Answers
Answer:
2 i think
Step-by-step explanation:
Related Questions
Is every relation also a function? Explain
Answers
Answer:
no
Step-by-step explanation:
they are not
Answer:
Step-by-step explanation:
In fact, every function is a relation. However, not every relation is a function. In a function, there cannot be two lists that disagree on only the last element. This would be tantamount to the function having two values for one combination of arguments.
HELP IT'S URGENT.
Please show workings.
No 4 (see image)
Answers
Answer:
(i) (b² - 2ac)/c²(ii) (3abc - b³)/a³Step-by-step explanation:
α and β are the roots of the equation:
ax² + bx + c = 0Sum of the roots is:
α + b = -b/aProduct of the roots is:
αβ = c/aSolving the following expressions:
(i)
1/α² + 1/β² =(α² + β²) / α²β² =((α + β)² - 2αβ) / (αβ)² = ((-b/a)² - 2c/a) / (c/a)² = (b²/a² - 2c/a) * a²/c² = b²/c² - 2ac/c² =(b² - 2ac)/c²----------------
(ii)
α³ + β³ =(α + β)(α² - αβ + β²) =(α + β)((α + β)² - 3αβ) = (α + β)³ - 3αβ(α + β) =(-b/a)³ - 3(c/a)(-b/a) =-b³/a³ + 3bc/a²= 3abc/a³ - b³/a³=(3abc - b³)/a³[tex] \huge \underline{\tt Question} :[/tex]
If α and β are the roots of the equation ax² + bx + c = 0, where a, b and c are constants such that a ≠ 0, find in terms of a, b and c expressions for :
[tex] \tt \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]α³ + β³[tex] \\ [/tex]
[tex] \huge \underline{\tt Answer} :[/tex]
[tex] \bf \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }[/tex][tex] \bf \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}[/tex][tex] \\ [/tex]
[tex] \huge \underline{\tt Explanation} :[/tex]
As, α and β are the roots of the equation ax² + bx + c = 0
We know that :
[tex] \underline{\boxed{\bf{Sum \: of \: roots = \dfrac{- coefficient \: of \: x}{coefficient \: of \: x^2}}}}[/tex][tex] \underline{\boxed{\bf{Product \: of \: roots = \dfrac{constant \: term}{coefficient \: of \: x^2}}}}[/tex][tex] \tt : \implies \alpha + \beta = \dfrac{-b}{a}[/tex]
and
[tex] \tt : \implies \alpha\beta = \dfrac{c}{a}[/tex]
[tex] \\ [/tex]
Now, let's solve given values :
[tex] \bf \: \: \: \: 1. \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\beta ^2 + \alpha ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\alpha ^2 + \beta ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \\ [/tex]
Now, by using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies \dfrac{(\alpha + \beta)^2 - 2 \alpha\beta}{(\alpha\beta)^2}[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \dfrac{\Bigg(\dfrac{-b}{a}\Bigg)^2 - 2 \times \dfrac{c}{a}}{\Bigg(\dfrac{c}{a}\Bigg)^2}[/tex]
[tex] \tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2c}{a}}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2ac}{a^{2} }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2 - 2ac}{a^2 }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{\cancel{a^2} } \times \dfrac{ \cancel{a^2}}{c^2}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{c^2 }[/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }}[/tex]
[tex] \\ [/tex]
[tex] \bf \: \: \: \: 2. \: \alpha ^3 + \beta ^3 [/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^3+ b^3 = (a+b)(a^2 -ab + b^2)}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha ^2 - \alpha\beta + \beta ^2)[/tex]
[tex] \tt : \implies (\alpha + \beta)(\alpha ^2 + \beta ^2 - \alpha\beta)[/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha + \beta)^2 -2 \alpha\beta - \alpha\beta)[/tex]
[tex] \tt : \implies (\alpha + \beta)((\alpha + \beta)^2 -3 \alpha\beta)[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg( \bigg(\dfrac{-b}{a} \bigg)^2 -3 \times \dfrac{c}{a}\Bigg)[/tex]
[tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3c}{a}\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3ac}{a^{2} }\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2 - 3ac}{a^2} \Bigg)[/tex]
[tex]\tt : \implies \dfrac{-b}{a} \times \dfrac{b^2 - 3ac}{a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b(b^2 - 3ac)}{a \times a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b^3 + 3abc}{a^3} [/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}}[/tex]
give me answer.1 to 100 plus. like:1+2+3+4+5+6+7+8+9+10+11.........
