For what value of k are the roots of the quadratic
equation kx²+ 4x+ 1=0 equals and reals."

Answers

Answer 1

Answer:

k ≥ 4

Step-by-step explanation:

A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,

[tex]\rm\implies kx^2 +4x +1=0[/tex]

With respect to Standard form of Quadratic equation :-

[tex]\rm\implies ax^+bx+c=0[/tex]

For real roots ,

[tex]\rm\implies Discriminant = b^2-4ac\geq 0[/tex]

Substitute the respective values ,

[tex]\rm\implies b^2-4ac \geq 0\\[/tex]

[tex]\rm\implies 4^2 - 4(k)(1) \geq 0 \\[/tex]

Simplify the LHS ,

[tex]\rm\implies 16 - 4k \geq 0 \\[/tex]

Add 4k both sides ,

[tex]\rm\implies 4k\geq 16 [/tex]

Divide both sides by 4 ,

[tex]\rm\implies \boxed{\blue{\rm k \geq 4}}[/tex]


Related Questions

Can someone help me on this

Answers

Answer:

The choose (C)

F(x)=x/ (x+1)(x-2)

i am having troubles solving this 4(x+3)=x+42 can i get some help please.

Answers

Answer:

x=10

Step-by-step explanation:

Step 1: Multiply 4 with X and 3. You'll get 4x+12=x+42

Step 2: Keep the variable on one side and the number on the other side. you would subtract X and subtract 12. You'll get 3x=30

Step 3: Divide by the 3 on both sides and you'll get x=10

Given:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ [/tex]

Solution:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ \\ \\ \tt⇢ 4x + 12 = x + 42 \: \: \\ \\ \\ \tt \: ⇢4x - x = 42 - 12 \: \\ \\ \\ \tt \: ⇢3x = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢x = \frac{30}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: \pink{ \pmb{ \mathfrak{⇢x = 10}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ [/tex]

Verification:

[tex] \\ ⇢ \tt \: 4(10+ 3) = 10+ 42 \\ \\ \\ \tt⇢ 40 + 12 = 10 + 42 \: \: \\ \\ \\ \tt \: ⇢52 = 52 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: ⇢ \purple{ \pmb{ \bold{L.H.S = R.H.S}}}\\ \\ \\ [/tex]

Hence Verified!

what is the solution to the equation below? sqrt x-7 = 5
A. 144
B. 12
C. 2
D. 4

Answers

Answer:

I think the answer is B.12

If this not correct, Sorry.

the ratio of 62 miles to 100 kilometers

Answers

9514 1404 393

Answer:

  0.99779328

Step-by-step explanation:

The exact conversion factor is ...

  1 mi = 1.609344

Then 62 miles is 62×1.609344 km = 99.779328 km.

The ratio of this to 100 km is ...

  99.779328/100 = 0.99779328 . . . . ratio of 62 miles to 100 km

Find the surface area of the composite figure

Answers

Answer:

384 cm^2

Step-by-step explanation:

Start with the prism (I multiply by 2 because some of the surfaces are more of):

4×15×2=1206×15×2=1806×4=24

The Triangular Prism (I divide by 2 because it is a triangle shape on the sides):

3×4/2*2=123×6=186×5=30

The Last Step (adding everything):

120+180+24+12+18+30=384

Classify the polynomial 5x3 + 4x - 2 by degree.

Answers

Answer:

3

Step-by-step explanation:

3 would be the degree of the polynomial since it has the highest degree.

Solve the following.
2x^2-7x-4/6x^2+7x+2<0
Can someone explain how to solve this.

Answers

Answer:

Which one have same variable gather or decrease up

Step-by-step explanation:

2x^2-4.6x^2=1.4x^2

-7x+7x=0

1.4x^2+2<0

x<0

A(-3,3),b(0,1) and c(-1,-4)

Answers

Step-by-step explanation:

domain (-3,0,-1)

range (3,1,4)

PT= 3x+4 and TQ=5x-8

Answers

Answer:

So if PT=TQ and TQ=7x-9

PT=5x+3=TQ=7x-9

5x+3=7x-9

minus 5x both sides

3=2x-9

add 9 both sides

12=2x

divide 2

6=x

PT=5x+3

PT=5(6)+3

PT=30+3

PT=33

PT=QT=33

x=6

Hoped I helped you.

