Answers
We will investigate how to graph a straight line on cartesian coordinate plane.
All equations of straight line are expressed in a general slope-intercept form as follows:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ slope} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]To graph any straight line we need the equation of the straight line or atleast two points that must lie on the line.
We are given the slope ( m ) and one of the points that lie on the line as follows:
[tex]\begin{gathered} m\text{ = -}\frac{2}{5} \\ \\ (\text{ -3 , 5 )} \end{gathered}[/tex]We need one another point that lies on the line to plot the graph of a straight line. To find another point we must completely express the equation of the straight line ( general form given above ).
We see that an equation of a straight line is defined by two parameters i.e ( m and c ). We are given the value of the slope ( m ). We will go ahead and plug it into the general slope-intercept form given above:
[tex]y\text{ = -}\frac{2}{5}\cdot x\text{ + c}[/tex]Now to determine the value of parameter ( c ) we must have atleast one point that lies on the line. We will use the point given to us and plug in the respective coordinates in the equation developed above and solve for ( c ) as follows:
[tex]\begin{gathered} (\text{ x , y ) }\to\text{ ( -3 , 5 )} \\ \\ 5\text{ = -}\frac{2}{5}\cdot(-3)\text{ + c} \\ \\ 5\text{ = }\frac{5c\text{ + 6}}{5} \\ \\ 25\text{ = 6 + 5c} \\ \\ c\text{ = }\frac{19}{5} \end{gathered}[/tex]We will go ahead and update the equation of the straight line as follows:
[tex]y\text{ = -}\frac{2}{5}\cdot x+\frac{19}{5}[/tex]Now to get one more point to graph the plot we will assume any value of the for either variable ( x or y ) and then determine the value of the other variable as follows:
[tex]\begin{gathered} x\text{ = 2} \\ \\ y\text{ = -}\frac{2}{5}\cdot(2)\text{ +}\frac{19}{5} \\ \\ y\text{ = }\frac{-4+19}{5} \\ \\ y\text{ = }\frac{-15}{5} \\ \\ y\text{ = -3} \end{gathered}[/tex]Therefore, we have the two points to plot the graph as follows:
[tex](\text{ -3 , 5 ) \& ( 2 , -3 )}[/tex]We can go ahead and select the above points on the given grid to construct the straight line!
Related Questions
A coin is flipped and a spinner is spun.What is the sample space of the experiment?
Answers
The sample space is the set of all different outcomes that can show up from the experiment.
Flipping a coin has two possible outcomes: heads or tails.
Spinning the spinner has three possible outcomes: A, B or C.
Draw a tree diagram to represent the sample space:
If we represent results using ordered pairs, the sample space is:
[tex]\mleft\lbrace(H,A\mright),(H,B),(H,C),(T,A),(T,B),(T,C)\}[/tex]Where H stands for heads and T stands for tails.
use the figures below what shows that rectangles are not similar PS.THIS IS JUST HOMEWORK THAT I NEED HELP WITH
Answers
Answer is option A
Because the other side (AB) is 15 and the other rectangle (JM) is 10, so the realation between them is 15/10 = 3/2
But, since DC and ML relation is NOT 3/2, then the rectanlges are not similar
Which statement correctly compares the function shown on this graph with the function y = 3x - 6?
Answers
The plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + c
where -
[m] is slope of line
[c] is y - intercept
Given is a equation of a straight line and a graph of a straight line.
We have the following equation -
y = 3x - 6
For this equation, the slope of the straight line will be [m] = 3 and the y - intercept would be [c] = - 6. Refer to the graph attached with green color for all the possible set of solution.
Now, the equation of the line plotted on graph -
m = (4 - 0)/(0 + 1.3)
m = 3.07
m = 3 (approx.)
Its y - intercept [c] = 4
Therefore, the equation of the plotted line -
y = 3x + 4
Now, both the lines are plotted on the graph. It can be seen from the graph and from the equation that they have same slope and hence, both the lines are parallel to each other.
Therefore, the plotted function and the function y = 3x - 6 represent a straight line and have have same slope and hence, both the lines are parallel to each other.
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[The complete question needs the plotted graph. It is attached at the end of the answer]
Find the equation of a parabola with a focus of (0, 9) and directrix y = –9.
Answers
Answer:
Step-by-step explanation:
Given that,
To find the standard form of the equation of the parabola with a focus at (0, 9) and a directrix y = -9.
What is a parabola?
