Mathematics, 16.07.2019 07:20 umadbro46111

Determine the better buy by comparing unit rates. 1. 20 pens for $1.60 or 25 pens for $2.25 2. 13 berries for $2.60 or 17 berries for $3.06

Answers: 2

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To find the better buy we have to find the cost per pen for each.

1. 20 pens for $1.60 -> 1.60/20 = .08 cents per pen.
25 pens for $2.25 -> 2.25/25 = .09 cents per pen.

The best buy is 20 pens for $1.60 because it's cheaper per pen.

2. 13 berries for $2.60 -> 2.60/13 = .20 cents per berry
17 berries for $3.06 -> 3.06/17 = .18 cents per berry

The best buy is 17 berries for $3.06 because it's cheaper per berry.

Answer from: abigaleschwartz

1. 20 pens for $1.60
2. 17 berries for $3.06

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.