Find the largest integer not greater than the following expression :
[tex]\displaystyle \large \boldsymbol{} \frac{2150}{2005} +\frac{2150}{2006} +\frac{2150}{2007 } + ...+\frac{2150}{2020}[/tex]

Answers

Answer:

17

Step-by-step explanation:

The number of terms:

2020 - 2004 = 16

Each term is greater than 1, so the expression is greater than 16:

2150/2005 = 1 + 145/20052150/2006 = 1 + 144/2006...2150/2020 = 1 + 130/2020

It's easy to note each of the numbers getting smaller like 145/2005 > 144/2006 etc. Taking the smallest fraction.

The sum is:

S > 16 + 16*130/2020 = 16 + 2080/2020 > 16 + 1 = 17

So the largest integer not greater than S is 17.

The equation y=2(x-1)^2-5y=2(x−1)
2
−5y, equals, 2, left parenthesis, x, minus, 1, right parenthesis, squared, minus, 5 is graphed in the xyxyx, y-plane. Which of the following statements about the graph is true?

Answers

Answer:

(b) It is symmetrical about [tex]x = 1[/tex]

Step-by-step explanation:

Given

[tex]y = 2(x - 1)^2 - 5[/tex]

See attachment for options

Required

True statement about the graph

First, we check the line of symmetric

[tex]y = 2(x - 1)^2 - 5[/tex]

Expand

[tex]y = 2(x^2 - 2x + 1) - 5[/tex]

Open bracket

[tex]y = 2x^2 - 4x + 2 - 5[/tex]

[tex]y = 2x^2 - 4x -3[/tex]

A quadratic equation [tex]y = ax^2 + bx + c[/tex] has the following line of symmetry

[tex]x = -\frac{b}{2a}[/tex]

By comparison, the equation becomes:

[tex]x = -\frac{-4}{2*2}[/tex]

[tex]x = \frac{4}{4}[/tex]

[tex]x = 1[/tex]

Hence, the line of symmetry is at: [tex]x = 1[/tex]

(b) is true.

Answer: It is symmetrical about x=1

Step-by-step explanation:

( 2 + 3 ) ^-1 x ( 2 ^-1 + 2^-1 )

Answers

Answer:

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }[/tex]

find H.C.F OF 4x²y and xy²​

Answers

Answer:

xy

Step-by-step explanation:

The HCF is known as the highest common factor. To find the HCF of two values, we have to take the greatest number that fits into all of their factors.

To start, we can list each value's factors.

For 4x²y, this can also be written as 4*x²*y = 4*x*x*y. In multiplication, we can take the factors of each value that is multiplied. Therefore, we can start with the factors of 4 and then go to the factors of x² and so on. Our factor list is thus 1,2,4,x,x²,y

Similarly, for xy² = x*y*y, our factors are x, y, and y²

The common factors for each of these are x and y. Assuming all values are positive and greater than 1, the x*y will be greater than either x or y. Therefore, the highest common factor would be x*y = xy

please helpp!!!!!!!!​

Answers

Step-by-step explanation:

the answer is in picture

Express 12 000 iin standard form?​

Answers

Answer:

the answer will be

1.2x10⁴

hope it helps

Answer:

We have been provided the number, 3430000. Therefore, the standard form is, 3430000=3.43×106, here, we have moved 6 places to the left. Hence, the standard form of 3430000 is 3.43×106. Note: It is important to note that the standard form of representing numbers is also called scientific form or standard index form.

Help!!!! Please!! Thanks

Answers

never saw an indian guy asking for help in so simple question

Step-by-step explanation:

ans of 3rd   given statement is true, conclusion, mb=nb

ans of 4th    given statement is true, conclusion alt int angles of paralel lines are equal

AB=BA
∠ABM=∠ABN
MB=NB
△AMB≌△ANB (SAS)

∠CBM=∠ADM
∠BCM=∠DAM
∠BMC=∠DMA
△BCM∽△DAM (AAA)

Hope my answer helped u :)

Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4

Answers

Answer:

x^2+3x+3

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x^2 + 4

f(x) + g(x) = 3x-1+ x^2 +4

                 Combine like terms

                   = x^2+3x+3

From the table below, determine whether the data shows an exponential function. Explain why or why not. x 3 1 -1 -3 y 1 2 3 4 a. No; the domain values are at regular intervals and the range values have a common sum 1. b. No; the domain values are not at regular intervals. c. Yes; the domain values are at regular intervals and the range values have a common factor 2. d. Yes; the domain values are at regular intervals and the range values have a common sum 1. Please select the best answer from the choices provided A B C D

Answers

A………………………………………………….

