The difference between the roots of the equation 2x^2−5x+c=0 is 0.25. Find c.

Answers

Answer 1

Answer:

[tex]c=\frac{99}{32}[/tex]

Step-by-step explanation:

The given quadratic equation is [tex]2x^2-5x+c=0[/tex].

Comparing this equation to:  [tex]ax^2+bx+c=0[/tex], we have a=2,b=-5.

Where: [tex]x_1+x_2=\frac{5}{2}[/tex] and [tex]x_1x_2=\frac{c}{2}[/tex]

The difference in roots is given by:

[tex]x_2-x_1=\sqrt{(x_1+x_2)^2-4x_1x_2}[/tex]

[tex]\implies 0.25=\sqrt{(2.5)^2-4(\frac{c}{2})}[/tex]

[tex]\implies 0.25^2=6.25-2c[/tex]

[tex]\implies 0.0625-6.25=-2c[/tex]

[tex]\implies -6.1875=-2c[/tex]

Divide both sides by -2

[tex]c=\frac{99}{32}[/tex]

Answer 2

Answer:

The value of c is 3.09375.

Step-by-step explanation:

Given : The difference between the roots of the equation [tex]2x^2-5x+c=0[/tex] is 0.25.

To find : The value of c?

Solution :

The general quadratic equation is [tex]ax^2+bx+c=0[/tex] with roots [tex]\alpha,\beta[/tex]

The sum of roots is [tex]\alpha+\beta=-\frac{b}{a}[/tex]

The product of roots is [tex]\alpha\beta=\frac{c}{a}[/tex]

On comparing with given equation, a=2, b=-5 and c=c

Substitute the values,

The sum of roots is [tex]\alpha+\beta=-\frac{-5}{2}[/tex]

[tex]\alpha+\beta=\frac{5}{2}[/tex] .....(1)

The product of roots is [tex]\alpha\beta=\frac{c}{2}[/tex] ....(2)

The difference between roots are [tex]\alpha-\beta=0.25[/tex] .....(3)

Using identity,

[tex]\alpha-\beta=\sqrt{(\alpha+\beta)^2-4\alpha\beta}[/tex]

Substitute the value in the identity,

[tex]0.25=\sqrt{(\frac{5}{2})^2-4(\frac{c}{2})}[/tex]

[tex]0.25=\sqrt{\frac{25}{4}-2c}[/tex]

[tex]0.25=\sqrt{\frac{25-8c}{4}}[/tex]

[tex]0.25\times 2=\sqrt{25-8c}[/tex]

[tex]0.5=\sqrt{25-8c}[/tex]

Squaring both side,

[tex]0.5^2=25-8c[/tex]

[tex]0.25=25-8c[/tex]

[tex]8c=25-0.25[/tex]

[tex]8c=24.75[/tex]

[tex]c=\frac{24.75}{8}[/tex]

[tex]c=3.09375[/tex]

Therefore, the value of c is 3.09375.


Related Questions

!!!!!PLEASE HELP!!!!

Find (f/g)(x) for: f(x)=(x+16)/x; g(x)=(2x)/(x+4)

Answers

Answer:

Step-by-step explanation:

All you have to do here is to divide polynomial f(x) = (x + 16)/x by polynomial g(x) = 2x / (x + 4), simplify the result and label the quotient properly.  Recall that division by a fraction involves inverting the divisor fraction and then multiplying.

               (x + 16)       (x + 4)      (x + 16)(x + 4)

(f/g)(x) = ------------- * ----------- = --------------------

                    x              2x                 2x^2

Note that this quotient is true for all x except x = 0.


What is the value of x?

Answers

Answer:

do you have any more information to solve this ?????????

Step-by-step explanation:

what is the actual equation it goes with??

What is (u+2ax)(2u+2ax)

Answers

Answer:

2u^2 +6aux+4ax

Step-by-step explanation:

2u^2 because u×2u

2aux cuz u× 2ax

4aux cuz 2ax×2u

4ax. cuz 2ax time 2ax

Final answer:

The multiplication of the binomials (u+2ax)(2u+2ax) can be solved using the FOIL method. The steps result in 2u^2 + 2uax + 4uax + 4a^2x^2. Combining like terms yields the final answer: 2u^2 + 6uax + 4a^2x^2.

Explanation:

The problem (u+2ax)(2u+2ax) is a mathematical multiplication of two binomial expressions. You may solve it by applying the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's walk through the steps to solve it:

First: Multiply the first terms in each binomial. u * 2u = 2u^2. Outer: Multiply the outer terms, which are u and 2ax. u * 2ax = 2uax. Inner: Multiply the inner terms, which are 2ax and 2u. 2ax * 2u = 4uax. Last: Multiply the last terms of each binomial. 2ax * 2ax = 4a^2x^2.

