What is the value of K?

What Is The Value Of K?

Answers

Answer 1
Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.

Explanation:

Given: A quadratic equation, kx2 - 14x + 8 = 0

Let the two zeros of the equation be α and β.

According to the given question, if one of the roots is α the other root will be 6α.

Thus, β = 6α

Hence, the two zeros are α and 6α.

We know that for a given quadratic equation ax2 + bx + c = 0

The sum of the zeros is expressed as,

α + β = - b / a

The product of the zeros is expressed as,

αβ = c / a

For the given quadratic equation kx2 - 14x + 8 = 0,

a = k, b = -14, c = 8

The sum of the zeros is:

α + 6α = 14 / k [Since the two zeros are α and 6α]

⇒ 7α = 14 / k

⇒ α = 2 / k --------------- (1)

The product of the zeros is:

⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]

⇒ 6α 2 = 8 / k

⇒ 6 (2 / k)2 = 8 / k [From (1)]

⇒ 6 × (4 / k) = 8

⇒ k = 24 / 8

⇒ k = 3

Related Questions

Which letter will correspond to the location of the following points when plotted on the number line below?

Answers

Answer:

A, E, B, D, C

Step-by-step explanation:

1) 6 is A

2) √83 = 9.11, so it is E

3) √40 = 6.3, so it is B

4) √64 = 8, so it is D

5) 7.5 is C

Solve 2(9-x) = 3 ( x +16 )

Answers

Answer: x=-6

Step-by-step explanation:

Let's solve your equation step-by-step.

2(9−x)=3(x+16)

Step 1: Simplify both sides of the equation by distribution

[tex]2(9-x)=3(x+16)\\(2)(9)+(2)(-x)=(3)(x)+(3)(16)\\18+-2x=3x+48\\-2x+18=3x+48\\[/tex]

Step 2: Subtract 3x from both sides.

[tex]-2x+18-3x=3x+48-3x\\-5x+18=48[/tex]

Step 3: Subtract 18 from both sides.

[tex]-5x+18-18=48-18\\-5x=30[/tex]

Step 4: Divide both sides by -5.

[tex]\frac{-5x}{-5} =\frac{30}{-5} \\x=-6[/tex]

2(9-x)=3(x+16)18-2x=3x+483x+2x=18-485x=-30x=-6

Gary has 24 sweets. He eats 3/8 of them.
Ben has 30 sweets. He eats 2/5 of them. Who has the most sweets left?

Answers

no of sweet gave to peny is 24×3/8 = 9 sweets

rest was ate by him

so the sweet ate by him is 24-9 = 15 sweet

hope this helps you kindly mark me as brainliest and follow me

Based on the amount of sweets eaten by Gary and Ben, the person with more sweets left is Ben.

Who has more sweets left between Ben and Garry?

The sweets left by Gary are:

= 24 - (24 x 3/8)

= 24 - 9

= 15 sweets

The sweet left by Ben are:

= 30 - (2/5 x 30)

= 30 - 12

= 18 sweets

In conclusion, Ben has more sweets left.

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Answer number 6 pleaseeeee

Answers

Answer:

20 people

Step-by-step explanation:

25% = 1/4 of 100

100 represents 200 people here, that means that if 25 = 1/4 to 100, then it is 1/8 to 200. 25x8=200

If 25% = 50, since 50x4=200 and 1/4 = 25% of 100%.

50... ok......

50 = 25%

Now, because there are 5 parts in 25, let's divide 5 by 50, that is 10. That means that 5 = 10 in that 50. 5% = 10 people

So, if 25-15=10

and then 5% = 10 people

5%+5%=10

10+10=20

That means, that 20 people more liked the movie than disliked it.

Answer A (20 people).
Survey 200. 25% (.25) enjoyed and 15% (.15) disliked.
So 25% of 200 is 50
So 15% of 200 is 30
We want enjoy minus dislike since we want difference or how many more.
50-30 is 20
This matches answer A.
Mark as best answer!

5. In the given sequence 32, 28, 24, 20, What rule is applied?
a. 10[tex]n[/tex]
b. 4[tex]n[/tex]
c. [tex]n[/tex]- 4
d. ([tex]n[/tex]+ 5) / 8​

Answers

Answer:

C

Step-by-step explanation:

A number is n, therefore you can start off with 32 and subtract 4 getting you 28. Subtract 4 and you get 24, and again 20.

Which products result in a difference of squares? select three options. (x minus y)(y minus x) (6 minus y)(6 minus y) (3 x z)(negative 3 x z) (y squared minus x y)(y squared x y) (64 y squared x squared)(negative x squared 64 y squared)

Answers

The three (3) products that resulted in a difference of squares are:

(3 + xz)(-3 + xz) (y² - xy)(y² + xy)(64y² + x²)(-x² + 64y²)

How to determine the difference of squares?

