Question

100 POINTSSSSS

If z(t)=2t^2+7t-4 find z(-7) and z(5) .

A. z(-7) = 143; z(5) = 131

B. z(-7) = 101; z(5) = 53

C. z(-7) = 45; z(5) = 81

D. z(-7) = -151; z(5) = 81

Answer 1

Alright, genius, grab your calculator or let's just flex those mental muscles. You've got z(t) = 2t^2 + 7t - 4, and you need to find z(-7) and z(5).

First off, z(-7):

Substitute t = -7 into the equation.

z(-7) = 2(-7)^2 + 7(-7) - 4

= 2 * 49 + (-49) - 4

= 98 - 49 - 4

= 45.

Ta-da! For z(-7), we've got 45. So, if an answer choice doesn't have 45 for z(-7), you can chuck it out the window.

Next up, z(5):

Substitute t = 5 into the equation.

z(5) = 2(5)^2 + 7(5) - 4

= 2 * 25 + 35 - 4

= 50 + 35 - 4

= 85 - 4

= 81.

Wow, you're still awake? Good, because we've got 81 for z(5).

So, z(-7) = 45 and z(5) = 81. That would be choice C, my friend. Time to celebrate, or, you know, keep doing math if that's your jam.

Answer 2

C. z(-7) = 45; z(5) = 81

Explanation:

We can find z(-7) and z(5) by substituting t = -7 and t = 5, respectively, into the function z(t).

`\begin{aligned} \textsf{z(-7) } &\sf = 2(-7)^2 + 7(-7) - 4 \\\\ &\sf = 2* 49 -49 - 5 \\\\ &\sf = 98 -49 -5 \\\\ &\sf = 49 - 4 \\\\ &\sf =45 \end{aligned}`

Similarly:

`\begin{aligned} \textsf{z(5) } &\sf = 2(5)^2 + 7(5) - 4 \\\\ &\sf = 2* 25 + 35 - 4 \\\\ &\sf = 50+ 35 -4 \\\\ &\sf = 85 - 4 \\\\ &\sf = 81 \end{aligned}`

Therefore, answer is:

C. z(-7) = 45; z(5) = 81