Given that Micheal is three times as old as Jean, but in seven years he will be twice old as she will be, to determine how old are they both at this time, the following calculation must be performed:

M = 3J

M + 7 = 2J + 7

7 = 1/3

7 x 3 = 21

21 + 7 = 28

7 + 7 = 14

21 / 7 = 3

28 / 14 = 2

Therefore, Michael is 21 years old while Jean is 7 years old.

5 0

3 years ago

Write an equation in slope intercept form that is perpendicular to 3x + 2y equals 12 and passes through the point (1,2)

Zigmanuir [339]

Answer:

The equation is y = (2/3)x + (4/3).

Step-by-step explanation:

First, you have to change the equation into slope-intecept formula to find its gradient (slope) :

$3x + 2y = 12$

$2y = - 3x + 12$

$y = - \frac{3}{2}x + 6$

Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :

$m1 \times m2 = - 1$

$- \frac{3}{2} \times m2 = - 1$

$m2 = - 1 \div - \frac{3}{2}$

$m2 = \frac{2}{3}$

Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :

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

$let \: x = 1,y = 2$

$2 = \frac{2}{3} (1) + b$

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

$b = \frac{4}{3}$

$y = \frac{2}{3} x + \frac{4}{3}$

5 0

3 years ago

What is the vertex of a parabola having the equation y = –2(x – 5)2 + 7? Which direction does the parabola open?

Vika [28.1K]

$y = -2(x-5)^2 + 7$

That's vertex form for a parabola $y=a(x-p)^2+q$ and we read off vertex (p,q) as

Answer: Vertex (5,7)

The negative a tells us this is a downward opening parabola (upside down from the usual $y=x^2$ . I remember CUP - Concave Up Positive; here a is negative so not a cup, instead concave down. The same rule applies to second derivatives in calculus so memorize it now and use it later.

Answer: downward

7 0

3 years ago