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3 years ago

What are the first four terms in tn=3n+2

1 answer:

3 0

For this question we are looking at arithmetic sequences. A sequence is any set of numbers in a particular order. An arithmetic sequence is a specific type of sequence where the difference between 2 consecutive terms is constant. The difference is called the common difference. In your problem...

t_n = 3n + 2

we need to find the common difference, then we can find the 1st four terms. Find the 1st term by replacing n with 1.

t_1 = 3(1) +2
t_1 = 3 +2 = 5

Find the second term by replacing n with 2

t_2 = 3(2) + 2 = 8

and so on

t_3 = 3(3) + 2 = 11

t_4 = 3(4) + 2 = 14

The 1st 4 numbers in the sequence are 5,8,11, and 14.

You can see the common difference is d=3. You could plug any number into the equation to find that number in the sequence. For example, the 100th number in the sequence would be

t_100 = 3(100) + 2 = 302

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Y=−4x−3 y=−2x+1 solve by graphing

Effectus [21]

Answer: (-2,5)

Step-by-step explanation: just graph both equations they are already set up in the form and find the point where they intersect

5 0

3 years ago

Read 2 more answers

4. Find the volume of the figure. The base is a square.

GREYUIT [131]

Answer:

A) 283500 ft³

B) 1057.26 π in³

Step-by-step explanation:

A) Volume of square based pyramid

= 1/3 × Area of the base × height

= 1/3 × (90 ft)² × 105 ft

= 283500 ft³

B) This figure is a composite figure

Step 1

Find the volume of the cone

=1/3 πr²h

r = radius = 8.5 in

h = height = 10 in

= 1/3 × π × (8.5 in)² × 10 in

= 240.83333333 π in³

≈ 240.83 π in³

Step 2

Find the volume of the cylinder

= πr²h

= r = radius = 8.5 in

h = height = 11.3 in

= π × (8.5 in)² × 11.3 in

= 816.425 π in³

≈ 816.43π in³

Volume of the figure = (240.83 π + 816.43 π) in³

= 1057.26 π in³

7 0

3 years ago

Pls help I’ll add extra points

Readme [11.4K]

Answer:

Step-by-step explanation:

4 0

2 years ago

Which system of linear inequalities has the point (3, –2) in its solution set? y less-than negative 3. y less-than-or-equal-to t

xxTIMURxx [149]

Answer:

$y > -3$ and $y \geq \frac{2}{3}x- 4$

Step-by-step explanation:

<u>The complete question is</u>

Which system of linear inequalities has the point (3,-2) in its solution set?

y < -3

y ≤ 2/3x - 4

y > -3

y ≥ 2/3x - 4

y < -3

y ≥ 2/3x - 4

y > -2

y ≤ 2/3x - 4

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

<em>Verify each case</em>

Case A) we have

$y < -3$ ----> inequality A

$y \leq \frac{2}{3}x- 4$ ----> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

$-2< -3$ ----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

$y > -3$ ----> inequality A

$y \geq \frac{2}{3}x- 4$ ----> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

$-2< -3$ ----> is true

Inequality B

$-2 \geq \frac{2}{3} (3)-4$

$-2\geq -2$ ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

$y< -3$ ----> inequality A

$y \geq \frac{2}{3}x- 4$ ----> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

$-2< -3$ ----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

y > -2 ----> inequality A

$y \leq \frac{2}{3}x- 4$ ----> inequality B

Substitute the value of x and y of the point (3,-2) in both inequalities and then compare the results

Inequality A

$-2> -2$ ----> is not true

therefore

The ordered pair is not a solution of the system D

9 0

3 years ago

Here are two similar solid toys.

Fiesta28 [93]

Answer:

13.7

Step-by-step explanation:

7*k²=9

k²=9/7

k=√9/7

k=1.133893419

20/1.133893419³=13.7

5 0

3 years ago