Answer:

C

Step-by-step explanation:

you find the variable

Please help explanation if possible

Answers

Answer:

17.6

Step-by-step explanation:

Answer:

80 pennies ; 160 nickels

Step-by-step explanation:

Given the 2 equations

0.01p + 0.05n = 8.80 → (1)

n = 2p → (2)

Substitute n = 2p into (1)

0.01p + 0.05(2p) = 8.80

0.01p + 0.1p = 8.80

0.11p = 8.80 ( divide both sides by 0.11 )

p = 80

Substitute p = 80 into (2)

n = 2 × 80 = 160

There are 80 pennies ; 160 nickels

If ∠AFB and ∠DFE are congruent, what term describes ∠BFE and ∠AFD?

Answers

Answer:

If you add a picture I can help

Step-by-step explanation:

I need to see what the figure looks like

The option which is not a solution of the equation 2x + 3y = 6 is:
(A) (0, 2)
(B) (1, 1)
(C) (-3, 4)
(D) (3, 0).​

Answers

Answer:

Step-by-step explanation:

B OR TRUE

Look at photo I tested each thing, your answer to this question in option B

please help me with that

Answers

Answer:

[tex]\frac{16}{81}[/tex]

Step-by-step explanation:

[tex](\frac{27}{8} )^{-\frac{4}{3} }[/tex]

[tex]=((\frac{3}{2} )^3)^{-4/3}[/tex]

[tex]=(\frac{3}{2} )^{-4}[/tex]

[tex]=(\frac{2}{3} )^{4}[/tex]

[tex]=\frac{16}{81}[/tex]

Answer:

16/81

Step-by-step explanation:

a negative exponent means 1/...

the number in the numerator means "to the power of".

the number in the denominator means take the root of that power.

so, we have to take the third root of the expression, or this then to the power of 4, and finally build 1/... if the whole result.

and the sequence is not making a difference.

the third root of of 27/8 = 3/2

this to the power of 4 = 81/16

this 1/... = 16/81

sin^6x + cos^6x = 1/4

Answers

Answer:

[tex]\displaystyle x = \frac{\pi}{4} + k\, \pi[/tex] for integer [tex]k[/tex] (including negative numbers.)

Step-by-step explanation:

Pythagorean Identity: [tex]\sin^{2}(x) + \cos^{2}(x) = 1[/tex]. Equivalently, [tex]\cos^{2}(x) = 1 - \sin^{2}(x)[/tex].

Rewrite the original equation and apply this substitution to eliminate [tex]\cos(x)[/tex]:

[tex]\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}[/tex].

Let [tex]y = \sin(x)[/tex] ([tex]-1 \le y \le 1[/tex].) The original equation is equivalent to the following equation about [tex]y[/tex]:

[tex]\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}[/tex].

Expand the cubic binomial in the equation:

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}[/tex].

Simplify to obtain:

[tex]\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}[/tex].

Rearrange and simplify:

[tex]12\, y^{4} - 12\, y^{2} + 3 = 0[/tex].

[tex]3\, (2\, y^{2} - 1)^{2} = 0[/tex].

[tex]2\, y^{2} - 1 = 0[/tex].

[tex]\displaystyle y^{2} - \frac{1}{2} = 0[/tex].

Solve for [tex]y[/tex]:

Either [tex]\displaystyle y = \frac{1}{\sqrt{2}}[/tex] or [tex]\displaystyle y = -\frac{1}{\sqrt{2}}[/tex].

If [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

On the other hand, if [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

Combine both situations to obtain:

[tex]\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi[/tex] for all [tex]k \in \mathbb{Z}[/tex].

Simplify: 0.9(2b-1)-0.5b+1

Answers

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

Hi there!  

