Answer:
10. 32 & 37
11. 3 & 4
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Sin O = 1 / csc O = 2/9
cos O = sqrt (1 - (2/9)^2) = sqrt 77/81 = sqrt77 / 9
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Line passes through (2, -4) & parallel to y = 3x+ 2
Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope. "M" is simply a place mat so if we look at our given line, the "m" value is 3. Therefore, our slope is 3.
We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our slope for our new line will be 3.
Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (2, -4) with a slope of 3.
y-y₁=m(x-x₁)
Let's start by plugging in 3 for m (our slope), 2 for x1 and -4 for y1.
y - (-4) = 3(x - 2)
Simplify.
y + 4 = 3x - 6
Simplify by subtracting 4 from both sides.
y = 3x - 10
~Hope I helped!~
Let us examine the speed of growth of the function. We have that the difference between successive terms is: 2, 4, 8, 16. These are powers of 2 and thus there is clearly an exponential increase in the parent function. In fact, the function can be modeled by f(x)=C+2^x where C is a constant.
We have that the new function is g(x). Translating upwards by 5 means that the new y-values are 5 units higher. Hence, we have that the pairs (x,f(x)) correspond to the pairs (x,f(x)+5) and thus the answer is that the f(x)/y-values will be increased by 5.
According to the above, we need to check the given values and see whether in some cases we have g(x)=f(x)+5; in layman's terms, we need to check whether for some x, the new y-value is bigger by 5 from the old one. This is the case only for (2,16) since the old point was (2,11).
Options A, C and D are functions.
In a function, for every number for 'x' there is only one 'y'. So, if you have two ordered pairs in a choice that have the same number for 'x', that is not a function.
Remember an ordered pair is written (x, y).
B is not a function as:
(x, y)
(1, -2)
(1, -3)
(1, -4)
^ All of the x-coordinates are the same.
E is not a function as:
(x, y)
(6, -1)
(6, -8)
^ Two of the x-coordinates are the same.
Thus, A, C and D are functions.