Then, add these results together: 2u^2 + 2uax + 4uax + 4a^2x^2. Combine like terms to get the final answer: 2u^2 + 6uax + 4a^2x^2.

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3 pizzas are shared equally between 10 people. What fraction of a pizza does each person receive?

Show your work, please!

Answers

Answer:

3/10 fraction of a pizza is received by each person.

Step-by-step explanation:

3 pizzas are shared among 10 people. We need to find the fraction of pizza each person receive.

No of pizzas = 3

Total People sharing = 10

Each person receive pizza = No of pizzas/ Total People sharing

                                             = 3/10

3/10 fraction of a pizza is received by each person.                                            

Answer:

dang

Step-by-step explanation:

2 years ago

If a-b=2 and b=2 find the value of a×b​

Answers

Answer:

a*b = 8

Step-by-step explanation:

a-b =2

Let b= 2

a-2 =2

Add 2 to each side

a-2+2 =2+2

a =4

We want to find a*b

4*2 = 8

a*b = 8

First substitute 2 in for b to get a - (2) = 2.

Now isolate a by adding 2 to both sides to get a = 4.

Since a = 4, substitute 4 in for a and 2 in for b to get 4 × 2.

Multiplying, 4 × 2 gives us a product of 8.

So the value of a × b is 8.

Bobby-Joe takes a 25-question test for which he receives 4 points for each correct answer and loses 1 point for each wrong answer. If Bobby-Joe answers all the questions and gets a passing grade of 65%, how many questions did he get right?

Answers

Answer:

Let x be the number of questions he gets right. Let y be the number of questions he gets wrong.

Then:

x + y = 25

4x - 1y = 65

Adding these two equations gives:

5x = 90

x = 90/5 = 18 right answers

y = 25 - 18 = 7 wrong answers

* Hopefully this helps:) Mark me the brainliest:)!!!

~ 234483279c20~

The number of right questions is 18

How to determine the right question?

Let the number of right questions be x, and the wrong questions be y

So, we have the following equations

x + y = 25

4x - y = 65

Add both equations

5x =90

Divide both sides by 5

x = 18

Hence, the number of right questions is 18

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HELP ME! DUE IN 5 MINUTES!
A group has an equal number of adults and children. When n oranges are given to the group, each adult gets two oranges while each child gets one orange and there are still 5 oranges left. Write an algebraic expression for the number of oranges given to the adults.

Answers

Answer:

Adults are given =

2n oranges

2n+n=once given

so

Step-by-step explanation:

Final answer:

The algebraic expression for the number of oranges given to adults in a group with an equal number of adults and children, with a specified distribution of oranges and a remainder, is 2A, where A represents the number of adults (or children, since they are equal).

Explanation:

The question requires us to find an algebraic expression for the number of oranges given to the adults in a group where there are an equal number of adults and children, and a specific distribution of oranges to adults and children with a remainder.

Let's denote the number of adults by A, and thus, the number of children will also be A since the group has an equal number of adults and children. If n oranges are distributed, and each adult receives 2 oranges, then the total number of oranges given to adults is 2A. Each child receives one orange, so the number of oranges given to children is A. Including the 5 oranges that are left, the equation representing the total number of oranges is: 2A (for adults) + A (for children) + 5 (leftover) = n (total oranges).

From this equation, if you want to isolate the expression that represents the number of oranges given to adults, it is simply 2A.

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find the distance between A(2,3,5) and B(6,7,-2)
(pictures of the answer above)

Answers

Answer:

I think it's B (Sorry if im wrong)

What is the solution to the equation 3/5(x+4/3) = 1.04

1. 3.0666
2. 0.4
3. -0.4888
4. -.0709333

Answers

Answer:

2. 0.4

Step-by-step explanation:

Solve for "x" by simplifying both sides of the equation, then isolating the variable.

The solution of the equation is x = 0.4.

What is an Equivalent Expression?The expression where equivalent result is produced by the both sides of the expression.It is used to solve many critical mathematical problems.

Given: Equation

[tex]\frac{3}{5}(x+\frac{4}{3})=1.04[/tex]

Now, we have to solve for x.

[tex]\frac{3}{5}(x+\frac{4}{3})=1.04[/tex]

Multiplying both sides by 5, we get:

⇒ 3(x + 4/3) = 1.04 × 5

⇒ 3x + 4 = 5.2

⇒ 3x = 5.2 - 4

⇒ 3x = 1.2

Dividing both sides by 3, we get:

⇒ x = 0.4

Therefore, the solution of the given equation is x = 0.4.

