Answers
Answer:
[tex] \alpha = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ \beta= \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \alpha +\beta = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} + \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 2b + 0}{2a} = \frac{ - 2b}{2a} \\ \therefore \: \alpha +\beta = - \frac{b}{a} \\ \alpha \times \beta = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \times \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ {b}^{2} - ( {b}^{2} - 4ac) }{4 {a}^{2} } \\ = \frac{4ac}{4 {a}^{2} } \\ \therefore \alpha \times \beta = \frac{c}{a} \\ (x - \alpha)(x - \beta) = 0 \\ {x }^{2} + (\alpha + \beta)x + \alpha\beta = 0\\\\Let \:D =\sqrt{ {b}^{2} - 4ac}\\ If \:D >0 \Rightarrow \alpha, \beta \in \mathbb R\:(2 \: real \:roots)\\ If D =0 \Rightarrow \alpha= \beta \in \mathbb R\: (one \:real\: root) \\ If D <0 \Rightarrow \alpha, \beta \in \mathbb C\:(complex\: roots)\\At least 4examples\\{(x-1)}^{2}=0\\{x}^{2}-x-1=0 \\{x}^{2}-2x+13=0\\7{x}^{2}-49x-7=0\\ Applications\\ut+g{t}^{2}=s\\a=g\\u=-\frac{b}{a}\\s=\frac{c}{a}[/tex]
Answer:
Step-by-step explanation:
1) Determining the nature of roots:
Quadratic equation: ax² + bx +c = 0
Find D (Discriminant) using the D = b² - 4ac
If D = 0 , then the two roots are equal.
If D > 0, then the equation has two distinct real roots.
If D < 0, then the roots are complex/ imaginary.
One can find the sum and product of the roots using the below mentioned formula.
1) sum of roots = [tex]\frac{-b}{a}[/tex]
2) Product of roots = [tex]\frac{c}{a}[/tex]
If sum and product of the roots are given, one can frame the quadratic equation by x² - (sum of roots)*x + product of roots = 0
2) i) x² - 6x + 9 = 0
a = 1 ; b = -6 and c = 9
D = (-6)² - 4 * 1 * 9 = 36 - 36 = 0
D = 0. So, two equal roots
ii) x² - 4x + 3 = 0
a = 1 ; b = -4 ; c = 3
D = (-4)² - 4 * 1 * 3 = 16 - 12 = 4
D > 0. So, two distinct real roots.
iii) x² - 4x - 3 = 0
a = 1 ; b = -4 ; c = -3
D = (-4)² - 4*1*(-3) = 16 + 12 = 28 > 0
D > 0. So, two distinct real roots.
iv) x² - 4x + 7 = 0
a = 1 ; b = -4 ; c = 7
D =(-4)² - 4 *1 *7 = 16 - 28 = - 12
D< 0. So, two imaginary/ complex roots.
Related Questions
Solve the equation:
3x + 2 = 6x - 7
Answers
Answer:
x=3
Step-by-step explanation:
1) Subtract 3x from both sides
2 = 6x - 7 - 3x
2) Simplify 6x - 7 - 3x to 3x - 7
2 = 3x - 7
3) Add 7 to both sides
2 + 7 = 3x
4) Simplify 2 + 7 to 9
9 = 3x
5) Divide both sides by 3
9/3 = x
6) Simplify 9/3 to 3
3 = x
7) Switch sides
x=3
What is 56 divided by 98
Answers
Answer:
0.571428571
Step-by-step explanation:
Simply go into a calculator app and say 56/98
You need $3,000 to buy a new stereo for your car. If you have $1,200 to invest at
6% compounded annually, how long will you have to wait to buy the stereo?
Answers
Answer:
15 years and 8 months
Step-by-step explanation:
I used the formula for compound interest as shown below and solved for the unknown, time.
Since our interest is compounded annually (So once a year) our m value is 1.
1^2/13x 5^2\5 answer the question
Answers
Answer:
5/13x
Step-by-step explanation:
BRO
The claim is that weights (grams) of quarters made after 1964 have a mean equal to 5.670 g as required by mint specifications. The sample size is n = 39 and the test
statistic is t= -3.276. Use technology to find the P-value. Based on the result what is the final conclusion? Use a significance level of 0.01.
