Show that 3x^2 -2x + 1 is always greater than 0.
( This is an Additional Math Question )

Answers

Answer 1

Answer:

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved

Step-by-step explanation:

3x^2 -2x + 1 =3(x^2-2/3x+1/3)

Consider x^2-2/3x+1/3

Remember that (a-b)^2 =a^2-2ab+b^2

x^2=a^2

a=x

-2/3x= -2*x*b

b=1/3

S0 (x-1/3)^2= x^2-2/3x+1/9

x^2-2/3x+1/3= x^2-2/3x+1/9+1/3-1/9= (x-1/3)^2+2/9

3x^2 -2x + 1 =3(x^2-2/3x+1/3)=3(x-1/3)^2+2/9*3= 3(x-1/3)^2+2/3

(x-1/3)^2 is greater or equal to zero

3(x-1/3)^2 is greater or equal to zero

and 2/3 is greater than zero

So there sum is greater than zero

Proved


Related Questions

A boy buys 2 packets each containing x biscuits. He eats 6 biscuits
How many biscuits does he have left?

Answers

Answer:

he have left 16 biscuits

Solve the system of linear questions by substitution

-3x + y = 1
4x + y = 8

Answers

Answer:

–3x + y =1

y= 1 +3x

4x + y =8 —> 4x + ( 1 + 3x ) = 8

7x + 1 = 8 —> 7x = 8 – 1 —> 7x = 7

x = 7/7 —> x = 1

y= 1 + 3x —> y = 1 + 3 (1) —> y = 1+ 3

y= 4

(x , y ) > ( 1 , 4 )

I hope I helped you^_^

Find the unknown sizes of the angle​

Answers

Answer:

b=58 ( vertically opposite angle)

58+65+x=180 (Beaing straight angle)

123+x=180

x=180-123

:.x=57

65+b+c=180 (beaing straight angle)

65+58+c=180

123+c=180

c=180-123

c=57

a=65 (beaing vertically opposite angle)

answer

:.b=57

:.c=57

:.a=65

a=65°
b=58°
c=180-65-58=57°

Hope my answer helped u :)

whate are the factors for the following 64,72,36,140​

Answers

Answer:

the greatest common factor is 8

PLz help :( i will mark barinliest
which best describes the meaning of the word theorem

A. A conjecture based on inductive reasoning

B. A statement that is accepted as true without proof

C. a statement explaining the meaning of a geometric term

D. A conclusion proved by deductive reasoning

Answers

Answer:

Step-by-step explanation:

It's D.

A theorem is true by some sort of mathematical logic.

It is not a definition. Not C

It is not in the end true because of inductive reasoning (a theorem may lend itself to inductive reasoning, but it must be proved.) Not A

It certainly not assumed to be true without proof. Not B

select the correct answer
which of these mappings is a function

Answers

Answer:

B. X

Step-by-step explanation:

the other functions have same x and different y which makes them non existant

B is the answer for this problem

Ethans solution and reasoning for solving an equation are shown below:

Given: 4/2x - 10 = 30

Which reason is incorrect?
(9th grade math Algebra 1)

Answers

Answer:

Reason 4 is wrong in Ethan's solution.

Step-by-step explanation:

Reason 4 is incorrect because at this step in the answer we already have one  variable which is unknown on the left side and then one constant which can be seen on the right. So, instead of multiplying the fractions the way Ethan is doing, all you need to do now is just simplify the expression instead of complicating the step.

Charlotte read a 608-page book in 16hours last month. How many pages per hour was that

Answers

Answer:

33

Step-by-step explanation:

608pages/16h = 33pages/h

2 1/6 x 4 1/2= and explain it

Answers

Answer:

9 3/4

Step-by-step explanation:

First you would want to multiply the whole number with their denominators and then add the numerator to that. 2*6+1 and 4*2+1  Then you keep the original denominator at the bottom of the fraction.

2*6+1/6  4*2+1/2 ---> 13/6 x 9/2

You would then simplify the crossing numbers 6 and 9. They both can be divided by three.

13/2 x 3/2 = 39/4

Now you would do long division where you divide 39 by 4

4 goes into 39 nine times subtracting 36 from 39.

You then end up with 1 which becomes you numerator, 4 is the new denominator and 9 is the whole number.

The answer of the given mixed numbers 2 1/6 x 4 1/2 is 9 3/4.

What is mixed numbers?

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers.

