Mathematics, 16.07.2019 08:30 AnastasiaJauregui

Valeria is filling her new fish tank with water. the tank measures 36 inches by 13 inches by 24 inches. she has a 3-gallon bucket that she can fill at the sink and then pour into the tank. what is the minimum number of times valeria needs to fill (or partially fill) the 3-gallon bucket in order to completely fill her fish tank? (hint: there are 231 cubic inches in a gallon.) she needs to fill up the 3-gallon bucket at least times in order to completely fill her tank.

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Answer from: JaredO

1) You are told the conversion of cubic inches to gallons, but first you need to find the volume of the fish tank in cubic inches.

The equation for the volume of a rectangular prism (shape of the fish tank) is V = lwh, where V = volume, l = length of the base, w = width of the base, and h = height of the tank. You know the dimensions are 36 inches by 13 inches by 24 inches. Plug these numbers into the equation to find the volume:
$V = lwh\\
V = (36)(13)(24)\\
V = 11232 \:in^3$

2) You know the conversion from cubic increase to gallon is 231 cubic inches in 1 gallon. That means the three gallon bucket is 231*3 = 693 cubic inches. Divide 11232 by 693 and round up (since you're partially filling it up once) to find the number of times Valeria needs to fill the bucket:
$11232 \div 693 = 16.21\: \rightarrow \:17$

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17 times

Answer from: Quest

$w\geq 14$

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

$2l+2w\geq 40$

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

$2\times 6+2w\geq 40$

now, we can solve for w

$12+2w\geq 40$

subtract both sides by 12

$12+2w-12\geq 40-12$

$2w\geq 28$

divide both sides by 2

and we get

$w\geq 14$

so,

the smallest possible measurement of the width is 14 feet

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'.

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