Let $z$ be a complex number such that $z^5 = 1$ and $z \neq 1.$ Compute
1 answer:
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Answer:
see explanation
Step-by-step explanation:
both linear equations will have the form
y = mx + c ( m is the slope and c the y- intercept )
Chef Mate
c(n) = mn + c
calculate m using the slope formula
m =
with (x₁, y₁ ) = (2, 14) and (x₂, y₂ ) = (3, 18.5) ← 2 ordered pairs from the table
m = =
= 4.5 , then
c(n) = 4.5n + c ( n represents ounces )
To find c substitute any ordered pair from the table into c(n)
using (4, 23 )
23 = 18 + c ⇒ c = 23 - 18 = 5
c(n) = 4.5n + 5 ← equation for Chef Mate
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Similarly for Grocery Gourmet
g(n) = mn + c
using (2, 23 ) and (3, 27 ) to find m
m = =
= 4 , then
g(n) = 4n + c
using (4, 31 ) to find c
31 = 16 + c ⇒ c = 31 - 16 = 15
g(n) = 4n + 15 ← equation for Grocery Gourmet
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Equate the 2 equations to find when cost is the same
4.5n + 5 = 4n + 15 ( subtract 4n from both sides )
0.5n + 5 = 15 ( subtract 5 from both sides )
0.5n = 10 ( divide both sides by 0.5 )
n = 20
Then when n = 20
c(n) = 4.5(20) + 5 = 90 + 5 = 95
g(n) = 4(20) + 15 = 80 + 15 = 95
Both Chef Mate and Grocery Gourmet charge $95 for 20 ounces of extract
Boys: x
gilrs: y
From the text of the task:
Replacing x:
So there are 28 girs and 20 boys
gilrs: y
From the text of the task:
Replacing x:
So there are 28 girs and 20 boys
It had taken a while for me to understand the problem. From what I understood, the given pairs of points are tabulated below:
x f(x)
-7 -11
-1 1
3 9
4 11
7 17
Then, the choices are equations in terms of x. The correct equation should yield the pairs tabulated above when the x-values are substituted into the equation. So, the solution is basically just substituting x to each of those equations, then you get the corresponding y values. Check which of those question has pairs similar to the given. I suggest that you tabulate the numbers so that it would be easier for you. For me, I used MS Excel as shown in the picture. Th x-values are in the first column gathered from the given. I applied the equations to get the f(x) values. As you can see, the pairs matched with the third column. Therefore, the answer is: f(x) = 2x+3.
x f(x)
-7 -11
-1 1
3 9
4 11
7 17
Then, the choices are equations in terms of x. The correct equation should yield the pairs tabulated above when the x-values are substituted into the equation. So, the solution is basically just substituting x to each of those equations, then you get the corresponding y values. Check which of those question has pairs similar to the given. I suggest that you tabulate the numbers so that it would be easier for you. For me, I used MS Excel as shown in the picture. Th x-values are in the first column gathered from the given. I applied the equations to get the f(x) values. As you can see, the pairs matched with the third column. Therefore, the answer is: f(x) = 2x+3.