what is the answer for the discriminant of this equation and what are the values of k
Answers
For having a discriminant equal to or larger than zero we must have:
k ≤ 2 and k ≥ 10
How to get the possible values of k?
For a quadratic equation of the form:
y = a*x^2 + b*x + c
The discriminant is:
D = b^2 - 4ac
And the equation has real roots only if the discriminant is equal to or larger than zero.
Here our equation is:
x^2 + (k - 2)*x + (2k - 4) = 0
The discriminant is:
D = (k - 2)^2 -4*1*(2k - 4)
D = k^2 - 4k + 4 - 8k + 16
D = k^2 -12k + 20
The solutions of :
k^2 -12k + 20 = 0
are:
k = (+12 ± √( (-12)^2 - 4*1*20))/(2)
k = (+12 ± 8)/2
The two values of k are:
k = 20/2 = 10
k = 4/2 = 2
The possible values of k are:
k ≤ 2 and k ≥ 10
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Related Questions
In a two-digit number, the units digit is 5 more than the tens digit. The number itself is three times the sum of its digits. What is this number?
Answers
Answer:
The number is 27.
Step-by-step explanation:
Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.
Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.
3 (1 + 6) = 21 does not work because 16 isn't the same as 21.
3 (2 + 7) = 27 does work because 3 * 9 is 27.
3 (3 + 8) = 33
3 (4 + 9) = 39
Evaluate The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1)
Answers
By evaluating The Triple Integral. Triple Integral 7x2 DV, Where T Is The Solid Tetrahedron With Verticies (0, 0, 0), (1, 0, 0), (0, 1, 0), And (0, 0, 1) the value calculated is 7/60.
Given:
= ∫∫∫7[tex]x^{2}[/tex] dV
T(x,y,z) : 0≤x≤1; 0≤y≤1-x; 0≤z≤1-x-y]
apply limits and solving we get:
= 7/2([tex](x^{3} /3+x^{5} /5-x^{4}/2)[/tex]
= 7/2(1/3+1/5-1/2)
= 7/2(1*5+1*3/15 - 1/2)
= 7/2(8/15 - 1/2)
= 7/2(16 - 15/30)
= 7/2*1/30
= 7/60
Therefore after evaluating the value of triple integral is 7/60.
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College freshmen were asked if they were currently enrolled in Composition I. The results are shown in the table.
How many females are currently enrolled in Composition I?
A) 46
B) 73
C) 75
D) 119
Answers
There are 73 females currently involved in the competition.
What is arithmetical operation?The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')
Given that, there is a table of male and female involved and not involved in a competition,
Female column total = 103
103-57 = 46
Female row total = 119
119-46 = 73
Hence, There are 73 females currently involved in the competition.
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Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm and
circle B has a diameter of 16 cm.
How much wider was the pair of
compasses when Alex drew circle A than
when he drew circle B?
Answers
Answer:
Circle B and 3.14 cm
Step-by-step explanation:
Not 100% sure but good luck :)
The length 1 cm wider was the pair of compasses when Alex drew circle A than when he drew circle B.
What is a diameter?A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.
Given:
Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm.
So, the radius is 18/2 = 9 cm.
And circle B has a diameter of 16 cm.
So, the radius is 16/2 = 8 cm.
To find how much wider was the pair of compasses when Alex drew circle A than when he drew circle B:
The difference in the radius,
= 9-8
= 1 cm
Therefore, when Alex drew circle A than when he drew circle B, the compass was wider 1 cm.
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0.75(8+e)=2−1.25e slove for E
Answers
The value of 'E' in the algebraic equation is -2
What is algebraic equation?Algebraic equation is a mathematical statement in which two expressions are set equal to each other.
Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e
Use 0.75 to open the bracket
6 + 0.75e = 2 -1.25e
Collect the like terms
0.75e+1.25e = 2-6
2e = -4
Divide both sides by 2
2e/ 2 = -4/2
e =-2
Therefore, the value of 'E' in the equation is -2
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POPULATION The projected population in thousands for a city over the next several years can be estimated by the
function P(x)=x³ + 2x² - 8x + 520, where x is the number of years since 2005. Use synthetic substitution to estimate
the population for 2015.
O 1,640,000
O 1,320,000
O 590,000
O 36,240,000
Answers
The population for 2015 is 1,640,000 ,so option A is correct.
Given:
The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.
where x is the number of years since 2005.
x = 2015 - 2005
x = 10
P(x) = x³ + 2x² - 8x + 520.
= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]
= 1000 + 2*100 - 80 + 520
= 1520 + 200 - 80
= 1720 - 80
= 1640.
Given the projected population in thousands so = 1640 * 1000
= 1640000.
Therefore The population for 2015 is 1,640,000 ,so option A is correct.
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The circumference of a circle is 47 cm. Find its radius, in centimeters.
