Answer:
Procedure:
1) Form a system of 3 linear equations based on the two zeroes and a point.
2) Solve the resulting system by analytical methods.
3) Substitute all coefficients.
Step-by-step explanation:
A quadratic function is a polynomial of the form:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
A value of [tex]x[/tex] is a zero of the quadratic function if and only if [tex]y = 0[/tex]. By Fundamental Theorem of Algebra, quadratic functions with real coefficients may have two real solutions. We know the following three points: [tex]A(x,y) = (r_{1}, 0)[/tex], [tex]B(x,y) = (r_{2},0)[/tex] and [tex]C(x,y) = (x,y)[/tex]
Based on such information, we form the following system of linear equations:
[tex]a\cdot r_{1}^{2}+b\cdot r_{1} + c = 0[/tex] (2)
[tex]a\cdot r_{2}^{2}+b\cdot r_{2} + c = 0[/tex] (3)
[tex]a\cdot x^{2} + b\cdot x + c = y[/tex] (4)
There are several forms of solving the system of equations. We decide to solve for all coefficients by determinants:
[tex]a = \frac{\left|\begin{array}{ccc}0&r_{1}&1\\0&r_{2}&1\\y&x&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]a = \frac{y\cdot r_{1}-y\cdot r_{2}}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x+x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]a = \frac{y\cdot (r_{1}-r_{2})}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]b = \frac{\left|\begin{array}{ccc}r_{1}^{2}&0&1\\r_{2}^{2}&0&1\\x^{2}&y&1\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]b = \frac{(r_{2}^{2}-r_{1}^{2})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x +x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
[tex]c = \frac{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&0\\r_{2}^{2}&r_{2}&0\\x^{2}&x&y\end{array}\right| }{\left|\begin{array}{ccc}r_{1}^{2}&r_{1}&1\\r_{2}^{2}&r_{2}&1\\x^{2}&x&1\end{array}\right| }[/tex]
[tex]c = \frac{(r_{1}^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1})\cdot y}{r_{1}^{2}\cdot r_{2}+r_{2}^{2}\cdot x + x^{2}\cdot r_{1}-x^{2}\cdot r_{2}-r_{2}^{2}\cdot r_{1}-r_{1}^{2}\cdot x}[/tex]
And finally we obtain the equation of the quadratic function given two zeroes and a point.
which lines are perpendicular ?
Answer:
Lines C and D
Step-by-step explanation:
For a pair of lines to be perpendicular ,
the product of their slope must be - 1 .
Slope of A:
[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{-2x}{-3} + \frac{6}{-3}\\\\[/tex]
[tex]y = \frac{2}{3}x - 2\\\\slope_A = \frac{2}{3}[/tex]
Slope of B:
[tex]3x - 2y = - 9\\\\-2y = - 3x - 9\\\\y = \frac{-3x}{-2} - \frac{9}{-2}\\\\y =\frac{3x}{2} + \frac{9}{2}\\\\slope_B = \frac{3}{2}[/tex]
Slope of C:
[tex]y = - \frac{3}{2}x - 5 \\\\slope_C = -\frac{3}{2}[/tex]
Slope of D:
[tex]y = \frac{2}{3}x + 2\\\\slope_D = \frac{2}{3}[/tex]
Product of the slopes = - 1
[tex]slope_A \times slope_B = \frac{2}{3} \times \frac{3}{2} = 1 \neq - 1 \\\\Therefore, not\ perpendicular.\\\\Slope_B \times slope_C = \frac{3}{2} \times \frac{-3}{2} = \frac{-9}{4} \neq -1\\\\Therefore , not \ perpendiucalr.\\\\Slope_C \times slope_D = -\frac{3}{2} \times \frac{2}{3} = - 1\\\\Therefore , perpendicular\\\\\\Slope_A \times slope_D = \frac{2}{3} \times \frac{2}{3} = \frac{4}{9} \neq 1\\\\therefore , not \ perpendicular.[/tex]
Solve each system of equations by substitution. Clearly identify your solution.