You should first multiply the entire number by the denominators of the other numbers, and then add the numerator to that result. 2*6+1 and 4*2+1 The original denominator is then kept at the bottom of the fraction.

(2*6+1)/6 x ( 4*2+1)/2 —-> 13/6 x 9/2

Next, you would streamline the intersection of numbers 6 and 9. They are both divisible by three.

13/2 x 3/2 = 39/4

You would now perform a long division by dividing 39 by 4.
4 multiplies 39 by 9 and subtracts 36 from 39.

In the end 3 becomes the numerator, 4 becomes the new denominator, and 9 is the total.

Therefore, 2 1/6 x 4 1/2 = 9 3/4.

To know more about the mixed numbers, click on the link

https://brainly.com/question/1746829

#SPJ2

A box of cereal states that there are 90 calories in 3/4 cup serving. How many calories are there in 4 cups of the cereal

Answers

Answer:

480

Step-by-step explanation:

Let x be the calories in 4 cups

Set it up

[tex]\frac{90}{\frac{3}{4}}=\frac{x}{4}[/tex]

Step 1: Switch sides

[tex]\frac{x}{4}=\frac{90}{\frac{3}{4}}[/tex]

Step 2: Apply fraction rule

[tex]\frac{x}{4}=\frac{90\cdot \:4}{3}[/tex]

Multiply

[tex]\frac{x}{4}=\frac{360}{3}[/tex]

Divide

[tex]\frac{x}{4}=120[/tex]

Step 3: Multiply both sides by 4

[tex]\frac{4x}{4}=120\cdot \:4\\\\=480[/tex]

There are 480 calories in 4 cups of the cereal.

What the picture says

Answers

Answer:

BCG

Step-by-step explanation:

This is because it is what you see when you look in the front of the shape.

HOPE THIS HELPED

What is the slope between the points (5.-7) and
(–7.1)?

Answers

This is your awnser have a great night awnser is in the picture below

6x-14(17+19x)=-11x+13

Answers

ANSWER: x=-251/271 or -0.926

Step by Step:
1) 6x-238-266x=11x+13 (multiply 14 with 17 and 19x)
2) -260x-238=11x+13 (like terms put together)
3) -260x-238-11x=13 (combine the x’s)
4) -260x-11x=13+238
5) -271x=13+238
6) -271x=251
7) divide both sides by -271

Hayden had 2 1/2 gallons of water in his watering can. The seed packet said to use 1/4 of a gallon for peppers and 5/8 of a gallon for tomatoes. Hayden then used some of the water for lettuce. If Hayden had 3/4 gallons of water left over, about how much water did he use for lettuce?

Answers

Answer:

7/8

Step-by-step explanation:

1/4 + 5/8 = 2/8 + 5/8 = 7/8

= amount used for pepper and tomatoes

2 1/2 - 3/4 = 5/2-3/4 = 10/4 -3/4 = 7/4

= total amount used

so

7/4 - 7/8 = 14/8 - 7/8 = 7/8 for lettuce

prove angle z = angle v​

Answers

Answer:

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

Step-by-step explanation:

angle z = angle v​ can be proved by the SAS (Side angle side) Property

XZ = TV (Given)

Angle Z = Angle V (as it is already said that ZY = VY and their ending points are Z and V respectively

ZY = VY ( Given )


find the value proportion :x : 35:98:60​

Answers

Answer:

x/35=98/60

x=7/6

The value of x is 7/6

If AB is parallel to cD and the slope of aD is -5, what is the slope of AB?

Answers

Answer:

-5

Step-by-step explanation:

According to formula:

m1 = m2

Since:

m2 = -5

∴ m1 = -5

Answer:

-5

Step-by-step explanation:

because -5 is parallel to AB

Help please.
Simplify: 5i/ 3 + 2i

Answers

Answer:

10+15i/13

Step-by-step explanation:

This question is about complex numbers.

so,

in this type of questions we have to multiply this fraction by the conjugate of the denominator

   conjugate of the denominator is  3-2i

    1)    5i(3-2i)/(3+2i)(3-2i)

   

    2) 15i-10i^2/9-4i^2   ( we know that i^2 = -1 )

    3) 15i+10/9+4

 

     4) 15i+10  / 13

   

Help me please broskies

Answers

From step 1 to step 2 they distributed the 2 (multiplied the inner numbers of the parentheses)
From step 2 to step 3 they added 6x to both sides,canceling out the -6x on the left side and adding 6x with the 5x
From step 3 to step 4 they subtracted 2 from both sides, canceling it out on the right side and subtracting 2 from 8 to get 6
From step 4 to step 5 they try and get x alone by dividing both sides by 11, canceling out the 11 on the right side and leaving a fraction the left
Leaving you with your answer of what x equals in the final step
Hope this helps!!

