Perform the indicated operations on the following polynomials.Add: 3x^3+4x^2-x+8 and x^3-7x^2+2x-16
Answers
Final answer:
To add the polynomials, combine like terms by adding the coefficients. The sum of the polynomials is 4x^3 - 3x^2 + x - 8.
Explanation:
To add the polynomials 3x^3+4x^2-x+8 and x^3-7x^2+2x-16, we combine like terms. We add the coefficients of the terms with the same degree of x.
Starting with the terms with degree 3, we have 3x^3 + x^3 = 4x^3.
Continuing with the terms with degree 2, we have 4x^2 - 7x^2 = -3x^2, and for the terms with degree 1, we have -x + 2x = x. Lastly, for the terms with degree 0 or the constant terms, we have 8 - 16 = -8.
Therefore, the sum of the polynomials is 4x^3 - 3x^2 + x - 8.
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When applied to a triangle, a dilation with a positive scale factor does not preserve __________. A. angle measure B. orientation C. shape D. length
If the equation for the regression line is y=-8x+3 then the slope of this line is
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x+3y=6
3y=-x+6 /:3
y=
y=ax+b
a is a slope
so a=
Answers
Your slope is 4/3
You y-intercept is -5
put it in slope intercept form which is y=MX+B
you get y=4/3x-5
2) 4x+6y=24 4x-y=10
3)2x-y=-3 x+3y=16
4) 2x+3y=7 3x+4y=10
Answers
First of all we have add both equation but to be sure that the value we want to eliminate are both in a way that would make it possible t be deleted.
3x+y=-1
5x-y= 9
8x = 8
x= 1
In this case we are able to eliminate y becuase if we add +y-y we get that our answer is 0. and 3x + 5x would be 8x and -1+9 would be equal to 8 and to find x we needed to divided giving us that the answer for x is 1 becuase 8/8 is 1.
Then to find y we substitude the value of x in any of the formulas.
3(1)+y= -1
3+y= -1
y= -1-3
y=-4
When we have our y value we can determine if it is correct by replace the values.
5(1)--4= 9
5+4= 9
9=9
Up until now we are fine. So we do the same with the other equation.
3(1)+-4=-1
3+-4=-1
-1=-1
So by this we can now detemine that.
x= 1
y= -4
2) 4x+6y=24 4x-y=10
4x+ 6y =24
4x-y=10 (*-1)
4x+6y=24
-4x+y=-10
7y= 14
y= 14/7
y= 2
In this case we are not able to delete any of the variables so we multiplied by -1 to be able to eliminate x.
Then to find x we substitute the value of y in any of the formulas.
4x-2=10
4x= 10+2
x= 12/4
x= 3
So we now know our variables so we substituted them to see if they are correct.
4(3)+6(2)=24
12+12=24
24=24
We do the same with the other equation.
4(3)-2=10
12-2 =10
10= 10
So we can assume that.
x= 3
y= 2
3)2x-y=-3 x+3y=16
(3*)2x- y= -3
x+ 3y = 16
6x -3y = -9
x+3y =16
7x= 7
x= 1
In this case we are not able to delete any of the variables so we multiplied by 3 to be able to eliminate y.
Then to find y we substitute the value of x in any of the formulas.
1+ 3y = 16
3y= 16-1
y= 15/3
y= 5
So we now know our variables so we substituted them to see if they are correct.
2(1)- 5 =-3
2-5= -3
-3= -3
We do the same with the other equation.
1+3(5)= 16
1+15=16
16=16
So we now are sure that
x= 1
y= 5
4) 2x+3y=7 3x+4y=10
2x+3y =7 ( * - 4)
3x+4y =10 ( * 3)
-8x -12y = -28
9x +12y = 30
x= 2
In this case we are not able to delete any of the variables so we multiplied one of teh quations by - 4 to be able to subtract in our sum and the other by 3 to have the same number on y to be able to eliminate y.
Then to find y we substitute the value of x in any of the formulas.
2(2)+3y= 7
4+3y=7
3y= 7-4
y= 3/3
y= 1
So we now know our variables so we substituted them to see if they are correct.
3(2)+4(1)= 10
6+4=10
10=10
We do the same for the other
2(2)+3(1)=7
4+3= 7
7=7
So with that we can say that.
x= 2
y= 1
Answers
Answer:15 seniors served on the student council during their freshman year, 14 seniors served during their sophomore year, 16 seniors served during their junior year, and 3 seniors have never served before.
Step-by-step explanation:
Final answer:
Using inclusion and exclusion principles, we find that 2 seniors served on the student council during each of the four years in high school.
Explanation:
The problem can be solved using the Principle of Inclusion and Exclusion (PIE), a common technique in combinatorial mathematics. First, we add the number of seniors serving in their freshman, sophomore, and junior years: 3 (never served) + 10 (junior) + 9 (sophomore) + 11 (freshman) giving us 33.
Then, we subtract the number of seniors who served during both sophomore and junior years, freshman and junior years, and freshman and sophomore years: 33 - 5 (sophomore and junior) - 6 (freshman and junior) - 4 (freshman and sophomore). This results in 18.
However, from the initial condition we know that there are 20 seniors in total. Therefore, the two 'extra' seniors must have served all four years in high school. Thus we find that 2 seniors served on the student council during each of the four years in high school.
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Answers