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Gnoma [55]
3 years ago
9

HELP? The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.

Mathematics
2 answers:
Andrej [43]3 years ago
6 0
36+12=48

48-16=32 

ive completed that lesson
Fittoniya [83]3 years ago
5 0

Answer : The volume blue prism in Model 1 is, 32in^3

Step-by-step explanation :

As we are given that:

Volume of Model 1 = Volume of Model 2

Given:

Volume of blue prism in Model 2 = 36in^3

Volume of orange prism in Model 2 = 12in^3

Volume of orange prism in Model 1 = 16in^3

Now we have to calculate the total volume of Model 2.

Total volume of Model 2 = 36in^3+12in^3 = 48in^3

Now we have to calculate the volume blue prism in Model 1.

Volume of Model 1 = Volume of Model 2

Volume of orange prism in Model 1 + Volume blue prism in Model 1 = Total volume of Model 2

16in^3 + Volume blue prism in Model 1 = 48in^3

Volume blue prism in Model 1 = 48in^3-16in^3

Volume blue prism in Model 1 = 32in^3

Thus, the volume blue prism in Model 1 is, 32in^3

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1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right  \\   \\ \Rightarrow  \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right  \\  \\ \Rightarrow10x=320 \\  \\ \Rightarrow x=32 \\  \\ \Rightarrow y=80-32=48
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.


2.) Volume of alcohol in the original mixture
\frac{35}{100} \times 40=14 quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
\frac{48}{100} \times (40+x)=14+x \\  \\ \Rightarrow19.2+0.48x=14+x \\  \\ \Rightarrow0.52x=5.2 \\  \\ \Rightarrow x=10

Therefore, 10 quarts of pure alcohol should be added


3.) Original proportion of white paint in the mixture
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Let x be the number of gallons of white paint to be added, then
\frac{5+x}{16+x}=\frac{2}{3} \\  \\ \Rightarrow3(5+x)=2(16+x) \\  \\ \Rightarrow15+3x=32+2x \\  \\ \Rightarrow x=32-15=17
Therefore, 17 gallons of white paint should be added.


4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 25 \\  \\ \Rightarrow3x=25\Rightarrow x=8.33
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.


5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\  \\ \Rightarrow t= \frac{180}{23} =7.83
Therefore, it will take 7.83 hours to get the tank filled up.
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exis [7]

Answer:

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Step-by-step explanation:

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Now, here coefficient of x^{2} is positive , so the parabola will be facing upwards and thus the function will be having a minimum.

Now, as we know that minimum value of a parabolic function occurs at

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here, a = 2 , b = -6

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