A parabola is a cross-section cut out of the cone and represented by an equation
Focus of the prabola = (h , k + F ) = (0, 9)
Since the directrix, y = -9
F = -9
k + F = 9
k = 0
Vertex of the parabola = (h, k )
= (0, 0)
Standard equation of the parabola
( y - k ) = 4a (x - h)²
( y - 0 ) = 4a (x - 0)²
y = 4 * 9 x²
y = 36 x²
Thus, the required expression for the parabola with focus at (0, -9) and a directrix y = 9 is y = 36x².
What is the ones digit in the number 2^2058. Hint: Start with the smaller exponents to find pattern
Answers
1) We need to find out a pattern for the powers that have a base 2:
[tex]\begin{gathered} 2^{1}=2 \\ 2^2=4 \\ 2^3=8 \\ 2^4=16 \\ 2^5=32 \\ 2^6=64 \\ 2^7=128 \\ 2^8=256 \\ (\ldots) \end{gathered}[/tex]Note that from 4 to 4 powers the last digit starts to repeat itself.
2) So, let's proceed with this dividing the exponent 2058 by 4:
Now, note that the remainder is 2, therefore we can state that:
[tex]2^{2058}=same\: ones\: digit\: as\colon2^2=4[/tex]QuestionWhich of the following expressions is equivalent to the verbal expression 'the quotient of 23x and 15t'?Select the correct answer below:23x · 15115123x0 23x + 151
Answers
Explanation
The quotient is the number obtained by dividing one number by another
for example:
the quotient of a and b is
[tex]a\text{ divided by b=}\frac{a}{b}[/tex]so
Step 1
Let
number 1=23x
number 2=15 t
so, the quotient would be
[tex]\frac{23x}{15t}[/tex]therefore, the answer is C:
[tex]\frac{23x}{15t}[/tex]I hope this helps you
Find an equation for the perpendicular bisector of the line segment whose endpoints are (3, -8) and (7,2).
Answers
ANSWER
[tex]y=-\frac{2}{5}x-1[/tex]EXPLANATION
We want to find the equation of the perpendicular bisector of the line segment with the given endpoints.
To do this, we first have to find the slope of the given line, since the slope of a line perpendicular to a given line is the negative inverse of the slope of the line.
Then, we have to find the midpoint of the given line since the line is a bisector, it passes through the midpoint of the given line segment.
To find the slope of the line, apply the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are the two endpoints of the line segment
Hence, the slope of the line is:
[tex]\begin{gathered} m=\frac{2-(-8)}{7-3}=\frac{2+8}{7-3} \\ m=\frac{10}{4} \\ m=\frac{5}{2} \end{gathered}[/tex]The negative inverse of this is:
[tex]\begin{gathered} -(\frac{1}{\frac{5}{2}}) \\ \Rightarrow-\frac{2}{5} \end{gathered}[/tex]To find the midpoint of the endpoints, apply the formula for midpoint:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Hence, the midpoint of the given endpoints are:
[tex]\begin{gathered} (\frac{3+7}{2},\frac{-8+2}{2}) \\ \Rightarrow(\frac{10}{2},\frac{-6}{2}) \\ \Rightarrow(5,-3) \end{gathered}[/tex]Now, we have the slope and an endpoint of the perpendicular bisector.
To find the equation of the line, we have to apply the point-slope method:
[tex]y-y_1=m(x-x_1)[/tex]Therefore, the equation of the perpendicular bisector of the line segment is:
[tex]\begin{gathered} y-(-3)=-\frac{2}{5}(x-5) \\ y+3=-\frac{2}{5}x+2 \\ y=-\frac{2}{5}x+2-3 \\ y=-\frac{2}{5}x-1 \end{gathered}[/tex]Last year, Tammy opened an investment account with $8200 . At the end of the year, the amount in the account had decreased by 7.5% . How much is this decrease in dollars? How much money was in her account at the end of last year?
Answers
1. The decrease in dollars, based on a 7.5 percent decrease, is $615.
2. The balance in the account at the end of last year was $7,585.
What is a percentage?A percentage is a ratio or proportion of a variable in another.
For instance, the percentage decrease in the investment account was 7.5%, which in dollar terms amounts to $615.
The percentage reference gives an idea of the investment status and the fractional effect that the decrease had on it.
Initial investment = $8,200
Decrease in investment = 7.5%
Decrease in dollars = $615 ($8,200 x 7.5%)
Balance = $7,585 ($8,200 - $615)
Thus, Tammy's investment account decreased to $7,585 by $615, representing a 7.5% decrease.
