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Insert 6 arthematic mean between 5 and -9

astraxan [27]

Answer:

see explanation

Step-by-step explanation:

Consider 5 and - 9 to be terms in an arithmetic sequence and we require to find the 6 terms between them.

The n th term of an arithmetic sequence is

$a_{n}$ = a + (n - 1)d ← d is required

Here a = 5 and $a_{8}$ = - 9, hence

5 + 7d = - 9 ( subtract 5 from both terms )

7d = - 14 ( divide both sides by 7 )

d = - 2

---------------------------------------------------------

The terms in the sequence are

5, 5 - 2, 5 - 4, 5 - 6, 5 - 8, 5 - 10, 5 - 12, - 9 , that is

5, 3, 1, - 1, - 3, - 5, - 7, -9

With the 6 arithmetic means being

3, 1, - 1, - 3, - 5, - 7

5 0

3 years ago

In simplest form …..

777dan777 [17]

Answer:

2 $\sqrt[3]{2}$

Step-by-step explanation:

$\sqrt[3]{54} - \sqrt[3]{2}$

$\sqrt[3]{2 * 3 * 3 * 3}$ - $\sqrt[3]{2}$ Prime factorization.

$3\sqrt[3]{2}$ - $\sqrt[3]{2}$ Simplify the radical.

2 $\sqrt[3]{2}$ Subtract.

8 0

3 years ago

Use a graphing calculator to solve the equation 3 tan 1/3 (theta) =8 in the interval 2 to pie.

abruzzese [7]

The answer to this may be C

3 0

3 years ago

Graph the system of inequalities presented here then use your graph to answer the following questions:

Nookie1986 [14]

Answer:

Part A) The graph in the attached figure (see the explanation)

Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

Step-by-step explanation:

Part 1) Graph the system of inequalities

we have

$y> 5x+5$ ----> inequality A

The solution of the inequality A is the shaded area above the dashed line $y=5x+5$

The slope pf the dashed line A is positive m=5

The y-intercept of the dashed line A is (0,5)

The x-intercept of the dashed line A is (-1,0)

$y>-\frac{1}{2}x+1$ ----> inequality B

The solution of the inequality B is the shaded area above the dashed line $y=-\frac{1}{2}x+1$

The slope pf the dashed line B is negative m=-1/2

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (2,0)

The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B

using a graphing tool

see the attached figure

Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

substitute the value of x and the value of y in each inequality

For x=-2, y=5

Verify inequality A

$5>5(-2)+5$

$5>-5$ ---> is true

so

The ordered pair satisfy inequality A

Verify inequality B

$5>-\frac{1}{2}(-2)+1$

$5>2$ ---> is true

so

The ordered pair satisfy inequality B

therefore

The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)

6 0

3 years ago

What does b stand for 11.3 > b/4.3 (Please show explanation)

lilavasa [31]

$11.3 > \frac{b}{4.3} \\ = >11.3 \times 4.3 > b \\ = > 48.59 > b$

Answer:

b < 48.59

Hope you could understand .

If you have any query, feel free to ask and sorry for my previous answer.

3 0

2 years ago