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arlik [135]
3 years ago
13

In a different dimension, cows have $x+3$ legs, with 3 toes on each leg. Chickens have $2x-4$ legs, with 7 toes on each leg. If

your farm only has two cows and one chicken, what is the expression for how many animal toes there are in total (not including yours)? Give your answer in simplest form.
Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
6 0

Answer:

20x-10

Step-by-step explanation:

Cows have x+3 legs and 3 toes on each leg, if we want to find the number of toes of ONE cow we have to multiply the legs by the toes giving the following:

3(x+3) \quad (1)

But we have two cows so (1) we have to multiply it by 2 giving a total of:

2(3(x+3))\\6(x+3)\\6x+18 \quad (2)

By the other hand chickens have 2x-4 legs and 7 toes on each leg, if we want to find the number of toes we have to multiply the legs by the toes giving the following:

7(2x-4)\\14x-28 \quad (3)

To find the total amount of toes we have to add (2) and (3)

(6x+18)+(14x-28)\\20x-10

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Answer:

f\left(x\right)=x^3-6x^2+3x+10 is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.

Step-by-step explanation:

Given the function

f\left(x\right)=x^3-6x^2+3x+10

As the highest power of the x-variable is 3 with the leading coefficients of 1.

  • So, it is clear that the polynomial function of the least degree has the real coefficients and the leading coefficients of 1.

solving to get the zeros

f\left(x\right)=x^3-6x^2+3x+10

0=x^3-6x^2+3x+10              ∵  f(x)=0

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Factor\:x^3-6x^2+3x+10\::\:\left(x+1\right)\left(x-2\right)\left(x-5\right)=0

so

\left(x+1\right)\left(x-2\right)\left(x-5\right)=0    

Using the zero factor principle

if  ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

x+1=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0

x=-1,\:x=2,\:x=5

Therefore, the zeros of the function are:

x=-1,\:x=2,\:x=5

f\left(x\right)=x^3-6x^2+3x+10 is the function of the least degree has the real coefficients and the leading coefficients of 1 and with the zeros -1, 5, and 2.

Therefore, the last option is true.    

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