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Pachacha [2.7K]
3 years ago
10

Which is equivalent to this expression (z+6)(2z^2+3z+5)

Mathematics
1 answer:
iVinArrow [24]3 years ago
5 0
(z + 6)(2z^2 + 3z + 5) = z(2z^2 + 3z + 5) + 6(2z^2 + 3z + 5) = 2z^3 + 3z^2 + 5z + 12z^2 + 18z + 30 = 2z^3 + 15z^2 + 23z + 30
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Write the explicit formula for the geometric sequence.
Savatey [412]

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 4 gives the next term. In other words:

 an = a1 * r ^ (n-1)

Now, knowing that a1 = 2, and r = 4

We check

a2 = 2 * 4 ^ (2-1) = 2 * (4 ^ 1) = 8

a3 = 2 * 4 ^ (3-1) = 2 * (4 ^ 2) = 32

a4 = 2 * 4 ^ (4-1) = 2 * (4 ^ 3) = 128

Therefore, this is the geometric function that this sequence fulfills.

5 0
4 years ago
How many days in 50 years
hodyreva [135]
We know what every year has 365 but once every four years has 366. We can simplify it by saying that every year has 365 and 1/4 days
Now, we just have to mulitiply 365 \frac{1}{4} *50=18262.5

So we can say that 50 years have 18262 days and chance to 18263 (depends when we started counting)
7 0
3 years ago
Read 2 more answers
Write a polynomial f(x) that satisfies the given conditions.
patriot [66]

Answer:

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

Step-by-step explanation:

Recall, if we have a polynomial of the form (x-a)^k \cdot (x-b)^m, then we say that a is a zero of multiplicity k and b is a zero of multiplicty m. For example, in the polynomial of the form (x+5)^10(x-2)^3 -5 is a zero of multiplicity 10 and 2 is a zero of multiplicity 3. If we want to know the degree of the polynomial,  just add the multiplicity of both zeros (13 in our example).

In this case, we know that the degree of our polynomial should be at least 3(multiplicity 2 and multiplicity 1). So, lets take the polynomial of the form

f(x)=(x-a)(x-b)^2).

In here, a is a zero with multiplicity 1 and b is a zero with multiplicity 2. We are also given that

f(0) = -1 = (0-a)(0-b)^2 = -a\codt b^2.

Which implies that 1 = a\cdot b^2. Since the square of any number is a positive number, it must happen that a>0. So, we have that

b= \pm \sqrt[]{\frac{1}{a}}.

We can choose any value of a and solve for b. Let us choose a=4. So we can have b=1/2 or b=-1/2. Let's use b=1/2. So our polynomial would be

f(x) = (x-4)(x-\frac{1}{2})^2 = x^3-5x^2+4.25x -1

which we can easily check that f(0)=-1.

6 0
4 years ago
Solve for 2.
Step2247 [10]

Answer:

(3x – 6)(-x + 3) = 0

=> 3x - 6 = 0 => x = 6/3 = 2

and

=> -x + 3 = 0 => x = 3

Hope this helps!

:)

5 0
3 years ago
Can you please help me answer questions 1-6 thank you
Veseljchak [2.6K]
3. Divide by 5
4. Add 12
5. Multiplying by -8
6.subtracting by -6
3 0
3 years ago
Read 2 more answers
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