| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
Which of the following statements about exponents is false?
b0 = 1 |
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b1 = b |
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all of these are false |
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b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Alex buys two shirts, each with a regular price of $27, how much will he pay for both shirts?
| $47.25 | |
| $6.75 | |
| $35.10 | |
| $36.45 |
By buying two shirts, Alex will save $27 x \( \frac{25}{100} \) = \( \frac{$27 x 25}{100} \) = \( \frac{$675}{100} \) = $6.75 on the second shirt.
So, his total cost will be
$27.00 + ($27.00 - $6.75)
$27.00 + $20.25
$47.25
What is \( \frac{1}{7} \) x \( \frac{4}{8} \)?
| \(\frac{3}{20}\) | |
| \(\frac{2}{15}\) | |
| \(\frac{1}{14}\) | |
| \(\frac{2}{27}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{7} \) x \( \frac{4}{8} \) = \( \frac{1 x 4}{7 x 8} \) = \( \frac{4}{56} \) = \(\frac{1}{14}\)
What is \( \frac{15\sqrt{21}}{3\sqrt{7}} \)?
| 5 \( \sqrt{\frac{1}{3}} \) | |
| 5 \( \sqrt{3} \) | |
| 3 \( \sqrt{\frac{1}{5}} \) | |
| 3 \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{15\sqrt{21}}{3\sqrt{7}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{21}{7}} \)
5 \( \sqrt{3} \)
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for division |
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distributive property for division |
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commutative property for multiplication |
The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).