Answers:
Part A: The value of x must be 0
Part B: The value of x can be any real number
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Explanation:
Part A) We have the equation (7^2)^x = 1 which simplifies to 7^(2x) = 1. The only way to get the left side equal to the right side is to have the exponent of 2x equal zero. If 2x = 0, then x = 0. So that's why x = 0 is the only solution here.
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Part B) Similar to part A above, but the exponent is slightly different now. We have (7^0)^x = 1 which turns into 7^(0*x) = 1. The exponent 0*x is really 0 no matter what x is. We can plug in any real number we want for x and the left side will always be 1. This is why the solution set to this equation is the set of all real numbers.
Answer:
10. Expanded vertically by 3, shifted left 2 and up 4.
11. Shifted right 6 and up 7.
Step-by-step explanation:
This sort of question involves matching patterns. You need to know what the various transformations look like, and what that means for a specific parent function.
Here are the transformations used in this problem:
- f(x -a) . . . . shift f(x) to the right by "a" units
- f(x) +a . . . . shift f(x) up by "a" units
- a·f(x) . . . . . vertically scale f(x) by a factor of "a"
For these problems, the parent function is f(x) = 1/x.
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10. The multiplier of 3 in the numerator (3/x) means the function has been scaled vertically (expanded) by a factor of 3.
The replacement of x with x+2 means the function has been shifted to the right by -2 units. That is the same as shifted left 2 units.
The addition of 4 to the function value means the function has been shifted up by 4 units.
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11. We note the numerator is still 1, so there is no vertical expansion. The replacement of x with x-6 means a right shift by 6 units. The addition of 7 to the function value means a shift up by 7 units.
Her first mistake was in step 2.
When taking an absolute value of some number let’s say x, equals to the distance it is from 0
So |x| = x as well as |-x|=x because they have the same distance from 0. 2 and -2 are both 2 unit from 0.
So in the problem, her second step was to add |-2| and |6| to get her first distance. She was supposed to remove the | | by taking the absolute value of |-2|, which is makes the equation 6+2 because |-2|=2. She just removed the signs without applying the function. Her answer should’ve been 8 for that distance not 4. Therefore her area should have been 32, not 16.
Answer:
19
Step-by-step explanation:
Its 19
9+10 is 19
Yeah
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