Answer:
Equivalent expressions are expressions which are equal. This means they simplify to the same expression. Simplify the two expressions -1.3x - (-8.9x) = 7.6x and -1.3 + (-8.9X) = -10.2x.
Then simplify each option to determine if it is equal -1.3x - (-8.9x), -1.3 + (-8.9X) or neither:
−1.3x−8.9x = -10.2x. This is equivalent to -1.3 + (-8.9X) .
8.9x+(−1.3x) = 7.6x This is equivalent to -1.3x - (-8.9x) .
−8.9x+(−1.3x) = -10.2x This is equivalent to -1.3 + (-8.9X) .
8.9x−(−1.3x) = 10.2x Neither
−1.3x+8.9x = 7.6x This is equivalent to -1.3x - (-8.9x) .
−8.9x+1.3x = -7.6x Neither
Step-by-step explanation:
Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
Answer:
y = 14/5x + 2
Step-by-step explanation:
is seems as though the y-intercept would be 2 and the slope is 2.8 which is
2 4/5 or 14/5
therefore, equation would be y = 14/5x + 2
Answer: 
Step-by-step explanation:
You need to draw a Right triangle as the one attached, where "x" is the lenght of a ladder Andrew will need to reach the top and be out of the flower bed.
You must apply the Pythagorean Theorem. This is:
Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.
If you solve for "a", you get:
In this case, you can identify in the figure that:
Therefore, knowing those values, you can substitute them into and then you must evaluate, in order to find the value of "x".
This is:
