Answer:
- c0 = 8
- c1 = 24
- c2 = 30
- c3 = 42
Step-by-step explanation:
It is convenient to notice that the pattern of coefficients that need to be multiplied and summed is a pattern of Xs.
For the constant, c0, only the constants need to be multiplied.
c0 = 4·2 = 8
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For the x-term coefficient, the constant of one series needs to be multiplied by the x-term of the other, and the two products added.
c1 = 4·5 +2·2
c1 = 24
If you draw real or imagined lines between the coefficients being multiplied, you see that they form an X.
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For the x²-term coefficient, the above X gets wider, and a vertical | is added. That is constant multiplies x² term and x-term multiplies x-term. The sum has three terms:
c2 = 4·3 +2·4 +2·5
c2 = 30
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For the x³ term, there are now two Xs, one wide and one narrower. Constant terms multiply x³ terms and x-terms multiply x² terms.
c3 = 4·3 +2·2 +2·3 +5·4
c3 = 42
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This sort of pattern of Xs can be used wherever polynomials (or multidigit numbers) are multiplied. It can help you ensure that all of the products that need to be included in a sum are accounted for.
Answer:
Step-by-step explanation:
let : x The length and y the width you have this system :
xy =60....(1)
x = y+10...(2)
put the value for x in (1): (y+10)y =60
the quadratic equation is : y² +10y - 60 = 0
Δ =b² - 4ac a = 1 b= 10 c= - 60
Δ =10² - 4(1)(-60) = 324 =18²
y 1 = (-10-18)/2 negatif...... refused
y 2 = (-10+18)/2 =4
the width is 4
Answer: I DON'T KNOW
Step-by-step explanation:
First you want to change the 4% to a fraction so 4/100. Then you have to figure out if 4/100 or 1/10 is larger. 4/100 reduces to 1/25. So the 1/10 or 1 in 10 is more often then the 1/25 or 1 in 25.
Answer:
x = $3.50; y = $2.25
Step-by-step explanation:
First, come up with your two equations where x= price of walnuts and y= price of chocolate chips: 8x + 4y = 37 and 3x + 2y = 15. Solve the first equation.
3x + 2y = 15
3x = 15 - 2y
x = (15 - 2y)/3
Plug in the answer to your second equation.
8(15 - 2y)/3 + 4y = 37
(120 - 16y)/3 + 4y = 37
120 - 16y + 12y = 111
120 - 4y = 111
-4y = -9
y = 2.25
Plug in your answer to find <em>x.</em>
3x + 2(2.25) = 15
3x + 4.5 = 15
3x = 10.5
x = 3.5
Check your equation.
1) 3(3.5) + 2(2.25) = 15
10.5 + 4.5 = 15
15 = 15
2) 8(3.5) + 4(2.25) = 37
28 + 9 = 37
37 = 37