Hence, option (2) is correct.

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A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = (x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.

y = x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17

Answers

Answer:

3y+4x=5

Step-by-step explanation:

step 1

Find the slope

we have

(–7, 11) and (8, –9)

m=(-9-11)/(8+7)

m=-20/15

m=-4/3

step 2

Find the equation of the line into point slope form

we have

m=-4/3

point (-7,11)

substitute

y-11=-(4/3)(x+7) ----> equation of the line into point slope form

Multiply by 3 both sides

3y-33=-4(x+7)

3y-33=-4x-28

3y+4x=33-28

3y+4x=5 -----> equation of the line into standard form

Answer:

The first and 4th option

Step-by-step explanation:

Just took it on edge

name a parallelogram that is neither a square, rhombus nor rectangle

Answers

With all due thinking...

I think a Diamond shape will befit your answer. So; The real answer is "Rhomboid"

The reason is that...

A rhomboid has four parallel sides. The opposite sides are equal, but the corners do not form right angles. Think of a rectangle that is slanted(a.k.a diamond) Thats what a Rhomboid is...

A parallelogram that dosent have equal sides is not a rhombus; and which dosent have Right angles are not rectangles and hence cannot be aquares either.

So in all Way a Rhomboid will mark the answer for your question.

Hope it helps..

Regards,

Leukonov/Olegion.

Answer;

TRAPEZOID

Step-by-step explanation:

Khaled and Wilma were asked to find an explicit formula for the sequence 1, 3, 9, 27. Khaled said the formula is f(n)=1*3^n-1 and Wilma said the formula is f(n)=1*3^n. Which one of them is right?

Answers

ANSWER

[tex]f(n) = 1 \times ( {3}^{n - 1} )[/tex]

EXPLANATION

The given sequence is 1, 3, 9, 27...

The first term of this sequence is

[tex]a = 1[/tex]

The common ratio is

[tex]r = \frac{3}{1} = \frac{9}{3} = \frac{27}{9} = 3[/tex]

The explicit formula for this geometric sequence is

[tex]f(n) = a ( {r}^{n - 1} )[/tex]

We substitute the first term and the common ratio to obtain,

[tex]f(n) = 1 ( {3}^{n - 1} )[/tex]

Answer:

khaled is correct. f(n)=1x3^n-1

Step-by-step explanation:

Solve Applications involving Uniform Motion
Question
Lorena walks the path around the park in 30 minutes. If she jogs, it takes her 20 minutes. Her jogging speed is 2 miles per
hour faster than her walking speed. Find Lorena's walking speed and jogging speed.

Answers

Answer:

6mph and 4mph

Step-by-step explanation:

because 2:3 is some as 3x:x in terms of speed

Answer: The speed of her walking is 4 mph and the speed of her jogging is 6 mph.

Step-by-step explanation:

Since we have given that

Time taken by Lorena to walk the path = 30 minutes

Time taken by Loren to jogs the path = 20 minutes

Let the speed of her walking be 'x'.

Let the speed of her jogging be 'x+2'.

Since distance would remain same, so it becomes,

[tex]30x=20(x+2)\\\\30x=20x+40\\\\30x-20x=40\\\\10x=40\\\\x=\dfrac{40}{10}\\\\x=4\ mph[/tex]

Hence, the speed of her walking is 4 mph and the speed of her jogging is 6 mph.

An olympian swam the 200-meter freestyle at a speed of 1.8 meters per second. An olympic runner ran the 200-meter dash in 21.3 seconds. How much faster was the runner’s speed than the swimmer’s speed to the nearest tenth of a meter per second?

Answers

Answer:

7.6m/s

Step-by-step explanation:

Find the time the Olympian swam

Speed=distance/time ⇒⇒Time=distance/speed

Distance=200m , speed= 1.8m/s   t= 200/1.8 = 111.11 seconds

Find the speed of the Olympic runner

Distance=200m  time = 21.3 sec  

s=200/21.3 = 9.4 m/s

Difference in speed= 9.4-1.8= 7.6m/s

Answer:

7.6 m/s faster

Step-by-step explanation:

Speed of swimmer = 1.8 meters per second

The distance covered by runner = 200

Time of runner = 21.3 sec

We have to find the speed of the runner first so that we can compare with the speed of swimmer.

Speed = Distance/Time

=> 200/21.3

=> 9.4 m/s

So we have to find the difference between both speeds

Difference = 9.4 - 1.8

=> 7.6 m/s

So the runner was 7.6 m/s faster..

