This goes up at a constant number between values, making it an arthmetic sequence. The first number is 2, with a difference of 3. Plugging this into the arithmetic equation you get A_n = 2 + 3 (n – 1). Plugging in 20 for n, you get a value of 59.

Looking at the sequence you can see that it doubles each term, making it a geometric sequence. Since it doubles r = 2 and the first term is 5. Plugging this into the geometric equation you get A_n = 5(2)^n–1. Setting n = 6, you get 160 as the 6th term.

The zeroes of the equation are where f(x) = 0 (aka x-intercepts). Setting the equation equal to zero you get x² = 9. Since a square makes a negative number positive, x can be equal to 3 or –3.

In order to solve for the x value you set both equations equal to each other (0.5x+3=3x-2). This gives you the x value for the point of intersection at x=2. Plugging x=2 into either equation gives you y=4.

Tommy's current age is represented by t, and Sara's is represented by s. In five years, both Tommy's and Sara's ages will be increased by five. Thus, in five years, we can represent Tommy's age as and Sara's as .

The problem tells us that Tommy's age in five years will be twice as great as Sara's in five years. Thus, we can write an algebraic expression to represent the problem as follows:

In order to solve for t, first simplify the right side by distributing the 2.

Then subtract 5 from both sides.

The answer is .

First we need the area or the rectangle. 24 * 8 = 192. So now we know that 10 gallons will cover 75 ft² and x gallons will cover 192 ft². We set up a simple ratio and cross multiply to find that 75x = 1920.

x = 25.6

The best way to solve this problem is to translate it into an equation, "decreased" meaning subtract and "increased" meaning add:

x – 7 = 10 + 7

x = 24

First find 2%3 = (2 * 3 + 3 * 2)/(6 * 2 * 3) = 12/36 = 1/3, then 3%2 = (2 * 2 + 3 * 3)/(6 * 3 * 2) = 13/36 which is greater.

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2x = 10

First, we need to find the possible values of k such that f(k) = 0.

We can use the definition of f(x) to write an expression for k.

f(x) = 2x³ + 7x² – 4x

f(k) = 2k³ + 7k² – 4k = 0

In order to solve this equation, we will want to factor as much as we can. We can immediately see that we could take out a k from all three terms.

2k³ + 7k² – 4k = 0

k(2k² + 7k – 4) = 0

Now, we need to factor 2k² + 7k – 4 by grouping. When we multiply the outer two coefficients we get (2)(–4) = –8. The middle coefficient is 7. This means we need to think of two numbers that multiply to give us –8, but add to give us 7. These two numbers are 8 and –1. We can now rewrite 2k² + 7k – 4 as follows:

2k² + 7k – 4 = 2k² + 8k – k – 4

Group the first two terms and the second two terms.

2k² + 8k – k – 4 = (2k² + 8k ) + (–k – 4)

Next, factor out a 2k from the first two terms and a –1 from the last two terms.

(2k² + 8k ) + (–k – 4) = 2k(k + 4) + –1(k + 4)

Then, factor out k + 4 from the 2k and the –1.

2k(k + 4) + –1(k + 4) = (k + 4)(2k – 1)

Thus, 2k² + 7k – 4, when fully factored, equals (k + 4)(2k – 1).

Now, let's go back to the equation k(2k² + 7k – 4) = 0 and substitute (k + 4)(2k – 1) for 2k² + 7k – 4.

k(2k² + 7k – 4) = k(k + 4)(2k – 1) = 0

We now have three factors, and we can set each equal to zero to find the possible values of k.

The first factor is k. This means k = 0 is one value for k.

The next factor is k + 4.

k + 4 = 0

k = –4

The last factor is 2k – 1.

2k – 1 = 0

2k = 1

k = 1/2

The values of k for which f(k) = 0 are 0, –4, and 1/2. However, we are told that k is positive, so this means that k can only be 1/2.

Ultimately, the problem asks us to find g(k). This means we must use the equation for g(x) to find g(1/2).

g(x) = 4x – x³

g(1/2) = 4(1/2) – (1/2)³

= 2 – (1/8)

= 15/8

The answer is 15/8.