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A cylindrical candle is to be made from 18 in 3 of wax. If the candle’s height is twice its
diameter, what radius and height should it have, to the nearest tenth?
Answers
The radius is 1.13 inches and the height of the cylinder is 4.52 inches.
How to calculate the value?From the information, it's important to use the volume of a cylinder to illustrate the information.
Use the volume of a cylinder.
V = πr²h
V = volume.
r = radius
h = height
where:
V = 18
h = 2(2r) = 4r
Plug in the values into the equation and solve for r.
18 = πr²(4r)
18 = 4πr³
Divide both sides of the equation by 4π.
9 / (2π) = r³
r³ = 1.43
r = 1.13 inches.
Finally, multiply the radius by 4 to get the height. This will be:
= 4 × 1.13
= 4.52 inches.
In conclusion, the height is 4.52 inches.
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NEED HELP WITH THIS MATH QUESTION QUICK!
Answers
Answer:
[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]
[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]
Step-by-step explanation:
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the dividend is divided.
Quotient: The result of the division.
Remainder: The part left over.
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
[tex]\textsf{Dividend}: \quad 10x^4-14x^3-10x^2+6x-10[/tex]
[tex]\textsf{Divisor}: \quad x^3-3x^2+x-2[/tex]
Therefore:
[tex]\large \begin{array}{r}10x+16\phantom{)}\\x^3-3x^2+x-2{\overline{\smash{\big)}\,10x^4-14x^3-10x^2+6x-10\phantom{)}}}\\{-~\phantom{(}\underline{(10x^4-30x^3+10x^2-20x)\phantom{-b)}}\\16x^3-20x^2+26x-10\phantom{)}\\-~\phantom{()}\underline{(16x^3-48x^2+16x-32)\phantom{}}\\28x^2+10x+22\phantom{)}\\\end{array}[/tex]
Solution:
[tex]10x+16+\dfrac{28x^2+10x+22}{x^3-3x^2+x-2}[/tex]
[tex]\textsf{The quotient is $\boxed{10}\;x+\boxed{16}$}[/tex]
[tex]\textsf{The remainder is $\boxed{28}\:x^2+\boxed{10}\:x+\boxed{22}$}[/tex]
1. Hay Story Problems Challenge Question Elliot delivered 630 newspapers in May. He delivered 35 more newspapers in June than May. Which equation can be used to find n, the number of newspapers Elliot delivered during these two months? A 630 + 35 x 2 = n B 630 + 35 = n C 630 + 630 - 35 = n D 630 + 630 + 35 = n Explain to your partner why your answer is correct.
Answers
Using elimination method, we get the result 630 + 630 + 35 = n
What is elimination method?
The elimination method involves removing one of the variables from a system of linear equations by adding or subtracting from the system and multiplying or dividing the variable coefficients.
You need an equation that can determine n, 630's total, and 35 more than 630.
More
The value "35 more in June than in May" refers to the value "35 more than 630." That value is represented by the sum (630 +35).
Total two months
In total, there will be two months' worth of delivered papers.
May deliveries + June deliveries = n
630 + (630 +35) = n
Eliminating parentheses, this expression is ...
630 + 630 + 35 = n
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Please help me I’ll mark u brainly
Answers
Answer:
a
Step-by-step explanation:
to rotate 180 degrees, simply invert both signs
To determine the value of tangent of 7 times pi over 8, which identity could be used?