Answers
Answer:
The radius (in centimeters) is 18.9999, or roughly 19 centimeters.
Step-by-step explanation:
If you need a step-by-step explanation, please let me know and I will help you. Thanks!
A parabola can be drawn given a focus of
(-8, 1) and a directrix of y=-1. What
can be said about the parabola?
The parabola has a vertex at
( , ) has a p-value of ( )
and it
Answers
We can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing up.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.A parabola refers to the shape that traces the equation of the form ax² + bx + c.
A parabola's directrix is a vertical or horizontal line that never contacts the parabola and is located at p distance from the vertex and 2p distance from the focus.
The parabola created when the directrix is on the y coordinate called a vertical parabola.
If the directrix value is greater than the corresponding focus or vertex, there will be a negative p and the parabola will face downhill.
If the directrix value is less than the corresponding focus or vertex, there will be positive p and the parabola will face up.
From the given definition of the directrix, we can find the value of p;
2p = y coordinate of focus - equation of the directrix
2p = 1 - (-1)
2p = 2
p = 1
Vertex, v(h, k) compared with f(h, k + p), we will get;
k + p = 1
k = 0
Therefore, the vertex is (-8, 0).
Thus, we can say about the parabola given a focus of (-8, 1) and a directrix of y = -1 is as:
The parabola is a vertical parabola and facing down.The vertex of the parabola is v(-8, 0).p value of the parabola is 1.To learn more about directrix of a parabola visit:
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what is 1/3 plus 4.1 in simplest form written as a mixed number
Answers
Hope it helps
QUESTION 10/10 HELP ASAPP
!WILL GIVE BRAINLIEST TO WHOEVER ANSWERS THE OTHER 9 TOO.!
Answers
Answer: tyhe image / screenshot
Step-by-step explanation:
Determine whether f(x) = 1 − x is linear. If so, give the slope and y-intercept.
A. yes
slope = −1
y-intercept = 1
B. false
C. yes
slope = 1
y-intercept = −1
D. yes
slope = 1
y-intercept = 1
Answers
Answer:
a
Step-by-step explanation:
f(x) = y, so y=1-x. the slope is always infront of the x, so if there is nothing infront of x then it'll be a 1. so in this cas slope is a -1 and the y intercept is 1.
Open-Ended Write an equation for the line in slope-intercept form. Use pencil and paper. Which part of writing
the equation is the most difficult? The easiest? Explain.
(Use integers or fractions for any numbers in the equation.)
Answers
The equation of the line in slope-intercept form is y = -5x
How to determine the equation of a line into slope-intercept form?From the question, we have the graph that can be used in our computation
On the graph, we have the following points
(0, 0) and (-1, -5)
Start by calculating the slope using
Slope = (y₂ - y₁)/(x₂ - x₁)
Where,
(x, y) = (0, 0) and (1, -5)
So, we have
Slope = (-5 - 0)/(1 - 0)
This gives
Slope = -5
The equation of the line is then calculated as
y= Slope * (x - X) + Y
So, we have
y = -5 * (x - 0) + 0
Evaluate
y = -5x
Hence, the equation is y = -5x
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A swimming pool is being filled with a hose. The hose fills the pool at a constant rate. The pool’s water level rises 30 inches in 15 hours.
What was the rate per hour of the water level change?
How long will it take for the water level to rise 4 feet?
Answers
Answer:
1. 2 inches per hr
2. 24 hrs
Step-by-step explanation:
30/15=2/1
4ft=48in
48/2=24
hope it helps
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
According to the Pythagoras theorem, the value of the other leg is, 15.7 cm
Pythagoras theorem:
Pythagoras theorem defines that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.
Here we need to find the measure of the other leg and round off it to nearest tenth.
Though the given question, we know that the value of
Hypotenuse = 16 cm
one leg = 3cm,
Then let us consider the length of the other leg as x.
So, according to the Pythagoras theorem,
It can be calculated as,
=> hypotenuse² = one leg² + other leg²
=> 16² = 3² + x²
=> 256 = 9 + x²
Here we need the value of x, so it can be rewritten as,
=> 247 = x²
=> x = √247
When we take square root for 247, then we get the value of x as,
=> x = 15.716
When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.
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Vickie Ewing deposits her savings of $2800 in an investment paying 6% ompounded quarterly and she leaves it there for 5 years. Find (a) the compound amount nd (b) the interest.
Answers
The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $2800
Rate of interest = 6% = 0.06
Compound quarterly n = 4
Time period T = 5 yeras
a)
Total amount = P(1 + R/n)^(nT)
Total amount = 2800(1 + 0.06/4)^(4 x 5)
Total amount = 2800(1.015)^20
Total amount = $3771.19
b)
Let's say the equivalent annual interest rate is r.
n = 1
3771.19 = 2800(1 + r/1)^(1 x 5)
3771.19 = 2800(1 + r)^5
1.061 = 1 + r
r = 0.06136 = 6.136%
Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".
