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4 years ago

The factorization of 8x3 – 125 is (2x – 5)(jx2 + kx + 25). What are the values of j and k

Mathematics

1 answer:

Inga [223]4 years ago

4 0

Answer:

$j=4\\k=10$

Step-by-step explanation:

$8x^3 - 125$

$\left(2x\right)^3-5^3$

Use this formula:

$x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)$

Where,

$x=2x\\y=5$

Substitute in the values.

$\left(2x\right)^3-5^3=\left(2x-5\right)\left(2^2x^2+5\cdot \:2x+5^2\right)$

$\left(2x-5\right)\left(4x^2+10x+25\right)$

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Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=

Alik [6]

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3 | 3 -5 -1 2

-------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3 | 3 -5 -1 2

-------------------------------------

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3 | 3 -5 -1 2

| -1

-------------------------------------

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3 | 3 -5 -1 2

| -1

-------------------------------------

3 -6

Again any number below the bar gets multiply to the number outside.

-1/3 | 3 -5 -1 2

| -1 2

-------------------------------------

3 -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3 | 3 -5 -1 2

| -1 2

-------------------------------------

3 -6 1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3 | 3 -5 -1 2

| -1 2 -1/3

-------------------------------------

3 -6 1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3 | 3 -5 -1 2

| -1 2 -1/3

-------------------------------------

3 -6 1 5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

7 0

4 years ago

The graph shows f(x)=(x-h)^2 what is the value of h ?

AVprozaik [17]

Answer: I think the value of k is equal to (-1.5).

Step-by-step explanation: When you plug it into the graphing calculator, you get that exact graph.

5 0

3 years ago

Read 2 more answers

. A shipyard makes a container ship that can withstand the total amount of weight W, which is normally distributed with mean of

Debora [2.8K]

Answer:

the maximum number of containers that the ship can load is 170

Step-by-step explanation:

Given the data in the question;

W ~ N( 600, 60 )

S ~ N( 4n, 0.4√n )

p( W > S ) = 0.90

⇒ P( W - S > 0) = 0.9 ------ let this be equation 1

now, since W and S are independent

Mean( W - S ) = Mean( W ) - Mean( S 0 = 600 - 4n

and

SD( W - S ) = √( var(W) + var(S) ) = √( 60² + 0.4²n)

hence;

W - S ~ N( 600 - 4n, √( 60² + 0.4²n) )

now, from equation one, P( W - S > 0) = 0.9

$P( \frac{(W-S)-Mean(W-S)}{SD(W-S)} > \frac{0-(600-4n)}{\sqrt{60^2 + 0.4^2n} }) = 0.90$

$P( z > \frac{0-(600-4n)}{\sqrt{60^2 + 0.4^2n} }) = 0.90$

from z- table

$P( z > \frac{0-(600-4n)}{\sqrt{60^2 + 0.4^2n} }) = P( z >-1.282)$

$\frac{4n - 600}{\sqrt{60^2 + 0.4^2n} } = -1.282$ ------------------ let this be equation 2

now, we square both sides of equation 2

$\frac{(4n - 600)^2}{60^2 + 0.4^2n} } = (-1.282)^2$

$\frac{(4n - 600)(4n-600)}{3600 + 0.16n} } = 1.643524$

we cross multiply

16n² + 360000 - 4800n = 1.643524( 3600 + 0.16n )

16n² + 360000 - 4800n = 5916.6864 + 0.26296384n

16n² + 360000 - 5916.6864 - 4800n - 0.26296384n = 0

16n² + 354083.3136 - 4800.26296384n = 0

16n² - 4800.26296384n + 354083.3136 = 0

solving the quadratic equation, we know that;

x = -b±√( b² - 4ac ) / 2a

so we substitute

x = [-(-4800.26296384) ±√( (-4800.26296384)² - (4 × 16 × 354083.3136)] / [2×16]

x = [ 4800.26296384 ±√( 23042524.522 - 22661332.0704 ] / 32

x = [ 4800.26296384 ±√(381192.4516) ] / 32

x = [ 4800.26296384 ± 617.4078 ] / 32

Hence;

x = [ 4800.26296384 - 617.4078 ] / 32 or [ 4800.26296384 + 617.4078 ] / 32

x = 131 or 170

Therefore, the maximum number of containers that the ship can load is 170

5 0

3 years ago

An alloy is composed of nickel, zinc, and copper in a5:4:8 ratio. How many kilograms of each metal are needed to make 3.4 kg of

lorasvet [3.4K]

5x+4x+8x=3.4
17x=3.4
x=0.2
Nickel 1 kg
Zinc 0.8 kg
Copper 1.6 kg

4 0

3 years ago

Read 2 more answers

What is the solution for x in the equation? -8x+11=35

liraira [26]

You need to make 11 a negative number and subtract it from 35 then you should get the answer 24! Next you divide -8 divided by 24 which is -3! BTW you don't need to use the original 11 because it gets cancelled out!

8 0

3 years ago

Read 2 more answers