Answers
Given:
[tex]\tan \frac{7\pi}{8}[/tex]To Determine: The identity that is equivalent to the given tangent
Note that, the identity rule below would be applied
[tex]\tan \frac{\alpha}{2}=\sqrt[]{\frac{1-\cos \alpha}{1+\cos \alpha}}[/tex]Also,
[tex]\tan \frac{\alpha}{2}=\frac{\sin \alpha}{1+\cos \alpha}[/tex]And also,
[tex]\tan \frac{\alpha}{2}=\frac{1-\cos \alpha}{\sin \alpha}[/tex]From the given tangent, we can re-write it as below:
[tex]\begin{gathered} \tan \frac{7\pi}{8}\cong\tan \frac{\frac{7\pi}{4}}{2} \\ \text{Note} \\ \frac{7\pi}{8}=\frac{\frac{7\pi}{4}}{2} \end{gathered}[/tex]Therefore:
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\sqrt[]{\frac{1-\cos\frac{7\pi}{4}}{1+\cos\frac{7\pi}{4}}}[/tex]Also:
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\frac{\sin \frac{7\pi}{4}}{1+\cos \frac{7\pi}{4}}[/tex]And also,
[tex]\tan \frac{\frac{7\pi}{4}}{2}=\frac{1-\cos \frac{7\pi}{4}}{\sin \frac{7\pi}{4}}[/tex]It can be observed from the option provided, the correct options is
I and III only
Crossfire Company segments its business into two regions—East and West. The company prepared a contribution format segmented income statement as shown below:
Total Company East West
Sales $ 1,120,000 $ 770,000 $ 350,000
Variable expenses 840,000 616,000 224,000
Contribution margin 280,000 154,000 126,000
Traceable fixed expenses 155,000 65,000 90,000
Segment margin 125,000 $ 89,000 $ 36,000
Common fixed expenses 70,000
Net operating income $ 55,000
Required:
1. Compute the companywide break-even point in dollar sales.
2. Compute the break-even point in dollar sales for the East region.
3. Compute the break-even point in dollar sales for the West region.
4. Prepare a new segmented income statement based on the break-even dollar sales that you computed in requirements 2 and 3. What is Crossfire’s net operating income (loss) in your new segmented income statement?
5. Do you think that Crossfire should allocate its common fixed expenses to the East and West regions when computing the break-even points for each region?
Answers
Choose the best answer. The diagonals of a rhombus:A. bisect each other and intersect at different anglesB. are the same length and intersect at a right angleC. are the same length and intersect at different anglesD. bisect each other at right angles
Answers
The property of a rhombus regarding the two diagonals states that they bisect each other at right angles.
Hence, option D is the correct answer.
Find each indicated value or measure assume that all segments that appear to be tangent are tangent.
Answers
Answer:
6
Step-by-step explanation:
Using the intersecting chords theorem,
[tex]x^2=36 \\ \\ x=6 (x>0)[/tex]
The expression 81 √ ⋅ 100√ represents the number of feet between home plate and first base. What is the distance, in feet, between home plate and first base? Answers are 19 30 80 and 810.
Answers
The distance between home plate and first base is -1 feet
what is distance ?
Distance is a numerical or occasionally qualitative measurment of how far apart objects or point are . in physics or everyday usage , distance may refer to a physical length.
How to determine the number
From the information given, we have that;
The expression for the number of feet between home plate and first base is given as;
√81-√100
Where;
√81 is the number of feet at home plate
√100 is the number of feet at the first base
To determine the distance, we take find the square root of the numbers and substitute, we have;
9 - 10 Find the difference
-1 feet
Thus, the distance between home plate and first base is -1 feet
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Under which transformation is size not preserved?A. reflectionB. dilationC. rotationD. translation
Answers
The philosophy of dilation is to resize uniformly the figure in question. Under this intuitive idea, dilation is the answer. Now, what does uniformly mean here?
It means that, as can be seen in the figure, the length of every side of the right triangle can be calculated by multiplying its corresponding side in the left ("small") triangle by a constant. However, this can be done from the right triangle to the left triangle; that's why I put a bidirectional arrow.
Finally, I want to give you some motivation for this concept: Every time you are resizing an image on your phone or in your computer, you're applying this concept.
Which one is the option to describe a piece wise function ?
Answers
.
A piece-wise function is a function that changes its value, based on the input
That is a function its range depends on the domain.
The correct answer is the third option
Look at the table. Is F(x) an exponential function? If so, Identify the base. if not, Why not?
Answers
ANSWER
YES, the base is 4 ......option B
A performer expects to sell 5000 tickets for an upcoming concert.
They plan to make a total of $311000 in sales from these tickets.
Assume that all tickets have the same price.
How much money will they make if they sell 7000 tickets?