State the null and alternative hypotheses
Hop
H.
(Type integers or decimals. Do not round)
Answers
Testing the hypothesis, we have that:
The null hypothesis is [tex]H_0: \mu = 5.67[/tex]The alternative hypothesis is: [tex]H_1: \mu \neq 5.67[/tex]The p-value of the test is of 0.002252.The p-value is 0.002252 < 0.01, which means that the final conclusion is that the mean weight of quarts made after 1960 is different than 5.67g.At the null hypothesis, we test if the mean is of 5.670g, that is:
[tex]H_0: \mu = 5.67[/tex]
At the alternative hypothesis, we test if the mean is different of 5.670g, that is:
[tex]H_1: \mu \neq 5.67[/tex]
The test statistic is t = -3.276, with the number of degrees of freedom given by:
[tex]df = n - 1 = 39 - 1 = 38[/tex]
The p-value is found using a t-distribution calculator, using a two-tailed test(as the alternative hypothesis is that the mean is different from the value), with t = -3.276 and 38 df. This p-value is of 0.002252.
The p-value is 0.002252 < 0.01, which means that the final conclusion is that the mean weight of quarts made after 1960 is different than 5.67g.
A similar problem is given at https://brainly.com/question/24146681
Assume three cards are drawn in succession and without replacement from an ordinary
deck of 52 cards. Find the probability of drawing a jack, a non-face card, and another
jack, in that order.
O A. 0.00483
OB. 0.00362
O C. 0.00341
OD.0.01086
Answers
Answer:O A. 0.00483
Step-by-step explanation:
The width of the rectangle is 0.4 meters less than the length. The perimeter of a rectangle is 53.2 meters. Find the dimensions of the rectangle (in meters). length m width m
Answers
Answer:...
Step-by-step explanation:...................
please helppppppppppppppppp
Answers
Answer:
seventeen plus twelve minus thirty
Step-by-step explanation:
17 + 12 - 30 = -1
Write 4/5 as an equivalent fraction in 3 different forms.
Answers
And-Which is a way to show sixteen?
Answers
Answer:
The answer will be 62
Step-by-step explanation:
52
{ } +10
61 (+1) 62 (+1) 63
{ } +10
72
Which is 3,200 divided by 40?
A.
6
B.
8
C.
60
D.
80
Answers
Answer:
80
Step-by-step explanation:
40 x 80 = 3200
The solution of the expression is, 80
We have to give that,
3200 divided by 40.
Now, Divide the numbers as,
⇒ 3200 ÷ 40
⇒ 3200 / 40
⇒ 320/4
⇒ 80
So, The solution after dividing is, 80
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A tennis player hits a ball hard and 0.4 s later hears the echo sound from a wall. The speed of sound in air is 330 ms. How
?far away is the player from the wall
Answers
The distance traveled by the echo is used to determine the player's distance from the wall
The player's distance from the wall is 66 m.
Reason:
Known parameter;
The time after which the tennis player hears the echo of the ball, t = 0.4 s
The speed of sound in air, v = 330 m/s
The distance of the player from the wall = Required
Solution:
Let d, represent the distance of the player from the wall
An echo is the reflection the wave of the sound of hitting the ball that
travels to the wall and back
The distance traveled by the sound to the wall, d, and back, (d again), is 2·d
[tex]Speed = \dfrac{Distance}{Time}[/tex]
Therefore;
[tex]The \ speed \ of \ the \ sound,\ v = \dfrac{2 \cdot d}{t}[/tex]Therefore;
[tex]330 = \dfrac{2 \cdot d}{0.4}[/tex]
330 × 0.4 = 2·d
[tex]d = \dfrac{330 \times 0.4}{2} = 66[/tex]
The distance of the player from the wall, d = 66 mLearn more here:
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The recommended calcium intake for men and women is about 1.2 grams per day.
A glass of milk contains about 0.27 gram of calcium. If a man drinks 3 glasses of milk,
how much additional calcium does he need from other food sources?
