49 is prime bcuz it can't be halfed
Answers:
A ' = (-2, -3)
B ' = (0, -3)
C ' = (-1, 1)
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Explanation:
To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.
Algebraically, the reflection rule used can be written as ![(x,y) \to (x,-y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2C-y%29)
Applying this rule to the three given points will mean....
- Point A = (-2, 3) becomes A ' = (-2, -3)
- Point B = (0, 3) becomes B ' = (0, -3)
- Point C = (-1, -1) becomes C ' = (-1, 1)
The diagram is provided below.
Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.
Answer: 0.1
Explanation: If the last digit in the fractional part of 0.05 is 5 or more and the first digit in the fractional part is less than 9, then add 1 to the first digit of the fractional part and remove the second digit.
Answer: Choice D) ![x \ge -6](https://tex.z-dn.net/?f=x%20%5Cge%20-6)
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Explanation:
Taking the square root of a negative number leads to a nonreal result.
So we want the radicand to be 0 or positive
Set the stuff under the square root to be 0 or larger. Solve for x.
![\frac{1}{3}x+2 \ge 0\\\\\frac{1}{3}x \ge 0-2\\\\\frac{1}{3}x \ge -2\\\\x \ge 3(-2)\\\\x \ge -6](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%2B2%20%5Cge%200%5C%5C%5C%5C%5Cfrac%7B1%7D%7B3%7Dx%20%5Cge%200-2%5C%5C%5C%5C%5Cfrac%7B1%7D%7B3%7Dx%20%5Cge%20-2%5C%5C%5C%5Cx%20%5Cge%203%28-2%29%5C%5C%5C%5Cx%20%5Cge%20-6)
If x is -6 or larger, then
is 0 or larger leading to some real number for f(x).
The inequality sign does not flip because we multiplied both sides by a positive number. The inequality sign only flips when we multiply both sides by a negative number.
Answer:
Rasheed bought 3 packages of chocolate and 5 packages of toffee.
Step-by-step explanation:
In this case we have to found the number of bars that multiplied by the fractions presented give us an integer number and meets with the fact that the bars are an odd number because the packages came in packs of two bars.
For the case of the chocolate we have to find a number that meets this characteristics, we try with the number 6:
![6*\frac{2}{3} =4](https://tex.z-dn.net/?f=6%2A%5Cfrac%7B2%7D%7B3%7D%20%3D4)
For chocolate Rasheed bought 3 packages, we can see that 6 bars meet the asked.
For the case of toffee, we try with number 10:
![10*\frac{3}{5} =6](https://tex.z-dn.net/?f=10%2A%5Cfrac%7B3%7D%7B5%7D%20%3D6)
For toffee Rasheed bought 5 packages, we can see that 10 bars meet the asked.
Rasheed bought 3 packages of chocolate and 5 packages of toffee.