In Mathematics, the standard form for a difference of two (2) squares is given by a² - b² = (a + b)(a - b).

(3 + xz)(-3 + xz) = (3 + xz)(xz -3)

(3 + xz)(xz -3) = 3xz - 9 + x²z² - 3xz.

(3 + xz)(xz -3) = x²z² - 9

Therefore, x²z² - 9a² - b²

(y² - xy)(y² + xy) = y⁴ + xy³ - xy³ - x²y²

(y² - xy)(y² + xy) = y⁴ - x²y²

Therefore, y⁴ - x²y² a² - b².

(64y² + x²)(-x² + 64y²) = (64y² + x²)(64y² - x²)

(64y² + x²)(-x² + 64y²) = 4096y⁴- 64y²x² + 64y²x² - x⁴

(64y² + x²)(-x² + 64y²) = 4096y⁴ - x⁴

Therefore, 4096y⁴ - x⁴ a² - b².

Read more on difference of squares here: https://brainly.com/question/24673551

Answer:

Step-by-step explanation:

At the park there
is a merry-go-round with a radius of 6 feet.
What is the circumference?

Answers

Answer:

Step-by-step explanation:

r=6ft; c=2pi(6)=12pi ft

put into calculator, you get 37.7 ft

You are considering buying the house next to your home in order to fix it up and
sell it to make a profit. Ypu estimate that you will need to invest about $8,000 to
make necessary repairs and upgrades. After these improvements, you should
be able to sell it for $215,000. If the general guideline for flipping is to buy at
least 20% below the market value, what is the most you should be willing to pay
for the home?

Answers

Answer:

s

Step-by-step explanation:

Which represents a perfect cube? 6 times 6 times 6 6 6 6 3 times 3 times 3 times 3 3 3 3 3 3

Answers

The expression that represents a perfect cube is expressed as: 6 × 6 × 6

What is a Perfect Cube?

A perfect cube, x, is such that x × x × x = x³ = ∛x.

Thus, we have:

6 × 6 × 6 = 216

Cube root of 216 = ∛216

∛216 = 6

We can then conclude that the expression that represents a perfect cube is: 6 × 6 × 6

Learn more about perfect cube on:

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Answer:

6x6x6

Step-by-step explanation:

will give brainliest if your answer IS CORRECT

Answers

Answer:

Reflection over the y-axis.

Step-by-step explanation:

All the x values will change sign so its over the yaxis

Answer:

a. The graph will be reflected over the y-axis

Step-by-step explanation:

When a function is reflected over the y-axis, the x-coordinates are divded by -1, and then the new points will become reflections of the y-axis. Because x was changed to -x in this problem, we know that the graph was relfected across the y-axis.

hope this helps :)

What is an equation of the line that passes through the points (4, -2) and (2, 3)?

Answers

Step-by-step explanation:

For this problem, you'll need two formulas:

Slope: y1 - y2/x1 - x2

Point Slope: y - y1 = m(x - x1)

First thing you need to use is the slope formula.

Plugging in your coordinates gives you:

[tex]\frac{-2-3}{4-2}[/tex] = [tex]\frac{-5}{-2}[/tex]

You can simplify this by getting rid of the negatives since two negatives make a positive.

Now to use the point slope formula.

For this formula, the slope we just found, [tex]\frac{5}{2}[/tex], replaces the m, and for the x1 and y1, you use one of the original points(either (4,-2) or (2,3)).

I'll be using the point (2,3). Now plug everything in:

[tex]y-3=\frac{5}{2} (x-2)[/tex]

First thing you should do is distribute the [tex]\frac{5}{2}[/tex]:

[tex]y-3=\frac{5}{2} x-5[/tex]

Next thing to do is get the y by itself by adding 3 to both sides, which gives you your answer of:

[tex]y=\frac{5}{2} x-2[/tex]

Hope this was helpful, good luck :)

Which expression is equivalent to cube root of 216 x superscript 27 ? 6x3 6x9 72x3 72x9

Answers

The expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).

How to find the equivalent expression?

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

To find the equivalent expression, simplify the given equation with the help of mathematical operations.

The expression given in the problem is,

[tex]\sqrt[3]{216\times {27}}[/tex]

Let the expression which is equivalent to the above expression is n. Thus,

[tex]n=\sqrt[3]{216\times {27}}\\n=\sqrt[3]{216}\times \sqrt[3]{27}\\n=\sqrt[3]{6\times6\times6}\times \sqrt[3]{3\times3\times3}\\n=6\times3[/tex]

Thus, the expression which is equivalent to cube root of 216 x superscript 27 is 6 times 3 (6x3).

