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3 years ago

In an arithmetic sequence, a1=5 and a6=-5. Determine an equation for an, the nth term of this sequence.

Mathematics

1 answer:

GalinKa [24]3 years ago

6 0

Answer: 7 - 2n

Step-by-step explanation:

a1 = 5

a6 = -5 = a + (n - 1)d = a + (6 - 1)d

a + 5d = -5

Since a1 = 5

5 + 5d = -5

5d = -5 - 5

5d = -10

d = -10/5

d = -2

Therefore, the equation to calculate the nth term of this sequence will be:

= a + (n-1)d

= a + (n - 1)-2

= 5 -2n +2

= 7 - 2n

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What is the inverse of the function y= x^2-12

aalyn [17]

Answer:

$y=\sqrt{x+12}$

Step-by-step explanation:

To find the inverse of a function, what I like to do is to switch the places of x and y, and then try to isolate y again like so:

$x=y^2-12$

$x+12=y^2$

$y=\sqrt{x+12}$

Hope this helps!

7 0

3 years ago

A principal of $3600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 6 years?

zaharov [31]

After 6 years the investment is $5555.88

Step-by-step explanation:

A principal of $3600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 6 years?

The formula used to find future value is:

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

where A(t) = Accumulated amount

P = Principal Amount

r = annual rate

t= time

n= compounding periods per year

We are given:

P = $3600

r = 7.5 %

t = 6

n = 1

Putting values in formula:

$A(t)=P(1+\frac{r}{n})^{nt}\\A(t)=3600(1+\frac{0.075}{1})^{6*1}\\A(t)=3600(\frac{1.075}{1})^6\\A(t)=3600(1.075)^6\\A(t)=3600(1.543)\\A(t)=5555.88$

So, After 6 years the investment is $5555.88

Keywords: Compound Interest formula

Learn more about Compound Interest formula at:

#learnwithBrainly

8 0

3 years ago

Angela earns $11.50 per hour. If she works more than 40 hours a week she earns double time. This week she worked a total of 48 h

WARRIOR [948]

Answer:

11.50 x 40 regular hours is $460

double time is 11.50 x 2 = $23 an hour

She makes $23 an hour for 8 hours = $184

$460 + $184 = $644 paycheck

5 0

3 years ago

If anyone knows how to do this please help, its for a test and I have to finish the course by 11:59 tonight

abruzzese [7]

The correct answer would be c. hope this helps

3 0

3 years ago

Read 2 more answers

What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?

Bess [88]

Answer:

(4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

4 0

2 years ago