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3 years ago

What is the common difference in the arithmetic sequence -3, -1, 1, 3, ...?

Mathematics

1 answer:

blagie [28]3 years ago

7 0

Answer:

Step-by-step explanation:

The common difference in an arithmetic sequence is the difference between any two terms

So, you could start by doing -3 + d = -1

-3 + d = -1

-3 + d +3 = -1 +3

d = 3 -1

d = 2

Now test it with other terms

-1 + d = 1

Substitute

-1 +2 = 1

2 -1 = 1

1 = 1

It works!!!

If you want you can try it with 1 and 3

1 + d = 3

1 + 2 = 3

3 = 3

I hope this helps!!!!

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PolarNik [594]

Answer: A. 70.50

Step-by-step explanation:

So 350*0.11 is 38.50. Add the $32.00 and you get $70.50

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3 years ago

Read 2 more answers

Which system or equation is represented in the graph?

melamori03 [73]

Answer:

$(A)\displaystyle \begin{array} {ccc} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{array}$

Step-by-step explanation:

<h3>Equation of the blue line:</h3>

since the line is horizontal and passes <u>-</u><u>2</u> the equation of the blue line should be

$\displaystyle \large y = - 2$

<h3>Equation of the red line:</h3>

remember The form of equation of a line

$\displaystyle \boxed{ \displaystyle y = mx + b}$

where m is slope of the line and b is the y-intercept we can clearly see that the red line crosses y-axis at (0,-3) therefore b=-3

to figure out m we can consider the following formula:

$\displaystyle m = \frac{ \Delta y}{ \Delta x}$

from the graph we acquire ∆y=1 and ∆x=2

thus substitute:

$\displaystyle m = \frac{ 1}{ 2}$

so we have figured out m and b

therefore our equation of blue line is

$\displaystyle y = \frac{1}{2} x - 3$

our given options are in standard form so

move -3 to left hand side and change its sign:

$\displaystyle y + 3= \frac{1}{2} x$

cross multiplication:

$\displaystyle 2y + 6= x$

move 6 to right hand side and x to left hand side and change its sign

$\displaystyle - x + 2y = - 6$

multiply both sides by -1:

$\displaystyle x - 2y = 6$

hence, our system of linear equation is

$\displaystyle \begin{cases} \displaystyle y = - 2 \\ x - 2y = 6\\ \end{cases}$

3 0

3 years ago

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

$A = P(1 + \frac{r}{n})^{nt}$

In which A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

$A = P(1 + \frac{r}{n})^{nt}$

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

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4 years ago

Wat is 2 and 3 7ths divided by 7

Alchen [17]

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4 years ago

Bobo and the Bouncing Ball Math Problem

leva [86]

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