The nature of roots of quadratic equation 5x²- 4x +5= 0
are unreal.
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, a and b are the coefficients, and c is the constant term.
Nature of Roots of the Quadratic Equation
The symbols alpha () and beta () are typically used to denote a quadratic equation's roots. Here, we'll learn more about how to identify a quadratic equation's nature without locating the equation's roots. Additionally, look at the formulas for calculating the product and sum of the equation's roots.
Without actually locating the roots (, ) of the equation, the nature of the roots of a quadratic equation can be determined. By using the discriminant value, which is a component of the quadratic equation solution formula, this is made achievable. The discriminant of a quadratic equation is denoted as "D" and has the value b2 - 4ac. Using the discriminatory value as a basis, the nature of the roots of the quadratic equation can be predicted.
Discriminant: D = b2 - 4ac
D > 0, the roots are real and distinct
D = 0, the roots are real and equal.
D < 0, the roots do not exist or the roots are imaginary.
From the given quadratic equation, we can observe that:
a = 5
b = -4
c = 5
On finding discriminant, we get:
D = b² - 4ac
D = (-4)² - (4 × 5 × 5)
D = 16 - 100
D = -84
We can notice that, D(-84) < 0, which means the roots are unreal. Therefore, no roots exist!
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The nature of roots of quadratic equation 5x²- 4x +5= 0
are unreal.
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, a and b are the coefficients, and c is the constant term.
Nature of Roots of the Quadratic Equation
Discriminant: D = b2 - 4ac
D > 0, the roots are real and distinct
D = 0, the roots are real and equal.
D < 0, the roots do not exist or the roots are imaginary.
From the given quadratic equation, we can observe that:
a = 5
b = -4
c = 5
D = b² - 4ac
D = (-4)² - (4 × 5 × 5)
D = 16 - 100
D = -84
We can notice that, D(-84) < 0, which means the roots are unreal. Therefore, no roots exist!
Ali's mom filled the cookie jar with 7 chocolate chip cookies, 6 peanut butter cookies, and 2 raisin cookies. She filled the candy jar with 14 peppermints and 12 caramels. If Ali randomly pulls one cookie and one candy from each jar, what is the probability that she pulls a raisin cookie and a peppermint?
Answer:
Probability: 131/195
Step-by-step explanation:
Total cookies:
7 + 6 + 2 = 15
Total candies:
14 + 12 = 26
Probability of raisin:
2/15
Probability of peppermint:
14/26 = 7/13
Probability of both:
2/15 + 7/13
131/195
students make a rectangular banner that is 2 feet 6 inches wide and 84 inches long what is the perimeter
Answer:
6 + 2 = 8 which is the width.
8 + 8 = 16
84 + 84 = 168
168 + 16 = 184 in
Answer:
228 inches
Step-by-step explanation:
2 feet 6 inches = 30 inches
2(30in+84in) =228 in
In October of 2010 it rained 4 inches. In October of 2011 it rained 2.6 inches. What is the percent decrease in October rainfall?
Which is the most accurate way to estimate 25% of 14?
A: 2/3 x 12
B: 1/4 x 12
C: 3/4 x 12
D: 1/2 x 12
Answer:
2/3 x 12=8
1/4 x 12= 3
3/4 x 12 =9
1/2 x 12 = 6
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Answer:
Hieight is 65m
volume is 35
Step-by-step explanation:
A 12 foot ladder is leaning against a wall and the foot of the ladder is 5 feet away from the wall. What is the angle between the ground and the ladder
Answer:
65.38degrees
Step-by-step explanation:
Given the following
Length of ladder = 12foot = hypotenuse
Distance of the ladder from the wall = 5ft = adjacent
Required
Angle between the ground and the ladder theta
Using the SOH CAH TOA identity
Cos theta = adj/hyp
Cos theta = 5/12
Cos theta = 0.41667
theta = arccos(0.41667)
theta = 65.38 degrees
Hence the angle between the ground and the floor is 65.38degrees
Find the equation of a line that is perpendicular to 4x+6y=1 and that has a greater intercept to the line 2x+3y=18
Answer:
The equation of the the line that is perpendicular to 4·x + 6·y = 1 and that has a greater intercept to the line 2·x + 3·y = 18 can be 2·y - 3·x = 14
Step-by-step explanation:
The line which is perpendicular to the required line = 4·x + 6·y = 1
The line with which the required line has a greater intercept = 2·x + 3·y = 18
Solution;
The relationship between the slope, m₁, of a straight line, y = m₁·x + c₁ perpendicular to another straight line, y = m₂·x + c₂, with slope m₂ is given as follows;
m₁ = -1/m₂
Rewriting the equation of the given line in slope and intercept form gives;
4·x + 6·y = 1
6·y = 1 - 4·x
y = 1/6 - 4·x/6 = 1/6 - 2·x/3 = 1/6 - (2/3)·x
∴ y = 1/6 - (2/3)·x
Therefore, the slope, 'm₁', of the line y = 1/6 - (2/3)·x, is m₁ = -(2/3)
The slope of the perpendicular line, is therefore, m₁ = -1/m₂
∴ m₂ = -1/m₁
m₂ = -1/(-(2/3)) = 3/2
The intercept of a straight line of the form y = m·x + c is 'c'
The intercept of the line 2·x + 3·y = 18 is obtained by rewriting the equation of the line in slope and intercept form as follows;
2·x + 3·y = 18
y = 18/3 - (2/3)·x = 6 - (2/3)·x
y = 6 - (2/3)·x = -(2/3)·x + 6
y = -(2/3)·x + 6
By comparing the above equation to the equation, y = m·x + c, we have;
c = 6
The intercept of the line y = -(2/3)·x + 6, which is the same line as 2·x + 3·y = 18 is 6
∴ The intercept of the required line, c₂ > 6
The equation of the required line in slope and intercept form, y = m·x + c, can therefore be;
y = (3/2)·x + 7
By multiplying by 2, we get;
2·y = 3·x + 14
∴ The equation of the line can be 2·y - 3·x = 14.
