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2 years ago

Find a formula for the nth term in this

Mathematics

2 answers:

amm18122 years ago

6 0

The formula for the nth term in this arithmetic sequence is:

-3n + 10

Eva8 [605]2 years ago

3 0

Answer:

$a_{n} = -3n + 10$

Step-by-step explanation:

The arithmentic function formula is:

$a_{n} = a_{1} + d(n-1)$

Let's plug in what we know. $a_{1}$ (the first term in our sequence) is 7. d (the common difference) is -3. This means we are subtracting 3 every time.

Plugging that in to the formula, we get

$a_{n} = 7 -3(n-1)$

Now we distribute and combine like terms.

$a_{n} = 7 - 3n +3$

$a_{n} = 10 - 3n$

Change the order to fit the format and you get

$a_{n} = -3n + 10$

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On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.

$P(x,y)$ - Original point.

$k$ - Scale factor.

$P'(x,y)$ - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

( $P(x,y) = (10, 40)$ , $Q(x,y) = (70, 120)$ , $O(x,y) = (0,0)$ , $k = 5$ )

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$

$P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]$

$P'(x,y) = (50,200)$

$Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]$

$Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]$

$Q'(x,y) = (350, 600)$

Then, the length of the resulting segment is determined by following Pythagorean identity:

$l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}$

$l_{P'Q'} = 500$

The length of the resulting segment is 500.

3 0

3 years ago

Which of the following phrases are inequalities?

Wewaii [24]

Answer:

11 > (w- 4)

y < 3

5 + 9 < 5.9

So these are the phrases which are inequalities.

6 0

4 years ago

Find the values of X and Y.

Natasha_Volkova [10]

Answer:

x = 90°

y = 43°

Step-by-step explanation:

We know that one angle equals 47°.

The two triangles are right triangles, so that makes x = 90°.

To find y, we add 90 + 47.

That would give us 137°.

All triangles add up to 180°.

180 - 137 = 43.

43° is the answer.

3 0

4 years ago

Read 2 more answers

A radio station had 228 tickets to a concert. They gave away 5 times as many tickets to listeners as to employees. How many tick

malfutka [58]

So you start off with 228 tickets. The listeners got 5 times the amount that the employees got. So the listeners plus the employees equals 228 which is your starting amount. So you have to plug in each answer to the equation 5x + y = 228 , the x being listeners and the y being the employees. You use the answer choice for the x and y and plug them in and solve until your answer becomes true. I hope that explains it as well as my picture

6 0

3 years ago

A retail outlet for calculators sells 900 calculators per year. It costs $2 to store one calculator for a year. To reorder, th

Rus_ich [418]

Answer:

In order to minimize cost the outlet must order 60 units 15 times a year.

Explanation:

Theoretically, the EOQ is the optimal order quantity that a firm should purchase in order to minimize its inventory costs (holding costs are included here), and costs of placing an order.

Mathematically:

EOQ= $\sqrt{2SD} /H$

Where:

D= demand

S= cost of placing an order.

H= holding cost (per unit and per year).

In the statement, we identify each of these values:

D= 900

S= 4

H= $2

EOQ= $\sqrt{2SD} /H$ =√2*4*900/2= 60

Times per year= 900/60= 15

5 0

3 years ago