help me please i dont get it

Answer:

16/45 for fraction, or 0.35 for decimal

Step-by-step explanation:

4/7 x 4/5 × 7/9

reduce numbers with greatest common factor 7

4 × 4/5 × 1/9

calculate the product = 4 × 4 × 1 = 16

5 × 9 = 45

16/45 or 0.35

Answer:

To Evaluate:

[tex] \\ { \displaystyle{ \rm \lim_{x \to1} \left \{ \frac{ {x}^{4 } - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right \} }}\\ \\[/tex]

Using L'Hospital's Rule

Let f(x) and g(x) be two common functions which are differentiable on an open Interval , at a point a where,

[tex]\\{ \displaystyle{ \lim_{x \to a}{ \rm{f(x)} = { \displaystyle{ \lim_{x \to a}}} \: { \rm{g(x)}} = 0 \: or \: \pm \infty}}}\\ \\[/tex]

Then,

[tex]\\{ \displaystyle{ \lim_{x \to a} \frac{{ \rm{f (x)}}}{{ \rm{g(x)}}} = { \displaystyle{ \lim_{x \to a }}} \frac{{ \rm{f '(x)}}}{{ \rm{g'(x)}}}}}\\ \\[/tex]

As x to 0 , we have:

[tex]\\{ \displaystyle{ \lim_{x \to 1}}} \left( \large\rm\frac{ {x}^{4} - {3x}^{2} + 2 }{ {x}^{3} - {5x}^{2} + 3x + 1} \right) = \frac{0}{0}\\ \\[/tex]

Therefore,

[tex]\\{ \large{ \displaystyle{ \lim_{x \to1}}} \left( \large \rm\frac{ {x}^{4} - {3x}^{2} + 2}{ {x}^{3} - {5x}^{2} + 3x + 1 } \right) = { \displaystyle{ \lim_{x \to1} { \small{\frac{ {4x}^{3} - 6x}{ {3x}^{2} - 10x + 3 }}} = { \small{\frac{4 - 6}{3 - 10 + 3} }} = - \frac{2}{ - 4} = - \frac{1}{2} }}}\\ \\[/tex]

Hence,

[tex]\\{ \displaystyle{ \lim_{x \to1}{\rm{ \left( \frac{ {x}^{4} - 3 {x}^{2} + 2 }{ {x}^{3} - 5 {x}^{2} + 3x + 1 } \right) = { \boxed{ \red{ - \frac{1}{2} }}}}}}}\\ \\[/tex]

Without using L'Hopital's rule:

Factorize the numerator.

[tex]x^4 - 3x^2 + 2 = (x^2 - 2) (x^2 - 1) = (x^2 - 2) (x + 1) (x - 1)[/tex]

Factorizing cubics is usually a bit trickier. But we know x = 1 makes the denominator vanish, so x - 1 is a factor of the cubic. So for some constants a and b,

[tex]x^3 - 5x^2 + 3x + 1 = (x - 1)^3 + a(x - 1)^2 + b(x - 1)[/tex]

Expanding the right side gives

[tex]x^3 - 5x^2 + 3x + 1 = x^3 + (a - 3)x^2 + (-2a + b + 3)x + a - b - 1[/tex]

Then

[tex]a - 3 = -5 \implies a = -2[/tex]

[tex]-2a + b + 3 = 3 \implies b = -4[/tex]

So we rewrite the limit as

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1) (x - 1)}{(x-1)^3 - 2(x-1)^2 - 4(x-1)}[/tex]

x is approaching 1 so x ≠ 1 and we can cancel out factors of x - 1 :

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \lim_{x\to1} \frac{(x^2 - 2) (x + 1)}{(x-1)^2 - 2(x-1) - 4}[/tex]

The simplified limand is continuous at x = 1, so we can now evaluate the limit by direct substitution.

[tex]\displaystyle \lim_{x\to1} \frac{x^4 - 3x^2 + 2}{x^3 - 5x^2 + 3x + 1} = \frac{(1^2 - 2) (1 + 1)}{(1-1)^2 - 2(1-1) - 4} = -\frac24 = \boxed{-\frac12}[/tex]

Answer:

$2.57

Step-by-step explanation:

divide 5,140 by 20,

5,140/20=257=2.57

Answer:

Colin spends 1/8 of an hour practicing each song

Step-by-step explanation:

Colin's piano lesson is 3/4 of an hour, long.

