Identify the common difference in the arithmetic sequence: 21, 15, 9, 3, -3, ...

Bob and Kathy want to save a total of $500,000 for retirement. Using the present value of a periodic deposit formula, how much s

victus00 [196]

The answer is $1,051.17 if I’m not mistaken

8 0

3 years ago

How do the lengths of line segments define the golden ratio?

NISA [10]

Answer:

$\frac{a+b}{a}=\frac{a}{b}$

Step-by-step explanation:

The golden ratio is a special number favored by the Greeks. Its ratio roughly equals 1.618. The ratio is formed by taking a line segment and dividing it into two parts labeled a and b. The golden ratio is formed when this proportion is true $\frac{a+b}{a}=\frac{a}{b}$ .

When you add a and b then divide by a, it will be the same as a divided by b. This will hold true only for specific lengths of a and b. This means you must divide the line segment in such a way that a and b meet this requirement.

Example:

If the line segment is 50 cm long. Split the segment into parts a and b where a = 30.9 and b = 19.1. Substitute the values into the proportion $\frac{a+b}{a}=\frac{a}{b}$ .

$\frac{30.9+19.1}{30.9}=\frac{30.9}{19.1}$

$\frac{50}{30.9}=\frac{30.9}{19.1}$

1.618 = 1.618

This is the golden ratio.

5 0

4 years ago

Please help explanation if possible

stira [4]

Answer:

$y = 2x + 7$

Step-by-step explanation:

Use Point Slope Form since we are given the slope and coordinates. Why is the slope 2x?

 In Depth: Parallel lines never touch so they are Lines that have same slope but different y intercept. An example is a square. A square has four parallel sides. The upper and lower sides will never touch because they are the same slope and they both have a finite distance vertically between them.

Back to the question, let use the Point Slope Form,

$y - y_{1} = m(x - x_{1})$

Where y1 is the y coordinate of the given point, m is the slope and x is the x coordinates of the given points.

Substitute

$y - ( - 1) = 2(x - ( - 4)$

$y + 1 = 2(x + 4)$

Simplify

$y + 1 = 2x + 8$

$y = 2x + 7$

4 0

3 years ago

HELP FAST PLEASE

gayaneshka [121]

Answer:

ok well your answer would be postive

Step-by-step explanation:

because it would go up the more you sell andlets say you didnt sell at lot to would be postive then slowly drift to negtive

5 0

3 years ago

Anybody know the correct answer?

earnstyle [38]

Since $\csc^2{x}=\frac{1}{\sin^2{x}}$ and $\cot^2{x}=\frac{\cos^2{x}}{\sin^2{x}}$ , we can rewrite the right side of the equation as

$\frac{1}{\sin^2{x}}-\frac{\cos^2{x}}{\sin^2{x}} =\frac{1-\cos^2{x}}{\sin^2{x}}$

Using the identity $\sin^2{x}+\cos^2{x}=1$ , we can subtract $\cos^2{x}$ from either side to obtain the identity $\sin^2{x}=1-\cos^2{x}$

substituting that into our previous expression, the right side of our equation simply becomes

$\frac{\sin^2{x}}{\sin^2{x}}=1$

We can now write our whole equation as

$3\tan^2{x}-2=1$

Adding 2 to both sides:

$3\tan^2{x}=3$

dividing both sides by 3:

$\tan^2{x}=1$

$\tan{x}=\pm1$

When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4

4 0

3 years ago