(-3x)²-(3x-2)²-6*(2x-1.5)

1 answer:

4 0

Without the instructions, I can only assume that you are to "expand the given expression."

Following order of operations rules requires that (3x-2)^2 and -6(2x-1.5) be evaluated first.

(3x-2)^2 = 9x^2 - 12x + 4 and -6(2x-1.5) = -12x + 9

Then we have 9x^2 - (9x^2 - 12x + 4) -12x + 9

the 9x^2 terms cancel, leaving us with 12x - 4 - 12x + 9 = 5 (answer)

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Which one of the following statements is true? (5 points)

DanielleElmas [232]

Answer:

None of these statements are true.

Step-by-step explanation:

a) The derivative of (fg)(x) is f'g +fg' according to the product rule for derivatives.

b) The derivative of |x² +x| is a 3-part piecewise linear function equal to 2x+1 for |x+1/2| > 1/2, and equal to -2x-1 for |x+1/2| < 1/2. It is undefined for x=0 and x=1.

c) for y = √f(x), y' = f'(x)/(2√f(x))

8 0

3 years ago

What is the sum of the geometric series

lbvjy [14]

If $S$ denotes the sum of the first $n$ terms of a geometric series with first term $a$ and common ratio $r$ , then

$S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}$
$rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n$
$\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n$
$\implies (1-r)S=a(1-r^n)$
$\implies S=a=\dfrac{1-r^n}{1-r}$

Using summation notation, you have

$S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}$

In this case, you have $a=2$ , $r=\dfrac12$ , and $n=16$ . So the value of the sum is

$\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67$

Rounded to the nearest whole number, the answer would be 3.

4 0

3 years ago

Read 2 more answers

In the accompanying diagram of parallelogram ABCD, LaTeX: m\angle A=x+17 m ∠ A = x + 17 and LaTeX: m\angle C=2x-4 m ∠ C = 2 x −

jek_recluse [69]

Answer:
x = 21

Explanation:
In a parallelogram, each two opposite angles are equal.

In the given parallelogram ABCD, we can note that angles A and C are opposite angles. This means that they have equal measures.

Therefore:
∠A = ∠C
x + 17 = 2x - 4
17 + 4 = 2x - x
x = 21

We can check:
angle A = 21 + 17 = 38°
angle C = 2(21) - 4 = 38°
They are equal

Hope this helps :)