the diffrence between the roots of the equation 2x^2-5x+c=0 is 0.25 find c

Answers

Answer 1

Answer:

c = 3.09375

Step-by-step explanation:

Standard for of quadratic equation:

ax² + bx + c = 0

We have

2x² - 5x + c = 0

Sum of the roots

x₁ + x₂ = - b/a = -(-5)/2 = 2.5

Product of the roots

x₁x₂ = c/a = c / 2

We have:

x₁ - x₂ = 0.25

The square of the above is:

(x₁ - x₂)² = (x₁ + x₂)² - 4x₁x₂

Substitute known values and solve for c:

0.25² = (2.5)² - 4(c/2) 2c = 6.25 - 0.06252c = 6.1875c = 3.09375
Answer 2

Answer:

c = 3.09375

Step-by-step explanation:

Factored form of a quadratic equation

[tex]y=a(x-r_1)(x-r_2)[/tex]

where:

a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the roots

Given quadratic:

[tex]2x^2-5x+c=0[/tex]

Therefore, the leading coefficient is:

[tex]\implies a=2[/tex]

Substitute the value of a into the formula:

[tex]\implies y=2(x-r_1)(x-r_2)[/tex]

Expand:

[tex]\implies y=2x^2-(2r_2+2r_1)x+2r_1r_2[/tex]

Compare the coefficients of x:

[tex]\implies -(2r_2+2r_1)=-5[/tex]

[tex]\implies 2r_2+2r_1=5[/tex]

[tex]\implies r_2+r_1=2.5[/tex]

If the difference between the roots is 0.25 then:

[tex]\implies r_2-r_1=0.25[/tex]

Add the two root equations to eliminate r₁:

[tex]\implies 2r_2=2.75[/tex]

[tex]\implies r_2=1.375[/tex]

Substitute the found value of r₂ into one of the root equations and solve for r₁:

[tex]\implies 1.375-r_1=0.25[/tex]

[tex]\implies r_1=1.375-0.25[/tex]

[tex]\implies r_1=1.125[/tex]

As c = 2r₁r₂ then:

[tex]\implies c=2(1.125)(1.375)[/tex]

[tex]\implies c=3.09375[/tex]

Learn more about factored quadratics here:

https://brainly.com/question/27783166

https://brainly.com/question/27934929


Related Questions

What is the product? 3a(8a - 6b)

24a² - 6b

24a² - 6ab

24a² - 18b²

24a² - 18ab

Answers

The answer is the last one.

Explanation:

3a(8a - 6b)
3a x 8a - 3a x 6b
24a^2 - 3a x 6b
24a^2 - 18ab

The product of expression is 24a² - 18ab.

What is Polynomial?

A polynomial is a sort of algebraic expression in which all variable exponents are whole numbers. Variable exponents in any polynomial must be non-negative integers. A polynomial is made up of constants and variables, however we cannot divide polynomials by variables.

We have,

3a( 8a - 6b)

Now, multiplying the expression as

= 3a(8a) - 3a(6b)

= 24a² - 18ab

Learn more about Polynomial here:

https://brainly.com/question/11536910

#SPJ5

MATH HELP CALC

LOOK AT IMAGE

Answers

The right Riemann sum for the given function is 2.5.

Firstly, we must find the width of each of the subintervals Δx,

We know n = 4, a = 0, b = 2

∴ Δx = b - a / n

Δx =  2 - 0 / 4

Δx = 1/2

The width of each rectangle is 0.5

Next, we must find the locations of the right endpoints of the rectangles -

x1 = a + Δx(1) = 0.5

x2 = a + Δx(2) = 1

x3 = a + Δx(3) = 1.5

x4 = a + Δx(4) = 2

Now that we have the width of each rectangle, Δx = 0.5, and the right endpoints for the rectangles, x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2.

we can compute the right Riemann sum.

Computing the sum of the areas of the rectangles:

∑Δx f(x) =  ∑ 0.5f(xi)

= 0.5 f(x1) + 0.5 f(x2) + 0.5 f(x3) + 0.5 f(x4)  

= 0.5 (0.5) + 0.5 (1) + 0.5 (1.5) + 0.5 (2)

= 2.5

[tex]\int\limits^2_0 {x^{3} } \, dx[/tex]   ≈ 2.5

To learn more about right Riemann from given link

https://brainly.com/question/29275224

#SPJ1

Question 3: Use the graph to fill in the blank with the correct number. f(3) =
10A
5

0
5

-5.
-10%
Your answer

Answers

Answer:

f(3) = 2

Step-by-step explanation:

See the attached graph.  f(3) = ____ is asking us to find the value of the function, f, at the point x = 3.  At x = 3, the value of y is 2.

Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost

Answers

23 dollar for each book

Answer:

each book cost=222-15=207/9=22.88 dollar

Find the value of x. Round to the nearest tenth.

Answers

Sin 21 = x/30
x = 30sin21 = 10.75 = 10.8 (to nearest tenth)

Clara baked a sheet cake with a length of 0.5 meters. She covered the cake in small 1 frosting polka dots that are the length of the cake. What is the approximate 100 length of a polka dot, in meters?​

Answers

Answer:

kkuguftfhbnkmom ugvtvtv uvbuub

Please answer quick! The question is in a file down below.

Answers

Answer:

perimeter= 9+9π cm

area= 40.5-10.125π cm²

Step-by-step explanation:

area of the square =9x9=81cm²

area of the two semicircles which have the same diameter =area of one circle

= (9÷2)²π =(81÷4)π

area of the whole shaded part = 81- (81÷4)π cm²

the area of each shaded part= (81-(81÷4)π)÷2

= 40.5-10.125π cm²

circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm

then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm

perimeter of each shaded part = (18+18π)÷2=

9+9π cm

im homeschooled and someone asked me if I was in school and I said "yes" and he asked if I was in "7th period" I literally dont know what that means :)

Answers

There is no 7th period, so no you aren't in 7th period.

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answers

Answer:

C) {6+√43, 6-√43}

Step-by-step explanation:

Applying,

x = [-b±√(b²-4ac)]/2a.................... Equation 1

From the question,

Given: a = 1, b = -12, c = 7

Substitute these values into equation 1

x = [-(-12)±√(-12²+4×1×7)]/2×1

x = [12±√(144+28)]/2

x = [12±√172]/2

either,

x = (12-√172)/2

x = (12-2√43)2

x = (6+√43)

or

x = (12+√172)/2

x = (12+2√43)/2

x = (6+√43)

Hence,

The right answer is C). {6+√43, 6-√43}

Cars enter a car wash at a mean rate of 4 cars per half an hour. What is the probability that, in any hour, exactly 4 cars will enter the car wash? Round your answer to four decimal places.

Answers

The probability that exactly 4 cars will enter the car wash in an hour is 0.195

What is the probability that, in any hour, exactly 4 cars will enter the car wash?

Generally, This is a Poisson process, where the mean number of cars entering the car wash is 4 cars per hour. The probability of exactly 4 cars entering in an hour is given by the Poisson probability mass function:

P(X = 4) = (e^(-4) * 4^4) / 4!

where e is approximately 2.71828, and 4! is

4 * 3 * 2 * 1 = 24.

Plugging in the values, we get:

P(X = 4) = (2.71828^(-4) * 4^4) / 24

P(X = 4) =0.195

Read more about probability

https://brainly.com/question/30034780

#SPJ1

6n = 21 what is the answer

Answers

Answer:

Decimal: n = 3.5

Fraction: n = 7/2

Step-by-step explanation:

6n = 21

n = 21/6

n = 7/2

n = 3.5

Answer:

3.15

Step-by-step explanation:

Divide 21 by 6

Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?

Answers

Answer:

$821.2

Step-by-step explanation:

cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2

Mark has 10 pens. Kate has 5 times as many pens as Mark.
Which equation below answers how many pens Kate has? (y = number of
Kate's pens)
10 = 5 x y
B
10 = 5 + y
c.
y = 5 x 10
D
y = 10 - 5

Answers

Answer:

The answer to this questions is A

The answer to this question is A

What type of triangle is 70 70 40?

Answers

70-70-40 is an isosceles triangle.

The isosceles triangle has three acute angles, which means that the angles are less than 90°.The summation of three angles of an isosceles triangle is always 180°. In an isosceles triangle, if two sides are equal, then the angles opposite to the two sides correspond to each other and are also always equal.The two equal sides are defined as the legs and the third side is defined as the base of the triangle.The two angles opposite the legs are equal and are always acute, so the categorization of the triangle as acute, right, or obtuse depends only on the angles between its two legs.

Read more about the isosceles triangle:

https://brainly.com/question/25812711

#SPJ4

A solution set always includes...

A. all the numbers that make the inequality false.

B. all the numbers that make the inequality true.

C. zero and infinity.

D. negative infinity.

Answers

I think the answer is going to be a

Answer:

A

Step-by-step explanation:

i got the same answer and got ir right

How do you find the sides of an isosceles triangle given the angles?

Answers

To find the sides of an isosceles triangle given the angles, use the Law of Cosines to calculate the length of each side.