PLS HELP I'LL GIVE BRAINLIEST

Answers

Answer:

$5,000

Step-by-step explanation:

Create a proportion:

11/100 = 550/x

100(550)/11

5,000= x

You have to form a proportion: [tex]\frac{part}{whole}[/tex]

Meals are only 11% for the vacation budget. This means that meals would go over 100% like this:

[tex]\frac{11}{100}[/tex]

You also know that you have $550 for meal (your part) but you want to know what your total vacation budget is(your whole)[tex]\frac{x}{550}[/tex] (x), so you would set it up like this

Now you sent them equal to solve for x:

[tex]\frac{11}{100} = [tex]\frac{550}{x}[/tex]

cross multiply:

11x = 55,000

x = 5,000

This means that your total vacation budget is $5,000

Hope this helped!

Which point is located at (4,-5)?

1. A

2. B

3. C

4. D​

Answers

Answer:

it is C

Step-by-step explanation:

A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?

Answers

Answer:

8  15/16 inches

Step-by-step explanation:

Multiply 3  1/4 inches by 2  3/4:

13      11

---- * ----- = 146/16 inches, or 8.9375 inches, or 8  15/16 inches.

 4       4

Answer:  The required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]

Step-by-step explanation:  Given that a customer wants you to enlarge a photo to [tex]2\dfrac{3}{4}[/tex] its current height and the photo’s current height is [tex]3\dfrac{1}{4}[/tex] inches.

We are to find the enlarged height of the photo in inches.

The enlarged height of the photo is given by

[tex]2\dfrac{3}{4}\times \textup{current height of the photo}\\\\\\=\dfrac{11}{4}\times3\dfrac{1}{4}\\\\\\=\dfrac{11}{4}\times\dfrac{13}{4}\\\\\\=\dfrac{143}{16}\\\\=8\dfrac{15}{16}.[/tex]

Thus, the required enlarged height of the photo is [tex]8\dfrac{15}{16}~\textup{inches}.[/tex]

need help asap!!!!! thank you!!

Answers

Answer:

1,2,20

take away 14 from 8 = 6

add 6 to 14 = 20

Hope I helped!

NOTE: MARK BRAINLIEST!!!! plz....

Answer:

8,4  

14,7

6,3

Step-by-step explanation:

A tessellation is an arrangement of repeating shapes that have what
characteristic?

Answers

Answer:

Option B is correct, (no spaces or overlaps exist between it's pieces).- APEX

Step-by-step explanation:

I hope this helps.

Answer: No spaces or overlaps exist between its pieces.

Would appreciate the help.

Answers

Answer:

[tex]x^{2}+(y+2)^{2}=9[/tex]

Step-by-step explanation:

The center of the circle is (0, -2). The dark-filled circle is the center and lies 2 units below the origin on the y-axis.

On the other hand, the radius of the circle is 3 units. If we count from the dark-filled circle, we have 3 complete squares to the left, to the right.

Now the standard equation of a circle with center (a, b) and radius r units is given by the formula;

[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]

Substituting the values obtained;

[tex]x^{2}+(y+2)^{2}=9[/tex]

and is our standard equation of the given circle

can someone help me with this

Answers

Answer:

19 m

Step-by-step explanation:

This is Geometric progression with

[tex]\left \{ {{u_1=1,\: u_2 =2} \atop {u_n=2^{n-1}u_1} \right.[/tex]

Then the fomular of sum is

[tex]S=u_1\frac{2^n-1}{2-1} =1\times(2^n-1)=2^n-1\\To\: save\: 1 \:million\: then \; our \:sum \: will \: be\: 1000000\\Hence,\\2^n-1=1000000\\2^n=1000001\\n=log_{2}{1000001}\approx19,9\\Thus, it\:would \;be \:19 \:months \:before\: we\: saved \:1000000 \:pounds[/tex]

A circuit contains three resistors rated at 100 Ω, 200 Ω, and 300 Ω that are connected in parallel. What's the total resistance of the circuit?

Answers

Answer:

total resistance is 54.54 ohms

Step-by-step explanation:

In parallel circuits, current can take various paths so the resistance are not added simply like that in series circuit, instead the reciprocal of total resistance in parallel circuit is calculated by adding the reciprocals of all the resistors connected parallel in circuit.

Given:

Resistor r1= 100

resistor r2 = 200

resistor r3= 300

The three resistors are connected in parallel  so the total resistance will be calculated by:

1/R= 1/r1 +1/r2 +1/r3

Putting the values of r1, r2, r3 in above we get

1/R= 1/100 + 1/200 +1/300

  = 0.01 + 0.005 + 0.0033

  = 0.0183

Taking reciprocal of both sides:

R=54.54

Hence total resistance is 54.54 ohms!

