If you divide one root of the equation 4x^2+bx-27=0 by the other root, the quotient will be -3. Find b.

Answers

Answer 1

There is no value of b that satisfies the condition that dividing one root of the equation by the other gives a quotient of -3.

Let's assume the roots of the quadratic equation \(4x^2 + bx - 27 = 0\) are r and s. According to the problem, if we divide one root by the other, the quotient is -3.

We know that the sum of the roots of a quadratic equation is given by the formula: r + s = -b/4 (coefficient of x term divided by 4)

And the product of the roots is given by the formula: rs = -27/4 (constant term divided by 4)

We are given that dividing one root by the other gives a quotient of -3, which can be expressed as r/s = -3.

From this information, we can set up the following equations:

r + s = -b/4 (Equation 1)

rs = -27/4 (Equation 2)

r/s = -3 (Equation 3)

From Equation 3, we can rewrite r in terms of s: r = -3s

Substituting r = -3s into Equation 1, we get:

-3s + s = -b/4

-2s = -b/4

s = b/8

Now we can substitute s = b/8 into Equation 2:

(-3s)(s) = -27/4

\(-3s^2 = -27/4\\s^2 = 27/12\\s^2 = 9/4\)

s = ±√(9/4)

s = ±(3/2)

Since r/s = -3, we have:

r/(b/8) = -3

r = -3b/8

Now we can substitute s = 3/2 and r = -3b/8 into Equation 1:

(-3b/8) + (b/8) = -b/4

-b/8 = -b/4

b/8 = b/4

1/8 = 1/4

However, we reached a contradiction since 1/8 is not equal to 1/4. Therefore, there is no value of b that satisfies the condition that dividing one root of the equation by the other gives a quotient of -3.

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Related Questions

hi may you help me with 1+1

Answers

Answer:

2

Step-by-step explanation:

3. John has a bag of marbles. The ratio
of red marbles to blue marbles is 3:7.
What percent of the marbles are red?

Answers

Answer:

Step-by-step explanation:

percentage is taken as out of 100 we have to do like this for finding any percentage for any given ratio.

add the given ration 7+3=10

now as ratio is given from red to blue so we have red=3 and blue=7.

now final step is that simply do this.....

if 10(total) is equal to 100 %

then 3(for red) is equal how many percentage?

so we know that it will be (3 x 100) / 10 = 30%

so 30 percent of marbles are red.

y=2x-2,2y=4x=4 substitution]

Answers

Answer: No solution

Step-by-step explanation:

Answer:

y=2x-2 , 2y+4x=4

Solve with Substitution:

x: 1

y: 0

Step-by-step explanation:

Plug in to check work

Part A
MONEY Samir plan to buy a new video game ytem which will cot at leat $450. He earn $6 per hour babyitting and $10 per hour tutoring. Let x be the number of hour babyitting and y be the number of hour tutoring. Part A Select the inequality that repreent the number of hour Samir could work to earn enough to buy the game ytem. Part A

Select the inequality that repreent the number of hour Samir could work to earn enough to buy the game ytem. A) y≥ − 0. 6x 45
B) y ≥ − 123x 75
C) y > 123x − 75
D) y > 6x 10

Answers

Answer:

Step-by-step explanation:

The required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system. which is the correct answer would be an option (A).

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The video game system will cost at least $450.

He earns $6 per hour babysitting and $10 per hour tutoring.

Let x be the number of hours babysitting and y be the number of hours of tutoring.

According to the given situation, we can write the inequality would be as:

⇒ 6x + 10y ≥ 450

Rearrange the terms of variables in the above inequality,

⇒ 10y ≥ 450 - 6x

Divided by 10 into both sides of the above inequality,

⇒ 10y/10 ≥ 450/10 - 6x/10

⇒ y ≥ 45 - 0.6x or

⇒ y ≥ - 0.6x + 45

Thus, the required inequality is y ≥ - 0.6x + 45 which represents the number of hours Samir could work to earn enough to buy the game system.

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Find the value of X??

Find the value of X??

