For what values of k does the equation (2k + 1)x^2 + 2x = 10x – 6 have two
real and equal roots?

Answers

Answer 1

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:

[tex]ax^2 + bx + c = 0[/tex]

has two equal solutions if [tex]\Delta = b^2 - 4ac[/tex] is 0.

------------------------------------

In this question:

The equation is:

[tex](2k+1)x^2 + 2x = 10x - 6[/tex]

Placing in the correct format:

[tex](2k+1)x^2 + 2x - 10x + 6 = 0[/tex]

[tex](2k+1)x^2 - 8x + 6 = 0[/tex]

Thus, the coefficients are: [tex]a = 2k + 1, b = -8, c = 6[/tex]

------------------------------------

Delta:

We want it to be positive, so:

[tex]\Delta = b^2 - 4ac[/tex]

[tex]\Delta = 0[/tex]

[tex]b^2 - 4ac = 0[/tex]

[tex](-8)^2 - 4(2k+1)(6) = 0[/tex]

[tex]64 - 48k - 24 = 0[/tex]

[tex]-48k + 40 = 0[/tex]

[tex]-48k = -40[/tex]

[tex]48k = 40[/tex]

[tex]k = \frac{40}{48}[/tex]

[tex]k = \frac{5}{6}[/tex]

The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]

A similar question is found at https://brainly.com/question/12144265


Related Questions

I need help i tried to do this but can't get it.

Answers

Answer: x=5, y=-1

Hope this helps

A basketball is shot into the air. Its height is represented by the polynomial equation h(t) = –16t2 + 35t + 5, where h is the height of the basketball at t seconds. What's the height of the basketball at 1.5 seconds?
Question 4 options:

20.2 feet


18.8 feet


21.5 feet


16.7 feet

Answers

Answer:

height = 21.5 ft

Step-by-step explanation:

Substitute t = 1.5 into h(t) and evaluate

h(1.5) = - 16(1.5)² + 35(1.5) + 5

        = - 16(2.25) + 52.5 + 5

       = - 36 + 57.5

      = 21.5 ft

Answer:

21.5 feet.

Step-by-step explanation:

Let t = 1.5

[tex]h(1.5)=-16(1.5)^2+35(1.5)+5\\h(1.5)=-36+52.5+5\\h(1.5)=21.5[/tex]

Therefore, at 1.5 seconds, the basketball is 21.5 feet in the air.

A man spends 880$ a month. Out of this, 26% goes to his rent. Find how much is his rent.

Answers

Answer:

$228.80 paid for rent.

Steps:

Divide the percentage by 100.

26/100=0.26

Multiply this amount by the principal amount, 880.

880*0.26=228.8 is 26% of 880

Answer:

26% of 880

= (26 x 880 )  /  100

= 228.80 ($)

Step-by-step explanation:

Have attached some composite functions completed to show you the whole unit. Hope it helps. The 2nd and third one are part of the same answer.

The forth one attached may help you most.

helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent​ "The product of 12 and a number y ​" mathematically.

Answers

Answer:

12y

Step-by-step explanation:

product means multiplycation so twelve times y is  12y


Solve for u.
– 22 = -8u + 6(u-7)
Simplify your answer as much as possible.

Answers

Step-by-step explanation:

- 22 = -8u + 6(u-7)

-22 = -8u + 6u - 42

8u - 6u = 22 - 42

2u = -20

u = -20/2

u = -10

Answer:

[tex] \boxed{ \boxed{ \mathrm{ \bold{ \blue{ - 10}}}}}[/tex]

Step-by-step explanation:

[tex] \mathrm{ - 22 = - 8u + 6(u - 7)}[/tex]

Distribute 6 through the parentheses

⇒[tex] \mathsf{ - 22 = -8u + 6u - 42}[/tex]

Collect like terms

⇒[tex] \mathrm{ - 22 = - 2u - 42}[/tex]

Swap the sides of the equation

⇒[tex] \mathrm{ -2u - 42 = - 22}[/tex]

Move constant to R.H.S and change it's sign

⇒[tex] \mathrm{ - 2u = - 22 + 42}[/tex]

Calculate

⇒[tex] \mathrm{ - 2u = 20}[/tex]

Divide both sides of the equation by -2

⇒[tex] \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }[/tex]

Calculate

⇒[tex] \mathrm{u = - 10}[/tex]

Hope I helped!