Find the height of the pyramid.
Answer:
hight is 158
Step-by-step explanation:
yall some hot cheetos with some fresh lime juice and Tajin be bussin P.S im eating some right now tehheee
what yall fav snack combo
Answer:
ruffles classic + those two bite cupcakes literally best thing to exist
Step-by-step explanation:
Answer:
Honestly, twinkies with twinkies
Step-by-step explanation:
#WhyNot
Math equations giving Brainliest
Last week, an information centre had 950 visitors. This week it had 1026 visitors. What is the percentage increase?
Answer:
8%
Step-by-step explanation:
Find the percent increase by dividing the difference in visitors by the original amount, then multiply it by 100
(76/950) x 100
= 8
So, the percent increase is 8%
Use the scatter plot of car resale values to answer the following question.
A graph titled Car Resale Values has age of car on the x-axis, from 0 to 10 in increments of 2, and percentage of sticker price on the y-axis, for 0 to 100. A line of best fit goes through points (2, 80) and (9, 20).
What can you say about the correlation between the age of a car and its resale value?
a.
The trend line slopes downward from upper left to lower right, so there is a negative correlation between a car’s age and its resale value.
b.
The trend line slopes downward from upper left to lower right, so there is a positive correlation between a car’s age and its resale value.
c.
The trend line slopes upward from lower right to upper left, so there is a positive correlation between a car’s age and its resale value.
d.
There is no correlation between a car’s age and its resale value.
Please select the best answer from the choices provided
A
B
C
D
Answer:
A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
taking the practice assignment
Please help me with this homework please
Answer:
x = 15
Step-by-step explanation:
x² = 12² + 9²
x² = 144 + 81
x² = 225
x = √225
x = 15
In circle O, mZR = 23. Find mzo. (The figure is not drawn to scale.)
e
R
O 46
23
67
157
Answer:
A. 46Step-by-step explanation:
m<R=23
m<NQ=2(23)=46
m<O=m NQ =46
hope it helps....
✏---------------
m∠R=23mNQ=2(23)=46m∠O=m NQ=46➜➜➜➜➜➜
hope it helps
have a great day!!
You pick from cards at random 2 4 5 6 7 8 9 Which is P(prime)
Answer:
2, 3, 5, 7
Step-by-step explanation:
They are all prime
Answer: 2,3,7,5
Step-by-step explanation:
2 is an exeption for a prime number but 3,7,5 are only diviusible by 1 and itself
help me please!!!
What is the value of -3x^5+ 2x^2+ x -5 when x = -1
Answer:
-1
Step-by-step explanation:
Plug in calculator
-3(-1)^5+2(-1)^2-1-5 = -1
Matthew wants to purchase a new couch, but he does not have enough money in his bank account to pay for one.
Which of these is not an option for Matthew?
He can save money and write a check once there is enough money in his account.
He can use his debit card to purchase the couch now.
He can use his credit card to purchase the couch now.
He can save money and pay cash once he has enough.
Answer:
He can use his debit card to purchase the couch now.
Step-by-step explanation:
The graph represents the piecewise function:
pls help asap! ill give brainliest:))
Answer:
the answer should be 38.75
Find the coordinates of the point which divides the join of (-1,7) and (4.-3) in the ratio 2:3 ??
Please don't post invalid answer ..
please
Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 ?
