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timurjin [86]
3 years ago
8

Mrs . Porcelli’s classroom bulletin board is 2/1/4 feet long. Ms .Smith bulletin board is 3 times as long Mrs . Porcelli’s.How l

ong is Ms.Smith’s bulletin board.
Mathematics
1 answer:
snow_lady [41]3 years ago
3 0

Answer:

6\frac{3}{4}\ ft

Step-by-step explanation:

we know that

To find out how long is Ms.Smith’s bulletin board, multiply Mrs . Porcelli’s bulletin board by 3

so

2\frac{1}{4}(3)

but first convert mixed number to an improper fraction

so

2\frac{1}{4}\ ft=2+\frac{1}{4}=\frac{9}{4}\ ft

substitute

\frac{9}{4}(3)=\frac{27}{4}\ ft

convert to mixed number

\frac{27}{4}\ ft=\frac{24}{4}+\frac{3}{4}=6\frac{3}{4}\ ft

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blsea [12.9K]

Option A: \sqrt{75}

Option C: \sqrt{15} \cdot \sqrt{5}

Option F: \sqrt{25} \cdot \sqrt{3}

Solution:

Given expression is 5 \sqrt{3}.

Option A: \sqrt{75}

\sqrt{75}=\sqrt{25\times3}

       =\sqrt{5^2\times3}

       =5\sqrt{3}

Hence \sqrt{75} is equivalent expression of 5 \sqrt{3}.

Option B: \sqrt{45}

\sqrt{45}=\sqrt{9\times5}

       =\sqrt{3^2\times5}

       =3\sqrt{5}

Hence \sqrt{45} is not equivalent expression of 5 \sqrt{3}.

Option C: \sqrt{15} \cdot \sqrt{5}

\sqrt{15} \cdot \sqrt{5}=\sqrt{15\times5}

              =\sqrt{75}

              =5\sqrt{3}    (proved in option A)

Hence \sqrt{15} \cdot \sqrt{5} is equivalent expression of 5 \sqrt{3}.

Option D: \sqrt{3} \cdot \sqrt{5}

\sqrt{3} \cdot \sqrt{5}=\sqrt{3\times5}

            =\sqrt{15}

Hence \sqrt{3} \cdot \sqrt{5} is not equivalent expression of 5 \sqrt{3}.

Option E: 75

75 is a whole number.

Hence 75 is not equivalent expression of 5 \sqrt{3}.

Option F: \sqrt{25} \cdot \sqrt{3}

\sqrt{25} \cdot \sqrt{3}=\sqrt{25\times3}

              =\sqrt{75}

              =5\sqrt{3}    (proved in option A)

Hence \sqrt{25} \cdot \sqrt{3} is equivalent expression of 5 \sqrt{3}.

Therefore, \sqrt{75},\ \  \sqrt{15} \cdot \sqrt{5}, \  \ \sqrt{25} \cdot \sqrt{3} are all equivalent expressions of 5 \sqrt{3}.

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a. A' means the complement with respect to Z? If so, then

To know A' you need to write all the elements in Z that are not in A.

A'= \{ u, v, w, x, y, z\}

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c. A \cup B = \{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t, w,x,y \} (Add to A the elements of B, or equivalently add to B the elements of A)

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