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KiRa [710]
2 years ago
7

Pls help i will mark brainliest

Mathematics
2 answers:
s344n2d4d5 [400]2 years ago
6 0

Answer:

(4,6)

Step-by-step explanation:

hope this helps you

adell [148]2 years ago
3 0
I was gonna comment but my answer is the same as the person above
You might be interested in
Need help with this one question
loris [4]

Answer:

71.6599

Step-by-step explanation:

I think if I’m wrong please tell me

wich ik I’m probably wrong

8 0
2 years ago
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 <em>f(x)</em> needs to satisfy

• x^3 divides f(x)

• (x-1)^3 divides f(x)^2

I'll also assume <em>f(x)</em> 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 <em>a</em> and <em>b</em> 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 is (f - 5)(-2) + 11f
n200080 [17]

Answer:

-2f+10+11f

= 9f+10

Step-by-step explanation:

just expand it

7 0
2 years ago
Read 2 more answers
would someone be able to explain to me how to solve these problems? I don't need the solutions, I just need an explanation. I ne
Leni [432]
The first 3  are examples of the difference of 2 squares so you use the identity 
a^2 - b^2 = (a + b)(a - b)
x^2 - 49 = 0 
so (x + 7)(x - 7) = 0
so either x + 7 = 0 or x - 7 = 0
giving x = -7  and 7.
Number 7 reduces to 3x^2 =12, x^2  = 4 so x = +/- 2
Number 8  take out GCf (d) to give 
d(d - 2)  = 0   so d = 0 ,  2
9 and 10 are more difficult to factor
you use the 'ac' method  Google it to get more details
2x^2 - 5x + 2
multiply first coefficient by the constant at the end 
that is 2 * 2 =  4
Now we want  2 numbers  which when multiplied give + 4 and when added give - 5:-    -1 and -4  seem promising so we write the equation as:-

2x^2 - 4x - x + 2 = 0

now factor by grouping 
2x(x - 2) - 1(x - 2) = 0

(x - 2) is common so

(2x - 1)(x - 2) = 0
and 2x - 1 = 0 or x - 2 = 0  and now you can find x.

The last example is solved in the same way.


8 0
3 years ago
Three forces of 300 N in the direction of N30E, 400N in the direction of N60E and
andreyandreev [35.5K]

Split up each force into horizontal and vertical components.

• 300 N at N30°E :

(300 N) (cos(30°) i + sin(30°) j)

• 400 N at N60°E :

(400 N) (cos(60°) i + sin(60°) j)

• 500 N at N80°E :

(500 N) (cos(80°) i + sin(80°) j)

The resultant force is the sum of these forces,

∑ F = (300 cos(30°) + 400 cos(60°) + 500 cos(80°)) i

… … …  + (300 sin(30°) + 400 sin(60°) + 500 sin(80°)) j N

∑ F ≈ (546.632 i + 988.814 j) N

so ∑ F has a magnitude of approximately 1129.85 N and points in the direction of approximately N61.0655°E.

4 0
2 years ago
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