Solution:-Let the given points be A(-1,7) and B(4,-3)
Now,
Let the point be P(x, y) which divides AB in the ratio 2:3
Here,
[tex] { \bf x \: = \frac{m_1 x_2 \: + \: m_1 x_1}{m_1 \: + \: m_2}} [/tex]Where,
[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3
[tex] x_1 [/tex] = -1 , [tex] x_2 [/tex] = 4
[tex] \therefore [/tex] Putting values we get,
x = [tex] \frac{2 \: × \: 4 \: + \: 3 \: × \: -1}{2 \: + \: 3} [/tex]
x = [tex] \frac{8 \: - \: 3}{5} [/tex]
x = [tex] \frac{5}{5} [/tex]
x = 1
Now,
Finding y
[tex] { \bf y \: = \frac{m_1 y_2 \: + \: m_2 y_1}{m_1 \: + \: m_2}} [/tex]Where,
[tex] m_1 [/tex] = 2 , [tex] m_2 [/tex] = 3
[tex] x_1 [/tex] = 7 , [tex] x_2 [/tex] = -3
[tex] \therefore [/tex] Putting values we get,
y = [tex] \frac{2 \: × \: -3 \: + \: 3 \: × \: 7}{2 \: + \: 3} [/tex]
y = [tex] \frac{-6 \: + \: 21}{5} [/tex]
y = [tex] \frac{15}{5} [/tex]
y = 3
Hence x = 1, y = 3
So, the required point is P(x, y)
= P(1, 3)
The coordinates of the point is P(1, 3). [Answer]_______________________________________
Note:- Refer the attachment.
_______________________________________
HELP HELP HELP!! ILL MARK BRAINLIEST
Answer: i think its the 3rd one
Step-by-step explanation:
ū= (5,8)
Find the direction angle of ū.
Enter your answer as an angle in degrees between 0 and 360° rounded to the nearest hundredth.
Assuming the angle made by a vector refers to the angle it makes with the positive horizontal axis, take the dot product of u with the vector (1, 0), and recall that
a • b = ||a|| ||b|| cos(θ)
where θ is the angle made by the vectors a and b. Then
u • (1, 0) = ||u|| ||(1, 0)|| cos(θ)
We have
u • (1, 0) = 5×1 + 8×0 = 5
||u|| = √(5² + 8²) = √89
||(1, 0)|| = √(1² + 0²) = √1 = 1
so that
5 = √89 cos(θ)
cos(θ) = 5 / √89
θ = arccos(5 / √89) ≈ 57.99°
What is the domain of the function graphed below?
Answer:
the answer is c
Step-by-step explanation:
Domain is [tex]{ x|x\neq -1,2,4}[/tex]
What is domain ?The domain of a function is the complete set of possible values of the independent variable.
The domain is the set of all possible x-values which will make the function "work", and will output real y-values
We need to find the domain of the function graphed
Domain are the values of x for which the function is defined.
For domain, we look at the x values of the graph.
We have graph for x values the graph goes close to x = -1 and x = 4 axis but does not cross x = -1 and x = 4axis. and at x =2 not define
So , domain is set of all x values [tex]{ x|x\neq -1,2,4}[/tex]
Hence, domain is [tex]{ x|x\neq -1,2,4}[/tex]
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What is 3/4 divided by 1/2
Respuesta: 3/2= 1 1/2
Answer:
1 1/2 or 1.5
Step-by-step explanation:
To divide a fraction, use the phrase, "keep, change, flip"
We keep the first fraction as it is, change the sign to multiplication, and flip the second fraction to its multiplicative inverse.
So 3/4 divided by 1/2 becomes:
3/4 x 2/1
= 6/4 = 1 1/2
Un cilindru circular drept are raza bazei egală cu 27 , iar înălțimea cilindrului este egală cu 11 . (unitatea de măsură o alegi tu). De aflat aria totală și volumul cilindrului. VA ROG URGENT
Answer:
1) 6447,55 unități pătrate
2) 25192,43 unități cubice
Step-by-step explanation:
1) Suprafața totală a unui cilindru
Formula = 2πr (r + h)
r = 27 de unități
h = 11 unități
Suprafața totală = 2 × π × 27 × (27 + 11)
= 6446.54813 unități pătrate
Aproximativ = 6447,55 unități pătrate
2) Volumul cilindrului
Formula = πr²h
= π × 27² × 11
= 25192,43 unități cubice
‼️ PLEASE HELPPPP ‼️
Answer:
blank 1- 2304
blank 2- 2736
Step-by-step explanation:
hope it helps
Which function has a graph with
x-intercepts of (-2, 0) and (7,0)?
The photo is the answers
Select all the expressions that equal 6 to the power of-10.
6−5⋅62
(16)5
(6−5)2
6−367
65⋅6−36−8
Answer:
I will say answer A but I don't know
Step-by-step explanation:
What is greater or are they equal
1. 8.13 or 8.4
2. 0.004 or 0.05
3. 0.4repeating or 0.4
Answer:
Step-by-step explanation:
8.13<8.4
.004<.05
.4 repeating>.4
What is the solution, and independent and dependent veribles?
Answer:
The independent variable is the cost of the item ([tex]d[/tex]), whereas the dependent variable is the change ([tex]c[/tex]) received by Darrel, since that quantity is calculated by subtracting the cost of the item from the value of the bill. The equation is the following linear equation: [tex]c = 20.00 - d[/tex]
Step-by-step explanation:
The independent variable is the cost of the item ([tex]d[/tex]), whereas the dependent variable is the change ([tex]c[/tex]) received by Darrel, since that quantity is calculated by subtracting the cost of the item from the value of the bill. The equation is the following linear equation: [tex]c = 20.00 - d[/tex]