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3 years ago

The polynomials that are given are P(x)=

Mathematics

1 answer:

natima [27]3 years ago

8 0

Answer:

Step-by-step explanation:

P(x)= x³ - x² - 18

Q(x) = P(2x-1)

= (2x-1)³ - (2x-1)² -18

= (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18

=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18

= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1 - 18

= 8x³ - 16x² + 10x - 20

Hint : (a-b)³ = a³-3a²b+3ab²-b³

(a-b)² = a² -2ab + b²

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Find the value of x and explain how you found it. Make sure to cite the problem and share what you see before you explain your s

klemol [59]

Answer:

THE VALUE OF X = 3 .

Step-by-step explanation:

From the Δ RQP and Δ TSP ;

⇒ ∠ TPS = ∠ RPQ ( since both are common angle )

⇒ RQ ≈ TS ( parallel lines )

⇒ ∠ PRQ = ∠ PST ( Corresponding angle )

∴ Δ RQP ≅ Δ TSP ( BY ASA RULE )

Now ,

$\frac{RP}{TP} = \frac{QP}{PS}$

$\frac{9 + X}{9} = \frac{6 + 2}{6}$

⇒ X = 3

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4 years ago

Solve this steps not needed

777dan777 [17]

Hi!

When you add a negative number, you really just subtract it. So let's solve this.

Convert the mixed numbers into improper fractions.

$\frac{434}{9} - \frac{351}{9}$

Solve

434 - 351 = 83

$\frac{83}{9}$

The sign of this fraction is positive

Hope this helps! :)

-Peredhel

4 0

3 years ago

Read 2 more answers

A city had population 67,255 on january 1, 2000, and its population has been increasing by 2935 people each year since then. A l

irina1246 [14]

We are given: On january 1, 2000 initial population = 67,255.

Number of people increase each year = 2935 people.

Therefore, 67,255 would be fix value and 2935 is the rate at which population increase.

Let us assume there would be t number of years after year 2000 and population P after t years is taken by function P(t).

So, we can setup an equation as

Total population after t years = Number of t years * rate of increase of population + fix given population.

In terms of function it can be written as

P(t) = t * 2935 + 67255.

Therefore, final function would be

P(t) = 2935t +67255.

So, the correct option is d.P(t) = 67255 + 2935t.

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3 years ago

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4.8/1 7/9 =(1.2b):6 2/3

Hunter-Best [27]

Answer:

b = 15

Step-by-step explanation:

Solve for b:

$\dfrac{4.8}{1\frac{7}{9}}=\dfrac{1.2b}{6\frac{2}{3}}$

Cross multiply:

$6\dfrac{2}{3}\cdot 4.8=1.2b\cdot 1\dfrac{7}{9}\\ \\\dfrac{6\cdot 3+2}{3}\cdot 4.8=1.2b\cdot \dfrac{9+7}{9}\\ \\\dfrac{20}{3}\cdot \dfrac{48}{10}=\dfrac{12b}{10}\cdot \dfrac{16}{9}\\ \\20\cdot 4=b\cdot \dfrac{16}{3}\\ \\5=b\cdot \dfrac{1}{3}\\ \\b=5\cdot 3\\ \\b=15$

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3 years ago

The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ

Nutka1998 [239]

Answer:

equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

(x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

-18-3 = -21
-18-1 = -19
-18+1 = -17
-18+3 = -15

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

(x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

4x +12 = -72 . . . . . collect terms

4x = -84 . . . . . . . . subtract 12

x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

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3 years ago