Answers
Answer:
0.39
Step-by-step explanation:
0.27 TIMES 3 is 0.60+0.21=0.81 then 1.2-0.81=0.39
if you dont give me brainliest i will find and eat your soul from a milk jar :D
1
1 point
Find the measure of the missing angle.
?
110°
Answers
Answer:
110
Step-by-step explanation:
Two lines are parallel and so:
Given angles are alternate exterior angles and the measurements ofalternate angles are equal so the measure of missing angle is 110 degrees.
Answer:
the value of the unknown angle is 110 degrees
Step-by-step explanation:
the unknown angle is alternate interior angle with 110
how many decimal points are in 131.6
Answers
Answer:
It just has 1 decimal point
Step-by-step explanation:
If it was a number like 14.454, then that would have 3 decimal points
Hope this helps!
What is the derivative of (x + 1) sin x?
Answers
[tex]\boxed{\sf \dfrac{d}{dx}x^n=nx^{n-1}}[/tex]
[tex]\boxed{\sf \dfrac{d}{dx}sinx=cosx}[/tex]
Now
[tex]\\ \sf\longmapsto \dfrac{d}{dx}(x+1)sinx[/tex]
[tex]\\ \sf\longmapsto 1+cosx[/tex]
sin x + x · cos x + cos x
Step-by-step explanation:
(x + 1) = u → u' = 1sin x = v → v' = cos xf(x) = u · v → f'(x) = u' · v + u · v'
f(x) = (x + 1) sin x
f'(x) = 1 · sin x + (x + 1) · cos x
f'(x) = sin x + x · cos x + cos x
What is the sum of the 10th square number and the 2nd square number?
Answers
Answer:
104
Step-by-step explanation:
10th square number is 100, 2nd square number is 4. 100+4=104
Question 10 of 10
Simplify 43.45
A. 168
B. 16.15
C. 48
O O
D. 415
SUBMIT
Answers
Answer:
C
Step-by-step explanation:
4^3 x 4^5 =4^8
You add the exponents together because they have the same base and it's multiplication sum.
I NEED HELP ASAP!!! (NO LINKS)
FULL EXPLANATION WILL GET BRAINLIEST!!!
#33
Answers
Answer:
35
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex]
with n = 7 and r = 3
7[tex]C_{3}[/tex]
= [tex]\frac{7!}{(7-3)!3!}[/tex]
= [tex]\frac{7!}{4!(3!)}[/tex]
= [tex]\frac{7(6)(5)(4)(3)(2)(1)}{4(3)(2)(1)3(2)(1)\\}[/tex] ← cancel 4(3)(2)(1) on numerator/denominator
= [tex]\frac{7(6))(5)}{3)2)(1)}[/tex]
= [tex]\frac{210}{6}[/tex]
= 35
help me with this asap please
Answers
Answer:
It is linear. The constant rate of change is 3 cents per hour.
Step-by-step explanation:
15/5 = 3
24/8 = 3
36/12 = 3
72/24 = 3
Animal
Is a bird can fly
✓
✓
✓
Pig
Penguin
Seagull
Tiger
Crow
Bat
Mosquito
✓
✓
✓
Let event A = The animal is a bird
Let event B = The animal can fly.
Which outcomes are in A and B?
O A. {seagull, crow}
O B. {penguin, seagull, crow, bat, mosquito}
O c. {penguin, seagull, crow}
☆
O D. (seagull, crow, bat, mosquito)
Need Helpp
Answers
Answer:
A. {seagull, crow}
Step-by-step explanation:
sorry im late but hopefully this helps anyone!
The option A is correct {seagull, crow}.
What is probability?Chance is represented by probability. A part of math manages the event of an irregular occasion. The value is expressed as a number from 0 to 1. Likelihood has been acquainted in Math's with anticipate how likely occasions are to occur. The extent to which something is likely to occur is basically what probability means. The probability distribution is also based on this fundamental probability theory.
Given a table shows relation in Animals is a bird and can fly
where, Let event A = The animal is a bird
Let event B = The animal can fly.
to find the outcomes are in A and B
According to the table, each of the two events provided by the problem describes a condition that must be verified. The first event specifies that it must be a bird, while the second event specifies that it must fly.
Accordingly, the creatures that have the two occasions confirmed in the table are he seagull and crow.
