The equation 12x² + 4kx + 3 = 0 has real and equal roots, if

Answers

Answer 1

Answer:

[tex]k=\pm3[/tex]

Step-by-step explanation:

[...] if you can write the LHS as a perfect square, or if you can't spot a factorization of it right away, if and only if the discriminant [tex]\Delta = b^2-4ac[/tex] (or, if b is an even number, 1/4 of it) is zero.

I see it! I see it!

Stare at it for a while. First term is [tex]3(2x)^2[/tex], third term is [tex]3(1)^2[/tex], we are missing a double product, but we can play with k. For the LHS to be [tex]3(2x\pm1)^2 = 3(4x^2\pm4x+1) = 12x^2\pm12x+3[/tex] you just need [tex]4k= \pm12 \rightarrow k=\pm3[/tex].

I don't see it...

Then number crunching it is. Set the discriminant to 0, solve for k

[tex]\frac{\Delta}4 = 4k^2-12\cdot 3 =0 \rightarrow 4k^2=36 \\k^2 = 9 \rightarrow k=\pm3[/tex]


Related Questions

A retirement account was opened with a $900 deposit. If the account earns 4.25% interest compounded continuously and has no other deposits or withdrawals, how long will it take the value to double?​

Answers

It will take 16.66years long for the money to double

The formula for calculating the compound amount is expressed as:

A = P(1+r)^t

A is the amount after t years  = 2(900) = $1800P is the amount invested = $900r is the rate in decimal  = 4.25% = 0.0425

Substitute into the formula to have:

1800 = 900(1+0.0425)^t

2 =(1+0.0425)^t

2 = 1.0425^t

ln2 = tln1.0425

t =  ln2/ln1.0425

t = 0.6931/0.0416

t = 16.66years

This shows that it will take 16.66years long for the money to double

Learn more on compound interest here: https://brainly.com/question/18483293

What is the solution to the system of equations?



y = 2x -1



y = -x +5

Answers

x= −2 and y=3

I can't explain this very well, sorry.

The solution is:

x= 4/3

y= 11/3.

Step by step: (substitution)



2x+1=-x+5

Add x to both sides.


3x+1=5.

Subtract 1.

3x=4.

Divide by 3.


x=4/3.

Use 4/3 instead of x to find y.

y=-(4/3)+5

y= 11/3.

Hope this helped!! :)

What is the slope in the equation y = 2/5x - 6?

Answers

Answer:

2/5

Step-by-step explanation:

y=2/5x-6

m=2/5

y=mx+b

Slope:  2/5

y-intercept:  6

Step-by-step explanation:

Just Did Now, Am not Really good at asking questions

what is the solution of the equation 9x+12=39

Answers

Answer:

X=3

Step-by-step explanation:

because 39-12=27 and 9x3=27 and 27+12=39

Answer:

x=3

Step-by-step explanation:

9x+12=39

9x=27

x=3

300 x 47 explain please

Answers

Answer:

I think u mean to just multiply 300 * 47 would equal 14,100

                          300

                        x  47

                                                            7*0 = 0          7*3=21   so 2,100

            40*0 = 0                since 40 has a 4 you can take 4*3 and put a 0 on the end               4*3= 12 so 40*3= 120 so with so with the bonus 0's it would be 12,000                                    

                                              12,000

                                            +  2,100

                                              14,100 so  that means

          300

        x   47

       14,100

train tickets cost $48 for adults and $32 for children there are 27 adults and 55 children on the train how much did the passengers pay to ride the train​

Answers

$3,056
work
adult tickets:48x27=1296
children tickets: 55x32=1760
add the two totals 1296+1760= 3056

(9u+w)^2
(use foil).................

Answers

Answer:

Step-by-step explanation:

(9u + w)(9u + w)

f: 9u * 9u = 81 u^2

o: 9u * w

i: 9u* w

l: w * w = w^2

Result

81u^2 + 9uw + 9uw + w^2

81u^2 + 18uw + w^2

please help me with this soon much appreciated.

