Part A: Solve –mk – 120 > 95 for m. Show your work.
2 answers:
Hello there!
Part A.) Solve -mk - 120 > 95 for m.
First, we need to understand that our primary goal is to isolate m on one side of the inequality.
-mk - 120 > 95
Currently, we have m being multiplied by -k and added to -120.
First, let's cancel out -120 by adding 120 to both sides.
-120 + 120 = 0
95 + 120 = 215
We now have:
-mk > 215
Divide both sides by -k. This is because m is being multiplied by -k. In order to cancel it out, you must perform the opposite order of operations.
-mk / -k = m
Remember, when you divide or multiply a number in an inequality, you must flip the sign to its opposite.
We now are left with:
m
This is your solution for part A.
Part B.) Solve 2c - 9f = 45 for f.
Remember that our primary goal is to isolate f on one side of the equation.
2c - 9f = 45
Since -9f is being added to 2c, perform the opposite order or operations on 2c.
+ 2c - 2c = 0
We now have:
-9f = -2c + 45
To solve for f, divide both sides by -9.
f =
or 
- 5
This is your solution for part B.)
I hope this helps!
Part A.) Solve -mk - 120 > 95 for m.
First, we need to understand that our primary goal is to isolate m on one side of the inequality.
-mk - 120 > 95
Currently, we have m being multiplied by -k and added to -120.
First, let's cancel out -120 by adding 120 to both sides.
-120 + 120 = 0
95 + 120 = 215
We now have:
-mk > 215
Divide both sides by -k. This is because m is being multiplied by -k. In order to cancel it out, you must perform the opposite order of operations.
-mk / -k = m
Remember, when you divide or multiply a number in an inequality, you must flip the sign to its opposite.
We now are left with:
m
This is your solution for part A.
Part B.) Solve 2c - 9f = 45 for f.
Remember that our primary goal is to isolate f on one side of the equation.
2c - 9f = 45
Since -9f is being added to 2c, perform the opposite order or operations on 2c.
+ 2c - 2c = 0
We now have:
-9f = -2c + 45
To solve for f, divide both sides by -9.
f =
This is your solution for part B.)
I hope this helps!
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Answer:
The quotient when is divided by
is
with no remainder, so x+2 is a factor of p(x).
Step-by-step explanation:
As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form . In this case, we may use synthetic division, since
is equal to
. I will use synthetic division here as it is slightly faster than long division.
The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.
The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.
Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.
This is the answer: the quotient is , and the remainder is zero (which indicates that x+2 is a factor of p(x)).
--
Edit: long division
We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since is equal to
, the first term in the quotient will be
. Since
is equal to
, we must now subtract that from
.
We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.
<em>I know this might be difficult to follow, so please comment if you have any questions.</em>