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Write an equation for the line in the slope-intercept form.
slope= 8/9, y-intercept=-4
A) f(x) = 9/8x +9/2
B) f(x) = -8/9x - 4
C) f(x) = 8/9x - 4
D) f(x) = -8/9x + 4
Answers
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
f(x) = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then
f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line
Please help!!!!! ASAP, thank you :)) I’ll give the right answers brainliest
Answers
Answer:
Step-by-step explanation:
ok
You work a basic week of 40 hours and your basic rate is $19.50 per hour. What is your basic wage for the week and showing working for this question.
Answers
If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer
19.50 x 40 = $ 780 a week.
I hope this helps!
What is the sum?
- 1 1/8 + (-1/2) = -1 1/8 + ( - 4/8) = ?
Answers
Answer:
[tex]-1\frac{5}{8}[/tex]
Step-by-step explanation:
-1 1/8 - 1/2 =- 1 1/8 -4/8
= -9/8-4/8
=-13/8
=-1 5/8
Hopes this helps please mark brainliest
Cross multiply the numbers
Answers
Answer:
2m/4m = 9m/xm
2m(xm) = 4m(9m)
2xm = 36m
A flagpole casts a shadow 18m long when the athlete of the sun is 54°. What is the height of the flagpole.
Answers
If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
In the question ,
it is given that ,
the length of the shadow of the flag pole = 18m
the angle of "elevation" of the sun = 54°
let the height of the flagpole be = "x" ,
The flagpole and the shadow form a right triangle ,
So , tan(54°) = (height of flag pole)/(shadow of flagpole)
Substituting the values from above ,
we get ,
tan(54°) = x/18
on cross multiplication ,
x = 18 × tan(54°)
x = 18 × 1.3763
x = 24.7734
x ≈ 24.8
Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
The given question is incomplete , the complete question is
A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?
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Puja Limbu did 8 out of 10 math problem and Raju Lama did 11 out of 15 imilar math problem. Expre the number of problem olved by each of them in fraction and identify who did better performance.
Answers
The person that has a better performance is Puja Limbu.
How to illustrate the information?From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:
= 8/10 × 100
= 80%
Raju Lama did 11 out of 15 similar math problem. This will be:
= 11/15 × 100
= 73%
Therefore, Puja has a better performance.
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Fourteen more than the product of x and y
Answers
Answer:
14+(x*y)
Step-by-step explanation:
Kyle has 80 potatoes he multiples them by 1900 than adds 100000 then he divides them by 53727282 then subtracts 1.5. How many potatoes does Kyle have?
Answers
Answer:
-1.49530965
Step-by-step explanation:
1 What is the cost to get into a Green Cab?
2 How much does it cost per mile for a Green Cab?
3 What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?
Answers
Answer:
1. $5
2. $1 per mile
3.y=x+5
Step-by-step explanation:
1. If you look at the graph you can see that the cost for 0 miles with the Green Cab is $5
2.If you look at the graph, for each mile traveled, the cost is $1
3. Since for each increase 1 increase in x, y increases by the same amount, the slope is 1
y=mx+b is the slope intercept form
m=slope
b=y intercept
since we know the slope is 1 we can put it in
y=1x+b
=y=x+b
to find the y intercept we can look at the graph and see what y equals when x is 0.
the y intercept is (0,5)
we can put that in so the equation in slope intercept form is
y=x+5
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1. Find the
radius of the circle to the nearest 10th.
Answers
The radius of the circle to the nearest 10th is 2.0537.
Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.
we know that,
radians = arc / radius
radius = arc/radians
= 19.1/9.3
= 191/10/93/10
= 191/93
≈ 2.0537
Therefore the radius of the circle to the nearest 10th is 2.0537.
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Use point-slope form to write the equation of a line that passes through the point (-7,-8) with slope -3/11
Answers
Answer:
y + 8 = -3/11(x+7)
Step-by-step explanation:
What is the point-slope form formula?
y-y1=m(x-x1) -------> y+8=-3/11(x+7)
HELP! PLEASE! I WILL NAME YOU THE BRAINLIEST!
Solve the system by graphing.
y = 1/3x - 1
x - 3y = 3
(6, 1)
(0, −1)
This system has no solutions.
This system has infinitely many solutions.
Answers
Answer:
This system has infinitely many solutions.
Step-by-step explanation:
The graphic in both functions is the same line, which means the system has many solutions
Leah makes $3.25 per hour. Lois makes $8.64 per hour. How much more does Lois make per hour than Leah
Answers
Answer:
$11.89 is the answer
Step-by-step explanation:
because $3.25 + $8.64 is $11.89
Hope this helps
What is the independent variable
Answers
Answer:
Your answer is correct.
Step-by-step explanation:
Answer:
p
Step-by-step explanation:
when p changes, it causes the equation to change