If [tex]x[/tex] is real and p=[tex]\frac{3(x^{2} +1)}{2x-1}[/tex], prove that [tex]p^{2}[/tex]-3(p+3) ≥ 0

Answers

Answer 1

Answer:

[tex]{ \tt{p=\frac{3(x^{2} +1)}{2x-1}}} \\ { \tt{p(2x - 1) = 3( {x}^{2} + 1) }} \\ { \tt{2px - p = 3 {x}^{2} + 3 }} \\ { \tt{3 {x}^{2} - (2p)x + (p + 3) = 0}} [/tex]

By factorization :

[tex]{ \tt{ ( {p}^{2} - 3)( p + 3) \: is \: the \: zero}}[/tex]

Since the roots are real, they're greater than zero ( 0 < x ≤ +∞ ):

[tex]{ \tt{ ({p}^{2} - 3})(p + 3) \geqslant 0}[/tex]


Related Questions

Giải phương trình
2x+6=0

Answers

Answer: x = -3

[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]

Answer:

x= -3

Step-by-step explanation:

Solve the equation:

2x +6 = 0

We have isolate 'x'.

First subtract 6 from both sides

2x = 0-6

2x = -6

Divide each side by 2

x = -6/2

x = -3

Type the correct answer in the box. Use numerals instead of words.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function p(g) =
.

Answers

Answer:

1g - 50 = p(g)

Step-by-step explanation:

The profit function is,

⇒ p(g) = g - 50

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Betty sets up a lemonade stand and charges $1 per glass.

It cost her $50 to set up the stand.

And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.

Now, The number of glasses of lemonade sold = g,  

And, A profit, p by function p(g)

Setup cost = $50

Since, Charges for 1 glass  = 1 $

Hence, Charges for g glasses = 1.g  = $g

Here, The cost = $50  

Hence, Profit  = $g - 50

⇒ p(g)  =  g - 50  

Therefore, The profit function is,

⇒ p(g) = g - 50

Learn more about the mathematical expression visit:

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What is 2:50 is simplest form

Answers

Answer:

0.04

Step-by-step explanation:

2 / 50 is the same as 1 / 25.

1 / 25 = 0.04

Answer:

0.04

Step-by-step explanation:

How do I solve this problem?

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Short answer: to solve this problem, follow directions.

a. Write the inequalities

Let c and p represent numbers of cakes and pies produced daily. Then the constraints are ...

  2c +3p ≤ 108 . . . . . . . . available hours of preparation time

  1c +0.5p ≤ 20 . . . . . . . available hours of decoration time

  p ≥ 0, c ≥ 0 . . . . . . . . . negative numbers of cakes or pies cannot be produced

__

b. Sketch the feasible region

It works well to let a graphing calculator do this.

The feasible region is the doubly-shaded area with vertices ...

  (0, 0), (0, 36), (3, 34), (20, 0)

__

c. Write the profit function

Profit is $25 per cake and $12 per pie, so is ...

  p = 25c +12p

__

d. Determine maximum profit

The attached table shows the profit for the various mixes of cakes and pies in the feasible region. The most profit is had by production of cakes only.

The maximum profit is $500 per day for production of 20 cakes.

_____

Additional comment

We have used x for cakes and y for pies in the attachment, because those are variables that the Desmos calculator prefers.

As is sometimes the case, the production point giving maximum profit leaves one of the resources (preparation time) only partially utilized.

Select the correct answer from the drop-down menu.
A
The diagram shows a stage in the construction of a line perpendicular to GH through point A.
The next step in this construction is
Reset
Next
2021 Edmentum. All rights reserved.

Answers

The diagram is missing and so i have attached it.

Answer:

Next step is;

to keep the same compass width and draw an arc centered at H crossing the previous arc in the image.

Step-by-step explanation:

A perpendicular line is to be drawn to line GH through point A.

The steps are;

1. Identification of the two end points of the line which has been done.

2. Place one leg of the compass at point G and draw a small arc above the line GH. This has been done.

3. Without changing the span of the compass, place the same leg of the compass at point H and draw another small arc above the line GH to intersect the previously drawn small arc.

