Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the
discriminant value, how many real number solutions does the equation have?
Discriminant = b2-4ac
Answers
Given -
x² + 4x + 1 = -3
To find -
the discriminant for the quadratic equation and to find how many real number solutions does the equation have. If it's discriminant = b² - 4ac
Concept applied -
As we know, Discriminant = b² - 4ac
A quadratic equation ax²+ bx + c = 0 has -
two distinct real roots, if b² - 4ac > 0 , two equal roots (i.e., coincident roots), if b²- 4ac = 0, and no real roots, if b² - 4ac < 0.Solution -
Solving the quadratic equation to bring it in the form of ax² + bx + c = 0,
➛ x² + 4x + 1 = -3
➛ x² + 4x +3 + 1 = 0
➛ x² + 4x + 4 = 0
Here,
a = 1, b = 4 and c = 4.
Putting the values in the the formula, b²- 4ac = 0.
➙ (4)²- 4(1)(4)
➙ 16- 16
➙ 0
As, b²- 4ac = 0 hence the quadratic equation will have two equal roots (i.e., coincident roots).
Answer:
1 aka b
Step-by-step explanation:
Related Questions
if a polynomial is divided by x-5, the quotient is 2x^2 +8x-9 and the remainder is 3 what is the original polynomial?
Answers
Answer:
[tex]P(x)=2x^3-2x^2-49x+48[/tex]
Step-by-step explanation:
Let the original polynomial be [tex]P(x)[/tex].
We know that when it is divided by [tex](x-5)[/tex], the quotient is [tex]2x^2+8x-9[/tex] and we get a remainder of 3.
Therefore, this means that:
[tex]\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}[/tex]
Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 over 3. We put the remainder over the divisor. This is the same thing for polynomials.
So, to find our original polynomial, multiply both sides by [tex](x-5)[/tex]:
[tex](x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})[/tex]
The left side will cancel. Distribute the right:
[tex]P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)[/tex]
Distribute:
[tex]P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)[/tex]
Combine like terms:
[tex]P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)[/tex]
Evaluate:
[tex]P(x)=2x^3-2x^2-49x+48[/tex]
And we're done!
Explanation:
Let a be the original polynomial
Where a/(x-5) = 2x^2 + 8x - 9 (remainder 3)
a = (2x^2 + 8x - 9)(x-5) + 3
a = 2x^3 - 10x^2 + 8x^2 - 40x - 9x + 45+3
a = 2x^3 - 2x^2 - 49x + 48
Zeroes of p(x)=x^-2x-3 are
Answers
Answer:
x=3 x= -1
Step-by-step explanation:
(x-3)(x+1)
x-3=0. x+1=0
x=3 x= -1
While playing football, John lost 4 yds, then gained 15 yds, then lost 4 yds. How many yards did he gain from the three plays?
Answers
Answe
Step-by-step explanation:
Simplify completely: (3 - 5i)(6 + i)
Answers
Answer:
9+6i
Step-by-step explanation:
3+6=9
5+1=6
a cube has a volume 512 cubuc feet. what is the side length?
Answers
Answer:
The cube is a 8x8x8
so a side length is 8
Thx guys (i will vote brainliest)
have an awesome day
djkal;fjkdla;jkdfl;ghkjhkjlhklkjlhkjl
Answers
Answer:
THANKS FOR THE POINTS!!!
Step-by-step explanation:
will give brainliest
Answers
Answer:
Pain Pain Pain Pain Pain now where is my brainliest you promised me
Step-by-step explanation:
AACB = ADCE
ZB = 61°, ZC = 57°, and ZD = 2x
D
E
A
с
X = [?]
B
Answers
Answer:
x = 31
Step-by-step explanation:
Given that the triangles are congruent, then corresponding angles are congruent, then
∠ D = ∠ A
The sum of the 3 angles in a triangle = 180° , thus
∠ A = 180° - (61 + 57)° = 180° - 118° = 62°
Thus
2x = 62 ( divide both sides by 2 )
x = 31
Cars are made in a factory for 24 hours every day.
In the factory a car is made every 209 seconds.
Work out an estimate for the number of cars made in the factory in one year.
