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Aneli [31]
3 years ago
11

A polynomial is to he constructed that will touch the x axis at most 4 times. What is the minimum degree of the polynomial?

Mathematics
1 answer:
AnnZ [28]3 years ago
7 0
At most 4 times
hmm
where it touches is when y=0
so just have lots of zeroes
y=(x-r1) is a zero
so 4 zeroes is
y=(x-r1)(x-r2)(x-r3)(x-r4)
if we expand it it is degree 4

minimum degree is 4th
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Since dimes + quarters = 22
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Let’s make d = dime, q = quarter
d + q = 22
0.10d + 0.25q = 4.00
Let’s use substitution
d + q = 22, get d or q by itself
d = 22 - q (plug into second equation)
0.10(22-q) + 0.25q = 4
2.2 - 0.10q + 0.25q = 4
2.2 + 0.15q = 4
0.15q = 1.8, q = 12
Since there are 12 quarters you know there are 10 dimes (22 in total)

Solution: 10 dimes, 12 quarters
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When Joey mowed lawns for 10 hours and walked dogo
ankoles [38]

The charges for mowing lawns are $5 per hour and charges for walking dogs are $3 per hour.

Step-by-step explanation:

Let,

x be the charge per hour for mowing lawns

y be the charge per hour for walking dogs

According to given statement;

10x+4y=62    Eqn 1

8x+5y=55      Eqn 2

Multiplying Eqn 1 by 5

5(10x+4y=62)\\50x+20y=310\ \ \ Eqn\ 3

Multiplying Eqn 2 by 4

4(8x+5y=55)\\32x+20y=220\ \ \ Eqn\ 4\\

Subtracting Eqn 4 from Eqn 3

(50x+20y)-(32x+20y)=310-220\\50x+20y-32x-20y=90\\18x=90

Dividing both sides by 18

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Putting in Eqn 1

10(5)+4y=62\\50+4y=62\\4y=62-50\\4y=12

Dividing both sides by 4

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The charges for mowing lawns are $5 per hour and charges for walking dogs are $3 per hour.

Keywords: linear equation, subtraction

Learn more about linear equations at:

  • brainly.com/question/2821386
  • brainly.com/question/2860697

#LearnwithBrainly

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