An isosceles triangle has two angles and two sides that are both equal.. To find the sides, you will need to use the Sine Law. The Sine Law states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal for all sides and angles of the triangle.

For example, if you have the angles A and B, and you know that they are both equal (i.e. they are the angles of an isosceles triangle), then you can use the Sine Law to calculate the length of the sides:

Side AB = Side BC = (Side AC) x (Sin A / Sin B)

Where A and B are the angles of the triangle and Side AC is the known side length.

Once you have calculated the length of the two equal sides, you can then use the Pythagorean Theorem to calculate the length of the third side (the base).

Learn more about isosceles triangle here

https://brainly.com/question/2456591

#SPJ4

Which of the following is correctly written in Standard Form?

Answers

Therefore , the solution to the given problem of equation comes out to be4x-3y = 6 as a standard equation in all the above options.

An equation's definition

An equation is a representation of two identical variables in mathematics, one on either side of an equals sign. Common difficulties can be solved using equations. We frequently seek pre algebra help when faced with obstacles in real life. Lessons in pre-algebra cover the basics of mathematics.

Here,

Given : 4x-3y = 6

-4x + 2y =8

=> y = 4/5x + 4

=> 4/5x + 2y = 6

Thus ,

From the above following equations we get ,

4x-3y = 6

as a standard equation in all the above options.

Therefore , the solution to the given problem of equation comes out to be 4x-3y = 6 as a standard equation in all the above options.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

What is the domain and range of √ X 2?

Answers

The domain of √ X  2 is X ≥ 4. The range is all real numbers.

Here is the proof, In order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the radicand is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all values of X that are greater than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any non-negative value is a real number.

Learn more about Domain and Range here:

https://brainly.com/question/2264373

#SPJ4

Molly bought a large basket of 60 apples.

When she got home, she found 4 rotten

ones. If she goes back and buys 200 more

apples, how many rotten apples would she

expect there to be?

Group of answer choices

20

24

13

8

Answers

Step-by-step explanation:

1. 60 apples

2. 60-4=56

3. 56+200=256

200/60

60/4

60+60=120

120+60=180

I think either 13.

What is the unknown fraction?

Answers

Answer:

47/100

Step-by-step explanation:

we will shift the 2/10 to the other side and change the sign to minus

PLS SOMEONE HELPP I NEED THIS ASAP

Answers

The rate of change for the graph, when x=0 and x=1 is 2 units.

What is average rate of change?

This expression represents the average rate of change of the function f(x) over the range a<=x<=b, is less than or equal to x, and is less than or equal to b -

[f(b)-f(a)]/b-a

The rate of change of graph is determined by the formula -

[f(b)-f(a)]/b-a

[f(1)-f(0)]/1-0

Here, in the graph it can be clearly seen that f(0)=-1 and f(1)=1.

Plugging in the values -

[1-(-1)]/1

(1+1)/1

2

Therefore, the rate of change is 2 units.

To learn more about average rate of change from the given link

https://brainly.com/question/8728504

#SPJ1

3 times one number minus a second is 8 and the sum of the numbers is 12

Answers

Answer: 3x-y=8

Step-by-step explanation:

In direct variation where y = kx, if y = 18 and x = 4, what is the value of x when y = 36 ?

Answers

Answer:

18/4x36/x

18x=4x36

18x=144

x=144/18

x=8

Answer:

x = 8

Step-by-step explanation:

Given

y = kx ← k is the constant of variation

To find k use the condition y = 18, x = 4 , then

18 = 4k ( divide both sides by 4 )

4.5 = k

y = 4.5x ← equation of variation

When y = 36, then

36 = 4.5x ( divide both sides by 4.5 )

8 = x

HELP ME PLEASE AND THANK YOUUU

Answers

Answer:

x=3 y=1

Step-by-step explanation:

-2/3x+3=2x-5

x=3

y=-2/3(3)+3

y=1

y=2(3)-5

y=1

What does → mean in math?

Answers

â' in mathematics refers to the hexadecimal representation of the number 10.

What does hexadecimal notation provide for?

In machine code and assembly programming languages, hexadecimal is widely utilised. It is frequently used to refer to memory addresses. It can be used to represent numbers kept in a CPU's registers or in main memory, as well as during the debugging phase of designing a computer programme.

How is the hexadecimal notation read?

Although there are six more digits to consider, counting in hex is very similar to counting in decimal. When a digit position exceeds "F," you roll that place over to "0" and increase the digit to the left by 1. And once you've reached 1F16, move on to 2016 and keep churning the right-most

To know more about hexadecimal notation visit:

https://brainly.com/question/14649964

#SPJ1

Frank earns an annual salary of $42,800. He pays 8% in total taxes. How much money will Frank pay in taxes each year?