Answer:
(-3, 5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)Terms/CoefficientsSolving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = x + 8
x + y = 2
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: x + x + 8 = 2Combine like terms: 2x + 8 = 2[Subtraction Property of Equality] Subtract 8 on both sides: 2x = -6[Division Property of Equality] Divide 2 on both sides: x = -3Step 3: Solve for y
Substitute in x [1st Equation]: y = -3 + 8Add: y = 5Answer:
x = - 3
y = 5
Step-by-step explanation:
y = x + 8 ------(I)
x + y = 2 -------------(II)
Substitute y = x + 8 in equation (II)
x + x + 8 = 2
Combine like terms
2x + 8 = 2
Subtract r from both sides
2x = 2- 8
2x = -6
Divide both sides by 2
x = -6/2
x = -3
Plug in x = -3 in equation (I)
y = -3 + 8
y = 5
Ronald brought a jacket on Friday that had original price if $45. It was on sale at 10% off its original price. Which formula shows what Ronald paid after 7% sales tax was added?
A. 1.07(45-10)
B. 1.03(45)
C. 1.07(45-45(.1))
D. 1.1(45-45(.7))
2p -5q=8.. 3p-7q=11 use substitution
Answer:
p = -1 q = -2
Step-by-step explanation:
3p - 7q = 11 -7q = -3p + 11 q = 3/7p - 11/7
2p - 5(3/7p - 11/7) = 8
2p - 15/7p + 55/7 = 8
-1/7p + 55/7 = 8
-1/7p = 1/7
p = -1
2(-1) - 5q = 8
-2 - 5q = 8
-5q = 10
q = -2
(e) Dhanu plays with his model railway from 06 50 to 11 15. He then rides his bicycle for 3 hours. Find the ratio time playing with model railway : time riding bicycle. Give your answer in its simplest form.
Answer:
53:36
Step-by-step explanation:
53:36
265:180
The ratio of time Dhanu spent playing with model railway to the time riding bicycle is 53 : 35.
What is the ratio of the time spent playing with model railway to the time riding bicycle ?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).
Time spent playing with the model railway = 4 hours 25 minutes.
Converting the time to minutes = (4 x 60) + 25 = 265 minutes
Time in minutes spent riding a bicycle = 60 x 3 = 180
Ratio of the minutes - 265 : 180
53 : 35
To learn more about ratios, please check: https://brainly.com/question/25927869
let's write the whole numbers from 90 to 100 . Select the appropriate number to form the following sets . Then , write the type of sets .
A={ even number}
B={ odd number}
C={ X:X is a prime numbers}
D={ y:y is a composite number}
E={z:z is a square number}
F={ cube number}
G={ multiples of 7}
H={ X:X is divisible by 11}
A={ even number}
B={ odd number}
C={ X:X is a prime numbers}
D={ y:y is a composite number}
E={z:z is a square number}
F={ cube number}
G={ multiples of 7}
H={ X:X is divisible by 11}
꧁Aɴsᴡᴇʀ꧂AThe even numbers between 90 and 100 are: 90, 92, 94, 96, 98, 100B The odd numbers between 90 and 100 are: 91, 93, 95, 97, 99C The prime number between 90 and 100 is: 97DThe composite numbers between 90 and 100 are: 91, 92, 93, 94, 95, 96, 98 and 99.EThe square numbers between 90 and 100 are:90 = 8100
91 = 8281
92 = 8464
93 = 8649
94 = 8836
95 = 9025
96 = 9216
97 = 9409
98 = 9604
99 = 9801
100 = 10000
F The answer for this is on the attached picture above. Kindly look at it. The cube numbers between 90 and 100. GThe multiples of 7 between 90 and 100 are: 91 and 98HDivisible by 11 (between 90 and 100) is: 99
✩ ⁱ ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ✩
Answer:
A
The even numbers between 90 and 100 are: 90, 92, 94, 96, 98, 100
B
The odd numbers between 90 and 100 are: 91, 93, 95, 97, 99
C
The prime number between 90 and 100 is: 97
D
The composite numbers between 90 and 100 are: 91, 92, 93, 94, 95, 96, 98 and 99.