Best regards!

plllllzzzzzzzz hellllllllpppp again...lol

Answers

Answer:

34

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

71 = z+37

Subtract 37 from each side

71 -37 =z

34 =z

Step-by-step explanation:

[tex]thank \: you[/tex]

PLEASE help me with this question! This is really urgent! No nonsense answers please.

Answers

Answer:

140°

Step-by-step explanation:

[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]

Which expression can be used to model the phrase “the sum of three and a number”?

Answers

Answer:

3+x

Step-by-step explanation:

lol im doing this on edge too

hope it helps

An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II

Answers

Answer:

The error made here is a Type I error.

Step-by-step explanation:

A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.

A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.

The hypothesis in this case is defined as follows:

H₀: The product does not change the height of the plant.

Hₐ: The product makes the plant grow taller.

The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.

So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.

Thus, the error made here is a Type I error.

GIVE ME A REAL ANSWER PLEASE! IT IS DUE NOW! Factor completely 3x^2 + 5x + 1.
(3x + 1)(x + 1)
(3x + 5)(x + 1)
(3x − 5)(x + 1)
Prime

Answers

Answer:

prime

Step-by-step explanation:

3x^2 + 5x + 1

it can't be factorizes with rational numbers

Answer:

Prime

Step-by-step explanation:

3x^2 + 5x + 1

3x^2  factors in to 3x and x

1 factors into 1 and 1

( 3x   + 1) ( x+1)

We need to verify the middle is 5

3x+1x = 4x

so this is not true

We cannot factor this so it is prime

Use the diagram below to answer the questions. Line q contains points J, K, and M. Point P is above line q between points K and M. A line connects points M and P. Another line connects points P and K. Point L is above point J. A line starts at point K and extends through point L. Which are shown on the diagram? Check all that apply. Line segment J L Ray K M Line J K Ray P K AngleLJK Ray M J

Answers

Answer:

2nd 3rd last one

Step-by-step explanation:

Angles, lines, rays, and segments can be found in a plane. The terms shown on the diagram are: Ray KM, Line JK, and Ray MJ

What are lines, rays, and segments?

A line is an unending, straight path that has no endpoints and travels in both directions along a plane. A line segment is a finitely long portion of a line with two endpoints. A line segment that goes on forever in one direction is known as a ray.

To identify the terms shown on the diagram, we need to note the following: A ray has no endpoint; it is represented with an arrow on one side line segment has two endpoints.

It is represented with dots on both sides. An angle is a space between intersecting lines, line segments, or rays. There is no connection between J and L. So, JL is not a line segment

Ray KM

KM has a dot at point K and an arrow that points in the direction of M. So, KM is a ray.

Line JK

JK has dots on both ends (at J and K). So, JK is a line.

Ray PK

PK has dots on both sides (at P and K). So, PK is a line; not a ray.

Angle LJK

There is no connection between points L, J, and K. Hence, LJK is not an angle.

Ray MJ

MJ has a dot at point M and an arrow that points in the direction of J. So, MJ is a ray.

The diagram is attached with the answer below.

Read more about lines, points, and rays at:

brainly.com/question/13486760

#SPJ5

Given that A is directly proportional to B and that A = 5/3 when B = 5/6, find A when B=1/3 and B when A =15/2.

Answers

Step-by-step explanation:

A is directly proportional to B is written as

A = kB

where k is the constant of proportionality

First we must find the relationship between the two variables

when

A = 5/3

B = 5/6

Substitute the values into the formula to find k

[tex] \frac{5}{3} = k \frac{5}{6} [/tex]

Multiply through by the LCM which is 6

That's

[tex]5 \times 2 = 5k[/tex]

5k = 10

Divide both sides by 5

k = 2

So the formula for the variation is

A = 2B

when B = 1/3

[tex]A = 2 \times \frac{1}{3} [/tex]

[tex]A = \frac{2}{3} [/tex]

When A = 15/2

[tex] \frac{15}{2} = 2B[/tex]

Multiply through by 2

[tex]4B = 15[/tex]

Divide both sides by 4

[tex]B = \frac{15}{4} [/tex]

Hope this helps you

solve 7 + x - 15=-2 2/3

Answers

Answer:

16/3 or 5 1/3

Step-by-step explanation:

7 + x - 15 = -2 2/3

x - 8 = -2 2/3

x = 16/3

Answer:

Let's solve your equation step-by-step.7+x−15=223

Step 1: Simplify both sides of the equation.

x−8=8/3

Step 2: Add 8 to both sides

.x−8+8=8/3+8x=32/3

Answer:x=10 2/3

i just answered this question on an algebra quiz and it was multiple choice, i hope this helps!

