Let f (x) = px 2 + qx - 4 p, where p 0. Find the number of roots for the equation f (x) = 0 . Justify your answer.

Answers

Answer 1

Answer:

f(x) = 0

px^2 + qx - 4p = 0

abc-Formula: x = (-b ± √(b^2 - 4·a·c))/(2·a)

x = (-q ± √(q^2 - 4·p·(-4p)))/(2·p)

x = (-q ± √(q^2 + 4^2·p^2))/(2·p)

Because q^2 + 4^2·p^2 > 0 there are two roots.


Related Questions

I NEED HELP FAST

image is the question :)

Answers

0.3x4= 1.2 is like multiplying 3x4=12

Garcia's bike rentals, it cost $38 to rent a bike for 9 hours. How many hours of bike use does the customer get per dollar. If necessary, round the answer to the nearest hundredth

Answers

From the question, we were told that Garcia's bike rentals cost $38 to rent bike for 9 hours.

We are to find how many hours will a customer use the bike per dollar.

This can also be likened to calculating miles per gallon.

if i can drive 300 miles on 10 gallons of gas then my miles per gallon is 300/10 = 30 mpg.

So, hours per dollar is also a division problem too.

(9 hours)/($38)

= 9/38

= 0.2368

= 0.24 hours per dollar (to the nearest hundredth)

The length of a rectangle is eight more than twice it's width. If the length is less than 34,then what is the width?

Answers

Answer:

width < 13

Step-by-step explanation:

let width of the rectangle = x

length = 8 + 2x

according to the question,

8+2x < 34

2x < 34-8

2x < 26

x < 13

Wasif spent 1/3 of his income on housing and 2/5 on daily expenditure and save the rest if he save 24600 what was his income altogether

Answers

Answer:

61500

Step-by-step explanation:

1/3 = 3/15

2/5 = 6/15

1 - 3/15 - 6/15 = 6/15

6/15 = 24600

24600 ÷ 6 × 15 = 61500

Answer:

92250

Step-by-step explanation:

Forming algebraic equation and solving:

Let the income  = x

Amount spent on housing = (1/3) of the income

                                             [tex]\sf = \dfrac{1}{3}x[/tex]

Amount spent of daily expenditure = (2/5) of the income

                                                          [tex]\sf =\dfrac{2}{5}x[/tex]

Income = Savings + housing expenditure + daily expenditure  

Income - housing expenditure - daily expenditure = savings

[tex]\sf x - \dfrac{1}{3}x-\dfrac{2}{5}x=24600\\\\\\\dfrac{x*15}{1*15}-\dfrac{1*5}{3*5}x-\dfrac{2*3}{5*3}x = 24600\\\\\\[/tex]

            [tex]\sf \dfrac{15}{15}x-\dfrac{5}{15}x-\dfrac{6}{15}x = 24600\\\\\\\dfrac{(15 -5 - 6)}{15}x = 24600[/tex]

              [tex]\sf \dfrac{4}{15}x = 24600[/tex]

                 [tex]\sf x = 24600 *\dfrac{15}{4}\\\\ x = 6150*15[/tex]

Income = 92250

       

a certain type of aluminum screen 2 feet in width has, on the average, three flaws in a 100-foot roll. we assume flaws occur randomly so the number of flaws follow some poisson distribution. what is the probability that the first 40 feet in a roll contain no flaws?

Answers

The probability of that the first 40 feet in a roll contain no flaws is ≈ .3012

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Calculation

Θ = μ = [tex]\frac{100 foot}{3 flaws}[/tex]

a ) We assume that the length until the first flaw follows an exponential distribution.

Probability density function of exponential distribution:

f(x) = [tex]\frac{1}{Θ} e^{\frac{-x}{Θ} } = \frac{1}{100/3}e^{-x/(100/3)} = \frac{3}{100}e^{-3x/100}[/tex]

The first 40 feet in a roll of 100 feet contain no flaws if the first flaw occurs after 40 feet.

The probability is the integral over the corresponding interval:

the further calculation has been shown in fig. attached

since equation was not possible to write here

b) We assume that the length until the first flaw follows an exponential distribution.

