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3 years ago

A recursive rule for the arithmetic sequence is a1=-3;an=an-1+7

1 answer:

8 0

The explicit rule for any arithmetic sequence is:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case a=-3 and d=7 so:

a(n)=-3+7(n-1)

a(n)=-3+7n-7

a(n)=7n-10

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5. Find the value(s) of x so that the line containing the points (2x + 3, x + 2) and (0, 2) is

Dvinal [7]

Answer:

x = -2 or -9

Step-by-step explanation:

You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).

<h3>Slope</h3>

The slope of a line is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

Using the formula, the slopes of the two lines are ...

m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)

and

m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)

<h3>Perpendicular lines</h3>

The slopes of perpendicular lines have product of -1:

$\dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}$

<h3>Solutions</h3>

The values of x that satisfy this equation are x = -2 and x = -9. The attached graphs show the lines for each of these cases.

4 0

1 year ago

0.005 ___ 0.05 < > = thanks :>

irinina [24]

0.005 >  0.05

<h2>hope it helps!</h2>

4 0

2 years ago

Read 2 more answers

You operate a gaming website, www.mudbeast.net, where users must pay a small fee to log on. When you charged $4 the demand was 5

sertanlavr [38]

A) Demand function

price (x)          demand (D(x))

4                      540

3.50                  810

D - 540          810 - 540
----------- = -----------------
x - 4               3.50 - 4

D - 540
----------- = - 540
x - 4

D - 540 = - 540(x - 4)

D = -540x + 2160 + 540

D = 2700 - 540x

D(x) = 2700 - 540x

Revenue function, R(x)

R(x) = price * demand = x * D(x)

R(x) = x* (2700 - 540x) = 2700x - 540x^2

b) Profit, P(x)

profit = revenue - cost

P(x) = R(x) - 30

P(x) = [2700x - 540x^2] - 30

P(x) = 2700x - 540x^2 - 30

Largest possible profit => vertex of the parabola

vertex of 2700x - 540x^2 - 30

When you calculate the vertex you find x = 5 /2

=> P(x) = 3345

Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.

5 0

3 years ago

Here are the ingredients for a cake. 0.225 kg butter 225 g sugar 225 g flour 0.2 kg eggs 250 g berries How much do the ingredien

viktelen [127]

Answer:

1125.

Step-by-step explanation:

I'm going to work out the answer is grams.

1kg = 1000g

0.225kg of butter = 225g, 225g of sugar, 225g of flour, 0.2kg of eggs = 200g, 250g of berries.

225 + 225 + 225 + 200 +250 = 1125.

Hope that helps. x

5 0

2 years ago

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A store has 2 times as hooded sweatshirt as crewneck sweatshirts. The total number of sweatshirts is 36. How many hooded sweatsh

svlad2 [7]

Answer:

Answer below

Step-by-step explanation:

It would be 36×2=72

since we're doubl8ng it so there would be 72 hooded sweatshirts

6 0

3 years ago

Read 2 more answers