MATHEMATICS MIDDLE SCHOOL

Is g(x) = (x-1)(x+1)(x-3i)(x+3i) the factored form of f(x) = x^4+8x^2-9

Answers

Answer 1

Answer:

Answer:

Yes

Step-by-step explanation:

(x-1)(x+1)(x-3i)(x+3i)

FOIL ( x-1) (x+1) = x^2 -x+x-1 = x^2 -1

FOIL (x-3i)(x+3i) = x^2 +3ix -3ix -9i^2 = x^2 -9(-1) = x^2 +9

(x-1)(x+1)(x-3i)(x+3i) = (x^2 -1) (x^2 +9)

FOIL again

x^4 +9x^2 -x^2 -9

x^2 +8x^2 -9

This is the factored form

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Is 96 fl oz greater than 8 pt

Answers

96 fl oz is greater than 8 pt :3

Yes, 96 fl oz is greater than 8 pt.

What is the pattern of 3.5, 13, 41.5, 127,,,, and the anwser

Answers

Answer with Step-by-step explanation:

We are given a sequence as:

3.5, 13, 41.5, 127,...

we have to determine the pattern

13= 3.5×3+2.5

41.5= 13×3+2.5

127= 41.5×3+2.5

Hence, the sequence is defined as next term in the sequence is 3 times the previous term of the sequence plus 2.5

i.e. $a_(n+1) =3a_(n) +2.5\ ;\ a_(1)=3.5$

Hence, Pattern is:

$a_(n+1) =3a_(n) +2.5\ ;\ a_(1)=3.5$

times 3 plus 2.5 is the pattern, and the next number is 383.5

Is the additiveinverse of a number always, sometimes, or
never negative? Justify your answer with an
example.

Answers

Answer: I think it's sometimes, since additive inverse's yield zero and you could possibly have a negative a value.

Step-by-step explanation:

Use the following graph of the function f(x) = 3x4 − x3 + 3x2 + x − 3 to answer this question: graph of 3 x to the fourth, minus x cubed, plus 3 x squared, plus x minus 3. What is the average rate of change from x = 0 to x = 1?

Answers

For this case we have the following function:
$f (x) = 3x ^ 4 - x ^ 3 + 3x ^ 2 + x - 3$
By definition we have that the average rate of change is given by:
$AVR = (f(x2)-f(x1))/(x2-x1)$
We evaluate the function for the given interval:
For x = 0:
$f (0) = 3 (0) ^ 4 - (0) ^ 3 + 3 (0) ^ 2 + (0) - 3f (0) = - 3$
For x = 1:
$f (1) = 3 (1) ^ 4 - (1) ^ 3 + 3 (1) ^ 2 + (1) - 3f (1) = 3$
Substituting values we have:
$AVR = (3-(-3))/(1-0)$
Rewriting we have:
$AVR = (3+3)/(1-0)$
$AVR = (6)/(1)$
$AVR =6$
Answer:
the average rate of change from x = 0 to x = 1 is:
$AVR =6$

Answer:

Average rat of change of function is 6 from x = 0 to x = 1.

Step-by-step explanation:

We are given a function:

$f(x) = 3x^4 - x^3 + 3x^2 + x - 3$

The attached image shows the graph for the given function.

Average rate of change of function =

$\text{Average rate of change} = \displaystyle(\delta y)/(\delta x) = (f(b)-f(a))/(b-a)$

Now we will evaluate f(1) and f(0).

$f(x) = 3x^4 - x^3 + 3x^2 + x - 3\nf(1) = 3(1)^4 - (1)^3 + 3(1)^2 + (1) - 3 = 3\nf(0) = 3(0)^4 - (0)^3 + 3(0)^2 + (0) - 3 = -3$

Putting the values, we get,

$\text{Average rate of change} = \displaystyle(f(1)-f(0))/(1-0)\n\n= (3-(-3))/(1-0) = (6)/(1) = 6$

Thus, the average rat of change of function is 6 from x = 0 to x = 1.

Complete the solution of the equation. Find the value of y when x equals -2. -4x+8y=-24

Answers

Answer:y=-4

Step-by-step explanation:

Multiply -4 by -2 you get positive 8 rewrite the equation subtract 8 from both sides that leaves you with 8y=-32 your final step is to divide both sides 8 that leaves you with -4 which is the answer.

Answer:

y=-4

Step-by-step explanation:

-4(-2)+8y=-24

The negatives cancel out to make a positive.

8+8y=-24

subtract the number without a variable from the answer.

-24-8=-32

You are taking more away from the negative.

8y=-32

Divide the 32 by 8 to get your answer

-32/8=-4

Therefor your answer is y=-4

Write an equation of the line that passes through (−4,−5) and is parallel to the line y=−4x−1.

Answers

Answer:

y = -4x -21

Step-by-step explanation:

Use slope intercept form:

y = mx + b

use slope from original line: y = -4x - 1 so slope is -4

use the given point (-4,-5) for the x and y values and solve for b

-5 = -4(-4) + b

-5 = 16 + b

-5 - 16 = b

-21 = b

substitute b value in slope intercept form

y = -4x - 21

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