Lilygrimm06idn
Answered

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Jane evaluates [tex]$x^2-3x+5$[/tex] for [tex]$x=-2$[/tex] below.

Step 1: [tex]$(-2)^2-3(-2)+5$[/tex]
Step 2: [tex][tex]$=4+6+5$[/tex][/tex]
Step 3: [tex]$=15$[/tex]

What, if any, was Jane's mistake?

A. Jane made no mistakes.
B. Jane incorrectly evaluated [tex]$(-2)^2$[/tex] in step 2.
C. Jane incorrectly added the terms in step 3.
D. Jane incorrectly substituted in [tex][tex]$x=-2$[/tex][/tex] in step 1.

Sagot :

GinnyAnsweridn
To evaluate the expression [tex]\(x^2 - 3x + 5\)[/tex] for [tex]\(x = -2\)[/tex], let's follow the steps:

1. Substitute [tex]\(x = -2\)[/tex] into the expression:
[tex]\[ (-2)^2 - 3(-2) + 5 \][/tex]

2. Evaluate each part of the expression:

- [tex]\((-2)^2\)[/tex]:
[tex]\[ (-2)^2 = (-2) \times (-2) = 4 \][/tex]

- [tex]\(-3(-2)\)[/tex]:
[tex]\[ -3 \times (-2) = 6 \][/tex]

- The constant term remains:
[tex]\[ 5 \][/tex]

So, the expression now is:
[tex]\[ 4 + 6 + 5 \][/tex]

3. Add the terms together:
[tex]\[ 4 + 6 = 10 \][/tex]
[tex]\[ 10 + 5 = 15 \][/tex]

Thus, the correct evaluation of [tex]\(x^2 - 3x + 5\)[/tex] for [tex]\(x = -2\)[/tex] is 15.

Jane made a mistake in Step 2. Instead of evaluating [tex]\((-2)^2\)[/tex] correctly as 4, Jane incorrectly evaluated it as -4. Therefore, the correct answer is:

Jane incorrectly evaluated [tex]\((-2)^2\)[/tex] in Step 2.
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