Answers

Answer:

x = 137

Step-by-step explanation:

Since this shape has 4 vertices, the angles will add up to 360 so:

x + 67 + 109 + 47 = 360

x + 223 = 360

x = 360 - 223

x = 137

Compared with the graph of the parent function, which equation shows only a vertical compression by a factor of ______ and a shift downward of 4 units?

Compared with the graph of the parent function, which equation shows only a vertical compression by a

Answers

Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

What is scale factor?

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

x and y represents the data points.SF represents the scale factor.

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

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Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

What are the coordinates of A after reflecting across the line x = 3?

What are the coordinates of A after reflecting across the line x = 3?

Answers

Answer:

It would be (3,2) since it is being reflected over the line it is already on

Step-by-step explanation:

Answer:(3,2)

Step-by-step explanation:Doube check make sure you double check and not click (3,-2) THAT IS NOT THE ANSWER THE ANSWER IS (3, 2)

Given y = 3x + 1 State the quadrants in which this graph is in. (Use the numbers 1-4)

Answers

Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

which two parts of the vehicle are most important in preventing traction loss

Answers

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Please, If you can help i will be grateful and give brainliest.

Please, If you can help i will be grateful and give brainliest.

Answers

Answer:

To complete the square, you always want to add \((\frac{a}{2} )^{2}\), where a is the coefficient of x.

In this case, the coefficient of x is -1.

Thus,

\(y=x^2-x+1\)

\(y=x^2-x+(\frac{-1}{2})^2 +1-(\frac{-1}{2})^2\)

\(y=(x-\frac{1}{2})^2+1-\frac{1}{4}\)

\(y=(x-\frac{1}{2})^2+\frac{3}{4}\)

determine the correct check digit for the upc 6-73419-23216-? (lego architecture set)

Answers

The correct check digit for the UPC code 6-73419-23216- is "3".

The check digit is used to verify the accuracy of the UPC code when it's scanned. It's the last digit of a UPC code and is calculated using a formula based on the first 11 digits.

The formula involves adding up the digits in the odd-numbered positions and multiplying the sum by three, then adding up the digits in the even-numbered positions, and subtracting the second sum from the first sum.

The check digit is then calculated by taking the difference and finding the smallest number that, when added to the difference, is a multiple of 10. The result of this calculation is the check digit.

In this case, the correct check digit is "3".

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Simplify 6 to the negative 3rd power over 6 to the 5th.

68

6−2

1 over 6 to the 8th power

1 over 6 to the 2nd power

Points earned on this question: 0

Answers

Answer:

The correct option is C) 1 over 6 to the 8th power. ·

Step-by-step explanation: · Apply the exponent rule: · Thus, the correct ...

·

PLEASE I NEED HELP WITH THIS!!!! Domain! I WILL MARK U AS THE BEST!

1. What is the domain of the graph linear function?
A- x > 1
B- x >= 1
C- x > -1

PLEASE I NEED HELP WITH THIS!!!! Domain! I WILL MARK U AS THE BEST!1. What is the domain of the graph

Answers

Answer:

c

Step-by-step explanation:

big brain and the world is not

-in a random physical Sciences experiment A and B are two different events it was found that
,P(A)=2/5,P(B)=3/8 and P(A or B)=5/7

-calculate the P(B).​

Answers

Answer:

3/8

Step-by-step explanation:

P(B) is given to you in the question.

12. Use a triple integral in cylindrical coordinates to evaluate the volume of the region bounded above by x² + y² + z² = 12 and bounded below by z=√x² + y² . (6)

Answers

The volume of the region bounded above by  x² + y² + z² = 12 and bounded below by z=√x² + y² is

Given :

x² + y² + z² = 12 ⇒ z = √(12- (x² + y²))

z=√x² + y²

It is known that :

r = √(x² + y²)

So the z values range from r ≤ z ≤ √(12-r²)

Also 0 ≤ θ ≤ 2π

Setting,

12- (x² + y²) = √x² + y²

r = 12 - r²

r² + r - 12 = 0

(r - 3)(r + 4) = 0

Or r = 3

So the value of r range from 0 to 3.

In the cylindrical coordinates :

Volume = \(\int\limits^{2pi}_0 \int\limits^3_0 \int\limits^{12-r^2}_r {dzrdr} \, dtheta\)

Simplifying,

Volume = 99π

Hence the required volume is 99π.

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Divide. Write in simplest form.

2/3 divided by 1/5

Answers

Answer:

3 1/3 or 3.3(repeated)

Step-by-step explanation:

2/3 ÷ 1/5

= 2/3 × 5

= 10/3

= 3 1/3 or 3.3(repeated)

I hope this helped!

in the morning Emily studied 40 minutes for a math exam later that evening Emily studied 4X more minutes answer any question that represents the total number of minutes, y, Emily study for the math exam.

Answers

Answer: y = 40 + x

In the morning, Emily studied 40 minutes for an exam

In the evening he studied additional x minutes

The initial minutes he studied = 40 minutes

The additional minutes = x minutes

The total minutes = initial minutes + additional minutes

y = 40 + x

Where y = total minutes studies

Therefore, the total minutes he studied is y = 40 + x

A graph is shown below. Does the graph shown represent a function? Why or why not?

Answers

Hey, this is not a complete question, there is not visible graph. You may wanna retry to set up your question and make sure the graph is there

Which of the following correctly classifies the number -5 to all of the number sets which it belongs?

Real, Rational, Integer, Whole

Answers

Answer:

Real, Rational, Integer,

Step-by-step explanation:

Real: Most numbers are real so they just naturally fall into this category

Rational: -5 can be written as a fraction so it falls here

Integer: An integer is a number that can be positive, negative, or 0. as long as it doesnt have decmal points, it's an integer

Its not a whole number because whole numbers cannot contain a fraction, decimal, or negative value

Hope this helps!

Form the perfect square trinomial in the process of completing the square. what is the value of c? x2 3x c = startfraction 7 over 4 endfraction c c =

Answers

While making a perfect square for the given quadratic equation \(\rm x^2+3x+c=\frac{7}{4} +c\) the value of c is 9/4

It is given that the quadratic equation  \(\rm x^2+3x+c=\frac{7}{4} +c\) while forming the perfect square.

It is required to find the value of c.

What is a quadratic equation?

It is defined as the equation of polynomial of degree two. The standard form of the quadratic equation is as follows:

\(\rm ax^2+bx+c=0\)  where \(\rm a\neq 0\)

We have a quadratic equation:

\(\rm x^2+3x+c=\frac{7}{4} +c\)

We know that we can make any quadratic equation into a perfect square by the perfect square trinomial method as follow:

\(\rm ax^2+bx+c=0\\\rm ax^2+bx=-c\\\rm ax^2+bx+(\frac{b}{2a})^2 =-c+(\frac{b}{2a})^2\\\)

So, the value of 'c' would be:

\(\rm c=(\frac{b}{2a})^2\\\)  here b=3 and a=1 by comparing the equation to the standard equation.

\(c=(\frac{3}{2\times1} )^2\\c=(\frac{3}{2} )^2\\c=\frac{9}{4}\)

Thus,  while making a perfect square for the given equation the value of c is 9/4

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Answer:

9/4

Step-by-step explanation:

correct on edge

Use this set of number to answer the question.
4, 11, 6, 9, 23, 34, 6, 19,
What is the median for this set of numbers?
A. 6
B. 10
C. 14
D. 16

Answers

Answer:

10

Step-by-step explanation:

arrange the number in order from smallest to largest, 4, 6, 6, 9, 11, 19, 23, 34. you then find the middle number, in this case there is no middle number, but 9 and 11 are the closest, so you add those to together to get 20, then divide by 2. this gives you ten

if you have any questions, leave them in the comments and i will try to answer them, if this helped pls give brainliest

Answer:

Hello There!!

Step-by-step explanation:

Median is ordering the numbers from smallest to biggest.

Ordered: 4,6,6,9,11,19,23,34

And there is no middle number so you have two add the two middle numbers 9+11=20 then divide by 2 which equals 10.

hope this helps,have a great day!!

~Pinky~

9 m
Not drawn to scale
Find the volume of the triangular prism.
6 m
6m

9 mNot drawn to scaleFind the volume of the triangular prism.6 m6m

Answers

Answer:

162 m³

Step-by-step explanation:

Volume of the prism is the product of the area of the base and the height of prism.

