Astore has sales of $500 in their first month. if sales increase at a rate of $10 each month, they can be modeled by this equation: an=500+(k-1)10 use summation notation to model and evaluate the sales for the first ten years. explain your steps.

131,400$

Step-by-step explanation:

The sale for first  month is $500.

The sale increases by $10 each month, as modelled by the equation:

a_k=500+(k-1)10

where, k = 1 (first month)

k = 2 (second month)

and so on.

we have to calculate the sale for the first 10 years, that means for 10*12 = 120 months (1 year = 12 months)

Total sales = ∑ a_k

∑ a_k = ∑ (500+(k-1)10)

= 500k + ∑ (10k - 10)

= 500k + 10∑k - 10k

= 490k + 10∑k

= 490k + 10 {k*(k+1)/2}

= 490k + 5{k*(k+1)}

= 490k + 5k^2 + 5k

= 5k^2 + 495k

∴∑ a_k = 5k^2 + 495k

For calculating the total sales of 10 years, we will put the value of k = 120 (120th month after the first month)

= 5*(120*120) + 495*120

= 72,000 + 59, 400

= 131,400$

ab: 2 n83b8eb7ebi. 8e yen in

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .