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Crazy boy [7]
3 years ago
13

How many gallons of a 50% antifreeze solution must be mixed with 70 gallons of 30% antifreeze to get a mixture that is 40% antif

reeze?
Mathematics
1 answer:
Colt1911 [192]3 years ago
5 0

Answer:

70 gallons

Step-by-step explanation:

x gallon of 50%

x * 0.5 + 70 * 0.3 = (x + 70) * 0.4

0.5x + 21 = 0.4x + 28

0.1x = 7

x = 70

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You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box
jenyasd209 [6]

Answer:

h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

Step-by-step explanation:

Given in the question a piece of cardboard having dimensions 32 by 40

Suppose we cut square of length x

When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths

<h3>Step 1</h3>

Formula for the volume of box

v = height * length  * width

v = x  (32-2x)  (40-2x)

v = 4x³ - 144x² + 1280x

<h3>Step 2</h3>

Find derivative and equal it to 0

dv/dx = 4(3)x² - (2)144x + 1280

      0 = 12x² - 288x + 1280

x1 = 18.110

x2 =5.88

<h3>Step 3</h3>

Select x and plug value of x to find dimension

(32-2x) > 0

2x < 32

 x < 16

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h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

6 0
4 years ago
3 fewer than 5 times a number is 17
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Step-by-step explanation:

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Answer:

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