4. Make use of a straight object to connect the point of intersection of the two small arcs to the point A.

This line is the perpendicular line to GH.

In the figure attached, they have just finished point 2 I wrote above. Thus, the next step is point 3.

Answer:

to keep the same compass width and draw an arc centered at H crossing the previous arc in the image.

Step-by-step explanation:

please help! will give brainliest if the answer is correct:) need the answers in order to move on in the lesson!

Answers

Answer:

Just use a calculator and wite the square root value in it

Step-by-step explanation:

Atempt this method with all options at last u will have ur answer

help on the circled problems, will mark brainliest :D

Answers

Answer:

see explanation

Step-by-step explanation:

(1)

x - (9x - 10) + 11 = 12x + 3(- 2x + [tex]\frac{1}{3}[/tex] ) ← distribute parenthesis on both sides

x - 9x + 10 + 11 = 12x - 6x + 1 ← collect like terms on both sides

- 8x + 21 = 6x + 1 ( subtract 6x from both sides )

- 14x + 21 = 1 ( subtract 21 from both sides )

- 14x = - 20 ( divide both sides by - 14 )

x = [tex]\frac{-20}{-14}[/tex] = [tex]\frac{10}{7}[/tex]

(3)

- 4x - 2(8x + 1) = - (- 2x - 10) ← distribute parenthesis on both sides

- 4x - 16x - 2 = 2x + 10

- 20x - 2 = 2x + 10 ( subtract 2x from both sides )

- 22x - 2 = 10 ( add 2 to both sides )

- 22x = 12 ( divide both sides by - 22 )

x = [tex]\frac{12}{-22}[/tex] = - [tex]\frac{6}{11}[/tex]

(7)

8(2x + 9) = 56 ( divide both sides by 8 )

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^4 +5x2 +4

Answers

Answer:

(x-5)(x+2)(x+4)

Step-by-step explanation:

I just did It

7. solve for x!
please help

Answers

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

¿Qué valor de m creará un sistema de líneas paralelas sin solución? y = mx - 6 8 x - 4 y = 12 Una cuadrícula de coordenadas con una línea etiquetada como 8 x menos 4 y es igual a 12. La línea pasa por un punto en (0, menos 3), (1, menos 1) y un punto en (1,5, 0). - 2 - 2

Answers

Answer:

Hello,

m=2

(0,-3) True

(1,-1) True

(1.5,0) True

(-2,-2) False

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&mx-6\\8x-4y&=&12\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}y&=&mx-6\\y&=&2x-3\\\end{array}\right.\\\\\\The\ slope\ must\ be\ the\ same:\ m=2\\\\\\\begin{array}{c|c}&y=2x-3\\---&--------\\x&y\\0&2*0-3=-3\\1&2*1-3=-1\\1.5&2*1.5-3=0\\-2&2*(-2)-3=-7\\\end{array}[/tex]

Delta math need help

Answers

Answer:

2.6

Step-by-step explanation:

We'll use the Pythagoras theorem to solve this, which states that in a right angle triangle:

h^2 = a^2 + b^2

4^2 = 3^2 +b^2

16= 9 +b^2

16-9= b^2

7= b^2

(take square root in both sides)

b= 2.65

round to nearest 10th = 2.6

answer by Gauthmath

Answer:

Missing side is 2.6

3^2 + x^2 = 4^2

9 + x^2 = 16

-9            -9

x^2 = 7

([tex]\sqrt{x}[/tex])^2 = [tex]\sqrt{7}[/tex]

x = 7

Find the approximation o the square root of 7 in fractions then carry out the long division.

Or

Approx. is 2 3/5 which equals 2 6/10 which equals 2.6

i have 17 coins. N of them are nickels and the rest are dimes. write an expression in two different ways for the amount of money that i have

Answers

Answer:

Step-by-step explanation:

(N)0.05 + (17-N)0.1 = M; M = amount of money I have.

Or 1.7-0.05N = M.

An expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

What is amount?

" Amount is defined as the total of any given quantity."

