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Daria states that the value of the expression –45 x 2 – x + 2.5 is sometimes negative. Which of the following values of x would support Daria’s claim? Select two that apply.

A.– 5/4
B.1
C.2.3
D.– 1.84

User Todd Mark
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1 Answer

1 vote

Final Answer:

The values of x that would support Daria's claim that the expression –45x2 – x + 2.5 is sometimes negative are A. –5/4 and D. –1.84.

Step-by-step explanation:

To ascertain whether the expression –45x² – x + 2.5 is sometimes negative, we'll assess the given values of x.

Starting with x = –5/4:

Substituting –5/4 into the expression:

–45 * (–5/4)² – (–5/4) + 2.5

First, let's evaluate the values:

–45 * (–5/4)² = –45 * 25/16 = –1125/16

–(–5/4) = 5/4

So, –1125/16 + 5/4 + 2.5 = –1125/16 + 20/16 + 40/16 = –1125/16 + 60/16 = –1065/16

The result, –1065/16, is negative, confirming that –5/4 satisfies the condition that makes the expression negative.

Moving on to x = –1.84:

Substituting –1.84 into the expression:

–45 * (–1.84)² – (–1.84) + 2.5

Evaluating the values:

–45 * (–1.84)² = –45 * 3.3856 = –152.352

–(–1.84) = 1.84

Now adding these up: –152.352 + 1.84 + 2.5 = –152.352 + 4.34 = –148.012

As –148.012 is also negative, –1.84 satisfies the condition for the expression to be negative.

Thus, both –5/4 and –1.84 are values for x that produce negative results in the expression, supporting Daria's claim.

Conversely, when substituting 1 and 2.3 into the expression:

For x = 1: –45 * 1² – 1 + 2.5 = –45 - 1 + 2.5 = –43.5 + 2.5 = –41 which is positive.

For x = 2.3: –45 * 2.3² – 2.3 + 2.5 = –45 * 5.29 – 2.3 + 2.5 = –238.05 – 2.3 + 2.5 = –238.05 – 0.8 = –238.85 which is also positive.

Therefore, options A) –5/4 and D) –1.84 are the values of x that support Daria's claim, while options B) 1 and C) 2.3 do not satisfy the condition of making the expression negative.

User Erynn
by
7.8k points
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