Answers
Answer:
$435,400
Step-by-step explanation:
Price of one ticket: $311,000/5,000
Price of one ticket: $62.20
Price of 7000 tickets: $62.20 x 7000
Price of 7000 tickets: $435,400
#1 Write the quadratic function in vertex
form given a vertex of (-1,-2) and a
second point on the graph at (3,-10)
A. y = -3(x - 1)² + 2
B. y=-34 (x + 1)² + 2
C. y = -2(x - 1)²-2
D. y=-2 (x + 1)²-2
Answers
The quadratic function in vertex form is y = -1/2(x + 1)^2 - 2
How to determine the quadratic function in vertex form?The vertex is given as
(h, k) = (-1,-2)
The point is also given as
(x, y) = (3, -10)
Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
Substitute (h, k) = (-1,-2) in y = a(x - h)^2 + k
y = a(x + 1)^2 - 2
Substitute (x, y) = (3, -10)
-10 = a(3 + 1)^2 - 2
So, we have
-10 = a(4)^2 - 2
Add 2 to all sides
-8 = a(16)
Divide by 16
a = -1/2
Substitute a = -1/2 in y = a(x + 1)^2 - 2
y = -1/2(x + 1)^2 - 2
Hence, the equation is y = -1/2(x + 1)^2 - 2
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What are the coordinates of the foci of the conic section shown below?(y + 2)² /16 - (x − 3)² /9 = 1A. (3, -2±5)B.(-2+5,3)C. (-2,3±5)D.(-2+√7,3)
Answers
SOLUTION
Given the question on the question tab;
Explanation:
[tex]\frac{(y+2)^2}{16}-\frac{(x-3)^2}{9}=1[/tex][tex]h=3,k=-2,a=3,b=4[/tex][tex]The\text{ }standardform\text{ }is\frac{\text{ }\left(y+2\right)^2}{4^2}-\frac{\left(x - 3\right)^{2}}{3^{2}}=1.[/tex][tex]The\text{ }linear\text{ }eccentricity\text{ }is\text{ }c=\sqrt{b^{2} + a^{2}}=5.[/tex][tex]\begin{gathered} The\text{ first focus is:} \\ \left(h,k−c\right)=\left(3,−7\right). \\ The\text{ second focus is:} \\ \left(h,k+c\right)=\left(3,3\right) \end{gathered}[/tex]Final answer:
Sammy has 125 saved from his lifegaurding job
Answers
Using a linear function, it is found that:
a) The table is completed in the first image at the end of the answer.
b) The function is: s(w) = 125 - 10.50w.
c) The graph of the function is given by the second image at the end of the answer.
Linear functionThe slope-intercept representation of a linear function is shown by the rule presented below:
y = mx + b
The coefficients of the function are presented as follows:
m is the slope of the function, representing the rate of change of the output y in relation of the input x of the function, i.e, by how much y changes when x changes by 1.b is the y-intercept of the function, representing the numeric value of the function when the input x is of 0.In the context of this problem, the slope and the intercept are given as follows:
Slope of -10.50, which is the cost of the bus fare.Intercept of 125, which is how much he has saved from the bus fare.Hence the function is given as follows:
s(w) = 125 - 10.50w.
The numeric values to complete the table are given as follows:
s(6) = 125 - 10.5(6) = 62.s(10) = 125 - 10.5(10) = 20.A similar problem, also focused on linear functions, is presented at https://brainly.com/question/24808124
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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]What is the average rate of change please write your answer as an integer or simplify fraction
Answers
Given:
f(x)=6x+3
Required:
To calculate the average rate
Explanation:
[tex]\begin{gathered} Average\text{ rate of change} \\ \\ y=6x+3\text{ at \lparen x=5\rparen} \\ \\ y=6(5)+3=33 \end{gathered}[/tex][tex]\begin{gathered} y=6x+3\text{ at\lparen x=10\rparen} \\ \\ y=6(10)+3 \\ \\ y=63 \end{gathered}[/tex][tex]\begin{gathered} average\text{ }rate\text{ }of\text{ }change \\ \\ y=63-33 \\ \\ y=30 \end{gathered}[/tex]Required answer:
30
A carton of 12 eggs costs $3.00. A carton of 18 eggs costs $4.32. Suppose a supermarket wants to sell the eggs individually. Is there a price the supermarket can charge per egg that is between the prices per egg for the two different-sized cartons? Explain
Answers
The price the supermarket can charge per egg that is between the prices of per egg for the two different-sized cartons is $0.245 per egg.
According to the question,
We have the following information:
Cost of 12 eggs in a carton = $3.00
Cost of 18 eggs in another carton = $4.32
Now, to find the charge per egg that is between the prices of per egg for these different-sized cartons, we will first find the charge per egg of both of them.
We know that to find the cost of 1 product we divide the given cost by the number of products.
Cost of 12 eggs in a carton = $3.00
Cost of 1 egg = $ (3.00/12)
Cost of 1 egg = $0.25
Cost of 18 eggs in another carton = $4.32
Cost of 1 egg = $(4.32/18)
Cost of 1 egg = $0.24
Now, we have to find the price of egg between 0.24 and 0.25.