Answers
Answer:
6,591,024,000
Step-by-step explanation:
Minutes in 24 hours=1,440
number of seconds in 24 hours=60*1440
=86,400..
number of cars made in each second=209
number of cars made in 86,400 seconds= 18,057,600
24 hours =one day
1 year =365 days
cars made in one year =365*18,057,600
=6,591,024,000
therefore, the number of cars made in one year =
6,591,024,000
The number of cars made in the factory in one year where cars are made for 24 hours every day is 150891.
What is the relation between work and time?The total time taken is inversely proportional to the rate of work. If a unit of work is done in total n number of days, then the total work done W in a day can is,
[tex]W=\dfrac{1}{n}[/tex]
In a factory, cars are made, where Cars are made for 24 hours every day. As, there is total 60 seconds in one minute and 60 minutes in one hour. Thus, the number of second in 24 hours is,
[tex]24\times60\times60=86400[/tex]
In the factory, a car is made every 209 seconds. Thus, the number of cars made in 86400 seconds (24 hours),
[tex]\dfrac{86400}{209}=431.4[/tex]
There is total 365 days (24 hours) in one year. Thus, the number of cars made in the factory in one year is,
[tex]431.4\times365=150891[/tex]
Thus, the number of cars made in the factory in one year where cars are made for 24 hours every day is 150891.
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At a baking competition, 0.5 dishes were cooked by Room 102, 3/10 were cooked by Room 104, and 1/5 were cooked by Room 106. What fraction of the dishes were cooked by Rooms 102 and 104? Express your answer in the simplest form.
Answers
Simplifying the fraction: 4/5
Answer would be 4/5 of the dishes were cooked by rooms 102 and 104
Hope it helps! Good luck!
Mark me as brainliest pls!
The fraction of the dishes were cooked by Rooms 102 and 104 is 4/5
Addition of fractionDishes cooked by Room 102 = 0.5 = 1/2Dishes cooked by Room 104 = 3/10Dishes cooked by Room 106 = 1/5Fraction of the dishes were cooked by Rooms 102 and 104 = 1/2 + 3/10
= (5+3) / 10
= 8 / 10
= 4 / 5
Therefore, the fraction of the dishes were cooked by Rooms 102 and 104 is 4/5 in the simplest form
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On a 30-question test, Janice answered four-fifths of the questions correctly. Which of the following is the number of questions she answered correctly?
(1) 24
(2) 25
(3) 26
(4) 28
Answers
Hi!
Your answer should be: (4) 28.
Hope this helps!
Yours truly,
~~~PicklePoppers~~~
You need a loan of $110 comma 000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices. Choice 1: 15-year fixed rate at 6% with closing costs of $1200 and no points. Choice 2: 15-year fixed rate at 5.5% with closing costs of $1200 and 4 points.
What is the monthly payment for choice 1? $
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answers
Answer:
Monthly payment for choice 1 is $6,600
Step-by-step explanation:
We will use following formula in order to calculate the monthly payment of choice 1
Value of Loan = Monthly payment x ( 1 - ( 1 + Interest rate )^-numbers of payments / interest rate
Where
Value of Loan = $110,000
Interest rate = 6%
Numbers of Payment = 15 years x 12 payments / year = 180 payments
Placing values in the formula
$110,000 = Monthly payment x ( 1 - ( 1 + 6% )^-180 ) / 6%
$110,000 = Monthly payment x 16.6662
Monthly Payment = $110,000 / 16.6662
Monthly Payment = $6,600.18
Monthly Payment = $6,600 (Rounded to whole number)
If angle 2 = 48, determine the measure of angle 5.
Answers
Answer:
Angle 2 = 48
we are going to divide 48 by 2 to get the Angle 1
Angle 1 = 24
then Angle 5 = (5×24)
Angle 5 = 120
Corey is reading a graph of equivalent ratios. If one of the ratios is represented as (3, 5), which could be another ratio?
Answers
Answer:
another ratio is 3:5=6:10 or 9:15
Explanation:
3:5×2=6:10
3:5×3=9:15
Answer:
(9,15) aka C
Step-by-step explanation:
3 times 3 is 9 and so you multiply the same number to the y-coordinate. 5 times 3 is 15!
