<h3>
Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.
Answer:
6 book purchases.
Step-by-step explanation:
As the bookstore sells frequent buyers discount cards at $ 12, which make the books that usually cost $ 9 cost $ 7, to determine from how many books a card-holder and a common buyer will spend the same amount of money is necessary perform the following calculation:
9 - 7 = 2
12/2 = 6
Therefore, after purchasing 6 books, both categories of buyers will have spent the same amount of money. This is verified with the following calculation:
Card holder = 12 + 7 x 6 = 54
Non-card holder = 9 x 6 = 54
Answer:
3.54>0.354
Step-by-step explanation:
2.80 is greater than 2.68 not less.
0.257 is greater than 0.1574 not less.
9.04 is less than 9.4 not greater.
The only correct answer is 3.54>0.354 because the 3 in 3.54 is greater than the 0 in 0.354.
X=46
Explanation:
You just have to make 3x-28 and x+64 equal to each other and x would be 46.
m∠1=44
Explanation:
You just have to subtract the 46 that u solved earlier from 90 degree so it’s 44
Remark
You'll see it a whole lot easier if you make a substitution so that it looks like something you have already seen
Solution
let y = x^2
x^4 = x^2 * x^2
x^4 = y * y
x^4 = y^2
Now the expression becomes
y^2 + 8 y - 9 = z
(y + 9)(y - 1) = z
Now put the x^2 back in.
(x^2 + 9) ( x^2 - 1) = z
x^2 - 1 becomes x + 1 and x - 1. At this level x^2 + 9 can't be factored.
Answer
(x^2 + 9) (x + 1)(x - 1)
