| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
If \( \left|z + 0\right| \) + 9 = -1, which of these is a possible value for z?
| -23 | |
| -10 | |
| -3 | |
| -16 |
First, solve for \( \left|z + 0\right| \):
\( \left|z + 0\right| \) + 9 = -1
\( \left|z + 0\right| \) = -1 - 9
\( \left|z + 0\right| \) = -10
The value inside the absolute value brackets can be either positive or negative so (z + 0) must equal - 10 or --10 for \( \left|z + 0\right| \) to equal -10:
| z + 0 = -10 z = -10 + 0 z = -10 | z + 0 = 10 z = 10 + 0 z = 10 |
So, z = 10 or z = -10.
Convert 0.0002105 to scientific notation.
| 2.105 x 10-3 | |
| 21.05 x 10-5 | |
| 2.105 x 104 | |
| 2.105 x 10-4 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0002105 in scientific notation is 2.105 x 10-4
a(b + c) = ab + ac defines which of the following?
distributive property for multiplication |
|
distributive property for division |
|
commutative property for division |
|
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.
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 11 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 170 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?
| 11 | |
| 10 | |
| 8 | |
| 6 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 20 large cakes are needed for the party so \( \frac{20}{12} \) = 1\(\frac{2}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 11 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 11 x 3 = 33 small cakes during that time. 170 small cakes are needed for the party so \( \frac{170}{33} \) = 5\(\frac{5}{33}\) 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 + 6 = 8 cooks.
What is \( \frac{7x^9}{9x^2} \)?
| \(\frac{7}{9}\)x4\(\frac{1}{2}\) | |
| \(\frac{7}{9}\)x7 | |
| \(\frac{7}{9}\)x-7 | |
| 1\(\frac{2}{7}\)x11 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{7x^9}{9x^2} \)
\( \frac{7}{9} \) x(9 - 2)
\(\frac{7}{9}\)x7