In that period, he practices 6 different songs, spending an equal amount of time on each one.

This means that each song gets the sixth part of the lesson duration. The fraction that expresses that amount is:

[tex]\displaystyle \frac{\frac{3}{4}}{6}=\frac{3}{24}=\frac{1}{8}[/tex]

Colin spends 1/8 of an hour practicing each song

Answer:

1/8

Step-by-step explanation:

Answer: a = b*r/n

Step-by-step explanation: Hope this helps :^)

Answer:

the anser is 1.3

have a nice day!

Answer:

8(15-m)

Step-by-step explanation:

just took the test

Answer:

59890

you just subtract

459909-400019

Step-by-step explanation:

please pass this on... ( #helpsavelives )

Who ever is reading this:

I love u.

U matter.

The world needs u

hang in there ik it may be bad but u deserve the world <3

ur beautiful no matter ur shape, size, color, gender.. anything

don't give up i need u to live.

i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me

Pls pass this on. Everyone deserves to know this. ♥️♥️

just copy and paste its not hard pls this could save someones life

Answer:

59890

Step-by-step explanation:

459909-400019

Answer:

=0

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Let us label these coordinates for our own ease:

A(0,0)

B(0,4)

C(4,5)

Area= [Ax(By-Cy)+Bx(Cy-Ay)+Cx(Ay-By)]÷2

Area = [0(4-5)+0(5-0)+4(0-4)]÷2

Area= [0+0-16]÷2

Area = -8

But since the value can not be negative we have consider a modulus in the formula, thus the value is 8

Answer:

The two factor pairs for 72 are the following:

Step-by-step explanation:

Of you take the answer to each equation only these two equal 72, leaving them as factors.

3 × 18 is equal to 54

8 × 8 is equal to 65

Which leaves them being the wrong answer

Answer:

a

  [tex]f(x)= 100 [x - 0.2050][/tex]

b

 [tex]P(X > 0.2125) =  0.25 [/tex]

c

  [tex]a = 0.2140[/tex]

d

Mean [tex]\mu  = 0.21[/tex]

Variance  [tex]\sigma ^2  =  0.0000083 [/tex]

Step-by-step explanation:

From the question we are told that

   The thickness of photoresist follows a uniform distribution

So

     [tex]X\   \~{}\ U \{  0.2050 , 0.2150 \}[/tex]

Generally the probability density function  is mathematically represented as

[tex]F(x) =  \left \{  \frac{1}{ 0.2150 - 02050} , 0.2150< x < 0.2150[/tex]

=>  [tex]F(x) =  \left \{   100 , 0.2150< x < 0.2150[/tex]

Generally the cumulative distribution function is

   [tex]f(x) =  \int\limits^{x}_{- \infty} {F(x)} \, dx[/tex]

Here [tex]- \infty[/tex] means the lower limit which in this case is  02050

So

    [tex]f(x) =  \int\limits^{x}_{0.2050} {100} \, dx[/tex]

    [tex]f(x) =  100 \int\limits^{x}_{0.2050} {1} \, dx[/tex]

=>   [tex] f(x)=100 [ x ] | \left \ x} \atop {0.2050}} \right.[/tex]

=>   [tex]f(x)= 100 [x - 0.2050][/tex]

Generally the proportion of wafers that exceeds 0.2125 is mathematically represented as

     [tex]P(X > 0.2125) =  1 - F(0.2125)[/tex]

=>  [tex]P(X > 0.2125) =  1- 100[0.2125 - 0.2050][/tex]

=>   [tex]P(X > 0.2125) =  0.25 [/tex]

Generally the thickness which is exceeded by 10% of the wafers is mathematically represented as

       [tex]P(X  > a ) =  0.10[/tex]

=>    [tex]1 - F(a) = 0.10[/tex]

=>     [tex]1 -100 (a - 0.2050) = 0.10[/tex]

=>     [tex]100(a -0.2050) =  0.90[/tex]

=>   [tex]a - 0.2050 =  0.009[/tex]

=>   [tex]a = 0.2140[/tex]

Generally the mean is mathematically represented as  

     [tex]\mu  =  \frac{ 0.2050 -0.2150 }{2}[/tex]