2. Describe the graph of the line y = 15. .
Answers
Answer:
it is a horizontal line resting at 15 on the y axis
Step-by-step explanation:
because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies
The graph of the function y=15 is the horizontal line resting at 15 on the y-axis
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the function y=15 is the horizontal line resting at 15 on the y-axis because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies.
Therefore the graph of the function y=15 is the horizontal line resting at 15 on the y-axis. The graph is attached with the answer below.
To know more about graphs follow
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??????????????????.?..
Answers
You have found a jackpot, say what ever you want
Answers
Answer:
haha
Step-by-step explanation:
doing this for points
Answer:
jackpot
Step-by-step explanation:
In 2005, MusicMart sold 14,550 CDs. In 2010, they sold 12,000 CDs. What is the rate of change in the number of CDs sold?
A) -2550 per yr B) -510 per yr C) -425 D) -2400 per yr
Answers
Answer:
B) -510 per yr
Step-by-step explanation:
2005 = 14,550 CDs sold
2010 = 12,000 CDs sold
Difference in years = 2010 - 2005
= 5 years
Difference in CDs sold = 12,000 - 14,550
= - 4,550
Rate of change in the number of CDs sold = change in the number of CDs / change in years
= -4,550 / 5
= -510 per year
The correct answer is B) -510 per yr
Given g(x) = 4x−8, find g(1/2).
Answers
Answer:
4(1/2) = 2
2-8 = -6
-6 is your answer
hope this helps!
For finding g(1/2) you need to substitute the value of x= 1/2
Thus , g(1/2):
[tex] = 4 \times \dfrac{1}{2} - 8[/tex]
[tex] = 2 - 8[/tex]
= [tex]\red{\bold{\large{-6}}}[/tex]
The area of the circle is 144π m2
What is the diameter of the circle?
Answers
Answer:
Step-by-step explanation:
Remember that
Area of Circle = [tex]\pi r^2[/tex]
[tex]\pi = pi \\r = radius[/tex]
They told us that for this circle, the area is [tex]144\pi m^2[/tex]
If you put it back into the formula for area of a circle we get:
Area of Circle = [tex]\pi r^2[/tex]
[tex]144\pi = \pi r^2[/tex]
Divide both sides by [tex]\pi[/tex].
144 = [tex]r^2[/tex]
Now we want to solve for r (r = radius).
You need to square root each side
[tex]\sqrt{144} = \sqrt{r^2}[/tex]
[tex]12 = r[/tex]
So now we know the radius, [tex]r = 12[/tex] metres
Also remember that
Diameter = [tex]2r[/tex]
So,
Diameter = 2 times 12 = 24 metres
The required diameter of the given circle is 24 meters.
What is an area circle?The area of the circle is given by the pie times square of the radius.
Area of circle = πr^2
Here,
The given area of the circle is 144π m²
And we know that,
Area = πr²
substitute the value of the area in the above expression,
144π = πr²
r² = 144
r = √144
r = 12 meters
Since,
Diameter = 2 × radius
Diameter = 2 × 12 = 24 meter
Thus, the required diameter of the given circle is 24 meters.
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Name 21 and 22 another way.
Answers
Answer:
B
Step-by-step explanation:
Bryan has $15 to spend on taxi fare. The
ride costs $5 plus $2.50 per mile. How
many mile can Bryan go without spending
all $15?
Answers
Answer:
3 full miles; anything less than 4 miles
Step-by-step explanation:
5 + 2.50x = 15
subtract 5 from both sides
2.50x = 10
divide both sides by 2.50
x = 4
4 miles is how long he can travel by spending all $15
Anything less will cost him less than $15
Answer:
4 miles
Step-by-step explanation:
well we have a budget of 15$. We use 5$ for the ride so we have 10$ left. 10/2.5 is 4.
PLEASE HELP MEEEEEE ILL GIVE MAX POINTS AND BRAINIEST TYSMMM <33333
Answers
Answer:
Please see below :)
Step-by-step explanation:
4 cubed + 8 is the sum.
y is the variable.
9/y is the quotient.
