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3 years ago

What is the coefficient of x2 in the expansion of (x + 2)3?

1 answer:

4 0

One way is that you can just factor it out: (x+2)(x+2)(x+2)
For the first pair, you get $x^2+4x+4$ .
Then do $(x^2+4x+4)$ * $(x+2)$
That will be $x^3+6x^2+12x+8$
So the answer is 6

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a mechanic worked 20 hours. another mechanic worked 15 hours. together they charged a total of $1950. what was the rate charged

Natasha_Volkova [10]

Answer: The mechanics both charged $70 and $45 per hour respectively

Step-by-step explanation: We shall start by calling the mechanics hourly rates x and y respectively. So if one worked for 20 hours and charged 20 times x dollars, and the other one worked for 15 hours and charged 15 times y dollars, totalling 1950 dollars, we can write the following expression,

20x + 15y = 1950

Also, if the sum of the two rates was 115 dollars, that means for working for an hour only, they both would earn

x + y = 115

We now have a pair of simultaneous equations

20x + 15y = 1950 --------(1)

x + y = 115 ------------------(2)

We shall use the substitution method for this problem.

From equation (2), make x the subject of the equation

x = 115 - y

Substitute for the value of x into equation (1)

20(115 - y) + 15y = 1950

2300 - 20y + 15y = 1950

By collecting like terms we now have

2300 - 1950 = 20y - 15y

(Note that when a negative value crosses to the other side of the equation, it becomes a positive value and vice versa)

350 = 5y

Divide both sides of the equation by 5

70 = y

We now substitute for the value of y into equation (2)

x + y = 115

x + 70 = 115

Subtract 70 from both sides of the equation

x = 45.

Therefore, the rate they charged per hour were $45 and $70 respectively.

7 0

3 years ago

I have 4 factors. Three of my factors are 1, 2, and 6. What is my fourth factor?

SIZIF [17.4K]

The 4th factor would be 3. You would find this out through a factor tree. If you don't know the original number when you start you look at your numbers. A factor of 1 usually goes with the highest number, assuming that the number 6 is the highest factor, that would be the original number. As 2 is the other known factor than we know that 3 has to be the last factor, because 2 x 3 = 6. It cannot be the number 12 because then there would be 6 factors not the needed 4.

7 0

3 years ago

Can u help me do this

chubhunter [2.5K]

There will be 2 books left over if he fills each box.
7 · 4 = 28
30 - 28 = 2

Good Luck

5 0

3 years ago

Midpoint Between Two Given Points

kondaur [170]

Answer:

(1, -7)

Step-by-step explanation:

the difference between -4 & 6 is 10 so you add 5 (half) to -4 or subtract from 6, this gives you 1

you do the same for -9 and -5, the midpoint for those being -7, I hope this helps

4 0

2 years ago

A measure of ________ for a numerical data set describes how its values vary with a single number

uysha [10]

The answer is variation.

6 0

3 years ago