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:
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16,000 grow 3% each year
Answer:
Step-by-step explanation:
[tex]y=ar^t\\ \\ y=16000(1.03^x)[/tex]
Juan threw a dart onto the board. Which of the following is most likely?
A. Juan scored 0 points.
B. Juan scored at least 2 points.
C. Juan scored at least 4 points.
D. Juan scored at least 8 points.
Answer:
I think the answer should be.
B
Answer:
B
Step-by-step explanation:Edg 2021
How many cubes with the side lengths of 1/4 cm does it take to fill the prism?
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Answer:
224 cubes
Step-by-step explanation:
In terms of 1/4 cm cubes, the dimensions of the prism are ...
(2 cm)/(1/4 cm/cube) = 8 cubes long
(7/4 cm)/(1/4 cm/cube) = 7 cubes wide
(1 cm)/(1/4 cm/cube) = 4 cubes high
The volume in 1/4-cm cubes is ...
V = LWH = (8)(7)(4) = 224 . . . cubes
224 cubes are required to fill the volume.
Matthew kennedy of urbana, ohio is single and has been working as an admissions counselor at a university for five years. mathhew owns a home values at 250,000 on which he owns 135,000. he has a two year old vehicle valued at 32,000 on which he owes 26,000. he has about 20,000 remaining on hisnstudent loans. his rerirment account has grown to 32,000, and he owns some stock valued at 9,000. matthew has no life insurance and is considering buying some. how much should he buy?
Answer:
10,000.
Step-by-step explanation:
The solution is, Total assets is 164754.
What is assets?Assets are resources controlled by the entity as a result of past events and from which future economic benefits are expected to flow to the entity (AAA).
here, we have,
we know,
Mortgage is recorded separated by the home and is treated as liability
Loan & Auto loan are also liabilities of Matthew
Credit cards balances are only his indication of capacity to buy which is if that happens said transaction would result into an obligation of Matthew to pay or simply his liability
we have,
Based on the data given, assets is computed as follows;
Cash (checking account)= 2000
Cash (savings account)= 10000
Home =120000
Investments =12789
Car= 19965
Total assets is = 164754
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complete question:
Matthew currently has $2,000 in his checking account and $10,000 in a savings account. He owns a home worth $120,000 and he owes $75,900 on his mortgage. His investments in a 401(k) are valued at $12,789. He owes $29,526 on his student loans and just bought a new car. The car is currently valued at $19,965. His auto loan balance is $19,156. He is carrying a balance on two credit cards that adds up to $5,234. What is the value of Matthew's total assets? (Do not include the $ sign or commas in your answer).
1
-
2 x(x-2x+4
Ayuda
Answer:
Simplified - 2x(-x+4), Solution - -2x(-x+4)
Answer this correctly and explain I’ll give u brainalist + 10 points (:
Answer:
It is A: 75
Step-by-step explanation:
No need
The sales tax rate is 8.5%. If Helen buys a pillow priced at $18, how much tax will she pay?
Answer:
$1.53 for tax
Step-by-step explanation:
18 times .085 = 1.53
I can’t find the answer pls help!!
Answer:
470 x 1.1 = 517
Step-by-step explanation:
Which graph shows a proportional relationship between X and y
please help me with this ASAP
Answer:
32
Step-by-step explanation:
15x+19=2(10x+2)
15x+19=20x+4
19-4=20x-15x
15=5x
x=3
PQ=QN
10x+2=
10(3)+2=
30+2=
32
need help asap provide explanation
Answer:
B is the correct answer
what value from the set makes x/6 =18
true?
A.3
B.12
C.54
D.108
Answer:
D
Step-by-step explanation:
Plug it in 108 divide by 6
what is the equation for the graph below?
Answer:
ummmm, i cant see the graph
Step-by-step explanation:
Does anyone know how to do this
csc x ( sin x + cos x) = 1 + cot x
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Explanation:
Use the identities ...