2. Marci bought 6 shirts at Old Navy. Her subtotal
(before tax) was $73.50. If each shirt was the same
price, how much did each shirt cost?

Answers

Answer:

12.25

Step-by-step explanation:

73.50 divided by 6 for each shirt is 12.25 a shirt

Examine the graph. What is the domain and range of the function represented by the graph? Select two answers: one for the domain and one for the range.

domain: (−∞,∞)
range: [−9,∞)
domain: (−2,4)
range: (−∞,∞)
range: (−2,4)
domain: [−9,∞)

Answers

Answers:

domain: (−∞,∞)

range: [−9,∞)

=========================================

Explanation:

The graph extends forever to the left and right. This means any x value can be plugged into the function to get some y value output. The domain is the set of all real numbers in which we write (−∞,∞)  when using interval notation. This is the interval from negative infinity to positive infinity. We exclude both endpoints as we cannot reach infinity.

The smallest y value possible is y = -9 as shown by the vertex point (1, -9) being the lowest point on the parabola. The range is the set of y values such that [tex]y \ge -9[/tex] so we say [−9,∞) in interval notation. This is the interval from -9 to infinity. The square bracket says to include -9 as part of the interval.

Answer: It is A, I did this question many times before.

(−∞,∞)

Step-by-step explanation:

helphelphelphelphelphelphelp

Answers

Answer:

P = 1,-10

Q=1,-1

R=7,-1

S=7,-10

By increasing the list price of a book by ₹10 a person can buy a 10 books less for ₹1200 Find the original list price of the book. ( form Quadratic equation for the question) ​

Answers

Answer:

cwbmwl2h2h2jl2bcek2k3cgwkel

A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points)

Answers

Answer:

(16x + 8)m²

Step-by-step explanation:

area of a rectangle = 2length + 2width

=2(3x + 5) + 2(5x-1)

=6x + 10 + 10x - 2

=(16x + 8)m²

Find the equation of a circle with PQ as diameter, where P(2,-6) and Q(-6,-4)​

Answers

Answer:

y=-¼x+⁴⁴/8

Step-by-step explanation:

p(2,-6). Q(-6-4)

p (x¹,y¹). Q(x²,y²)

1) find the gradient(slope)

gradient=y²-y¹

x²-x¹

gradient = -4-(-6)

-6-2

gradient= -4+6

-6-2

gradient=²/-8

2)equation is supposed to be in the form of y=mx+c

where m is the gradient

thus.

gradient=y²-y¹

x²-x¹

when finding the equation we only use one of the values of the coordinates leaving the other as an unknown value.

2 = y-(-4)

-8 x-(-6)

2 =y+4

-8. x+6

remove the denominators by cross multiplying that is:

2(x+6)= -8(y+4)

2x+12= -8y-32

express in the format y=mx+c

2x+12+32=-8y

2x+44=-8y.

divide all sides by -8 to remain with y

²/-8x+⁴⁴/-8=y

-¼x+ -⁴⁴/8=y

y=-¼x-⁴⁴/8

Help, Answer ASAP; will give brainliest

Answers

Answer:

Step-by-step explanation:

measure of a = 9 degree

angle POM = 48 degree = angle NMO [ AIA}

HOPE IT HELPS

Answer:

Below

Step-by-step explanation:

We are given that <PMO= (3a+15)° and NMO= (6a-6)°

Notice that the sum of <PMO and <NMO gives a right angle.

● <PMO+<NMO = 90°

● 3a+15+6a-6 = 90

● 9a + 9 = 90

Substruct 9 from both sides

● 9a +9 -9 = 90 -9

● 9a = 81

Divide both sides by 9

● 9a/9 =81/9

● a = 9

So the value of a is 9°

■■■■■■■■■■■■■■■■■■■■■■■■■■

MN and PO are parallel since MNOP is a rectangle.