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Answer:

A

Step-by-step explanation:

Is 2x 4/3 equal to 4x 2/3

Answers

[tex]2x \times \frac{4}{3} = 4x \times \frac{2}{3}[/tex]

[tex] \frac{8x}{3} = \frac{8x}{3} [/tex]

Both are equivalents

Simplify the following.


I need to see a step by step answer on both questions to see how it actually works.

Answers

Answer:

See below ~

Step-by-step explanation:

27. (B)

3a/5b + 4a/15bTake the LCM to be 15b3a(3) + 4a / 15b13a/15b

27. (C)

(3²)³ × 3⁰ ÷ 3⁴3⁶ x 1 ÷ 3⁴3²3 x 39

Answer:

1,

[tex] \frac{13a}{15b} [/tex]

2,

[tex]9[/tex]

Step-by-step explanation:

[tex] \frac{3a}{5b} + \frac{4a}{15b} [/tex]

[tex] \frac{45a}{75b} + \frac{20a}{75b} [/tex]

[tex] \frac{13a}{15b} [/tex]

2,

[tex] {3}^{6} \times {3}^{0} \div {3}^{4} [/tex]

[tex]729 \times 1 \div 81[/tex]

[tex]729 \div 81 = 9[/tex]

I NEED THIS ASAP!!
Solve for X and find the angle relationship!!
(WILL GIVE BRAINIEST)
THIS IS RLY IMPORTANT

Answers

Answer:

Vertical anglesx = 1484°

Step-by-step explanation:

The indicated angles are vertical angles since formed by two intersecting lines.

We know the vertical angles are congruent. Use this property to find the value of x and the angle measure

6x = 3x + 426x - 3x = 423x = 42x = 42/3x = 14

The angle measure

6*14 = 84

Opposite angles are equal

6x=3x+426x-3x=423x=42x=42/3x=14

please help me...asap

Answers

Answer:

Your answer is D. 5 children, 12 teens, and 3 adults.

Step-by-step explanation:

45 children, 108 teens, and 27 adults.

x - children , y-teens, z-adults

45x + 108y + 27z

GCF for 45, 108, 27 is 9 so factory out 9 to all.

[tex]\frac{45}{9} ,\frac{108}{9} ,\frac{27}{9} \\5,12,3[/tex]

5 children, 12 teens, and 3 adults.

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


[tex]\large\text{It seems like all of your numbers are apart of the 9 factors. So, we will }\\\large\text{DIVIDE each of your numbers by 9 until we find out the total}\\\large\text{population (also known as your result to this equation)}[/tex]


“[tex]\large\text{45 children, 108 teens, \& 27 adults}[/tex]”


[tex]\large\textbf{Equation \# 1.}\\\\\large\boxed{\rm{\dfrac{45\ children}{9\ children}}}\\\\\\\large\boxed{= \rm{45 \ children \div 9 \ children}}\\\\\\\large\boxed{\rm{= 5\ children\ in\ total}}[/tex]


[tex]\large\textbf{Equation \# 2.}\\\\\large\boxed{\rm{\dfrac{108\ teens}{9\ teens}}}\\\\\\\large\boxed{= \rm{108\ teens \div 9 \ teens}}\\\\\\\large\boxed{= \rm{12 \ teens \ in \ total}}[/tex]


[tex]\large\textbf{Equation \# 3.}\\\\\\\large\boxed{\rm{\dfrac{27\ adults}{9\ adults}}}\\\\\\\large\boxed{\rm{= 27\ adults \div 9 \ adults}}\\\\\\\large\boxed{\rm{= 3\ adults\ in\ total}}[/tex]

[tex]\huge\textbf{Therefore, your answer is:}\\\\\huge\boxed{\textsf{Option D. 5 children, 12 teens, 3 adults}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]



~[tex]\frak{Amphitrite1040:)}[/tex]

Which is an x-value of a solution to the system

Answers

Answer:

Option B I.e -1/2

Step-by-step explanation:

Option B I.e -1/2

solve the volume for the triangular prism

Answers

Answer:

9.5 cubic units

Step-by-step explanation:

You need to multiply everything together and divide by 2.

5 x 2 x 1.9/2 = v

19/2 = v

9.5 cubic units

At a soccer game the snack bar sells hot dogs for 4 dollars and slices of pizza for 6 dollars. The snack bar sold 70 hot dogs and slices of pizza all together for $342 dollars.
Part A: Enter the total number of hot dogs sold.
Part B: Enter the total number of slices of pizza sold.