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
__
[tex]\csc(x)(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{1}{\sin(x)}(\sin(x)+\cos(x))=1+\cot(x)\\\\\dfrac{\sin(x)}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}=1+\cot(x)\\\\1+\cot(x)=1+\cot(x)[/tex]
50 POINTS QUICK Given that ab = x, evaluate the following:
1.) [tex]a^{2b}[/tex]
2.)[tex]a^{b+2}[/tex]
Answer:
2)The answer is x*a^2 because the equation is saying a^b*a^2. And if we knew that a^b = x, then the answer is x*a^2
Step-by-step explanation:
what is the answer to y+5<9
Answer:
I think the answer would be y<4
Enya is building a storage cupboard in the shape of a rectangular prism. The rectangular prism has a square base with side lengths of 2.6 feet and a height of 3.4 feet. Use percentage to compare the amount of paint she would use to paint all but the bottom surface of the prism to the amount she would use to paint the entire prism. Round your final answer to the nearest tenth.
(I will mark the person who gets the answer correct as brainliest)
Answer:
89.7 is the percent
Step-by-step explanation:
38.41/43.7=0.879 (87.9%).
how do you write 2 divided by 3 as a fraction
Answer: 2/3
Step-by-step explanation:
8. Find the value of
8^x/2^y
if 3x - y = 4,
a map has a scale of 1 cm :15.5 km two cities are 2.3 cm apart on the map. to the nearest tenth of a kilometer,whatis the actual distance corresponding to the map distance
What is the common denominator of 4/12
Answer:
lcm of
Step-by-step explanation:
it is 12and 2.........
Please answer this problem 3x−9<6
Answer:
your answer is five
Step-by-step explanation:
and stay safe and happy
The base of the right prism is a hexagon composed of a rectangle and two triangles. Find the volume of the right
hexagonal prism using the formula V = Bh.
3 in
in
Answer:
Correct
Step-by-step explanation:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Will 3in,4in,7in form a triangle.
Will 3in, 4in, 6in form a triangle
Will 1m, 2m, 3m form a triangle
Yes or no
Answer:
No, Yes, No
Step-by-step explanation:
3in by 4in by 5in will not make a triangle.
3in by 4in by 6in will make a triangle.
1m by 2m by 3m will not make a triangle.
The reason two of these triangles cannot be form is because the side lengths do not adhere to the triangle inequality theorem. This theorem states that the sum of the side lengths of any 2 sides of a triangle must exceed the length of the third side.
1.What is the total interest you will have paid for the scenario below?
The home you purchased was sold for $141,000 with a fixed APR of 1.035% across 40 years. The down payment required was 6.0%.
help what is it
Answer:
la respuesta que buscas es bastante simple pero no lo sé
Step-by-step explanation:
if (-1 ,5 ) satisfies the equation 3x + Ky =7 then k =?
Answer:
k = 2
Step-by-step explanation:
3(-1) + k(5) = 7
-3 + 5k = 7
5k = 10
k = 2
The value of K in the equation 3x + Ky =7 is 2.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Equation 3x + Ky =7.
And we have also given that (-1, 5) satisfies the equation.
That means,
(-1, 5) is a solution of the equation.
To find the value of K;
Substitute the value of x = -1 and y = 5
So,
3x + Ky =7,
3(-1) + K(5) =7
-3 + 5K = 7
5K = 10
K = 2
Therefore, the value of K is 2.
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f(x) = -x^2- 4x + 10
in the standard form
f(x) = a(x – h)^2 + k
Answer:
y = - ( x + 2 )² + 14
Step-by-step explanation:
f(x) = ax² + bx + c
f(x) = a(x - h)² + k (where (h, k) are coordinates of the vertex.
h = - [tex]\frac{b}{2a}[/tex]
~~~~~~~~~~~~
f(x) = - x² - 4x + 10
a = - 1, b = - 4, c = 10
h = - [tex]\frac{-4}{2(-1)}[/tex] = - 2
k = - ( - 2)² - 4( - 2) + 10 = 14
(h, k) = ( - 2, 14 )
y = - ( x + 2 )² + 14
PLEASE HELP QUICKK!!!! TYSM!!!
Answer:
The answer for the question is 3/10
Julie buys 3 kg of apples and 5 kg of pears for £12.20.
The pears cost £1.60 per kilogram.
What is the price per kilogram.
What is the price per kilogram of the apples?
You must show your working ou.
Answer:
here you go its in the image the answer
Step-by-step explanation:
pogchamp kiddies