| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.80 |
| Score | 0% | 56% |
What is \( 3 \)\( \sqrt{112} \) + \( 4 \)\( \sqrt{7} \)
| 12\( \sqrt{16} \) | |
| 12\( \sqrt{7} \) | |
| 16\( \sqrt{7} \) | |
| 12\( \sqrt{112} \) |
To add these radicals together their radicands must be the same:
3\( \sqrt{112} \) + 4\( \sqrt{7} \)
3\( \sqrt{16 \times 7} \) + 4\( \sqrt{7} \)
3\( \sqrt{4^2 \times 7} \) + 4\( \sqrt{7} \)
(3)(4)\( \sqrt{7} \) + 4\( \sqrt{7} \)
12\( \sqrt{7} \) + 4\( \sqrt{7} \)
Now that the radicands are identical, you can add them together:
12\( \sqrt{7} \) + 4\( \sqrt{7} \)Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 19 small cakes per hour. The kitchen is available for 4 hours and 22 large cakes and 340 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 9 | |
| 12 | |
| 8 | |
| 7 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 22 large cakes are needed for the party so \( \frac{22}{12} \) = 1\(\frac{5}{6}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 19 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 19 x 4 = 76 small cakes during that time. 340 small cakes are needed for the party so \( \frac{340}{76} \) = 4\(\frac{9}{19}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 5 = 7 cooks.
What is 7a5 x 7a6?
| 49a-1 | |
| 14a11 | |
| 14a5 | |
| 49a11 |
To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:
7a5 x 7a6
(7 x 7)a(5 + 6)
49a11
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for division |
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distributive property for multiplication |
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commutative property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?
distributive property for multiplication |
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commutative property for division |
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commutative property for multiplication |
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distributive property for division |
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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).