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2 years ago

How to factorise 9a^2bc^3 -27abc

Mathematics

1 answer:

olga2289 [7]2 years ago

3 0

Answer:

9abc(ac² - 3)

Step-by-step explanation:

Given polynomial:

9a²bc³ -27abc

Factors of the terms:

9a²bc³ = 3*3*a*a*b*c*c*c
27abc = 3*3*3*a*b*c

Common factors of the above:

3*3*a*b*c= 9abc

So the answer:

9a²bc³ -27abc = 9abc(ac² - 3)

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What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?

Anestetic [448]

Answer:

-12

Step-by-step explanation:

Let b = -1 and a = -3

The average rate of change = $\frac{f(b) - f(a)}{b - a}$

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

$\frac{f(b) - f(a)}{b - a}$ = -24/2 = -12

4 0

2 years ago

Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37

Mandarinka [93]

Answer:

The general rule is $a_n = -2 - 5(n-1)$

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

$a_{n} = a_1 + (n-1)d$

In which $a_1$ is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

$a_n = a_m + (n-m)d$

a3 = -12 and a8 = -37

First we find the common difference. So

$a_n = a_m + (n-m)d$

$a_8 = a_3 + (8-3)d$

$-37 = -12 + 5d$

$5d = -25$

$d = -\frac{25}{5}$

$d = -5$

$a_n = a_1 - 5(n-1)$

Finding the first term:

$a_n = a_1 - 5(n-1)$

Since $a_3 = -12$

$a_n = a_1 - 5(n-1)$

$a_3 = a_1 - 5(3-1)$

$a_1 = a_3 + 10 = -12 + 10 = -2$

So the general rule is:

$a_n = a_1 - 5(n-1)$

$a_n = -2 - 5(n-1)$

6 0

2 years ago

The ends of a pipe when measured with a tape measure that has marks every millimeter are exactly at the 0 mark and the 15 meter

exis [7]

If the ends span from the 0 to the 15 meter mark, then the length of the pipe is 15 meters. However, you should report it using the right amount of significant figures. It is mentioned in the problem that millimeter marks are calibrated between meters. Since millimeter is 1/1000 of a meter, you should add three decimal places to the 15 meters. Hence, you should report it as 15.000 meters.

3 0

3 years ago

Help me please help with this problem

vodomira [7]

It would be x=-4 have a good day

5 0

3 years ago

Given that F(x) = x2 + 2, evaluate F(1) + F(5).

gavmur [86]

Answer:

F(1)+F(5)= 30

Step-by-step explanation:

F(1)=1^2+2=1+2=3

F(5)=5^2+2=25+2=27

27+3=30

6 0

3 years ago