Hence the {seagull, crow} are outcomes are in A and B.
Learn more about probability;
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How many tenths are there in ⅘
Answers
Answer:
8
Step-by-step explanation:
4/5 = ?/10
4/5 * (2/2) = ?/10
8/10 = ?/10
Answer:
8
Step-by-step explanation:
multiply the denominator and numerator, you get 8/10
The area beneath the normal density curve is separated into three regions by the values
and
. Set the mean of the normal density curve to 6.4, the standard deviation to 0.7, and the -value
of
to 6.7. First, determine the value of the area to the right of .
Place
so that it equally divides the area to the left of
. What is the -value
of ?
Answers
The value of the area to the right of X > 6.7 calculated from the normal distribution principle is 0.334
Given the Parameters :
Mean, μ = 6.4Standard deviation, σ = 0.7X = 6.7Using the Zscore formula for a normal distribution :
Zscore = (X - mean) / standard deviationThe Zscore, when X = 6.7
Zscore = (6.7 - 6.4) / 0.7 = 0.4286The area to the right of the distribution :
P(Z > 0.4286) = 1 - P(Z < 0.4286)Using a normal distribution table or calculator :
P(Z > 0.4286) = 1 - 0.66589 = 0.334Therefore, the probability value of P(X < 6.7) is
P(Z > 0.4286) = 0.334Learn more :https://brainly.com/question/8165716
The function h(x) is a transformation of the square root parent function, f(x)= sqrt x . What function is h(x) ?
Answers
Answer:
You can actually change it however you want I just happen to add two underneath the radical which shifted the graph to the left and I subtracted five on the outside of the radical which shifted the graph down five
The function h(x) is a transformation of the square root parent function, f(x)= √x then the function h(x) is√x+2 - 5
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
f(x) = √x
f(x) is a parent function.
a parent function is the core representation of a function type without manipulations such as translation and dilation.
We have to find the function h(x) which is obtained by transforming the function f(x)
From the given graph, the function f(x) is moved up about 2 units and the shifted left of 5 units
h(x) =√x+2 - 5
Hence, the function h(x) is a transformation of the square root parent function, f(x)= √x then the function h(x) is√x+2 - 5
To learn more on Graph click:
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2+31×1/10+14×1/100 is greater smaller or equal to 2.324 and 14+72×1/10+4×1/1000 is greater than smaller than or equal to 21.24 and 0.3×10 to the second power +0.007×10 to the third power is bigger than small that are equal to 0.3×10+0.7×10 to the second power
Answers
Answer:
3457
Step-by-step explanation:670
x2−5x+8 if x=3 plz help
Answers
Answer:
Step-by-step explanation:
if its x to the second power:
(3)^2-5(3)+8= 9-15+8=17-15=2
if it is 2x
2(3)-5(3)+8=6-15+8 =-1
Dylan saves 7% of his $1450.00 bi-weekly net pay. Determine how many periods it will take for Dylan to have $5800.00 saved.
Answers
Answer:
Here,
2 weeks savings is 1450×(7/100) dollars = 101.5 dollars
So, Dylan can save,
101.5 dollars in 1 periods
1 dollars in 1/101.5 periods
5800 dollars in 5800/101.5 periods = 57.142 or 58 periods
Answer = 58 periods
Step-by-step explanation:
...................................................
Answers
Answer:
....................................
Step-by-step explanation:hope i helped
Help me with this math question. Please no links.
Answers
I cant read it, the picture is blurry
Steven uses a
caliper that has an absolute error of 0.02 millimeters. An object's width is measured
using the caliper, which records a width of 14.5 millimeters. What equation would represent the situation?
A. |x-0.02|=14.5
B. |x-14.5|=0.02
C. |0.02-x|=14.5
D. |14.5-0.02|=x
Answers
The relationship between the measured value, error and actual width of the object is |x - 14.5| = 0.02
The measurement error = 0.02 millimeters The measured width of caliper = 14.5 millimetersIf the actual width of the caliper is represented as x
The measurement error is an absolute value which can be calculated thus :|Actual value - measured value| = absolute error |x - 14.5| = 0.02Therefore, the equation which represents the scenario described is |x - 14.5| = 0.02
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