Mathematics, 25.03.2020 02:14 1315055427

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B.

Which equation represents Grant’s path?

y = 2 – 4x

y = 4 – X over 2

y = 6 – X over 4

y = 8 – 2x

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point

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Answer from: brae72

The equation of Grant's path is y = 4 - x over 2 ⇒ 2nd answer

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slope of the lineb is the y-intercept (value y at x = 0)

The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ Grant's path is a line from point A to point B

∴ The equation of AB represents Grant's path

Lets find the slope of AB using the formula of the slope above

∵ A = (8 , 0)

∵ B = (-4 , 6)

∴ $x_{1}$ = 8 and $x_{2}$ = -4

∴ $y_{1}$ = 0 and $y_{2}$ = 6

∵ $m=\frac{6-0}{-4-8}=\frac{6}{-12}$

∴ $m=-\frac{1}{2}$

Substitute the value of m in the form of the equation

∵ y = m x + b

∴ y = $-\frac{1}{2}$ x + b

∵ b is the value of y at x = 0

∵ y = 4 at x = 0 ⇒ from the figure

∴ b = 4

∴ y = $-\frac{1}{2}$ x + 4

We can write $-\frac{1}{2}$ x as $-\frac{x}{2}$

∴ y = $-\frac{x}{2}$ + 4

- Switch the two terms of the right hand side

∴ y = 4 - $\frac{x}{2}$

The equation of Grant's path is y = 4 - $\frac{x}{2}$

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

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step-by-step explanation:

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