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2 years ago

Algebra 1 please help!

Mathematics

1 answer:

Leona [35]2 years ago

5 0

Answer:

a. geometric

b. an = 2(2)^n-1 or an = 2^n

c. an+1 = an x 2

Step-by-step explanation:

The sequence, 2, 4, 8, 16, 32,...

a. The sequence is geometric because there is a common ratio in the numbers of the sequence. Each number is made by multiplying the common ratio and the previous number.

b. The explicit formula that can be used to find any term is an = 2(2)^n-1 or an = 2^n

Note: the variable n and number 1 is written in italics to show that it should be in subscript

an = a1 (r)n-1

With the common ratio of n being 2 and first number being 2, we have:

an = 2(2)^n-1

an = 2^n

c. The recursive formula for the sequence is an+1 = an x 2

an+1 = an x r

Plugging in the values, we have

an+1 = an x 2

Your welcome, and comment if you have any questions! If you could mark this answer as brainliest, I would appreciate it very much!

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3 years ago

Y=x^2-6x-16 in vertex form

satela [25.4K]

Answer:

$y=(x-3)^{2} -25$

Step-by-step explanation:

The standard form of a quadratic equation is $y=ax^{2} +bx+c$

The vertex form of a quadratic equation is $y=a(x-h)^{2} +k$

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

$h=\frac{-b}{2a}$

In this case, our quadratic equation is $y=x^{2} -6x-16$ . Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

$h=\frac{-b}{2a}$ ⇒ $h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3$

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is $y=x^{2} -6x-16$

$y=x^{2} -6x-16$ ⇒ $y=(3)^{2} -6(3)-16$ ⇒ $y=9-18-16$ ⇒ $y=-25$