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muminat
4 years ago
12

Veronica got 3 times as many gifts as Natalie. Together Veronica and Natalie got a total of 12 gifts how many gifts did Natalie

(x) and Veronica (y) each get
Mathematics
1 answer:
fenix001 [56]4 years ago
5 0
The equation we'll use for this is:Total Gifts = Veronica's Gifts (v) + Natalie's Gifts (n).
12 = v + n
The problem says Veronica got 3 times as many gifts as Natalie.
You can directly translate this into an equation!
v = 3 * n = 3n.  This means we can replace any v with 3n.
So, 12 = v + n = 3n + n = 4n
12 = 4n
3 = n.  Natalie got 3 gifts.
We can now plug back in for Veronica's gifts:
v = 3n
v = 3(3)
v = 9.  Veronica got 9 gifts.
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3 0
4 years ago
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Factorize x^3-10x^2-53x-42
pochemuha

Answer:

(x+1)(x-14)(x+3)

Step-by-step explanation:

The first step in factorising polynomials is to find the smallest factor first. The way to do this is with trial and error. Lets see if x+1 is a factor.

According to the factor theorem, (x-a) is a factor of P(x) if and only when P(a) = 0

In this case we will use f(x) = ((x)^3)-((10x)^2)-53x-42

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Therefore (x+1) is a factor of the polynomial.

Now we divide the polynomial with (x+1) via long division to get (x^2)-11x-42.

We now factorise (x^2)-11x-42 using whatever method you would like. I'm going to use the AC method, where we find a number that multiplies to AC and adds to B, In this case AC = -42, and B = -11.

Therefore (x^2)-11x-42 factosied is (x-14)(x+3)

Now merge (x+1) with (x-14)(x+3)

The final answer is (x+1)(x-14)(x+3)

If this has helped, please consider making this the Brainliest answer!

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3 years ago
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