Answers
Answer:
5,050
Step-by-step explanation:
Use sigma notation to add all the numbers together (∑)
(PLEASEEE HELP I DONT UNDERSTAND) Which of the following equations represents a linear NON-proportional function?
A) y=3x+0
B) y=x/4
C) y=7x
D) y=2/5x+7
Answers
A nonproportional relationship is a linear line that doesn’t go through the origin.
y=3x+0 does go through the origin because the y-intercept (the b) is 0
Y=x/4 also has a y-intercept of 0
Y=7x also has a y-intercept of 0.
y=2/5x+7 does not go through the origin because the line passes the y-axis at (0,7) which is the y-intercept.
Solving equations with like terms -8 -3y + 2y =32
Answers
Answer:
y= -40
Step-by-step explanation:
does opposites name the same location on a number line.
Answers
Answer:
I'm not sure but maybe this will help
Step-by-step explanation:
- 3 and 3 are located on opposite sides of zero. They are the same distance from zero. 3 and -3 are called opposites.
Sally buys a pair of shoes that are discounted 60% off the original price. If Sally pays $50 for the shoes, what was the original price of the shoes?
Answers
Answer:
90$
Step-by-step explanation
Step 1: You need to find how much was the 60% discount
Step 2: To find that multiply .6 by 50 you will get 30
Now you know how much was 60% discount
Step 3: Add 30(the discount) + 50(the prce sally pays) = 90 (the oriagnal price)
Need help pls like I really need help
Answers
Answer:
4
Step-by-step explanation:
PLZ MARK BRAINLIEST
Answer:
y=1.5x
Step-by-step explanation:
3/2=1.5
9/6=1.5
HELP ME PLEASE! how do you write 0.0370 as a scientific notation
Answers
Hope that helped
Help please it’s needed!
Answers
phoebe, andy and polly share €270
phoebe gets three times as much as and who gets twice as much as polly
work out how much they each get
Answers
Answer:
Polly=30
Andy=60
Phoebe=180
Step-by-step explanation:
Polly=x
Andy=2x
Phoeby 3(2x)=6x
x+2x+6x=270
9x=270
x=30
Polly=x=30
Andy = 2x=60
Phoebe=6x=180
what plus 80 and 70 equals 180
Answers
Answer:
30
Step-by-step explanation:
Take 80 and 70 and add them together to get: 130
Then subtract 130 from 180
To get: 30
:)
Answer:
30
Step-by-step explanation:
80 + 70 = 150
180- 150 = 30
therefore 80 + 70 + 30 = 180
Samantha paid $26.25 for three books that all cost the same amount. What was the cost per book?
Answers
Answer:
$8.75 per book
Step-by-step explanation:
26.25/3 = 8.75
Answer:
$8.75
Step-by-step explanation:
26.25 divided by 3 = 8.75
PLZ HELP ME ILL GIVE U 20 POINTS!!!!!!!!!!!!!!!!
Answers
Answer:
1. y < 4
2. x </= -3
3. y >/= 2
4. x > -2
5. x </= 2
6. x < 0
7. t > -2
8. N >/= 3
9. n < -4
10. x < 5
Step-by-step explanation:
Graph a scatter plot using the given data.
Answers
Answer:
Here is the answer.
