Which is the correct algebraic expression for each phrase? (Image) Please answer ASAP!

3х + 4 = 9x - 8 What is the value of X to make the equation true?

givi [52]

Answer:

x=2

Step-by-step explanation:

5 0

3 years ago

NEED THE ANSWER PLEASE...

sesenic [268]

Answer:

The correct answer option is D. $\frac { 3 n ^ { 3 } } { 5 m ^ { 2 } }$ .

Step-by-step explanation:

We are given the following expression and we are to simplify it:

$\frac { 3 m ^ { - 2 } } { 5 n ^ { - 3 } }$

Here the variables $m$ and $n$ are having negative powers. So to change these powers from negative to positive, we will take their reciprocals to get:

$\frac { 3 n ^ { 3 } } { 5 m ^ { 2 } }$

7 0

3 years ago

Read 2 more answers

(5) Rewrite the integral Z 1 0 Z x 0 Z √ 1−x2 0 z dz dy dx in the order dy dx dz, and evaluate it. Hint: You will need a reasona

Natalija [7]

Looks like the integral is supposed to read

$\displaystyle\int_0^1\int_0^x\int_0^{\sqrt{1-x^2}}z\,\mathrm dz\,\mathrm dy\,\mathrm dx$

The same integral in the required order is

$\displaystyle\int_0^1\int_0^{\sqrt{1-z^2}}\int_0^xz\,\mathrm dy\,\mathrm dx\,\mathrm dz$

5 0

3 years ago

According to the rational root theorem, which answer is not a possible rational root of x^3+9x^2-x+8=0

Readme [11.4K]

Answer:

6

Step-by-step explanation:

The rational root theorem states that the roots must be factors of p/q

where p is the constant and q is the coefficient of the highest order term

p = 8 which has factors ±1, ±2,±4,±8

q = 1 which has factors ±1

The possible roots are ±1, ±2,±4,±8

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

±1

which simplifies to

±1, ±2,±4,±8

6 is not a possible root

7 0

3 years ago

What is a quick and easy way to remember explicit and recursive formulas?

Oliga [24]

I always found derivation to be helpful in remembering. Since this question is tagged as at the middle school level, I assume you've only learned about arithmetic and geometric sequences.

First, remember what these names mean. An arithmetic sequence is a sequence in which consecutive terms are increased by a fixed amount; in other words, it is an additive sequence. If $a_n$ is the $n$ th term in the sequence, then the next term $a_{n+1}$ is a fixed constant (the common difference $d$ ) added to the previous term. As a recursive formula, that's

$a_{n+1}=a_n+d$

This is the part that's probably easier for you to remember. The explicit formula is easily derived from this definition. Since $a_{n+1}=a_n+d$ , this means that $a_n=a_{n-1}+d$ , so you plug this into the recursive formula and end up with

$a_{n+1}=(a_{n-1}+d)+d=a_{n-1}+2d$

You can continue in this pattern, since every term in the sequence follows this rule:

$a_{n+1}=a_{n-1}+2d$
$a_{n+1}=(a_{n-2}+d)+2d$
$a_{n+1}=a_{n-2}+3d$
$a_{n+1}=(a_{n-3}+d)+3d$
$a_{n+1}=a_{n-3}+4d$

and so on. You start to notice a pattern: the subscript of the earlier term in the sequence (on the right side) and the coefficient of the common difference always add up to $n+1$ . You have, for example, $(n-2)+3=n+1$ in the third equation above.

Continuing this pattern, you can write the formula in terms of a known number in the sequence, typically the first one $a_1$ . In order for the pattern mentioned above to hold, you would end up with

$a_{n+1}=a_1+nd$

or, shifting the index by one so that the formula gives the $n$ th term explicitly,

$a_n=a_1+(n-1)d$

Now, geometric sequences behave similarly, but instead of changing additively, the terms of the sequence are scaled or changed multiplicatively. In other words, there is some fixed common ratio $r$ between terms that scales the next term in the sequence relative to the previous one. As a recursive formula,

$a_{n+1}=ra_n$

Well, since $a_n$ is just the term after $a_{n-1}$ scaled by $r$ , you can write

$a_{n+1}=r(ra_{n-1})=r^2a_{n-1}$

Doing this again and again, you'll see a similar pattern emerge:

$a_{n+1}=r^2a_{n-1}$
$a_{n+1}=r^2(ra_{n-2})$
$a_{n+1}=r^3a_{n-2}$
$a_{n+1}=r^3(ra_{n-3})$
$a_{n+1}=r^4a_{n-3}$

and so on. Notice that the subscript and the exponent of the common ratio both add up to $n+1$ . For instance, in the third equation, $3+(n-2)=n+1$ . Extrapolating from this, you can write the explicit rule in terms of the first number in the sequence:

$a_{n+1}=r^na_1$

or, to give the formula for $a_n$ explicitly,

$a_n=r^{n-1}a_1$

6 0

3 years ago