=>   [tex]\mu  = 0.21[/tex]

Generally the variance  is mathematically represented as

    [tex]\sigma ^2  =  \frac{1}{12} [0.2150 - 0.2050]^2[/tex]

=>  [tex]\sigma ^2  =  0.0000083 [/tex]

I'm not 100% sure but it's not u

Answer:

16.2

Step-by-step explanation:

0.6 * 27

Answer:

  $625,000

Step-by-step explanation:

The maximum revenue will be found where the derivative of the revenue function is zero.

  r'(x) = 50 -2x = 0

  50 = 2x

  x = 25

When 2500 gallons are sold, the revenue is ...

  r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands

The maximum revenue is $625,000.

Answer:  [tex]y=\frac{1}{3} x[/tex]

Answer:

42

Step-by-step explanation:

5*5+6*3-1

25+6*3-1

25+18-1

43-1

=42

I hope this helped, please give me Brainliest if it did. :)

Answer:

5*4=9 and if thats -5*7=35 and adding those together gets 35+9=44

Step-by-step explanation:

Answer:

Hello there buddy

Your answer is

35+9=44

Hope it’s helps you buddy

Step-by-step explanation:

~Awesome Jayden

Answer:

$4

Step-by-step explanation:

It was 4 dollars because you bought one notebook worth two dollars and six-packs of crayons. 26-2 is 24, and 6x4 is 24, so it is worth four dollars.

Answer:

Option C, 20 is the answer.

Step-by-step explanation:

Let g(x) = 2x and h(x) = x² + 4

We have to evaluate (h ο g) ( -2 )

Since ( h ο g )x = h [ g(x) ]

                       = ( 2x)² + 4

                       = 4x² + 4

( h ο g ) ( -2 )  = 4 ( -2 )² + 4

                       = 4 × 4 + 4

                       = 16 + 4

                       = 20

Answer:

Check the pic

Given parameters:

Normal selling price off the bicycle = $440

Discount fraction  = [tex]\frac{3}{4}[/tex]

Unknown:

Sale price of the bicycle = ?

Solution:

The discounted sale price of the bicycle;

                      = normal selling price x discount fraction

Input the parameters and solve;

           Discounted sale price of the bicycle  =[tex]\frac{3}{4}[/tex] x 440

                                                                        = 3 x 110

                                                                        = $330

The discounted sale price of the bicycle is $330

Answer:

V = 3^3 = 5^3

Volume of each cube is side^3. To find the volume of both cubes just add the two volumes together.

Step-by-step explanation: Your welcome.

Answer:

total volume = 152 units³

given:

using this formula:

total volume = first cube volume + second cube volume

total volume = 3³ + 5³

total volume = 27 + 125

total volume = 152 units³

Answer:

She will earn 720 in December(Sorry, can't use the dollar sign.)

Step-by-step explanation:

1/5 of 600 is 120, so you want to add 120 to 600, which would be 720. Hope this helps!

Answer:

A U B = {2,3,4, 5}

Step-by-step explanation:

Union means join together

A U B = {2,3,4, 5}

Answer:

3

Step-by-step explanation:

eq.

1/5(12×5/6+5)

=1/5×(10+5)

=1/5×15

=3

Answer:

3

Step-by-step explanation:

Answer:

22 - 3 × 6 + 52 = 56

Step-by-step explanation:

Multiply

3×6 = 18

22-18+52

Add and subtract

22-18 = 4

4+52 = 46

Answer:

56

Step-by-step explanation:

To solve we must use the order of operations which is PEMDAS.

P-Parenthesis

E-Exponents

M-Multiplication

D-Division

A-Addition

and S-Subtraction

First we multiply -3 and 6 which gives us -18. So our equation is now 22-18+52.

Next we do addition. -18+52 is 34, plus 22 gives us 56.

Hope this helps :)

Answer:

Step-by-step explanation:

Completing the square

The blanks are

Answer:

(x^2-4)^2 = 9

Step-by-step explanation:

First, isolate the constant:

x^2-8x = -7

Then, since (a-b)^2 = a^2-2ab+b^2, you should add 16(4^2) to both sides:

x^2-8x+16 = 9

Now, we can rewrite the right-hand side as (a-b)^2:

(x-4)^2 = 9