Problem 13
If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.
- Example: x^3 times x^3 = x^6 in the top left corner
- Another example: 2x times x = 2x^2 in the bottom right corner.
This is known as the box method to keep track of all the terms multiplied.
Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).
The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2
x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.
Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.
So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.
They need at least $510 to purchase the new gaming station.
Therefore,
12x + 9y ≥ 510
Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.
Therefore,
y ≤ 2x
Also, Fabio will walk at least 25 dogs.
Therefore,
y ≥ 25
Hence, the constraints are:
12x + 9y ≥ 510
y ≤ 2x
y ≥ 25
Hello!!
So the product is when numbers or variables are multiplied together. So if we have 12 * 3/4 then that equals 12/1*3/4=(12*3)/4=36/4=9
So we can see that the product of 12*3/4 is less than 12. We can see this right from the start by noticing that to be at least 12, then 12 would have to be multiplied by at minimum 1 meaning 12*1=12 anything less than 1 would result in a lesser value than 12.
Hope this helps!! Any questions please just ask!! Thank you!!!
Answer:
a, c, b, a
Step-by-step explanation:
There are 60 players on football team that are not seniors.
Step-by-step explanation:
<u>Method 1:</u>
Given
Total students = 84
Also given that
2 out of 7 are seniors
Which is 2/7
So in order to find the total number of seniors we will multiply the whole number of students to 2/7
So there are 24 seniors on the football team.
Players that are not seniors = 84 - 24 = 60
There are 60 players who are not seniors.
<u>Method 2:</u>
We can divide the total number by 7, to get how many sets of 7 players will be there
= 84/7 = 12
Now,
Multiplying 12 with 2 will give us the number of seniors in football team.
12*2 = 24 seniors
So,
Not seniors =84-24 = 60
Keywords: Percentage, Units
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