According to the question,

Total number of coins = 17

Number of nickels coins = N

Number of dimes coin = 17 - N

'Y' express the amount of money

Represent amount of money in cents

1 dime = 10 cents

1 nickel = 5 cents

Expression to represents amount of money in cents,

5N + 10 (17 -N)  = Y cents

Expression to represents amount of money in nickels,

1 dime = 2 nickel

N + 2(17 - N) = Y nickels

Hence, an expression two different ways to  the amount of money is equals to

1. 5N + 10 (17 -N)  = Y cents

2. N + 2(17 - N) = Y nickels

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CAN A KIND SOUL PLEASE HELP ME OUT??!!!!!!!!!!!!!!

The translation (x, y)->(x + 10, y – 6) is applied to triangle ABC to create a new image triangle A’B’C’. Graph triangle A’B’C’ on the coordinate plane.

please show how you got it so I can see if the answer makes sense!!!!

Answers

Answer:

First find the coordinates of the vertices. A=(-8,8), B=(-8,3) and C=(-4, 4). Next apply transformation, A'=(2, 2), B=(2, - 3) and C=(6, - 2). Next map this and join them to get the required triangle

Two thirds of the students in a class have pets. There are
36 students in the class. How many of the students have pets?

Answers

I am so sorry if this is wrong. But I hope it helps u.


Answer is - 24

I did 2/3x 36 =24
Answer:

24 of the students have pets

Step-by-step explanation:

Two thirds of the students in a class have pets =

2/3 of the students in a class have pets

If there’re 36 students in the class, how many of the students have pets?

Step 1. Convert 2/3 as a decimal

2/3 = 66.6

Step 2. Use part/whole = part/whole

66.6%/100% = ?/36

Let ? represent the amount of students who have pets in class

Step 3. Divide 66.6/100

0.666

Step 4. Then multiply it by 36

24
••••••••••••••••••••••••••••••••••••
doomdabomb: All brainliest
and thanks are appreciated
and would mean a lot to me,
thanks!

need help with this !!

Answers

Answer:

1

5

4

2

3

Step-by-step explanation:

1 combines the sets A and B. that symbol there stands for U like "union". so, all values of x, where x is either < 1 or >= 5.

2 is again a union. A and C are combined. C contains only one element : x=5.

3 is again a union. B and C are combined. but the element of C (x=5) is already part of B (x>=5), so the union does not change anything, the result is simply B again.

4 is doing a "cross section" between the sets A and B. only elements that are in both sets are in the result. but x < 1 and x >= 5 don't have any elements in common. so, the result is an empty set.

5 is again a cross section. the only shared element between B and C is x=5.

If A=(prime number less than 10)list the element of set A and find n(A)​

Answers

A=(2 3 5 7)
N(A) =4


( sorry I need the points)

Identify the sequence that lists the sides of △MNO in order from shortest to longest.

Answers

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

10-7+12 dived (2^3-6) hope you can answer

Answers

Answer:

The answer is 7.5

A motorboat travels 81 miles in 3 hours going upstream. It travels 135 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Answers

Answer:

27, 18

Step-by-step explanation:

Here's why

Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height

pls help​

Answers

Answer:

8% out of 175 = ( 8 ÷ 100 ) × 175 = 14

175 cm - 14 = 161 cm

...............

Help me pls

Find the missing segment in the image below

Answers

Answer:

The answer is 12

Step-by-step explanation:

You see its because.

Answer:

?=12

Step-by-step explanation:

Using the Thalès's theorem:

[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]

Find the distance between the two points.
(-5,1)
(0,0)
[?]
Enter the number that
goes beneath the
radical symbol.

Answers

Answer:

[tex]{26}[/tex]

Step-by-step explanation:

[tex] \sqrt{(0 - ( - 5) ){}^{2} + (0 - 1) {}^{2} } [/tex]

[tex] = \sqrt{ {(5)}^{2} + {( - 1)}^{2} } [/tex]

[tex] = \sqrt{25 + 1} [/tex]

[tex] = \sqrt{26} [/tex]

Answered by GAUTHMATH

Answer:

26

Step-by-step explanation:

(-5, 1) (0, 0)

sqrt(5^2 + (-1^2))

sqrt(25 + 1)

sqrt(26)

So, 26 goes under the radical.