»»————- ★ ————-««

I believe your answer is:

1.3b + 0.1

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\0.9(2b-1)-0.5b+1\\--------------\\\rightarrow 1.8b - 0.9 - 0.5b + 1\\\\\rightarrow 1.8b - 0.5b - 0.9 + 1\\\\\rightarrow \boxed{1.3b +0.1}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

Let be the density function for the shelf life of a brand of banana which lasts up to weeks. Time, , is measured in weeks and . Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place. Mean

Answers

The question is incomplete. The complete question is :

Let [tex]p(t) = -0.0375t^2 + 0.225t[/tex]  be the density function for the shelf life of a brand of banana which lasts up to 4 weeks. Time, t, is measured in weeks and [tex]$0 \leq t \leq 4$[/tex]. Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place.

Answer:

2.4

Step-by-step explanation:

 Given :

[tex]p(t) = -0.0375t^2 + 0.225t[/tex]

Mean :

[tex]$=\int_0^4 tp (t) \ dt$[/tex]

[tex]$=\int_0^4 t (0.0375 t^2 + 0.225t) \ dt$[/tex]

[tex]$=-0.0375 \int_0^4 t^3 \ dt + 0.225 \int_0^4 t^2 \ dt$[/tex]

[tex]$=-0.0375 \left[ \frac{t^4}{4} \right]^4_0 + 0.225 \left[ \frac{t^3}{3} \right]^4_0$[/tex]

[tex]$=-0.0375 (64) + 0.225 \left( \frac{64}{3} \right)$[/tex]

[tex]$=-2.5 + 4.8$[/tex]

= 2.4

Therefore, the mean is 2.4


There is a sequence of rigid transformations that takes A to A', B to B', and C to "
same sequence takes D to D'. Draw and label D':

Answers

Answer:

I think it's D

Step-by-step explanation:

Answer:  I think its D

Step-by-step explanation:

Rigid transformation moves a shape without changing the size of the shape.

See attachment for the diagram that shows the position of D'

Harold used 6 centimeters of tape to wrap 3 presents. What is the unit rate?

Answers

Answer:

2cm/present is the unit rate

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Harold used \underline{\underline{6 centimeters of tape}} to wrap}\\\huge\text{\underline{\underline{3 presents}}. \underline{\underline{\underline{What is the unit rate?}}}}[/tex]

[tex]\huge\boxed{\star \ Formula: \mathsf{\dfrac{a}{b}= unit\ rate \ }\star}[/tex]

[tex]\huge\boxed{\mathsf{Equation\boxed{\rightarrow}\ \dfrac{6}{3} = \boxed{unit\ rate}}}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{6}{3} = \boxed{\bf unit\ rate}}}\\\\\\\huge\boxed{\mathsf{ 6 \ \boxed{\div} \ 3\ \boxed{= } \ \bf\boxed{\bf unit\ rate}}}\\\\\\\\\huge\boxed{\boxed{=} \bf \ 2}[/tex]

[tex]\huge\boxed{\star\ \textsf{Therefore, the UNIT RATE IS: \bf \boxed{\bf 2}}\ \star}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: the unit rate is \bf \boxed{\underline{\underline{\underline{\underline{\bf 2}}}}}}}}\huge\checkmark\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\huge\boxed{\frak{Amphitrite1040:)}}[/tex]

If mAngleVUW = (4x + 6)° and mAngleWUT = (6x – 10)°, what is the measure of AngleWUT?

Answers

Answer:

2 is the answer........

Answer:

the answer is 38 degrees

Step-by-step explanation:

just took test on ed

What is the result of rounding 8,888,888 to the nearest ten?

Answers

Answer:

8,888,890

Step-by-step explanation:

yup yup

Find the approximate side length of a square game board with an area of 145 in 2 Plz help!

Answers

Answer:

Side length ≈ 12.04

Step-by-step explanation:

145 = x²

144 is the closest  square, with the root 12

The square root of 145 is approximately 12.04

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The approximate side length is 12.0 in

Step-by-step explanation:

The area of a square is given by

A = s^2  where s is the side length

145 = s^2

Taking the square root of each side

sqrt(145) = sqrt(s^2)

12.04159458 = s

The approximate side length is 12.0 in

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