Which of the following expressions are equivalent to this expression:

Mathematics

2 answers:

tatyana61 [14]3 years ago

8 0

Answer:

A: -1[4+(-4)]

Gekata [30.6K]3 years ago

6 0

The original expression is equal to 0 because anything multiplied by 0 is equal to 0. Solve inside the brackets for the possible answer choices to find what will equal 0.

Start with the first expression. Add 4 and negative 4 will become 0, and -1 times 0 is equal to 0. Let's solve for the others just to be sure.

In the second expression, solving inside the brackets gives you 8. -1 times 8 is equal to -8.

Adding 4 and negative 4 in the third expression leaves you with 0. But, 1 + 0 is equal to 1.

Adding negative 4 and negative 4 gives you the answer of -8, and -1 times -8 is equal to 8.

Your answer is the first expression, or A.

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8 0

2 years ago

Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The

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a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

$\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\$

$\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft$

$\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft$