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Question 203028: I am so confused!
From the given polynomials, identify the polynomials of degree one.
a. 11y2 – 5 – 4y
b. (3x2)1/2 + 12
c. 7 – (12)1/2x
d. 2x + 13x2
e. 5x + 7y + 8
f. (12)1x1
g. x3 + 2x - 10
h. 3x + 4x - 4
Solve the following:
i. 2x = -3x + 9
ii. 3x/5 = -6
iii. y/4 + 2 = 7
iv. 16 = -2x/3
v. Find f(1) for f(x) = 2x3 - 3x2 + x – 21
vi. A function gives the value of C as 2 × (22/7) × r. Find C when r = 7 cm and r = 91 cm.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a. 11y2 – 5 – 4y
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this would be a polynomial of degree 2 because the highest exponent is 2.
by the way, y squared is usually shown as y^2 rather than y2. I think you mean y squared.
^ is shift 6 on your keyboard.
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b. (3x2)1/2 + 12
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degree of 2 because highest exponent is 2
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c. 7 – (12)1/2x
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not a polynomial because the x variable is in the denominator.
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d. 2x + 13x2
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degree of 2 because the highest exponent is 2
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e. 5x + 7y + 8
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this is a mixed polynomial. each term is looked at separately (5x is a term, 7y is a term). this would be degree 1 because the highest exponent is 1. any variable shown by itself is a degree 1 polynomial. x = x^1, etc.
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f. (12)1x1
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degree of 1 because highest exponent is 1.
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g. x3 + 2x - 10
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degree of 3 because the highest exponent is 3.
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h. 3x + 4x - 4
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degree of 1 because the highest exponent is 1.
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to be a polynomial, all exponents has to be a positive integer. 0 is a positive integer.
the degree of the polynomial is the highest exponent used in the polynomial.
mixed polynomials have the degree equal to the highest sum of exponents in each term.
example:
x^5 + x^4 = degree 5
x^5*y^2 + x^4*y^4 would be degree 8 because the sum of the exponents in the second term is greater than the sum of the exponents in the first term.
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variable that are multiplied together are called a term.
variables that are added together form separate terms.
x^2*x^3 = one term = degree of 5 because the exponents add up to 5.
x^2 + x^3 = 2 terms = degree of 3 because 3 is the highest exponent.
x^2*y^3*z^3 = one term = degree of 8 because the exponents add up to 8.
x^2 + y^3 + z^3 = 3 terms = degree of 3 because the highest exponent in any one term is 3.
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Solve the following:
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i. 2x = -3x + 9
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add 3x to both sides of the equation to get:
2x + 3x = 9 which becomes 5x = 9
divide both sides of equation by 5 to get:
x = 9/5
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ii. 3x/5 = -6
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multiply both sides of the equation by 5 to get:
3x = (-6)*5 which becomes 3x = -30
divide both sides of the equation by 3 to get:
x = (-30)/3 which becomes x = -10
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iii. y/4 + 2 = 7
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subtract 2 from both sides to get:
y/4 = 7 - 2 which becomes y/4 = 5
multiply both sides by 4 to get:
y = 4*5 which becomes y = 20
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iv. 16 = -2x/3
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multiply both sides of the equation by 3 to get:
3*16 = -2x which becomes 48 = -2x
divide both sides of the equation by (-2) to get:
48 / (-2) = x which becomes -24 = x
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v. Find f(1) for f(x) = 2x3 - 3x2 + x – 21
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you substitute 1 for x and solve:
f(1) = 2*(1^3) - 3*(1^2) + 1 - 21
since 1 to any power = 1, this becomes:
f(1) = 2*1 - 3*1 + 1 - 21 which becomes:
f(1) = 2 - 3 + 1 - 21 which becomes:
f = (-12)
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vi. A function gives the value of C as 2 × (22/7) × r. Find C when r = 7 cm and r = 91 cm.
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your formula is:
C = f(r) = 2*(22/7)*r
This means that the value of C is a function of r and can be found by the formula 2*(22/7)*r.
C if a function of r means that the value of C depends on what the value of r is.
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When r = 7, then f(r) becomes f(7).
You have C = f(7) = 2*(22/7)*7 = 44 cm.
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When r = 91, then f(r) becomes (f(91).
You have C = f(91) = 2*(22/7)*91 = 572 cm.
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