<span>1. B. The equation for the perimeter is P = 5n + 14
2. C. Decreasing; Linear
3. C. y = 3^x
4. C. y = (x+5)^2
1. Look at the 3 figures. You'll notice that in all three figures, there is always 2 sides of length 7 exposed and 1 side of length 5 exposed for each individual triangle. So the formula is 7*2 + 5n which simplifies to 14 + 5m. Looking at the available options, only option "B" is equivalent.
2. Looking at the table, as the number of teams a person belongs to, the number of free hours gets smaller, so the function is decreasing. To check if the function is linear, check if the change in the value of the function has a constant ratio with the change in the input. So let's see
Input changes from 0 to 1 for a change of 1. Output changes from 46 to 39, for a change of -7. -7/1 = -7
Input changes from 1 to 2 for a change of 1. Output changes from 39 to 32, for a change of -7, -7/1 = -7
Input changes from 2 to 3 for a change of 1. Output changes from 32 to 25, for a change of -7, -7/1 = -7
So the change in the output is always -7 for each change of 1 in the input. Therefore the function is linear.
Therefore the answer is "C. Decreasing; Linear"
3. Let's check each option and see what fits.
A. y=x^3
* We have the pair (1,3). 1^3 = 1. And 1 is not equal to 3, so this option doesn't fit and is therefore wrong.
B. y = 3x
* We have the pair (1,3) 3*1 = 3. 3 and 3 fit. So far, so good. Let's check the next pair.
(2,9). 3*2 = 6. And 6 is not equal to 9. So this option too is wrong.
C. y = 3^x
Checking (1,3). 3^1 = 3. Good
Checking (2,9). 3^2 = 9. Good
Checking (3,27). 3^3 = 27. Good
Checking (4,81). 3^4 = 81. Good
Checking (5,243). 3^5 = 243. Good
This matches all the points given. So this is the correct answer. But let's check option D just to make sure.
D. y = x+2
Checking (1,3). 1+3 = 3. Good
Checking (2,9). 2+3 = 5. Not a match. So this isn't a good choice.
4. Same method as #3 above. Just check each option against the order pairs we have and see if all of them fit.
A. y = x^2
Checking (1,36). 1^2 = 1. Not a match. Bad option.
B. y = 36x
Checking (1,36). 36 * 1 = 36. Good.
Checking (2,49). 36 * 2 = 72. Not a match. Bad option.
C. y = (x+5)^2
Checking (1,36). (1+5)^2 = 6^2 = 36. Good.
Checking (2,49). (2+5)^2 = 7^2 = 49. Good.
Checking (3,64). (3+5)^2 = 8^2 = 64. Good.
Checking (4,81). (4+5)^2 = 9^2 = 81. Good.
Checking (5,100). (5+5)^2 = 10^2 = 100. Good.
They all match, so this is the correct option.
D. y = (x+6)^2
Checking (1,36). (1+6)^2 = 7^2 = 49. Not a match. Bad option.</span>
It depends on how b approaches 0
If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.
On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.
The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.
Answer:
5x^2-25x+2x-10
5x^2-23x-10
Step-by-step explanation:
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