E
The square numbers between 90 and 100 are:
90 = 8100
91 = 8281
92 = 8464
93 = 8649
94 = 8836
95 = 9025
96 = 9216
97 = 9409
98 = 9604
99 = 9801
100 = 10000
F
The answer for this is on the attached picture above. Kindly look at it. The cube numbers between 90 and 100.
G
The multiples of 7 between 90 and 100 are: 91 and 98
H
Divisible by 11 (between 90 and 100) is: 99
Could anyone help me out with this?
Answer: they are abt the same its all abt percentage now- Pitcher A
Step-by-step explanation: more water lessens the strength
18x-108
-----------
6x-54
simplify the expression
A.
B.
C.
D.
Answer:
3x-2
---------
x-1
Step-by-step explanation:
simplify 18x/6x = 3x/1x
simplify 108/54 = 2/1
1. Slope and the properties of perpendicular and parallel can be used to confirm that a polygon is a specific type of
quadrilateral.
What types of quadrilaterals can you determine by using these properties? List at least two types of quadrilaterals.
2. Choose one type of quadrilateral from your answer to Question 1. Explain in complete sentences how you can use
properties of perpendicular and parallel lines, together with slope, to confirm that a given polygon is the type of
quadrilateral you chose. Be sure to clearly state the properties that you need to use.
Please number your responses to the questions as they are shown (1 and 2).
NOTE from Ms. Kliban:
I found this answer on the Internet. *If it were an original answer, below is how I would grade it and why
1. The two would be rectangle and trapezium
2. You can determine with the properties that are given, that it's a polygon because with the slope already known that gives
a in to see which lines are perpendicular to which lines and which aren't. Also, with the properties you can tell if everything
Is parallel lines with the slope formula. Some slopes might be different but doesn't mean the polygon Isn't perpendicular
because two sides can have the same slope and the other two won't
GRADE: First off, in the United States, we don't use the word "trapezlum."
For part 2, it says, you can determine with the properties that are given." What properties? There are no properties given.
There are shapes. The next thing said in part 2 is that the slope is already known. No, it's not. You have to find the slope.
PLEASE HELP!!!!! 70 points !!!!
The grammar is bumpy. In other words, I stumbled over it when I tried to read it.
In order to do well on this assignment, part one only needs to have two quadrilaterals stated. You don't even have to have it
In a sentence.
For part 2. you do need to use complete sentences. You need to explain how to find slope and why you need to find the
slope. Then also explain how parallel and perpendicular lines help you to make sure you have the shape you stated in part
sat
Answer: Rectangle and Trapezium
Step-by-step explanation:
If you have the slopes, then you can tell when two lines are parallel.
A rectangle has two pairs of parallel sides
A trapezium has exactly one pair of parallel sides
We can determine whether a quadrilateral is a rectangle or a trapezium using the slope and the properties of parallel and perpendicular lines.
2. How are the slopes of perpendicular sides related?Product of the slopes of perpendicular lines = -1.
M₁ * M₂ = -1 .
How are the slopes of parallel sides related?Slopes of parallel lines are equal.
M₁ = M₂.
How do we determine a rectangle?Suppose we have a quadrilateral ABCD.
AB and CD are one pair of opposite sides.
BC and DA are another pair of opposite sides.
AB is adjacent to BC. BC is adjacent to CD. CD is adjacent to DA. DA is adjacent to AB.
Slope AB = M₁
Slope BC = M₂
Slope CD = M₃
Slope DA = M₄
For ABCD to be a rectangle, by properties opposite sides need to be parallel and adjacent sides need to be perpendicular.
∴ If M₁ = M₃, M₂ = M₄ (for opposite sides to be parallel)
and if M₁.M₂ = -1, M₂.M₃ = -1, M₃.M₄ = -1, and M₄.M₁ = -1 (for adjacent sides to be perpendicular) then the given quadrilateral ABCD is a rectangle.