Answers

Answer:

1 : 2

Step-by-step explanation:

this is a 30-60-90 triangle which is a special right triangle. the ratio of the sides is x: x*sqrt(3): 2x, in the order short leg: long leg: hypotenuse. so the ratio of the short leg to the hypotenuse is x:2x or 1:2

Solve for s.



s
4
− 2
= 2


s =

Answers

Answer:

is 2

Step-by-step explanation:

is 2 why yes

find 50% of 20
Find the answer I need it for Get More Math

Answers

Answer:

10

Step-by-step explanation:

1/2 of 20 is 10

Answer:

10

Step-by-step explanation:

Use the binomial formula to find the coefficient of the q^4 p^17
term in the expansion of (29+p)^21

Answers

Recal the binomial theorem:

[tex]\displaystyle (a+b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

Then

[tex]\displaystyle (2q+p)^{21} = \sum_{k=0}^{21} \binom{21}k (2q)^{21-k} p^k = \sum_{k=0}^{21} \binom{21}k 2^{21-k} q^{21-k} p^k[/tex]

We get the q⁴p¹⁷ term when k = 17, and its coefficient would be

[tex]\dbinom{21}{17} 2^{21-17} = \dfrac{21!}{17!(21-17)!} 2^4 = \dfrac{21\cdot20\cdot19\cdot18}{4\cdot3\cdot2\cdot1}\cdot2^4 = \boxed{95,760}[/tex]

PLSSSSSSS HELPPPPPPPP ASAPPPP

Answers

Answer:

Answer should be choice 4

Step-by-step explanation:

4. Elie took $200 to spend during summer vacation. She spent $32 a day for 5 days. Then she bought gelato for her and three friends for $6 each. How much did she have left at the end of the trip?​

Answers

Answer:

$16

Step-by-step explanation:

32×5=160

6×4=24

160+24=184

200-184=16

Elie was left with $16 at the end of the trip

What is a expression? What is a mathematical equation? What is Equation Modelling?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Elie who took $200 to spend during summer vacation. She spent $32 a day for 5 days. Then she bought gelato for her and three friends for $6 each.

Assume that she is left with $[x]. Then, we can write the equation as -

x = 200 - {(32 x 5) + (6 x 4)}

x = 200 - {160 + 24}

x = 200 - 184

x = 16

Therefore, Elie was left with $16 at the end of the trip.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

During a recent rainstorm, 8 centimeters of rain fell in Dubaku's hometown, and 2.362, points, 36 centimeters of rain fell in Elliot's hometown. During the same storm, 15.1915, point, 19 centimeters of snow fell in Alperen's hometown.
How much more rain fell in Dubaku's town than in Elliot's town?
centimeters

Answers

Answer:

Hence, 5.64 centimeters of more rain fell in Dubaku's town than in Elliot's town.

Step-by-step explanation:

The amount of rain that fell in Dubaku's hometown is: 8 centimeters.

Amount of rain that fell in Elliot's hometown is: 2.36 centimeters.

We are asked to find how much more rain fell in Dubaku's town than in Elliot's town so it is calculated as the difference between the rain in both of there towns and is given by:

Difference in rain= 8-2.36

Difference in rain= 5.64 centimeters.

Simplify the expression.

Answers

Answer:

[tex]21x^{2}[/tex]

Step-by-step explanation:

It would be 3x*7x

3x*7x

=21x*x

=[tex]21x^{2}[/tex]

Answer:

21x^2 ( twenty-one x squared)

Step-by-step explanation:

What is the slope for this table?

Answers

Do u have a graph?
Sheeeeeeeeeeeeeeeeeeeeeeeesh

i don't know what this is

Answers

Answer:

Me U Hungry Hungry Me Im Mad Me U Angry Me U Way Mad U Talk Mad Me Angry U:(

Step-by-step explanation:

False

True

Ture

False

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

Someone, please help me with this MATH question.

Answers

Answer:

A

Step-by-step explanation:

An operation is defined as p*q=-5q+p2 evaluate. 2*(7*3)

Answers

Answer:

- 166

Step-by-step explanation:

First step is to evaluate 7*3

7*3 ( with p = 7 and q = 3 )

= - 5(3) + 7²

= - 15 + 49

= 34

Now evaluate

2*34 ( with p = 2 and q = 34 )

= - 5(34) + 2²

= - 170 + 4

= - 166

Give the simplified radical form for each side length requested.


