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11111nata11111 [884]
3 years ago
15

A. Is the sum of two polynomials always a polynomial? Explain

Mathematics
1 answer:
IgorLugansk [536]3 years ago
6 0

Answer:  The answers for both (a) and (b) is YES.


Step-by-step explanation: A polynomial is an algebraic expression containing   two or more algebraic terms, i.e., the sum of several terms that contain different powers of the same variable or variables with real coefficients.

For example, p(x) = 4x²+x+2 is a polynomial in variable 'x'.

(a) Yes, the sum of two polynomials is again a polynomial. For example,

if p(x) = ax² + bx + c  and  q(x) = dx² + ex + f, where, a, b, c, d, e and f are real numbers, then their sum will be

p(x) + q(x) = (a+d)x²+(b+e)x+(c+f), which is again a polynomial in 'x' with real coefficients.

(b) Yes, the difference of two polynomials is again a polynomial. For example,

p(x) - q(x) = (a-d)x²+(b-e)x+(c-f), which is again a polynomial in 'x' with real coefficients.

Thus, the answer is YES.

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Two separate bacteria populations that grow each month at different rates are represented by the functions f(x) and g(x). In wha
denis23 [38]

Step-by-step explanation:

This is confusing, what does g(x) equal? There's a bunch of random numbers there. I'll just assume.

They stated that f(x) needs to exceed g(x), so make an inequality plugging in the values

3x > 7x + 6

You see, function f(x) needs to be higher than function g(x)

Subtract 7x from both sides to get:

- 4x > 6

Divide both sides by -4, when you divide by a negative number the signs switch so it is now less than.

x < -1.5

And obviously that's not an answer up there, so you made a mistake stating the values of the functions

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Which outcomes are in A or B ?
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B...........................

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A baby elephant weighs 250 lb,
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Tons would be 0.125
and Kg would be 113.636
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The sales tax in your city is 4.4% and a item costs 3$ before tax. How much tax would you pay
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4 0
3 years ago
Please show your work this question what made you come to the conclusion. Thank you
AveGali [126]

Answer:

B the range, the x- and y-intercept

Step-by-step explanation:

the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).

but the range changes, as for the original function y could only have positive values - even for negative x.

the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.

the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.

the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.

the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.

the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)

3 {b}^{x + 1}  = 2

{b}^{x + 1}  = 2 \div 3

log_{b}(2 \div 3)  = x + 1

x =  log_{b}(2 \div 3)  - 1

8 0
3 years ago
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