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Shalnov [3]
3 years ago
7

Write an equation to represent the N'th term of the sequence (2,-1.-4,-7,...)

Mathematics
1 answer:
mr_godi [17]3 years ago
7 0

Answer: a(n) = 5 - 3n

the sequence has:

a1 = 2

a2 = -1

a3 = -7

.........

we can see that: a2 - a1 = a3 - a2 = -3

=> the sequence is a  arithmetic sequence

=> the distance between the numbers is d = -3

because this sequence is a  arithmetic sequence

=> a(n) = a1 + (n - 1)d = 2 + (n - 1).(-3) = 5 - 3n

Step-by-step explanation:

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A portion of the graph of f(x) = −x2 − 2x + 8 is shown. Which of the following describes all solutions for f(x)?
Naily [24]

Answer:

(x,-x^2-2x+8) where −5 ≤ x ≤ 3

Step-by-step explanation:

The given function is f(x)=-x^2-2x+8.

We want to select the option that describes all the solutions to the parabola.

The domain of the parabola is −5 ≤ x ≤ 3.

This means that  any x=a on −5 ≤ x ≤ 3 that satisfies (a,f(a)), is a solution.

This can be rewritten as (a,-a^2-2a+8)

Therefore for x belonging to −5 ≤ x ≤ 3, all solutions are given by:

(x,-x^2-2x+8) where −5 ≤ x ≤ 3.

7 0
4 years ago
Make the indicated trigonometric substitution in the given algebraic expression and simplify(x-25)/x = Sin y0
Strike441 [17]

Answer:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

Step-by-step explanation:

Let's solve and simplify for x,

(x − 25 )/ x  = sin(y)

Let's multiply both sides by x

((x − 25 )/x) *x= sin(y)*x

Then,

x − 25 = sin(y) * x

Let's add 25 to both sides

x − 25 + 25 = sin(y) * x + 25

If simplify again,

x = sin(y) * x + 25

Then we need subtract sin y x from both sides

x − sin(y) * x = sin (y)* x + 25 − sin (y)* x

It will equal:

x − sin (y)* x = 25

Factor x−sin(y) x: x(1−sin(y) ), then we get:

x (1 − sin(y)) = 25

Finally we need divide both sides by 1 − sin(y) ; y ≠π /2 + 2πn

And it will give us this equation:

x = 25 /(1 − sin(y )) and y ≠ π/2  +2πn

3 0
4 years ago
Given A(-3,6) and B(5,-6) find the distance and midpoint between each
xenn [34]
14.42 is your distance formula 
(1,0) is the midpoint 
if you need the forma for distance it is x2-x1 squared + y2-y1 squared then square root it 
7 0
4 years ago
Read 2 more answers
What is the product of 5/12 x 3
Sliva [168]
5/12 x 3/1 = 15/12 = 1 3/12
Simplified
1 1/4
Not simplified
1 3/12
4 0
3 years ago
The amount of water in a lake decreased by 12.8 feet over the last 4 weeks. How much did the water level change by each week?
Keith_Richards [23]

Answer:

3.2 feet.

Step-by-step explanation:

Since the total amount of water that was decreased is equal to 12.8, we would divide it by 4 to see how much it decreased in 1 week assuming it was constant. So, 12.8 divided by 4 is 3.2.

8 0
3 years ago
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