Step-by-step explanation:
Identify the real and imaginary parts of the given number. Then identify whether the number belongs to each of the following sets: real numbers, imaginary numbers, and complex numbers.
−9 + 9i
The real part of −9 + 9i is ____ and the imaginary part is ____.
The number −9 + 9i belongs to which of the following sets. Select all that apply.
A real numbers
B imaginary numbers
C complex numbers
See image.
Answers
Answer:
-9 is real, 9i is imaginary, C
Step-by-step explanation:
-9 is real because you can literally draw nine things.
9i is imaginary because i is √-1 and square roots of negatives are imaginary.
It is complex because complex expressios are written as a+bi.
How would you graph the solution to -5w + 9 = 14 on a number line?
Answers
Answer:
Step-by-step explanation:
w= -1
Your circle will be on the -1
Answer:
Taft
Step-by-step explanation:
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answers
Answer:
-12
Step-by-step explanation:
Answer:
-12
Step-by-step explanation:
Its -12 for sure!!!!!
y= (x + 4)2 + 8
how do you simplify this equation
Answers
Answer:
Step-by-step explanation:
you could distribute and combine like terms
y=(x+4)2+8
y=2x+8+8
y=2x+16
Performance Matters
Welcome, Sanjay McCall!
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Question 3 of 20 -
E
ZahraouiAziz Midterm Geometry Pt 1 2020-2021 Question: 134
A line segment has an endpoint at (4.6). If the midpoint of the line segment is (1,5), what are the.coordinates of the point at the other endorine ne segment?
O (3, 1)
O (-2,4)
O (7.7)
O (5, 11)
Chrome OS. 28m)
Switched network connection
Your connection
has switched td al
Previous
O
Fo
Answers
Answer: most likely be (7,7) not sure right or wrong but i tried so yeah
Step-by-step explanation:
plz help!! serious answers only
Answers
Answer:
line t = -9/8
Step-by-step explanation:
Parallel lines have the same slope, so line t will have a slope of -9/8 as well
The question is Find the constant of proportionality in the graph below
Answers
Answer:
4.5
Step-by-step explanation:
i need the answer asap i’ll make you the brainliest
Answers
Answer
the second one
HELP ASAP WILL MARK BRAINLIEST UTS DUE IN 5!!!
Find the slope of the line.
O -2/5
O 2/5
O 5/2
O None of the above
Answers
Answer: 2/5
Step-by-step explanation:
PLEASE HELP HURRY!! What is the value of x?
Answers
Hope this helps!✌
the cost of 3 boxes is
Answers
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A. g(x) = f(x) - 5
B. g(x) = f(x - 5)
C. g(x) = f(x) - 2
D. g(x) = f(x + 2)
Answers
Answer:
A.
Step-by-step explanation:
It just is trust
please help i will give brainliest
Answers
Answer:
n<-0.6
Step-by-step explanation:
7.2>0.9(n+8.6)
8>n+8.6
-0.6>n
n<-0.6
So there would be an open circle at the point -0.6 (because the "less than" sign shows that -0.6 is not included), and then an arrow pointing left to show solutions that are less than -0.6
I will assume you know what buttons to press.
Answer:
Step-by-step explanation:
7.2>0.9(n+8.6)
n< -0.6
(-∞,-0.6)
open circle on -0.6 and go to the left
Which of the following correctly lists the following equations in order from most steep to least steep?
Answers
You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car for the given years.
A. 5 years.
B. 8 years.
Answers
Answer:
a is 840 ,b is 525
Step-by-step explanation:
At the end of each year, its value is down to 79%, which is 0.79 times its value at the start of the year. Keep this up for n years and the value is
V(n) = $20,000 (0.79)n,
where n is the number of years elapsed from when the value was $20,000. Just plug in n=5 and n=8, evaluate, and get your 2 answers.
Answer:
A. 5 years
Step-by-step explanation:
21% of 20,000 is 4200, mutiply that by 5 and get $20,000