6xy+4x-3y-2=0 solve the equation

Answer:

We know that P(x) = 30*x^3 + k*x^2 + 1

a) If (3x - 1) is a factor, let's find the value of k.

Because the degree of the original polynomial is 3, and the degree of the factor is 1, we should multiply it by a polynomial of degree 2.

Then:

30*x^3 + k*x^2 + 1 = (3*x - 1)*(a*x^2 + b*x + c)

30*x^3 + k*x^2 + 1  = 3*a*x^3 + 3*b*x^2 + 3*c*x - a*x^2 - b*x - c

30*x^3 + k*x^2 + 1 = 3*a*x^3 + (3*b - a)*x^2 + (3*c - b)*x - c

The terms with the same exponent should be equal, then:

30*x^3 = 3*a*x^3

30 = 3*a

30/3 = a = 10

k*x^2 = (3*b - a)*x^2

k = (3*b - 10)  

0*x = (3*c - b)*x

0 = (3*c - b)

b = 3*c

and

1 = -c

then:

c = -1

Replacing this in the equation: b = 3*c

we get: b = -3

Replacing this in the equation for k, we get:

k = (3*b - 10) = (3*-3 - 10) = -19

k = -19

And we can write:

P(x) = (3*x - 1)*(10*x^2 - 3*x - 1)

b) Now we want to write P(x) as a product of its linear factors.

Then we need to factorize the quadratic part:

We need to solve

10*x^2 - 3*x - 1 = 0

We can use the Bhaskara's equation to get the solutions:

[tex]x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*10*(-1)} }{2*10} = \frac{3 \pm 7}{10}[/tex]

Then the two zeros of that polynomial are

x = (3 + 7)/10 = 1

x = (3 - 7)/10 = - 4/10 = -2/5

So we can write the polynomial as:

10*(x - 1)*(x - (-2/5))

Replacing this in the equation of P(x) we get:

P(x) = (3*x - 1)*10*(x -1)*(x + 2/5)

     = 10* (3*x - 1)*(x -1)*(x + 2/5)

So P(x) is written as a product of lineal factors.

C) The zeros of the polynomial are the values of x such that one of the factors becomes equal to zero.

For the first factor, we have a zero at x = 1/3

for the second, we have a zero at x = 1

for the third one, we have a zero at  x = -2/5

Answer:

25%

Step-by-step explanation:

An easy way to figure this out is just by dividing the initial amount of students (18) by the current amount of students (24), and then subtracting 1.

So, 18/24 = 0.75 (aka 75%), and  1 - 0.75 = 0.25 (aka 25%)

Answer:

6

Step-by-step explanation:

f(s) = x^2 - 3

f(-3) = 6

f(0) = -3

f(1) = -2

f(2) = 1

(1, -2)

The vertex is simply the turning point.

Answer:

x=-1

Step-by-step explanation:

5x=-5

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

Answer:

The constant is: 3.14

Multiplying 2 by 3.14 which would get you to 6.28

Multiply each one by 3.14

Answer:

the answer is 69.93

hope this helps!

Answer:

yessss

Step-by-step explanation:

Answer: mabey

Step-by-step explanation: mabey

Answer:

14x + 6

step by step explanation:

Answer:

numbers are 7 and 6

Step-by-step explanation:

7+6=13

7x6=42

Answer:

The answer is "Hot dog buns".

Step-by-step explanation:

In the given scenario, it increased the hot dog prices result in a reduction in hot dog bun production. Complementary products are hot dogs including hot dog buns. Therefore the curve of demand is moving to the left. Please find the image file in attached.

Answer:

2x+5

Step-by-step explanation:

Formula for the perimeter of a reactangle= 2(l+b)

So,

2(l+b) = 10x+18

2(3x+4 + b) = 10x+18

Rearrange and solve

3x+4+b = 5x+9

b = 5x+9 - 3x - 4

b = 2x+5

Thus the measurement of the width = 2x+5

Hope this helps

Answer:

484

Step-by-step explanation:

484=22^2

Answer:

X= -243

Used Math.way

We can find percent by dividing savings by total earned. 28/350=8%

8%

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

Answer:

C

Step-by-step explanation:

Considering the situation, the hypotheses set that would determine if the proportion of households that support starting school earlier has changed this year is given by:

[tex]H_0: p = 0.65, H_\alpha: p \neq 0.65[/tex]

At the null hypotheses, it is tested if there has been no change, that is, the proportion is still of 0.65 = 65%, hence:

[tex]H_0: p = 0.65[/tex]

At the alternative hypotheses, it is tested if there has been a change, that is, the proportion is not of 0.65 = 65% anymore, hence:

[tex]H_\alpha: p \neq 0.65[/tex]

More can be learned about an hypotheses test at https://brainly.com/question/26454209

Answer:

Equivalent / Equal

Step-by-step explanation:

Answer:

v = 135.5 cm³

Step-by-step explanation:

v = 1/3bh = 1/3(16)(25.4) = 135.5 cm³

Answer:

(a+b)^2+(a-b)^2=2(a^2+b^2)

expanding:

a² + 2ab + b² + a² -2ab + b² = 2a² + 2b²

2a² + 2b² = 2a² + 2b²

Answer:

with what?

Step-by-step explanation:

Answer:

x = 42,33°

Step-by-step explanation:

3x + 1° + 52° = 180° [angles on a straight line]

3x + 53° = 180°

3x = 180° - 53°

3x = 127°

divide both sides by 3

x = 42,33°

Answer:

certain

Step-by-step explanation:

Jai rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that he will roll a number between 1 and 6 (including 1 and 6)?

There are 6 possible outcomes for rolling a die numbered from 1 to 6: {1, 2, 3, 4, 5, 6}.

Within that set of outcomes, there are 6 possible ways of rolling a number between 1 and 6 (including 1 and 6): {1, 2, 3, 4, 5, 6}.

6 out of 6 is 1. When something will occur all the time, we say it is certain.

Answer:

x = 3

Step-by-step explanation:

The angle measuring 5x and the angle measuring 165° are a linear pair, so they are supplementary. Their measures add to 180°.

5x + 165 = 180

5x = 15

x = 3

Answer:

.............. just for filling 20 characters

Answer:

g= - 3x/x-2

Step-by-step explanation:

Answer:

a= 135

Step-by-step explanation:

18*15=135

Answer:

2x radius I believe

Tell me if im wrong and I will remove this