Learn more about quadrilaterals, the slope of parallel lines, and the slope of perpendicular lines at
https://brainly.com/question/23935806
https://brainly.com/question/26172639
https://brainly.com/question/1362601
#SPJ2
This is the last question for the 12 point
9514 1404 393
Answer:
WR ≅ WX
Step-by-step explanation:
To use the SAS postulate, you need congruent sides bounding a congruent angle.
Here, side WP is one side of one of the vertical angles, ∠PWR, so you need the other side of that angle: WR. The corresponding side in triangle VWX is WX. That is, for SAS, you need WR ≅ WX.
help leee plzzzzzzzbbbnbbbb
In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the sqaure?
Answer:
For completing the square, you need the coefficient of the x^2 term to be 1.
http://www.1728.org/quadr2.htm
Step-by-step explanation:
Find the circumference of this circle
using 3 for TT.
C = ?
[tex]{ \bf{ \underbrace{Given}}}[/tex]:
Diameter of the circle "[tex]d[/tex]" = [tex]36[/tex]
Value of [tex]π[/tex] = [tex]3[/tex]
[tex]{ \bf{ \underbrace{To\:find}}}[/tex]:
The circumference "[tex]C[/tex]" of the circle.
[tex]{ \bf{ \underbrace{Solution }}}[/tex]:
[tex]\sf\pink{The\:circumference \:"C"\:of\:the\:circle\:is\:108.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]
[tex] = 3 \times 36[/tex]
[tex] = 108[/tex]
Therefore, the circumference of the circle is [tex]108[/tex].
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Answer:
[tex]\Longrightarrow: \boxed{\sf{108}}[/tex]
Step-by-step explanation:
Apply the formula for the circle's circumference.
[tex]\text{Circumference circle formula:}[/tex]
[tex]\Longrightarrow: \sf{C=\pi d}[/tex]
[tex]\Longrightarrow:\sf{C=?}\\\\\Longrightarrow:\sf{\pi =3}\\\\\Longrightarrow:\sf{d=36}[/tex]
Multiply.
[tex]\sf{3*36=\boxed{\sf{108}}[/tex]
Therefore, the correct answer is 108.I hope this helps! Let me know if you have any questions.
How do you work out the volume of a cube
Answer:
V=a cubed
Step-by-step explanation:
write 36,438 correct to 2 significant figure
(show how you did it)
Answer:
36,000
Step-by-step explanation:
Rounding Significant Figures Rules
Non-zero digits are always significant Zeros between non-zero digits are always significant Leading zeros are never significant Trailing zeros are only significant if the number contains a decimal pointRounding Rules
When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.
Example: 356 rounded to 2 significant digits is 360
This calculator rounds down if the next digit is less than 5 and rounds up when the next digit is greater than or equal to 5.
In the table below 305.459 is rounded from 0 to 6 significant figures. For comparison the same number is rounded from 0 to 6 decimal places. You can see the difference between rounding for significant figures and rounding to decimal places.
question in picture | Math
Answer:
Y=4/-2
Step-by-step explanation:
Find the measure of the indicated side
Does anyone know how to solve these?
Answer:
1st graph: slope is -1 and equation is y=-x+5
2nd graph: slope is 2/5 and equation is y=2/5x-3
Step-by-step explanation:
y=mx+b is slope-intercept form.
It's call that because this forn tells us the slope,m, and the y-intercept,b.
The first graph you have identified b as 5 since you said the y-intercept was (0,5).
Now we just find slope by finding rise/run.
(0,5) is marked and we see another point has been marked, I will start at (0,5) go down 2 and right 2. This means rise=-2 and run=2 which means the slope=-2/2 and that reduces to -1.
The equation for first graph is y=-1x+5 or y=-x+5.
So again you have no problem identifying the y-intercept which is b=-3.