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I NEED HELP ASAP

What is the slope-intercept equation for the linear function represented by the
table?
A. y = -x +4
B. y =
-x-4
C. y = x-4
OD. y=x+4
0
x
2 4 6 8
y -4 -1 258

Answers

Answer: C : y = 3/2 - 4

Step-by-step explanation:

Find the Slope (Slope Formula)

(4,2) (6,5)

m = (5-2)/(6-4)

m = 3/2

Find "b"

y = mx + b (Slope intercept form)

2 = 3/2(4) + b

2 = 6 + b

-4 = b

If the perimeter of the square is 48 m. Find the area of a
circle whose circumference is the same as the square.

Answers

The area of the circle is 201 m².

What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the area of the circle:

The perimeter of square: 4aCircumference of the circle: 2πr

We know that 4a = 2πr, now calculate r as follows:

4a = 2πr48 = 2πrr = 48/2πr = 48/2(3.14)r = 48/6.28r = 7.64

Rounding off: 8m

Area of circle:

πr²3.14(8)²3.14(64)200.96

Rounding off: 201 m²

Therefore, the area of the circle is 201 m².

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what is the Riemann Hypothesis??

Answers

Answer:

lie on a certain vertical straight line

Step-by-step explanation:

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics.

when an integer is subtracted from 8 times the next consecutive integer, the difference is 71. Find the vale of the greater integer.

Answers

10.

First, define variables for the integer and the next consecutive integer. Then set up an equation that represents the problem. Solve for x. Since x+1 is greater than x, insert your value into the expression and evaluate.

See details:

The value of the greater integer will be 10.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The algebraic expression is,

'' An integer is subtracted from 8 times the next consecutive integer, the difference is 71.''

Now,

Let a number = x

Then, Its consecutive number = (x + 1)

So, We can formulate;

⇒ 8 (x + 1) - x = 71

Solve for x as;

⇒ 8x + 8 - x = 71

⇒ 7x + 8 = 71

⇒ 7x = 71 - 8

⇒ 7x = 63

⇒ x = 9

Thus, The value of greater number = x + 1

                                                      = 9 + 1

                                                       = 10

Therefore, The value of the greater integer will be 10.

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 If I stated 2 * - 3    OR  -10/-5   what steps would you follow to find the factor/quotient and its sign? You may use these examples to explain. ​

Answers

If I stated 2 * - 3    OR  -10/-5  then the factor/quotient and its sign is given by -6 and 2

What is a quotient in math?

The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient

What is quotient formula?

The quotient formula is given as follows: Dividend ÷ Divisor = Quotient (if the remainder is zero) The general formula for any division problem is given by: Dividend ÷ Divisor = Quotient + Remainder.

2 * -3 = -6  or -10/-5= 2

Thus the quotient is -6 and 2

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scores on the wechsler adult intelligence scale for the 20 to 34 age group are approximately normally distributed with mean 110 and standard deviation 15. how high must a person score to be in the top 5% of all scores? enter your answer as a whole number.

Answers

The person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

What is defined as the normal distribution?A normal distribution is a data set arrangement in which the majority of values cluster inside the center of the range and the remainder taper off symmetrically toward any extreme.A histogram inside a normal distribution curve is sometimes used to design the curve.

The formula for the normal distribution is;

z = (x - μ)/σ

where,

z = z- score, taken fro tableMean μ = 110Standard deviation σ = 15Sample mean x.

If we want to be in the top 5%, we must outperform 95% of the remaining scores. So we must investigate.

In with us standard normal probability table, look up 0.95 and get the Z score that corresponds to that.

z = 1.7

Put the value in formula ad find x.

1. 7 = (x - 110)/15

x = 25.5 + 110

x = 135.5

x = 136 (whole number)

Thus, the person must score 136 to be in the top 5% of all scores in wechsler adult intelligence scale.

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Which is an equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3?

Answers

The value that will be equivalent to the expression will be 5625³.

What is an expression?

It should be noted that an expression is simply used in Mathematics to illustrate or show the relationship between the variables.

The equivalent expression for (3 to the power of 2 • 5 to the power of 4) to the power of 3 will be illustrated as:

= (3² × 5⁴)³

= (9 × 625)³

= 5625³

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Marine biologist studies the population of seals in research area. how many Seals are in the research area?​

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello..as fast a possible I need the ans pls ​

Answers

Answer:

I think it's because the triangle sides are isometrics so that's why the sides are equal

would you put a closed dot or an open dot on a number line for n > -8?

