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3 years ago

Factor the expression: 6a + 24

Mathematics

2 answers:

Len [333]3 years ago

8 0

6 ( a+4 )

Step by step explanation :

Ber [7]3 years ago

4 0

Answer:

6 (a+4)

Step-by-step explanation:

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How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?

Arturiano [62]

Answer:

$y = \frac{2}{3} x + 2$

Step-by-step explanation:

Start by finding the slope of the given line.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of given line

$= \frac{5 - ( - 1)}{ - 2 - 2}$

$= \frac{5 + 1}{ - 4}$

$= \frac{6}{ - 4}$

$= - \frac{3}{2}$

A perpendicular bisector cuts through the line at its midpoint perpendicularly.

The product of the slopes of two perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

$- \frac{3}{2} m = - 1$

$m = - 1 \div ( - \frac{3}{2} )$

$m = - 1 \times ( - \frac{2}{3} )$

$m = \frac{2}{3}$

$y = \frac{2}{3}x + c$ , where c is the y-intercept.

To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$

Midpoint of given line

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

$=( \frac{0}{2} , \frac{4}{2} )$

= (0, 2)

$y = \frac{2}{3} x + c$

When x= 0, y= 2,

2= ⅔(0) +c

2= 0 +c

c= 2

Thus, the equation of the perpendicular bisector is $y = \frac{2}{3} x + 2$ .

7 0

3 years ago

This is a literal equation.

Aleksandr [31]

Assuming this is the equation you want to operate on:
$v^{2} = (v_0)^{2} + 2\cdot a \cdot \Deltax$
$2\cdot a \cdot \Delta x = v^{2} - (v_0)^{2}$
$a = \frac{v^{2} - (v_0)^{2}}{2\cdot \Delta x}$
Before final operation we have to assume that x is not equal to 0. :)

6 0

3 years ago

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Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machin

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