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Fofino [41]
1 year ago
10

What value of c makes x2 6x c a perfect square trinomial? c = If x2 6x c = (x d)2, then d =.

Mathematics
1 answer:
Mariana [72]1 year ago
3 0

\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^2 \pm \stackrel{\stackrel{2\sqrt{x^2}\sqrt{c^2}}{\downarrow }}{6x} +c^2~\hspace{10em}6x=2\sqrt{x^2}\sqrt{c^2}\implies 6x=2xc \\\\\\ \cfrac{6x}{2x}=c\implies 3=c\implies 9=c^2~\hfill \boxed{(x\pm 3)^2}

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The question is incomplete. Here is the complete question:

What is the volume of this triangular prism?

Base length = 22.4 cm

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Length = 28 cm

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Answer:

V=5,676.16\ cm^3

Step-by-step explanation:

Given:

The base of the prism is triangular with base length equal to 22.4 cm and height 18.1 cm. The length of the prism is 28 cm.

The volume of a triangular prism is defined by the formula:

V=(Area\ of\ base)\times (length)

Here, the base is triangular and the area of a triangle is:

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Therefore,  the volume of the triangular prism is given as:

V=\frac{1}{2}(base\times height\times length)

Now, plug in the given values and solve for the volume 'V'.

V=\frac{1}{2}(22.4\ cm\times 18.1\ cm\times 28\ cm)\\\\V=\frac{1}{2}(11,352.32\ cm^3)\\\\V=5,676.16\ cm^3

Therefore, the correct answer is the third option.

V=5,676.16\ cm^3

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