MO is crossing MN and PO so <POM and < NMO are alternate interior angles wich means that they have the same size.

● <NMO = <POM

● <POM = 6a-6

The value of a is 9°

● <POM = 6*9-6 = 48°

So <POM = 48°

Simplify: squrt 18x⁷

Answers

Answer:

3x^3 ⋅ √2x

Step-by-step explanation:

draw a figure for the triangle with ab

Answers

Step-by-step explanation:

figure for the triangle with ab

Jack picks 3 liters of berries in 8 minutes. Jill picks 4 liters of berries in 10 minutes. Working together, how many berries can they pick in 1 minute?

Answers

Answer:

they can pick 27 berry's

Step-by-step explanation:

I think-

They can pick 1.29 liters of berries in 1 minute working together.

--------------------------------------------

The together rate is the sum of each separate rate. In this question:

We want to find the together rate.Jack's rate is [tex]\frac{3}{8}[/tex]Jill's rate is [tex]\frac{4}{10}[/tex]

--------------------------------------------

Together, they can pick x liters, and the rate is: [tex]\frac{1}{x}[/tex]

Then

[tex]\frac{1}{x} = \frac{3}{8} + \frac{4}{10}[/tex]

[tex]\frac{1}{x} = \frac{15 + 16}{40}[/tex]

[tex]\frac{1}{x} = \frac{31}{40}[/tex]

Applying cross multiplication:

[tex]31x = 40[/tex]

[tex]x = \frac{40}{31}[/tex]

[tex]x = 1.29[/tex]

They can pick 1.29 liters of berries in 1 minute working together.

A similar question is given at https://brainly.com/question/23323624

Vanessa owed her friend $24. She paid back $8. How much more does Vanessa need to pay before her account is at zero?

Answers

Answer:

$16

Step-by-step explanation:

$24 - $8 = $16

Answer:

$ 16

Step-by-step explanation:

$ 24 - $ 8 = $ 16

I need help with this question. PLZZ HELP!!!

Answers

Answer: The solution of these inequalities are similar because they begin at two, however they are different because in the first inequality two cannot be an answer hence the open circle ⭕️, but the second inequality can have two as a solution hence the closed circle.

Step-by-step explanation:

URGENT, WILL GIVE BRAINLIEST IF CORRECT.
8 and 13
11.5 and 23.6
22 and 15

Answers

Answer:

5 < x < 21

Step-by-step explanation:

I did this bfore.


what is meaning of rate?

Answers

Answer:

1.a measure, quantity, or frequency, typically one measured against another quantity or measure.

Step-by-step explanation:

2.a fixed price paid or charged for something.

Answer:

a measure, quantity, or frequency typically one measured against another quantity or measure.

Assign a standard or value to (something) according to a particular scale.

Which number has the greatest value?
A) 12.2
B) 12.25
C) 12.5
D) 12.52

Answers

The Answer is the letter D, 12.52

Answer:

The answer is letter D, 12.52

whats a square + b square I don't know thats why I am asking u dude

Answers

Answer:

.............................

NEED HELP ASAP solve for x : 3/5 = x-1/8
a.5 b.29/5 c.23/5 d.19/5

Answers

Answer:

[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{ \frac{29}{5} }}}}}[/tex]

Option B is the correct option.

Step-by-step explanation:

[tex] \sf{ \frac{3}{5} = \frac{x - 1}{8} }[/tex]

Apply cross product property

⇒[tex] \sf{ 5(x - 1) = 3 \times 8}[/tex]

Distribute 5 through the parentheses

⇒[tex] \sf{5x - 5 = 3 \times 8}[/tex]

Multiply the numbers

⇒[tex] \sf{5x - 5 = 24}[/tex]

Move 5 to right hand side and change it's sign

⇒[tex] \sf{5x = 24 + 5}[/tex]

Add the numbers

⇒[tex] \sf{5x = 29}[/tex]

Divide both sides of the equation by 5

⇒[tex] \sf{ \frac{5x}{5} = \frac{29}{5} }[/tex]

⇒[tex] \sf{x = \frac{29}{5} }[/tex]

Hope I helped!

Best regards!!

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