + 3y + 9)
The equation becomes
(y - 3)(y^2 + 3y + 9) = 9y(y - 3)
If we divide both sides of the equation by (y - 3), it becomes
(y - 3)(y^2 + 3y + 9)/(y - 3 = 9y(y - 3)/(y - 3)
y^2 + 3y + 9 = 9y
y^2 + 3y - 9y + 9 = 0
y^2 - 6y + 9 = 0
We would solve the quadratic equation by applying the method of factorisation. We would find two terms such that their sum or difference is - 6y and their product is 9y^2. The terms are - 3y and - 3y. The equation becomes
y^2 - 3y - 3y + 9
y(y - 3) - 3( y - 3) = 0
(y - 3)(y - 3) = 0
y - 3 = 0 twice
y = 3 twice
Identify the graph of the ellipse given by the equation below.
Answer options are also attached :)
Answers
The required graph below which represents the given equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1. Which is the correct answer would be option (C).
What is an ellipse?An ellipse can be defined as a shape that looks like an oval circle.
The equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1 which is given in the question.
An asymptote is a line that a curve approaches, but never touches. Find the horizontal, vertical, and oblique asymptotes.
Center of the ellipse : (−7,5)
Vertex 1: (0,5)
Vertex 2: (−14,5)
We have attached the required graph below which represents the given
equation of the ellipse is (x +7)²/49 + (y-5)²/25 = 1.
Hence, the correct answer would be an option (C).
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