Answers

Answer:

Part A: Enter the total number of hot dogs sold. 70 of sold hot dogs

Part B: Enter the total number of slices of pizza sold. 50 slices of pizza

Step-by-step explanation:

Have a great day✧◝(⁰▿⁰)◜✧

The total cost for one year at the state university is $22,500. a student has the following help in covering the costs of school. an academic scholarship for $10,000. other scholarships and grants for $4,400. parents pay $1,800. what is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months?

Answers

Answer:

$630 Per Month

Step-by-step explanation:

$22,500-$10,000=$12,500-$4,400=$8,100-$1,800=$6,300/10Months

=$630

Which of the following rational functions is graphed below?
5
10
A. F(X) =
OB. F(x)=
O C. F(x) =
D. F(X) =
(x + 1)
(x + 2)(x-2)
(x+1)
(x-1)(x+2)
2x
x(x - 2)
(x-1)
x(x-2)
ڈے

Answers

Answer:

B.  F(x) = (x+1)/(x-1)(x+2)

Step-by-step explanation:

See attached graph.  Note how the two vertical lines at x = -2 and 1 match plot B

The following graph is of the rational function [tex]F(x) = \frac{x+1}{(x-1)(x+2)} \\[/tex]

What are asymptotes?

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance.

The rational function does not exist at x = 1 and x = -2 ( as observed in graph). Thus, the denominator of the function consist (x-1) and (x+2). It is only in option B, thus it is correct.

Learn more about asymptotes here

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Erica sells magazine subscriptions and makes a flat rate of $5.35 for each subscription she sells. if erica made $42.80 on monday, $64.20 on tuesday and $74.90 on wednesday, how many subscriptions did she sell in the three days? a. 32 b. 33 c. 34 d. 35 please select the best answer from the choices provided a b c d

Answers

Answer:

c. 34

Step-by-step explanation:

1) Add all the given prices on each day.

= 42.80 + 64.20 + 74.90

= 181.90

2) Set up an equation since we do not know how many magazine subscriptions she sold, but we know how much money she made.

Let x = number of magazine subscriptions sold

5.35x = 181.90

x = [tex]\frac{181.90}{5.35}[/tex]

x = 34

Solve for x . 8x-3 & 4x+3
8x-3+4x+3=180
?x+_=180

Answers

Answer:

x = 15

Step-by-step explanation:

the 2 angles are a linear pair and sum to 180° that is

8x - 3 + 4x + 3 = 180

12x = 180 ( divide both sides by 12 )

x = 15

The angles are supplementary angles. Then the value of the variable 'x' will be 15.

What is an angle?

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The angles are 8x - 3 and 4x + 3. And they are supplementary angles. Then the equation is given as,

8x - 3 + 4x + 3 = 180

Simplify the equation, then we have

8x - 3 + 4x + 3 = 180

12x + 0 = 180

x = 15

The angles are supplementary angles. Then the value of the variable 'x' will be 15.

More about the angled link is given below.

https://brainly.com/question/15767203

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Katie is selling lemonade for $1.50 per cup. She decides to put them on sale for $0.90. What percent discount did she give on her lemonade? *

Answers

Answer:

40%

Step-by-step explanation:

1.50 - 0.90 = 0.60

0.60 cents are saved.

[tex]\frac{0.60}{1.50} = 0.4[/tex]

0.4 = 40%

hope this helps :)

If one mile is aprox 1.6 kilometers the how many miles is the race

Answers

I need to know how many miles the race is

Find the equation of the lines a and b

Answers

Step-by-step explanation:

A ) 3x-2

B ) -4x+5

I HOPE IT HELPED YOU

8. In July 2008, the united states had a population of approximately 302,00,000 people. How many Americans were there in July

Answers

Answer: 302,000,000 people

help me plsss i need to do it fast 12 min left help me pls

Answers

Answer:

$44

Step-by-step explanation:

She has 79 AFTER her grandfather gave her 35. So you would subtract 35 from the 75 and get $44

Answer:

you're correct it's 44 you do 79 - 35 and you get 44

Help me plssss!
[tex]-124x+102=-126x-90[/tex]

Answers

Answer:

x=-96

Step-by-step explanation:

isolate x by moving -124x to the other side by adding -124x to -126x = -2x

then it will look like: 102= -2x-90

add 90 to both sides: 192= -2x

divide both sides by -2 to isolate x

x= -96

x = 96


-124x+126x = -90-102

2x = -90-102

2x = -192
divide both sides by 2

x = -96 !!

hope this helps <33

What is the equation of the line that passes through the point (8,-6) and has a
slope of o?

Answers

The slope or gradient has this formula when two points are given: m = y1 −y x1 −x In this case we have the points (-6,-8) and (-7,y) and m=-8.

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