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olganol [36]
3 years ago
12

Find the explicit formula for the sequence: 2,5,8,11,14

Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
4 0

Step-by-step explanation:

Given sequence is: 2,5,8,11,14

Here first term a = 2

Common Difference d = 3

\because \:  t_n = a +(n-1) d \\  \\  \therefore \: t_n = 2+(n-1) 3 \\  \\ \therefore \: t_n = 2+3n- 3 \\  \\  \huge \purple{ \boxed{\therefore \: t_n = 3n- 1}} \\  is \: the \: required \: explicit \: formula\\

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7,854,000

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What system of linear inequalities is shown in the graph?<br><br> Enter your answers in the boxes.
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Y > = -1/2x + 2
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Which ordered pairs are solutions to the inequality 2x+y&gt;−4?
hichkok12 [17]

we will proceed to resolve each case to determine the solution

we have

2x+y>-4

y>-2x-4

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

<u>case a)</u> (5,-12)

Substitute the value of x and y in the inequality

-12>-2*5-4

-12>-14 ------> is True

therefore

the ordered pair (5,-12) is a solution of the inequality

<u>case b)</u> (-3,0)

Substitute the value of x and y in the inequality

0>-2*-3-4

0>2 ------> is False

therefore

the ordered pair (-3,0) is not a solution of the inequality

<u>case c)</u> (-1,-1)

Substitute the value of x and y in the inequality

-1>-2*-1-4

-1>-2 ------> is True

therefore

the ordered pair(-1,-1) is a solution of the inequality

<u>case d)</u> (0,1)

Substitute the value of x and y in the inequality

1>-2*0-4

1>-4 ------> is True

therefore

the ordered pair (0,1) is a solution of the inequality

<u>case e)</u> (4,-12)

Substitute the value of x and y in the inequality

-12>-2*4-4

-12>-12 ------> is False

therefore

the ordered pair (4,-12) is not a solution of the inequality

<u>Verify</u>

using a graphing tool

see the attached figure

the solution is the shaded  area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality


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