Answers

Answer:

a opened because a closed means that number ond more

Step-by-step explanation:

WILL AWARD BRAINLIEST

Answers

M= 1/3. The equation would be y= 1/3x + 2

a couple has four children. neither the father nor the mother is bald; one of the two sons is bald, but neither of the daughters is bald. (a) if one of the daughters marries a nonbald man and they have a son, what is the chance that the son will become bald as an adult? (b) if the couple has a daughter, what is the chance that she will become bald as an adult?

Answers

If one of the daughters marries a non-bald man and they have a son, the chance that the son will become bald as an adult is 0%

If the couple has a daughter, the chance that she will become bald as an adult is 0%

In the question, we have been given that the neither the father nor the mother is bald, and out of the four children only one son is bald, but the other son and the two daughters are not bald, now we solve the following:

Part a

A chance that the son will become bald as an adult:

If the daughter has no bald gene (XX), and she marries a non bald man then there is 0% chance that the son will become bald as an adult because neither the mom nor the dad has the baldness gene

Part b

The chance that she will become bald as an adult:

If the daughter having a bald gene ([tex]X^{b} X[/tex]) marries a non bald (XY)man then also there is a 0% chance that the daughter will be bald as an adult. As the baldness is a recessive trait, for the daughter to be bald she needs to have two baldness gene( one from father and one from mother). And since this is not the case the daughter might have baldness gene but the phenotype will be non-bald.

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the denominator of a fraction is two more than the numerator. if both numerator and denominator are increased by ten, the simplified is 9/10. find the original fraction. (Do not simplify).

Answers

Give to each part of the fraction a variable (a letter)

Numerator: n

Denominator: d

the denominator of a fraction is two more than the numerator:

[tex]d=n+2[/tex][tex]\frac{n}{d}=\frac{n}{n+2}[/tex]

both numerator and denominator are increased by ten, the simplified is 9/10:

[tex]\frac{n+10}{n+2+10}=\frac{9}{10}[/tex]

Use the equation above to find the value of n:

[tex]\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}[/tex]

As n is equal to 8 find the value of d:

[tex]\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}[/tex]

The original fraction is:

[tex]\frac{8}{10}[/tex]

need help again with a question

Answers

Answer: x = 58

Step-by-step explanation:

The angles are alternating interior angles. This means that the angles are equal.

So x = 58

Find the volume of the cylinder (rounded to the nearest tenth).9 in.3 in.

Answers

We have the next formula to calculate the volume of the cylinder

[tex]V=\pi r^2h[/tex]

where

r is the radius

h is the height

in our problem

r=3in

h=9in

we substitute the values

[tex]V=\pi(3)^2(9)=254.46in^3[/tex]

the volume round to the nearest tenth is V=254.5 in ^3

Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent. Show work
A. 16%
B. 38%
C. 40%

Answers

The percentage of the students that like rap are also in grades 9–10 is 32%.

Determining the percentage of rap in grades 9-10

Given data:

Grade 9-10 for Rap = 40

Row total for grade 9-10 = 125

Now let determine the percentage of rap in grades 9-10 using this formula

Percentage of rap in grades 9-10 = Grade 9-10 for Rap / Row total for grade 9-10

Let plug in the formula

Percentage of rap in grades 9-10 = 40 /125

Percentage of rap in grades 9-10 = 0.32 × 100

Percentage of rap in grades 9-10 = 32%

Therefore we can conclude that 32% is the percentage of rap grade 9-10.

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Find the values of x and y.

Answers

Answer:

x=71 y=109

Step-by-step explanation:

explain 8 - 5 * 3 from a 7th grader

Answers

Answer:

-7

Step-by-step explanation:

5 * 3 = 15. 15 - 8 = 7; so, 8 - 15 = -7.

Can you simplify 6:4 ?

Answers

yes, it is the same than 3:2. And we can not simplify it more

-9^2 x 3
evaluate the experssion!!

Answers

Answer:

243

Step-by-step explanation:

-9^2 = -9 * -9 = 81

81 * 3 = 243

Solve the system of linear equations using the substitution method.

