prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k
The roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
The equation is given as:
x^2 + (1 - k).x+k-3 = 0
For an equation to have real root, then the following must be true:
[tex]b^2 \ge 4ac[/tex]
In x^2 + (1 - k).x+k-3 = 0, we have:
a = 1
b = 1 - k
c = k - 3
So, we have:
[tex](1 - k)^2 \ge 4 * 1 * (k - 3)[/tex]
Evaluate
[tex]1 - 2k + k^2 \ge 4k - 12[/tex]
Collect like terms
[tex]k^2 - 2k - 4k + 1 + 12 \ge 0[/tex]
[tex]k^2 - 6k + 13 \ge 0[/tex]
Using a graphing calculator, the value of k is all real numbers
Hence, the roots of x^2 + (1 - k).x+k-3 = 0 are real for all real values of k
Read more about real values at:
https://brainly.com/question/6499629
In order to determine whether or not there is a significant difference between the mean hourly wages paid by two companies (of the same industry), the following data have been accumulated.
Company A Company B
Sample size 80 60
Sample mean $16.75 $16.25
Population standard deviation $1.00 $.95 The p-value is:_________
a. 0.0084.
b. 0.0042.
c. 0.0026.
d. 0.0013
Answer:
The p-value is;
d. 0.00131
Step-by-step explanation:
The given question parameters are;
Company A [tex]{}[/tex] Company B
Sample size 80[tex]{}[/tex] 60
Sample mean [tex]{}[/tex] [tex]\overline x_1[/tex] $16.75 [tex]\overline x_2[/tex] $16.25
Population standard deviation [tex]{}[/tex] σ₁ $1.00 σ₂ $0.95
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}+\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Therefor, we have;
[tex]z=\dfrac{(16.75-16.25)-(0-0)}{\sqrt{\dfrac{1^{2} }{80}+\dfrac{0.95^{2}}{60}}} \approx 3.0128[/tex]
The p-value = 1 - 0.99869 (the area to the right of 3.01) = 0.00131
Write in summation notation.
11) -2+ 1 + 4+...
+ 13
I’ll give brainliest to whoever answers correctly first
find the quotient 1 7/8 / 5 5/8
please write an equation of a line in slope-intercept form with the given slope and y-intercept.
A. slope: -6, y-intercept: -2
B. slope: 1, y-intercept: -12
I need help understanding problem number 2
Step-by-step explanation:
(2×2) . 2×2×2×2 . 2×2×2
=(4) . 16 . 8
Which function is represented by the graph below?
Answer:
Step-by-step explanation:
y=-4x+2
Answer:
y=2x-4
Step-by-step explanation:
Becuase the x axis croses -4, so you would draw a line starting at the bottom through negative 4. Then since their is a positive 2 you would keep drawing the line on the untill you see a 2 which would be on the y axis.
I need help ASAP ! I’ll give anyone 5 stars for the correct answer
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 2x - 10 \\ f( - 2) = { (- 2)}^{2} + 2( - 2) - 10 = \\ = 4 - 4 - 10 = - 10[/tex]
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the u.s. landfill contained a total of 200 million tons of trash how many more million tons of trash has been paper than Rubber and leather?
Answer:
9,160,000 tons
what is the equation to 3x+2x+-x
Answer:
the answer qould be 4x if you are just simplifying
Find the radius of a circle in which the central angle, a, intercepts an arc of the given length
a = 30°, s = 9in
Answer:
17.2 in
Step-by-step explanation:
The formula for arc length is s = rФ. Here we are to find r. Solving this formula for r, we get:
r = s/Ф
So, in this problem, r = (9 in) / (π/6) = 54/π in ≈ 17.2 in
The volume of a large aquarium is 210 ft it is 3 3/5ft wide and 2 4/5 ft high what is the length of the aquarium
Answer:
21 ft
Step-by-step explanation:
Solve for x Enter the solutions from least to greatest . (x - 4)(- 5x + 1) = 0 lesser x = greater x =
Answer:
dont know maybe someone else can help u
:€
Answer:
lesser x=1/5
greater x =4
Step-by-step explanation:
Please refer to the attachment
Tell whether the angles are adjacent or vertical. Then find the value of x. (4x-25)
Answer:
i dont see the angles but heres how to solve for X
Step-by-step explanation:
Solve for n.
2(n + 5) = 18, n=
Answer:
n=14
....................
Answer:
n = 4Step-by-step explanation:
See the steps:
2(n + 5) = 182n + 10 = 182n = 18 - 102n = 8n = 8/2n = 4The perimeter of a rectangular lawn is 24m. If
the area of the lawn is 35m2; how wide is the
lawn?
Answer:
.
Step-by-step explanation:
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what's the value of s for s + 10 = 6?
-4 is the value for s
which is equivalents to 9/8
Answer:
12
Step-by-step explanation:
Answer: 9/8 , 18/16 , 27/24 , 36/32 , 45/40 , 54/48 , 63/56
Help me answer this please!!
Answer:
Step-by-step explanation:
Alyssa will correctly label the numbers 48.8 48 48.09 and 48 on the number line below Which number will be located closest to 48
Answer:
the answer is (6*10^6)
Step-by-step explanation:
Multiply the beginning numbers and add the exponents.
Plz help I put a pic there for u
Answer:
5
Step-by-step explanation:
because it takes 4 1/5 paint for each canvas 5 times 4 1/5 is 21.
write the ordered pair for each point. PLS! I will give 20 points did correct same goes with brainliest. DO NOT TYPE THAT YOU DON'T KNOW OR I WILL FLAG, REPORT AND GET MAD!
Answer:
M=(0.75,1.25)
H=(-1.5,-0.5)
D=(1,-1.75)
Step-by-step explanation:
Hope this helps.
Question 1 (10 points) What is the sum of two fractions: 3/4 + 1/6
Answer: 11/12 or 0.916
Step-by-step explanation: hope this helps!
Write a question that represents the following equation. 5 · n = 35. plssss help hurry
Answer:
what is the value of {n}to get product 35?
Step-by-step explanation:
(n is seven by the way!!)
Answer:
James is buying lemons for his grandmother, if 5 lemons cost $35, then how much does 1 cost? (n=7 if you are solving)
Step-by-step explanation:
16,000 grow 3% each year
Answer:
Step-by-step explanation:
[tex]y=ar^t\\ \\ y=16000(1.03^x)[/tex]
Complete this page STEP BY STEP
Answer:
Sample space is the collection of all possible events.
So, sample space of tossing two coins, S=(H,T),(T,T),(T,H),(H,H)
Step-by-step explanation:
I don’t know what to do
Answer:
i think it would be the first one i am not 100% sure just a gues
Step-by-step explanation:
4/9x6= (write in simplest form)
Answer:
24/7
Step-by-step explanation:
Answer:
8/3
Step-by-step explanation:
4 * 6 = 24 8
9 9 3
Answer this correctly and explain your answer and I’ll give u brainalist + 10 points
Answer:
D: 43
Step-by-step explanation:
No need
Select all the expressions that are solutions to 9 = 1/3x
Answer:
first and last expressions are correct.