(a-3b)^5 expand the binomial please

1 answer:

6 0

Expand the binomial:
( a - 3 b ) ^5 =
= a^5 - 5 * a^4 * ( 3 b ) + 10 * a^3 ( 3 b ) ^2 - 10 * a^2 ( 3 b)^3 + 5 *a*( 3 b ) ^4 -
- ( 3 b )^5 =
= a^5 - 15 a^4 b + 90 a^3 b^2 - 270 a^2 b^3 + 405 a b^4 - 243 b^5

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A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that

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The slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis is $\frac{3}{4}$ .

Step-by-step explanation:

<h3>Definition of slope of a line:</h3>

The slope of a line describes its steepness. In mathematical terms, for a line passing through two points with known coordinates, the slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates.

<h3>Formula for the slope of a line:</h3>

Let 'm' represent the slope of a line passing through two points with coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$ . So, according to the definition, the slope of the line can be written as follows,

$m=\left|\frac{y_{2}-y_{1} }{x_{2}-x_{1}}\right|$

<h3>Calculation of slope:</h3>

According to the information given in the question, the school conducts $27$ tests in $36$ weeks.

Now, any point on the $x-$ axis is given by the general form $(x,0)$ , where $x$ represents any numerical value on the axis. Similarly, any point on the $y-$ axis is given by the general form $(0,y)$ , where $y$ represents any numerical value on the axis.

It is given that the time in weeks is represented on the $x-$ axis, so $36$ weeks can be represented as coordinates as $(36,0)$ . Likewise, the number of tests conducted, i.e., $27$ can be represented as coordinates as $(0,27)$ .