Note the difference between these two charges is 0.01.
We will divide it by 2 to find the exact middle charge:
0.01/2 = 0.005
We can add this in $0.24 or subtract it from$ 0.25.
$0.24 + $0.005 = $0.245
Hence, price the supermarket can charge per egg is $0.245.
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write an equation, in factored form, of degree 6 polynomial that has four x-intercepts and a y-intercept of 64
Answers
ANSWER :
f(x) = (3x-2)(x-3)(x-4)(x-2)^3
EXPLANATION :
A polynomial with a degree of 6 has 6 factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - e)(x - f) with 6 roots or x-intercepts.
But the problems states that it has 4 x-intercepts, so we will reduced the number of roots but maintaining the number of factors.
f(x) = (x - a)(x - b)(x - c)(x - d)(x - a)(x - a).
From here, we still have 6 factors but only 4 x-intercepts, the last two factors (x - a) is the same as the first factor.
So we can rewrite this as :
[tex]f(x)=(x-a)^3(x-b)(x-c)(x-d)[/tex]Next is to have a y-intercept of 64, y-intercept is the value of f(x) when x = 0
Substitute 0 to the function.
[tex]\begin{gathered} f(0)=(0-a)^3(0-b)(0-c)(0-d) \\ f(0)=a^3(b)(c)(d) \end{gathered}[/tex]Now we have f(0) = a^3bcd and f(0) = 64 as the definition from above.
We need to find the factors of 64,
64 = 8 x 4 x 3 x 2/3
And we can rewrite the equation as :
[tex]\begin{gathered} f(0)=a^3bcd \\ 64=a^3bcd \\ 8\times4\times3\times\frac{2}{3}=a^3bcd \end{gathered}[/tex]From here, we can observe that,
a^3 = 8 ⇒ a = 2
b = 4
c = 3
d = 2/3
So the function will be :
[tex]\begin{gathered} f(x)=(x-2)^3(x-4)(x-3)(x-\frac{2}{3}) \\ f(x)=(x-2)^3(x-4)(x-3)(3x-2) \end{gathered}[/tex]Explanation in 2/3
Since we only need 4 distinct factors of 64.
8 x 4 x 3 x 2/3
8 x 4 = 32
The product of the 3rd and 4th factor should be 2, in order to get 64.
Since from the first
Could you teach me how to solve this problem without using a graphing calculator? (My algebra teacher doesn’t allow graphing calculators on the test.)
Answers
The type of function we are going to work with here is an exponential function. These functions are given by equations like:
[tex]f(x)=a\cdot b^x+c[/tex]Where x is the variable and a, b and c fixed parameters. In this case c=0, a=1 and b=13/4. This number b, i.e. the one affected by the exponent is called the base so I'm going to refer to it with that word.
All exponential functions have similar graphs, they pass from being very close, almost pararel to the x-axis and then they begin to rapidly increase toward infinite y values. In the following picture you can see the graph of two exponential functions:
The red graph tends to zero for positive x values, this means that its equation has a negative sign in the exponent:
[tex]\text{red(x)}=b^{-x}[/tex]The blue graph on the other hand tends to zero for negative x values which means that there's no negative sign in the exponent. This is the case of our function r(x) so we can discard the upper left option.
Another thing to take into account is the offset of the function, that number that I labeled as "c" in the first equation. This offset translates the graph upwards or downwards depending on its sign.
For example, in this image the graphs decrease for negative x values which means their exponents don't have a negative sign but they all tend to different values which means their offsets are different. Blue's offset is 0 since it tends to 0 while gray's offset is 1 because it tends to 1. The same way you can deduce that the orange graph has an offset of -2. In the case of our problem, function r(x) doesn't have an offset which means that in one direction it has to tend to 0. This means we can discard the lower rigth option.
We have already discarded two options, if we discard one more we have the answer.
Now let's take r(x) and evaluate it in x=0:
[tex]r(0)=(\frac{13}{4})^0=1[/tex]You don't need a calculator for this because any number raised to 0 lays 1. This means that at x=0 ,i.e. the y-intercept of the graph, the function has y=1.
Lower left graph intercepts the y-axis in 1 while the upper right does it closer to 0 so we can discard this last option.
In summary, we have only one possible option left, the one in the lower left. This is the correct option.
what’s the correct answer answer asap for brainlist
Answers
Answer:
B
I hope that this helps