2d + 8y = 20 and y = 2

A. (1, 1)

B. 4, 4

C. (1, 2)

D. (2, 2)

Answers

Answer:

D

Step-by-step explanation:

2d + 8y = 20

y = 2

substitute y = 2 into the other equation

2d + 8(2) = 20

2d + 16 = 20 ( subtract 16 from both sides )

2d = 4 ( divide both sides by 2 )

d = 2

solution is (2, 2 )

answer-> D. (2,2)

Given,

2d + 8y = 20  .............................................(Equation i)

y = 2 .............................................................(Equation ii)

substituting y = 2 in equation i, we get

2d + 8(2) = 20

2d + 16 = 20

2d = 20 - 16

2d = 4

d = 2

Hence the correct answer would be option D. (2,2)

We have used the substitution method to solve the given system of linear equations.

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Write the perimeter of the triangle as a simplified polynomial. Then factor the polynomial.

Answers

Answer:

4x² + 29x + 7 = (4x + 1)(x + 7)

Step-by-step explanation:

Simplify the polynomial:

Like terms are terms with same variable and same power.

       Perimeter = sum of all the sides

                         = 3x² + 1 + 15x + 6 + x² + 14x

                         = 3x² + x² + 15x + 14x + 1 + 6

Combine like terms,

                        = 4x² + 29x + 7

Factorize:

        Sum = 29

  Product = 4*7 = 28

   Factors = 1 , 28    {28 + 1 = 29 & 28*1 = 28}

Rewrite the middle term using the factors,

                           = 4x² + x + 28x + 7

                           = x(4x + 1) + 7(4x + 1)

                           = (4x + 1)(x + 7)

solve each linear equation 7+2x=4x-3

Answers

Answer:

Simplifying

7 + 2x = 4x + -3

Reorder the terms:

7 + 2x = -3 + 4x

Solving

7 + 2x = -3 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

7 + 2x + -4x = -3 + 4x + -4x

Combine like terms: 2x + -4x = -2x

7 + -2x = -3 + 4x + -4x

Combine like terms: 4x + -4x = 0

7 + -2x = -3 + 0

7 + -2x = -3

Add '-7' to each side of the equation.

7 + -7 + -2x = -3 + -7

Combine like terms: 7 + -7 = 0

0 + -2x = -3 + -7

-2x = -3 + -7

Combine like terms: -3 + -7 = -10

-2x = -10

Divide each side by '-2'.

x = 5

Simplifying

x = 5

A table is made using the following two patterns.

Pattern x: Starting number: 3, Rule: add 3

Pattern y: Starting number: 6, Rule: add 6

Complete the table for the given patterns.

And then it asks to graph the points from 3 points

Answers

The rules of the patterns are 3 + 3x and 6 + 6y

How to complete the pattern?

The patterns are given as:

Pattern x: Starting number: 3, Rule: add 3Pattern y: Starting number: 6, Rule: add 6

For pattern x, we have the following highlights:

Start = 3

Rule = Add 3

This means that the nth term of pattern x is:

Pattern x = 3 + 3x

For pattern y, we have the following highlights:

Start = 6

Rule = Add 6

This means that the nth term of pattern y is:

Pattern y = 6 + 6y

The complete table

For pattern x, set x = 0, 1, 2 and 3

So, we have

3 + 3x = 3 + 3(0) = 3

3 + 3x = 3 + 3(1) = 6

3 + 3x = 3 + 3(2) = 9

3 + 3x = 3 + 3(3) = 12

For pattern y, set y = 0, 1, 2 and 3

So, we have

6 + 6x = 6 + 6(0) = 6

6 + 6x = 6 + 6(1) = 12

6 + 6x = 6 + 6(2) = 18

6 + 6x = 6 + 6(3) = 24

Next, we plot the graphs of both patterns (see attachment) where the blue line represents pattern 1, and the other represents the second pattern

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2-3x + 4 + x = -2x + 1

Answers

Answer:

No solution

Step-by-step explanation:

2- 3x + 4 + x = -2x + 1

2  -3x  + 4 + x = -2x + 1

6  -3x + x = -2x + 1

6  -3x + x = -2x + 1

6  -2x = -2x + 1

6  -2x = -2x + 1

move -2x to the right by adding 2x on both sides

6  -2x = -2x + 1

+2x         +2x

6  =  + 1

is 6 equal to 1?

No, so No solution

 

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