Geometry, please answer question ASAP

Answers

9514 1404 393

Answer:

  D.  5.4

Step-by-step explanation:

The point U divides segment SP into the ratio 1 : 2. So, segment SU is 1/2 the length of segment UP.

  SU = UP/2 = 3.6/2 = 1.8

The length of PS is ...

  PS = PU +US = 3.6 +1.8

  PS = 5.4

__

Additional comment

If you were asked to find the value of x, you would discover x=1. That is not what you're asked here.

David has a part-time job. He earns $9.40 per hour. How much will he earn when he works 9 hours?

Answers

Answer:

$84.60

Step-by-step explanation:

$84.60 is what david will earn in 9 hours becuz 9.40 times 9 is 84 dollars and 60 cents

An airplane flies a distance of 800km from A to B. If its average speed is 600km/h, how long does it take to cover that distance?​

Answers

Answer:

1 hour 33 minutes

Step-by-step explanation:

distance/speed= time

d =800/600

d=1.33

The aeroplane takes 1.33 hours to traverse a distance of 800 km.

What is the speed of an object?

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: An airplane flies a distance of 800 km with an average speed of 600 km/h

Thus the time taken by the aeroplane to cover that distance is

t=800/600

t=4/3

t=1.33 hours

Hence, The aeroplane takes 1.33 hours to traverse a distance of 800 km.

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The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.​

Answers

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

➯Question:

The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.

Answer:

Both numbers are 25 and 400.

Step By Step Explanation:

Given that:

The product of two numbers is 10000.

One number is 16 times the other number.

To Find:

Both numbers?

Solution:

Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.

According to the Question :

[tex]\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}[/tex]

Hence,

1st number = n = 25

2nd number = 16n = 16 × 25 = 400

∴ Hence, both numbers are 25 and 400.

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

(25, 400) or (-25, - 400)

Step-by-step explanation:

Let the numbers be x and y.

We have:

y = 16xxy = 10000

Substitute y and solve for x:

x(16x) = 1000016x² = 10000x² = 10000/16x² = 625x = √625x = ± 25

Then y is:

y = ± 25*16 = ± 400

The numbers are:

25 and 400 or -25 and - 400

Mr lim had just enough money to buy 6 similar lamps. However, he bought 3 such lamps and had $950 left. How much money did mr lim have at first?

Answers

Let the cost of a lamp = x

6 lamps would cost 6x

He bought 3 lamps at 3x plus Thad 950 left.

3 lamps plus the 950

Would be the same amount as 6 lamps:

Set up an equation and solve for x:

3x + 950 = 6x

Subtract 3x from both sides:

950 = 3x

Divide both sides by 3:

X = 316.67

Each lamp was $316.67

Multiply the price of a lamp by 6:

316.67 x 6 = 1900

He had $1900

Answer: $1900

Step-by-step explanation:

Mr Lim had enough money to buy 6 similar lamps. However he only bought 3 such lamps. That means he had only spent half of his money (6-3=3).

So, if he take money remaining with him = x = $950

Amount of money he first had = 2x =$950×2 = $1900

write 1.4888... as a mixed number

Answers

Answer:

1861÷1250

Step-by-step explanation:

This is the simplified version

Cinco litros de agua se divide en cuatro partes iguales, me tomo 2 partes ¿Cuánto me queda?

Answers

Answer:

2 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

5 ÷ 4 = 1 [tex]\frac{1}{4}[/tex]

1 [tex]\frac{1}{4}[/tex] × 2 = 2 [tex]\frac{2}{4}[/tex] = 2 [tex]\frac{1}{2}[/tex]

5 - 2 [tex]\frac{1}{2}[/tex] = 2 [tex]\frac{1}{2}[/tex]

respuesta: 2 [tex]\frac{1}{2}[/tex]

a trader is given 15% discount on goods bought from a factory. If the original price of an item in the factory is 45000. Calculate the amount the trader paid for them​

Answers

Answer:

38,250

Step-by-step explanation:

Its a 15% discount so youre only paying 85% of the original 45,000. You then multiply 45,000 by .85 to find what youre paying because the decimal version of 85% is .85. You can find the decimal version of a percentage by dividing the percentage by 100; 85/100=.85. Once you multiply 45,000 by .85 you get 38,250.

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