Which polynomials are prime? Check all that apply. 2x2+ 7x + 1 5x2 – 10x + 5 3x2 + 8 4x2 – 25 x2 + 36

(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:

4321 = 1234 * 3 + 619

1234 = 619 * 1 + 615

619 = 615 * 1 + 4

615 = 4 * 153 + 3

4 = 3 * 1 + 1

Now we will express 1 as a linear combination of 4321 and 1234:

1 = 4 - 3

1 = 4 - (615 - 4 * 153) = 4 * 154 - 615

1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234

1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234

This reduces to

1 ≡ -1082 * 1234 (mod 4321)

Thus, the inverse is

-1082 ≡ 3239 (mod 4321)

(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.

 x = 27 + 3 √ 129/ 4, 27 − 3 √ 129/ 4

Please note: the entire equation mentioned is divided by 4, not only the last term. 

 x approximates to 15.26836251, − 1.76836251

That concludes my response. I hope this is helpful. You will still need to work on finding y and z, which can be quite challenging:)

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

-------------------------------------------------------------------------------------------------

Time elapsed since the balloon starts descending

This is the correct interpretation.

---------------------------------------------------------------------------------------------------

Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

---------------------------------------------------------------------------------------------------

(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

-------------------------------------------------------------------------------------------------

Time since descent began is incorrect because that is represented by t.

---------------------------------------------------------------------------------------------------

Time to reach the ground is inaccurate since a(t) is altitude, not time.

---------------------------------------------------------------------------------------------------

(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

---------------------------------------------------------------------------------------------------

The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

---------------------------------------------------------------------------------------------------

It is not the time needed to reach the ground.

---------------------------------------------------------------------------------------------------

5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.