Answers

Answer:

$3424

Step-by-step explanation:

42800 x .08

.08 = 8%

(PLEASE HELP)
Which expression is represented on the number line?

Answers

Answer:

F .0-(-8) I think so..........................

Answer:

F is represented on the number line

The table below shows the number of minutes played (x) by various basketball players and the number of rebounds (y) they had.

Scatter plot that has 2 through 20 for x and 1 through 10 for y.



a. Draw a scatter plot of the data. Label the axes.



b. Find an equation for a line of best fit.



c. Use your equation from part b above to predict how many rebounds a player would have if they played 30 minutes in the game.

I will give all my points to the first person that answers.

Answers

Answer:

A

Step-by-step explanation:

What is the value of x? Solve for x. You may build and solve the equation on your Equation Mat. Or you may solve the equation algebraically (to the right). Of this -2x-2=3 (-x+2 )

Answers

Answer:

[tex] - 2x - 2 = 3( - x + 2) \\ - 2x - 2 = - 3x + 6 \\ - 2x + 3x = 6 + 2 \\ x = 8[/tex]



anyone help please?

Answers

Answer:

The transformation is a reflection over the y axis

Other Questions
15 minutes for 5 songs = minutes per song Given parallelogram ABCD Find the area Your brain needs glucose to function properly. How much of your body'sglycogen is used for brain function? *60%75%89%55% Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has A. An area of 12 cubic units, and its sides could measure 12 units and 2 units B. An area of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 units O C. A volume of 12 cubic units, and its sides could measure 12 units and 2 units D. A volume of 24 cubic units, and its sides could measure 2 units, 3 units, and 4 unit What is the surface areaof the square pyramid?9 in6 in Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle UStartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFractionStartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle UStartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction What films were filmed at Durham Cathedral? Which development plan would cause the least harm to the existing forest ecosystem?A. Spread the houses out evenly so that there is as much forest as possible between each of the housesB. Place the houses close together and use the remaining forest as a natural common areaC. Build some big houses on large lots and some small houses on small lots so that families with different incomes can live togetherD. Build several small clusters of homes in different places so that each house will have a few close neighbors estimate the product of 5,398 x 47 by rounding to the nearest thousand and ten.a) 200,000b)250,000c)253,706d)300,000pls help me i will give you Brainliest if its correct What is the highest point on the wave called? A fitness center is interested in the average amount of time a client exercises in the center each week.Match the vocabulary word with its corresponding example.The average amount of exercise time for the 45 clients from the fitness center whoparticipated in the studyThe average amount of time that all clients from the fitness center exerciseAll 45 exercise times there were recorded from the participants in the studyAll clients at the fitness centerThe amount of time that any given client from the fitness center exercisesb The 45 clients from the fitness center who participated in the studydaca. Datab. Samplec. Populationd. Variablee. Statisticf. ParameterTextbook Pages Sep Obtain Information What are the Limitations to Making Progress with Engineering Better Batteries ? What progress have Battery Engineers Made? Sheffield Corp. is planning to sell 1070 boxes of ceramic tile, with production estimated at 800 boxes during May. Each box of tile requires 44 pounds of clay mix and a 0.50 hour of direct labor. Clay mix costs $0.40 per pound and employees of the company are paid $17 per hour. Manufacturing overhead is applied at a rate of 110% of direct labor costs. Sheffield has 3300 pounds of clay mix in beginning inventory and wants to have 5400 pounds in ending inventory. What is the total amount to be budgeted for direct labor for the month 50 POINTS Answer the following questions and draw a rough sketch of the function: f(x)=-x^4+8x^3+8x^2-96x-144What is the functions general shape?Does the function face up or down?What is the functions y-intercept?If one of the factors is (6), how would you show that on the graph? Who is Boxer an allegory for in Animal Farm? which pair of triangles? multiple choice You have just secured a job at a web development company. You get paid $19.50 an hour and work35 hours per week. Your take home pay will be 60% of your total income. You are planning to makea budget and have estimated that your rent will be about 29% of the total budget. How much moneywill you need to pay rent? Answer to the nearest cen PLEASE HELP ASAP AND IF U SEND A LINK = REPORT 5. How does Audre Lorde use repetition to develop thetheme in "Hanging Fire"? b. The original amount on the gift card was $200. Does Arleen haveenough left on the card to buy awheelbarrow for $50? Explain. Which process is responsible for causing this column of rock to form?A. crystallizationB. depositionC. sedimentationD. weathering