Arectangular picture frame is 5 inches wide and 10 inches tall. you want to make the area 6 times as large by increasing the length and width by the same amount. find the number of inches by which each dimension must be increased.

Step-by-step explanation:

let length and width be increased by x>0

(10+x)(5+x)=6×10×5

50+10 x+5x+x²=300

x²+15x-250=0

x²+25 x-10x-250=0

x(x+25)-10(x+25)=0

(x+25)(x-10)=0

x=-25(rejected),10

so x=10

so both the dimensions should be increase by 10 inches.

it is 10 inches

Step-by-step explanation:

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

hiking down a winding trail.

step-by-step explanation: