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3 years ago

10.6 - 3x when x is equal to 4.5.

Mathematics

2 answers:

Elenna [48]3 years ago

8 0

10.6-3(4.5)
10.6-13.5
=-2.9

diamong [38]3 years ago

5 0

Answer:

The answer is 2.6

Hope this Helps!!!

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Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

2 years ago

What are the solutions to 0=x^2-x+1?

kumpel [21]

Answer: No solutions

Step-by-step explanation:

There are no solutions to 0 = x² - x + 1.

[Method One]

We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.

[Method Two]

I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$\displaystyle x=\frac{1\pm\sqrt{(-1)^2-4(1)(1)} }{2(1)}$

$\displaystyle x=\frac{1\pm\sqrt{-3} }{2}$

-> Negative numbers don't have real square roots, so there is no solution

4 0

1 year ago

I would appreciate if someone answered these.

Firlakuza [10]

Answer:

1. no solution

2. any value of x makes the equation true

3. x=1

4. any value of x makes the equation true

Step-by-step explanation: hope that answers your question :)

7 0

2 years ago

What is the approximate area of a circle with radius 6 cm?

Vlad1618 [11]

Answer:

the answer in 36cm squared

Step-by-step explanation:

pie r squared

4 0

2 years ago

-20y + 15 = 2 - 16y + 11

shtirl [24]

In order to answer this, we will first need to combine like terms on each side. on the left, you can leave them alone. however on the right, we will need to combine 2 and 11. this is 13. the right side becomes 13-16y. after that, we can add 20y to both sides. that equals 15=13+4y now we can subtract 13 from both sides. 2=4y. then we divide by 4 on both sides to find y. y=.5

7 0

3 years ago

10.6 - 3x when x is equal to 4.5.​

10.6 - 3x when x is equal to 4.5.