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3 years ago

Which number is an integer, a whole number, and a counting (natural) number? a) 0 b) -1 c) 15 d) 0.5

1 answer:

7 0

C. 15

-1 is not a natural number so B is not your answer

0.5 is not a whole number so D is not your answer

0 is not a natural number so A is not your answer

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Prove that an = 4^n + 2(-1)^nis the solution to

olga nikolaevna [1]

Answer:

See proof below

Step-by-step explanation:

We have to verify that if we substitute $a_n=4^n+2(-1)^n$ in the equation $a_n=3a_{n-1}+4a_{n-2}$ the equality is true.

Let's substitute first in the right hand side:

$3a_{n-1}+4a_{n-2}=3(4^{n-1}+2(-1)^{n-1})+4(4^{n-2}+2(-1)^{n-2})$

Now we use the distributive laws. Also, note that $(-1)^{n-1}=\frac{1}{-1}(-1)^n=(-1)(-1)^{n}$ (this also works when the power is n-2).

$=3(4^{n-1})+6(-1)^{n-1}+4(4^{n-2})+8(-1)^{n-2}$

$=3(4^{n-1})+(-1)(6)(-1)^{n}+4^{n-1}+(-1)^2(8)(-1)^{n}$

$=4(4^{n-1})-6(-1)^{n}+8(-1)^{n}=4^n+2(-1)^n=a_n$

then the sequence solves the recurrence relation.

4 0

3 years ago

Calculate the size of each interior angle of a regular polygon with 14 sides

Ierofanga [76]

Answer:

154.285

Step-by-step explanation:

The sum of the interior angles of a 14-gon = (14-2)*180 = 2,160 degrees. There are 14 vertexes (vertices) for a 14-gon. It is 'regular' so all these angles are equal. By dividing 2160 (sum of all angles) by 14 (total amount of angles) we can see how much each angle is worth. So the interior angle of each is 154.285 degrees.

4 0

3 years ago

Simplify completely. (w^15/w^5)^4 <br> HELP PLEASE

Umnica [9.8K]

Answer:

$w^{40}$

Step-by-step explanation:

To simplify recall exponent rules:

1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.

2. When we multiply terms with the same bases, we add exponents.

3. When we divide terms with the same bases, we subtract exponents.

4. When we have a base to the exponent of 0, it is 1.

5. A negative exponent creates a fraction.

6. When we raise an exponent to an exponent, we multiply exponents.

7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.

We will use these rules to simplify.

Use rule #3 to simplify inside the parenthesis first.

$\frac{w^{15}}{w^5} = w^{10}$

Now simplify the exponent of 4 using rule 6.

$(w^{10})^4 = w^{40}$

8 0

3 years ago

If angle B is two more than three times the measure of angle C, and angle B are

GalinKa [24]

Set up a system of equations:

B=2+3C

B+C=90

The variable B is already solved, so plug into bottom equation:

2+3C+C=90

2+4C=90

4C=88

C=22

Plug C back in:

B+22=90

B=68

So B is 68 degrees and C is 22 degrees

Hope this helped!

6 0

3 years ago

Solve using the quadratic formula: 2n^2= 6n - 2

bekas [8.4K]

Answer:

$n_1=(3 + 1\sqrt{5} )/2\\\\n_2=(3 - 1\sqrt{5} )/2$

Step-by-step explanation:

$2n^2= 6n - 2\\\\2n^2-6n+2=0\\\\a=2\\\\b=-6\\\\c=2$

$n=(-b \pm \sqrt{b^2-4ac} )/2a\\\\n=(-(-6) \pm \sqrt{(-6)^2-4(2)(2)} )/2(2)\\\\n=(6 \pm \sqrt{36-16} )/4\\\\n=(6 \pm \sqrt{20} )/4\\\\n=(6 \pm 2\sqrt{5} )/4\\\\n=(3 \pm 1\sqrt{5} )/2\\\\n_1=(3 + 1\sqrt{5} )/2\\\\n_2=(3 - 1\sqrt{5} )/2$

3 0

3 years ago