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3 years ago

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Plzz hellp :( i will mark you the brainlist if some on helps (A rectangular prism has a length of 1 1/4 yards, a width of 2 1/2

yards, and a height of 4 yards.
Enter the volume of the prism as a mixed number in simplest form in the box.

1 answer:

Veseljchak [2.6K]3 years ago

4 0

The volume of rectangular prism is the product of its length, width and height.
So the volume V of prism with length $1 \frac{1}{4}$ yards, width $2 \frac{1}{2}$ yards and height of 4 yards will be:

$V=1 \frac{1}{4} * 2 \frac{1}{2} *4 \\ \\ 
V= \frac{5}{4}* \frac{5}{2}*4 \\ \\ 
V= \frac{25}{2} \\ \\ 
V=12 \frac{1}{2}$

Thus the volume of prism as a mixed number in simplest form will be $12 \frac{1}{2}$ cubic yards

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Complete the table of values

Agata [3.3K]

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, $3^{-2} =
\frac{1}{3^{2} }$ .
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, $(\frac{3}{4}) ^{3} = \frac{ 3^{3} }{4^{3} }$ .
3) The zero exponent rule<span> says that any number raised to zero is 1. For example, $3^{0} = 1$ .
</span>

Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is $y = 4^{-x}$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = 4^{-x}$ to find letter a:
$y = 4^{-x}\\
y = 4^{-0}\\
y = 4^{0}\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = 4^{-x}$ to find letter b:
$y = 4^{-x}\\ 
y = 4^{-2}\\ 
y = \frac{1}{4^{2}} \\ 
y= \frac{1}{16}$
<span>
3) x = 4
</span>Plug this into $y = 4^{-x}$ to find letter c:
$y = 4^{-x}\\ 
y = 4^{-4}\\ 
y = \frac{1}{4^{4}} \\ 
y= \frac{1}{256}$
<span>

Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is $y = (\frac{2}{3})^x$ . The x-values are:
<span>1) x = 0
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter d:
$y = (\frac{2}{3})^x\\
y = (\frac{2}{3})^0\\
y = 1$
<span>
2) x = 2
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter e:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\
y = \frac{4}{9}$
<span>
3) x = 4
</span>Plug this into $y = (\frac{2}{3})^x$ to find letter f:
$y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}$
<span>
-------

Answers:
a = 1
b = </span> $\frac{1}{16}$ <span>
c = </span> $\frac{1}{256}$
d = 1
e = $\frac{4}{9}$
f = $\frac{16}{81}$

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