Hope this helps!
Answer:
Please see below :)
Step-by-step explanation:
4 cubed + 8 is the sum.
y is the variable.
9/y is the quotient.
Hope this helps!
In the diagram shown below PS is perpendicular to RT and the two lines intercept at W. Ray WQ is drawn. Which of the following statements about angle pairs in incorrect?
Answers
Answer:
D. angle SWT and angle QWT are complementary
Step-by-step explanation:
The angles formed at W when the two lines, PS and RT, which are perpendicular to each other intercept at W are right angles.
Thus, let's analyse each given statements to see which is true or not true about the angle pairs formed:
Statement 1: "angle PWQ and angle QWT are complementary".
m<PWT = 90°.
m<PWQ + m<QWT = m<PWT (angle addition postulate)
m<PWQ + m<QWT = 90° (definition of complementary angles)
Therefore, statement 1 is CORRECT.
Statement 2: "angle PWR and angle TWP are supplementary".
m<PWR = 90°
m<TWP = 90°
m<PWR + m<TWP = 180° (definition of supplementary angles)
Therefore, statement 2 is CORRECT.
Statement 3: "angle RWQ and angle TWQ are supplementary".
<RWQ and <TWQ are angles on a straight line and are a linear pair.
m<RWQ + m<TWQ = 180° (definition of supplementary angles)
Therefore, statement 3 is CORRECT.
Statement 4: "angle SWT and angle QWT are complementary".
m<SWT = 90°
Therefore, m<SWT + m<QWT ≠ 90°
The sum of both angles does not give 90°. Therefore, statement 4 is INCORRECT.
(03.03 HC)
The table shows the outputs, y, for different inputs, x:
Input (x) 1 2 3 4
Output (y) 5 5 7 9
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Answers
inverse function of f(x)=100+4x
Answers
Answer:
[tex]f(x)^{-1} =\frac{x}{4} -25[/tex]
Step-by-step explanation:
This is the inverse function of f(x)=100+4x
if 5y - 8 < 12, what is the maximum possible value of 10y ?
Answers
Answer: The maximum possible value of y is 30 ;)
Please help! Solve for m in the mathematical formula y=m x+b.
Answers
Answer:
[tex]\frac{y-b}{x}[/tex]=m
Step-by-step explanation:
y=mx+b
-b -b
y-b=mx
[tex]\frac{y-b}{x}[/tex] = [tex]\frac{mx}{x}[/tex]
[tex]\frac{y-b}{x}[/tex]=m
What is the value of k?
M
115°
Y
Z
(4k+5)
(6k + 10)
Answers
Answer:
please add the image coz it's not clear
An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles, using this property we get, the value of k is: k = 10.
Here, we know that, an exterior angle is equal to the sum of the two opposite inside angles.
The picture shows an exterior angle of 115 degrees.
It's two opposite inside angles are the two equations.
This means:
(4k +5) + (6k+10) = 115
Combine like terms:
10k + 15 = 115
Subtract 15 from both sides:
10k = 100
Divide both sides by 10:
k = 100/10
k = 10
Hence, The value of k is: k = 10.
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complete question:
attached
An ice skating show earned 15,385 in one night. Tickets for the show cost $25 for adults and $15 for children. The number of adults who attendee the shw was 41 more than the number of children who attended the show. How many adults and children attended the show?
Answers
Answer:
Number of adults that attended the show = 400
Number of children that attended the show = 359
Total people who attended the show = 759
Step-by-step explanation:
Total earned = 15,385
Adults = $25
Children = $15
Let
Adults = A
Children = C
The number of adults who attendee the show was 41 more than the number of children who attended the show
A = C + 41
25A + 15C = 15,385
Substitute
A = C + 41
25(C+41) + 15C = 15,385
25C + 1,025 + 15C = 15,385
40C + 1,025 = 15,385
40C = 15,385 - 1,025
40C = 14,360
Divide both sides by 40
C = 14,360 / 40
= 359
C = 359
Substitute C = 359 into
A = C + 41
A = 359 + 41
= 400
A = 400
Number of adults that attended the show = 400
Number of children that attended the show = 359
Total people who attended the show = 759