Now just count the rise/run to the other point. Starting at y-intercept we have to go up 2 and right 5 to get to the other point so m=2/5.
30 POINTS !!!
what is the total surface area of the square pyramid? 5in height abs 8in base
20
40
104
144
Point M is the midpoint of AB. The coordinates of point A are (-8, 3) and the coordinates of M are (-2, 1). What are the coordinates of point B?
.
.
.
May you please show me the work?
Answer:
the coordinates of point B are (-5, 2)
Step-by-step explanation:
1. use midpoint formula to find the midpoint (equation attached below)
2. plug in the numbers
[tex](\frac{-8+(-2)}{2},\frac{3+1}{2})[/tex]
3. solve
[tex](\frac{-8-2)}{2},\frac{3+1}{2})[/tex]
[tex](\frac{-10}{2},\frac{4}{2})[/tex]
[tex](-5,2})[/tex]
8) A pyramid has a rectangluar base with length 12 km and width of 5 km. If the volume is 200
cubic kilometers, what is the height?
Hi there!
[tex]\large\boxed{h = 10km}[/tex]
We know that the equation for the volume of a pyramid is:
V = 1/3(bh)
We know that:
V = 200 km³
b = 12 × 5 = 60 km²
We can plug these into the equation:
200 = 1/3(60)(h)
Simplify:
200 = 20h
Divide both sides by 20:
200/20 = 20h/20
h = 10 km
Find the other endpoint of the line segment with the given endpoint and midpoint. I
nearest tenth.
Endpoint (-8, 8) Midpoint (5,-3)
Please answer the question that is attached below
Refer to the picture in the question for reference.
A statement-reason format is used to solve this problem. Statements are in normal print, reasons are bolded.
Statement Reason
1. AD = AE Given
<B = <C
2. <A = <A Reflexive Property
3. ΔABE = ΔACD Angle - Angle - Side
The given information refers to the information that is given with the problem.
The reflexive property states that if two polygons share a part (a side or an angle), then this part called in one of the polygons is congruent to itself in the other polygon.
Finally, the (angle-angle-side) congruence theorem states that if two triangles have two congruent angles and a congruent side between them, then the triangles as a whole are congruent to each other.
Pls help before the clock hits 50 :(
Use the following graph of the function f(x) = 3x4 − x3 + 3x2 + x − 3 to answer this question: What is the average rate of change from x = -1 to x = 0
Answer:
-6
Step-by-step explanation:
3 1/2 divided by 2 1/6=
Answer:
21/13
Step-by-step explanation:
3 1/2 = 7/2
2 1/6 = 13/6
7/2 divided by 13/6
7/2 X 6/13 = 42/26 = 21/13
Answer:
Step-by-step explanation:
3 1/2 = 7/2 and 2 1/6 = 13/6
7/2 divided by 13/6 = 7/2 x 6/13
42/26
21/13 is your final answer.
The transformation from the function ƒ(x) = 3x to the function ƒ(x) = 3x + 4 indicates:
Answer:
Moving 4 to the right on the x axis
Identify a horizontal or vertical stretch or compression of the function by observing the equation of the function .
A small point deduction applies if a participation activity's question is not answered correctly the first time?
Answer: False
Step-by-step explanation:
There is no such deduction when a participation's questions are not answered correctly the first time. Whatever answer is given is part of the learning curve and ensures that the activity can be improved upon.
Had there been a small point deduction then there would be no opportunity to learn because there would be too much fear associated with the wrong answer.
worth 10 points please help me ASAP!
Answer:
(-1,-1)
Step-by-step explanation:
If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).
what is the slope of the graph?
Answer:
The slope is 1.5
Step-by-step explanation:
To get the slope of the graph, we proceed to select any two points lying on the given line, and applying the slope formula
The two selected points are as follows;
(x1,y1) = (-4,0)
(x2,y2) = (-2,3)
m = (y2-y1)/(x2-x1)
m = (3-0)/(-2-(-4)
m = 3/2 = 1.5