Final answer:

The total resistance of three resistors rated at 100 Ω, 200 Ω, and 300 Ω connected in parallel is approximately 54.64 Ω. This is calculated using the reciprocal formula for parallel resistances.

Explanation:

When you have a circuit with resistors connected in parallel, the total (or equivalent) resistance of the circuit is found by using the reciprocal formula:

Rtotal = 1/(1/R1 + 1/R2 + 1/R3)

For the given resistors of 100 Ω, 200 Ω, and 300 Ω in parallel, you calculate the total resistance like this:

Rtotal = 1/(1/100 Ω + 1/200 Ω + 1/300 Ω)
= 1/(0.01 Ω-1 + 0.005 Ω-1 + 0.0033 Ω-1)
= 1/(0.0183 Ω-1)
= 54.64 Ω

The total resistance of the circuit would therefore be approximately 54.64 Ω.

Simplify the following expression.

A. 64
B. 12
C. 1/12
D. 1/64​

Answers

We have

[tex]a^b\cdot a^c=a^{b+c}[/tex]

[tex]a^b\div a^c=a^{b-c}[/tex]

So, in your case, we have

[tex]4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}} = 4^{-\frac{11}{3}+\frac{2}{3}} = 4^{-\frac{9}{3}}=4^{-3} = \dfrac{1}{4^3} = \dfrac{1}{64}[/tex]

Answer:

Option D. 1/64

Step-by-step explanation:

We have to simplify the following expression

[tex]4^{-\frac{11}{3} }[/tex] ÷ [tex]4^{-\frac{2}{3} }[/tex]

= [tex]\frac{4^{-\frac{11}{3} } }{4^{-\frac{2}{3} } }[/tex]

= [tex][4^{-\frac{11}{3}}[/tex] × [tex]4^{\frac{2}{3}}][/tex] [since [tex]\frac{1}{A-1}[/tex]=a]

= [tex]4^{(-\frac{11}{3}+\frac{2}{3})}[/tex] [since [tex]a^{b}[/tex] × [tex]a^{c}[/tex] = [tex]a^{(b+c)}[/tex]]

= [tex]4^{-\frac{9}{3}}[/tex]

= [tex]4^{-3}[/tex]

= [tex]\frac{1}{4^{3} }[/tex]  [[tex]a^{-1}=\frac{1}{a}[/tex]]

= [tex]\frac{1}{64}[/tex]

Option D. 1/64 is the answer.

3/8(2x-8/3x)=21 solve the equation for x​

Answers

Answer:

[tex]\boxed{\bold{x=-84}}[/tex]

Explanation:

Multiply Both Sides By 8:

= [tex]\bold{8\cdot \frac{3}{8}\left(2x-\frac{8}{3}x\right)=21\cdot \:8}[/tex]

Simplify:

= [tex]\bold{-2x=168}[/tex]

Divide Both Sides By -2:

= [tex]\bold{\frac{-2x}{-2}=\frac{168}{-2}}[/tex]

Simplify:

= [tex]\bold{x=-84}[/tex]

//Mordancy //.

X= -84 this would be your answer also use photomath :)

Mrs. Piper is driving Anna, Jo, and Mai home from school. All of them want to ride in the front seat. How can she make a fair decision about who rides in the front seat?

Answers

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The question is on probability

We have three students, Anna, Jo and Mai

We have 1 seat at the front

P(S)=3

P(A)=1/3

P(J)=1/3

P(M)=1/3

I am trying to find the next number in this number sequence and I dont know how! its like this, 2,9,37,149,597,2389, ... whats the next number?

Answers

[tex]\bf 2~~,~~\stackrel{2(4)+1}{9}~~,~~\stackrel{9(4)+1}{37}~~,~~\stackrel{37(4)+1}{149}~~,~~\stackrel{149(4)+1}{597}~~,~~\stackrel{597(4)+1}{2389}~~,~~\boxed{\stackrel{2389(4)+1}{9557}}[/tex]

help me plz and god bless :/

Answers

Upper quartile would be 4.5. The interquartile range could be 6.

How can you tell whether or not a question is a statistical question?

Answers

A statistical question is one for which you don't expect to get a single answer. Instead, you expect to get a variety of different answers, and you are interested in the distribution and tendency of those answers. For example, "How tall are you?" is not a statistical question. But "How tall are the students in your school?" is a statistical question.

I could probably figure this out but I have way too much homework so It'd be nice to finish this pathway.

Answers

Yeah that's right always be a hardworking person

Mathematics probability

Answers

Do you have a specific question or something like that which you need answering?

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