A compact-disc case, or jewel case is 14 cm long, 12.5 cm wide, and 1 cm tall. What is the volume of the jewel case?

Mathematics

1 answer:

puteri [66]3 years ago

4 0

V = 14 × 12.5 × 1 => V = 175 $cm^{3}$ is the volume of the jewel case.

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Harrison went out to buy coffee for his classmates. There are 23 students in his class, counting Harrison himself. Some wanted m

NemiM [27]

Step-by-step explanation:

Let's represent the number of mochas bought with the variable $M$ , and the number of lattes bought with the variable $L$ .

Since there are $23$ students, the total number of mochas and lattes bought must be $23$ . This can be represented with the following equation:

$M + L = 23$

We can also set up another equation based on the total amount spent on the coffe:

$4.30M + 3.50L = 87.70$

If we rearrange the first equation, we can solve for $M$ :

$M = 23 - L$

If we substitute this into the second equation, we can solve for $L$ :

$4.30(23 - L) + 3.50L = 87.70$

$98.9 - 4.3L + 3.5L = 87.7$

$98.9 - 0.8L = 87.7$

$0.8L = 11.2$

$L = 14$

Subtituting this back into the original equation, we can solve for $M$ :

$M + L = 23$

$M + 14 = 23$

$M = 9$

Therefore, 9 mochas and 14 lattes were bought.

3 0

3 years ago

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Y is directly proportional to square root of x<br> If y=56 when x=49 find,<br> y when x=81

STALIN [3.7K]

$\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}$

$\stackrel{\begin{array}{llll} \textit{"y" directly}\\ \textit{proportional to }\sqrt{x} \end{array}}{y = k\sqrt{x}}\qquad \textit{we know that} \begin{cases} y = 56\\ x = 49 \end{cases}\implies 56=k\sqrt{49} \\\\\\ 56=7k\implies \cfrac{56}{7}=k\implies 8=k~\hfill \boxed{y=8\sqrt{x}} \\\\\\ \textit{when x = 81, what is "y"?}\hfill y=8\sqrt{81}\implies y=8(9)\implies y=72$