First, we need to find the area of its triangular base:

A = bh/2 = 9*6/2 = 27 m²

Now we can find the volume:

V = 27*6 = 162 m³

Area of base

1/2BH1/2(9)(6)9(3)27m²

Volume

Area of base×Height27(6)162m³

Which radical expression is equivalent to k^2/9. Please give me a step-by-step explanation.

Answers

Answer:

Apply the rule x^m/n = n√ x^m to rewrite the exponentiation as a radical.

9√k^2

Let's simplify

\(\\ \rm\Rrightarrow \dfrac{k^2}{9}\)

\(\\ \rm\Rrightarrow \dfrac{k^2}{3^2}\)

\(\\ \rm\Rrightarrow (\dfrac{k}{3})^2\)

When a metal is placed in an a........ there is a chemical reaction. lol this is not maths

Answers

Step-by-step explanation:

you are my 7 year old are the only ones 6th in a world to make it to make a simple decision about you are you fresh out there in the United kingdom of America you have a great life in a country in the United kingdom of the world and inventor of the world is a good thing to be a great person but you can also find the right to be able and the way of the freash

HOW DO I SOLVE THIS 20POINTS

HOW DO I SOLVE THIS 20POINTS

Answers

The solution of the system of equations f(x) = 2^x + 1 and g(x) = 3^x is x = 1

Determining the solution of the system of equations

From the question, we have the following parameters that can be used in our computation:

f(x) = 2^x + 1

g(x) = 3^x

The above expression is a system of exponential equations

We are required to solve by graph

That implies that we graph the equations in the system on the same plane and write out ordered pairs from the point of intersection of the equations in the system

Next, we plot the graph

See attachment for the graph of the equations

The ordered pairs of the intersection point is (1, 3)

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HOW DO I SOLVE THIS 20POINTS

find in centimeters the circumference of a circle with a diameter of 0.15 m give and exact answer in terms of pi

Answers

Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. If you spin this spinner 1000 times, how many times do you expect it to land on Red?

Answers

Answer:

83 spins

Step-by-step explanation:

Number of red spins = n

Number of orange spins = 8n

Number of yellow spins = 3n

Total number of trials = 240

Total number of spins :

(n + 8n + 3n) = 240

12n = 240

n = 240 / 12

n = 20

Number of red spins = 20

(1000/240) * n

4.1666666 * 20

= 83.333

= 83 spins

In a study of canine attacks, the probability that the victim was under 18 years of age is 80%. the probability that the attack occurred on the dog owner's property was 64%. the probability that the victim was under 18 years of age or the attack occurred on the dog owner's propery was 95%. what is the probability that the victim was under 18 years of age and the attack occurred on the dog owner's property?

Answers

The probability that the age of the victim of a canine attack was under 18 years and that the attack took place at the property of the dog owner is 49/100

Let the event of the canine attack victim being under 18 years of age be X.

Let the event of the canine attack occurring at the dog owner's property be Y.

It is given that

the probability of X or, P(X) = 80%

= 8/10

Also, P(Y) = 64%

= 64/100

P(X or Y) = 95%

or, P(X ∪ Y) = 95%

= 95/100

We need to find the probability that the victim was under 18 years old, and that the attack occurred on the dog owner's property.

= P(X and Y) = P(X ∩ Y)

We already know the probability law that

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

or, P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

Henceforth,

P(X ∩ Y) = P(X) + P(Y) - P(X ∪ Y)

= 80/100 + 64/100 - 95/100

Since they have a common denominator we can write

= (80 + 64 - 95)/100

= (144 - 95) / 100

= 49/100

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The question in the photo
Pls help

The question in the photoPls help

Answers

I went on Doyourmath, and it helps me if the image didn't help then I am sorry, but I am truly hoping I answered your question.

The question in the photoPls help

Layla calculates the mean of the ages of 10 students on her bus, and she discovers the average(mean) age is 12.8. What will happen to the mean if she includes her bus driver's age of 56 in her data set? *
A.The mean will stay the same.
B.The mean will decrease.
C.The mean will increase.
D.There isn't enough information.

Answers

Answer:

The mean will increase

Step-by-step explanation:

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