Pls answer only if you can explain and if your sure it’s the right answer.

I need help in understanding how to work it myself so please make sure you explain well.

Answers

Answer:

See below

Step-by-step explanation:

30×60×90 right triangle has side ratios as:

s : l : h = 1 : √3 : 2, where s- short leg, l - long leg, h - hypotenuse

45×45×90 right triangle has side ratios as:

l : l : h = 1 : 1 : √2, where l- legs, h- hypotenuse

If you know one of the sides its easy to find the missing ones.

a) 30×60×90 right triangle

Given l = 12s : 12 : h = 1 : √3 : 2CB = s = 12 / √3 = 12√3/3 = 4√3 AB = h = 2s = 2*4√3 = 8√3

b) 45×45×90 right triangle

Given l = √22BC = l = √22AB = l√2 = √22×√2= √44 = 2√11

c)  30×60×90 right triangle

Given h = 20√6s : l : 20√6 = 1 : √3 : 2BC = s = h/2 = 20√6/2 = 10√6AC = l = s√3 = 10√6×√3 = 10√18 = 10×3√2 = 30√2

Please help me asap
DO NOT USE LINKS

Answers

1. a = 8

2. b = 7

3. c = -3

4. d = 6

5. e = 1

6. f = 2

use the GCF to factor 16+6

Answers

Answer:

2 x (8 + 3)

Step-by-step explanation:

b) 16 + 6 = 2 x (8 + 3)

=> 22 = 2(11)

=> 22 = 22

Therefore, 2 x (8 + 3) is your answer.

if a wire of length 2 meters costs $10. find the cost of a wire of length 35cm $1.75

Answers

Answer:

$1.75

Step-by-step explanation:

if a wire of length 2 meters costs $10. find the cost of a wire of length 35cm $1.75

2m = 200 cm

200 : 10 = 35 : x

x = 10 * 35 : 200

x = 1.75

PLEASE HELP THIS IS DUE TOMORROW

Answers

Answer:

Step-by-step explanation:

three are 6 blades on each windmill. how many total blades are on 7 windmills? use a fives fact to solve

Answers

Answer: 42 I think

Step-by-step explanation:

I did 6 times 7

Suppose that a department contains 7 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men

Answers

Answer:

7502040

Step-by-step explanation:

you can have 6 women,5 women and 1 men,4 women and 2 men,

in first case,you can place women in 15*14*13*12*11*10 ways

in second case

15*14*13*12*11*7

and in third case

15*14*13*12*7*6

and you need to sum all this numbers

Question 11 Objective: Solve for unknown side lengths of right triangles using trigonometric ratios. A right triangle has one angle that measure 27. The adjacent leg measures 29.6 cm and the hypotenuse measures 40 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = 1/2bh а​

Answers

Answer:

A≈ 268.76 sq cm.

Step-by-step explanation:

sine 27 = opposite side/hypotenuse

sine 27 = x/40

sin 27(40) = x

18.15961999 =x

18.16 = x

A = 1/2(29.6)(18.1596199)

A = 268.7623759

A≈ 268.76 sq cm.

radius of a circle with 11,304 circuference

Answers

Answer:

1799.08748

Rounded version: 1799

Step-by-step explanation:

Report me if its wrong mark me Brianliest if its right.

look at the screenshots please and thank you I really don't understand it please I need help with this

Answers

Answer:

1. 2/9

2. 3/7

3. 1/5

Step-by-step explanation:

For each graph look at where the line comes to a point and look at first the y coordinate, then the x coordinate, the answer should be y / x for that graph. My class was recently going over this so I know this for sure.

Tell me if I'm wrong :)

9 is what percent of 45?​

Answers

Answer:

20%

Step-by-step explanation:

9/45 = 0.2

0.2*100 = 20

9:45*100 =

( 9*100):45 =

900:45 = 20

So it’s 20
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