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QveST [7]
3 years ago
11

Jayne says that 0.45 is equal to 4/10. Is she correct? Explain.

Mathematics
2 answers:
Diano4ka-milaya [45]3 years ago
7 0
0.45 =  \dfrac{45}{100}

\dfrac{4}{10} =  \dfrac{4 \times 10}{10 \times 10} =  \dfrac{40}{100}

\dfrac{45}{100}  \neq  \dfrac{40}{100}

They are not the equal.
yKpoI14uk [10]3 years ago
4 0
No, 4/10 is equal to 0.40 and not 0.45 since 4/10 goes in tens.
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What is the height, width, and length
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so, let's say the length is "L".

width = 2 shorter than L = L - 2.

height = 9 more than twice L = 2L + 9.

check the picture below.

keeping in mind that the volume of a <u>rectangular prism</u> is simply the product of its length, width and height, and since we know the volume has to be 45.


\bf 45=(L)(L-2)(2L+9)\implies 45=(L)(2L^2+5L-18) \\\\\\ 45=2L^3+5L^2-18L\implies 0=2L^3+5L^2-18L-45 \\\\\\ \stackrel{\textit{now let's do some grouping}}{0=(2L^3+5L^2)-(18L+45)}\implies \stackrel{\textit{common factor}}{0=L^2(2L+5)-9(2L+5)}


\bf \stackrel{\textit{again common factor}}{0=\underline{(2L+5)}(L^2-9)}\implies \stackrel{\textit{difference of squares}}{0=(2L+5)\stackrel{\downarrow }{(L^2-3^2)}} \\\\\\ 0=(2L+5)(L-3)(L+3)\implies L= \begin{cases} -\cfrac{5}{2}\\[1em] \boxed{3}\\ -3 \end{cases}


from those 3 factors, we get those solutions/zeros.

we can't use -5/2, or -3, because the length can't be a negative value, so L = 3.

that means the width = 3 + 2, and the height = 2(3) +9.

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