What fractional part of the bar is blue? ill mark brainliest!


Group of answer choices


1/6


2/6 or 1/3


3/6 or 1/2


4/6 or 2/3

Answers

Answer:

3/6 or 1/2

Step-by-step explanation:

⇒ out of 6 blocks 3 are shaded so, it will be 3/6

⇒ out of 6 blocks 3 are shaded (3 is half of 6) so, it will be 1/2

Answer:

Answer: 3/6 or 1/2

Step-by-step explanation:

Basically there are six bars and we are to find the fractional part of the blue bars. The fractional part of the blue bars is 3/6 or 1/2.

5.6x+1.5=0.8x+25.5

What is x?

Answers

Answer:

x = 5

Step-by-step explanation:

Let me know if you need the work

hi how to solve this question 3n-5;where n=-1​

Answers

Answer:

[tex]3n - 5 \\ 3( - 1) - 5 \\ = - 3 - 5 \\ = - 8[/tex]

I hope I helped you^_^

Answer:

hope it's help you

Step-by-step explanation:

3(-1)-5                                                                                                                         =-3-5                                                                                                                                           =-8

The chorus sang for 27 minutes. If each song lasted an average of 412 4 1 2 minutes, how many songs did the chorus sing?

Answers

Answer:

It would be 15 songs if each song was 412 seconds, not minutes.

Step-by-step explanation:

5, 317, 000 in scientific notation

Answers

Hi ;-)

[tex]5 \ 317 \ 000=\\\\=5,317\cdot1 \ 000 \ 000=\boxed{5,317\cdot10^6}[/tex]

Step-by-step explanation:

[tex]5317000 = 5.317 \times {10}^{6} \\ thank \: you [/tex]

3(s-5)/4 -3 = 4s- (s-3)/2
pls answer fast​

Answers

Answer:

[tex]s = \frac{9± \sqrt{ - 39} }{4} [/tex]

Step-by-step explanation:

[tex] \frac{3(s - 5)}{4 - 3} = \frac{4s \times (s - 3)}{2} [/tex]

➡️ [tex] \frac{3(s - 5)}{1} = 2s \times (s - 3)[/tex]

➡️ [tex]3s - 15 = 2 {s}^{2} - 6s[/tex]

➡️ [tex]3s - 15 - 2 {s}^{2} + 6s = 0[/tex]

➡️ [tex]9s - 15 - 2 {s}^{2} = 0[/tex]

➡️ [tex] - 2 {s}^{2} + 9s - 15 = 0[/tex]

➡️ [tex]2 {s}^{2} - 9s + 15 = 0[/tex]

➡️ [tex]s = \frac{ - ( - 9)± \sqrt{( - 9 {)}^{2} - 4 \times 2 \times 15} }{2 \times 2} [/tex]

➡️ [tex]s = \frac{9± \sqrt{81 - 120} }{4} [/tex]

➡️ [tex]s = \frac{9± \sqrt{ - 39} }{4} [/tex]

➡️ [tex]s∉ℝ[/tex]

How to solve multi step equations

Answers

Answer:

x = –2

Step-by-step explanation:

– 6(1+4x) = –x +40

–6 – 24x = –x +40

24x –x = –6 –40

23x= – 46

x= – 46 / 23

x= – 2

I hope I helped you^_^

Which expression is equivalent to(2^3)^-5

Answers

Answer:

23

Step-by-step explanation:

Answer:

1/32

Step-by-step explanation:

First you must multiply the 3 and the -5 because the -5 is out of the parenthases. then you will get 2^-15. You cannot have a negative exponent so you chance it to 1/2^15. Then simplify to get the answer

Find the value of y and RT if S is between RT. RT = 7y + 7, RS = 11, and ST = 5y + 6.​

Answers

Answer:

78  

Step-by-step explanation:

show your work

where can i find the answers?

Answers

Answer:

I don't know where can you find this question's answer.

V36 What smallest number should be multiplied to 288 in order to make it a perfect cube?​

Answers

Answer:

6

Step-by-step explanation: We observe that if 288 is multiplied by (2 x 3), then its prime factors will exist in triples. Thus, the required smallest number by which 288 be multiplied to make it a perfect cube i: (2 x 3)=6. 1,331 is a perfect cube.

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