Can someone please do this for me

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

7 0

Next time please indicate which problem you want to work on.

One example of an equation with variables present on both sides is

y-b = m(x-a). Given the slope of a line and one point (a,b) through which the line passes, you can come up with an equation of the line.

Or, given the numeric value of y-b and that of x-a, you could obtain the slope of the line thru the points (x,y) and (a,b).

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Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Nezavi [6.7K]

Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

Two vectors $(x_1,\, y_1)$ and $(x_2,\, y_2)$ are parallel to one another if and only if the ratio between their corresponding components are equal:

$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.