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3 years ago

How do I find the volume of this right triangular prism?

Mathematics

1 answer:

frozen [14]3 years ago

8 0

I’ll try to make a step by step demonstration! Feel free to skip to step 5 for the answer, though
1. The formula for a right triangular prism is (1/2)*base*height*length, and we know what the base (4 cm) and length (8 cm) are, but not the height
2. To find the height we must divide the side triangle into two, which then gives us two right triangles
3. Focusing on just one of the right triangles, its base will be 2 cm rather than 4 (as it has been divided by two) and its hypotenuse will be 4 cm; using Pythagorean’s theorem (a^2 + b^2 = c^2), solve for the missing side (the height), which should end up being √12
4. Multiply! (1/2)4*√12*8 ≈ 55.425
5. Round to the nearest tenth —> 55.4
I hope this helped somewhat! Comment if clarification is needed

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3 years ago

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A store owner spends 7x + 13 dollars on two orders of boxes of light bulbs, including shipping.

Alex Ar [27]

Answer:

$B = 4x + 8$

A box = $11

Step-by-step explanation:

Given

$Total = 7x + 13$

Represent the first order with A and the second with B.

So, we have:

$A = 3x + 5$

Solving (a): Find B.

To find B, we make use of:

$A + B = Total$

Make B the subject

$B = Total - A$

Substitute values for Total and A

$B = 7x + 13 - (3x + 5)$

Open bracket

$B = 7x + 13 - 3x - 5$

Collect Like Terms

$B = 7x - 3x + 13 - 5$

$B = 4x + 8$

Solving (b): Cost of a box of light bulb

This means that:

$Total = 90$

Substitute 7x + 13 for Total

$7x + 13 = 90$

Collect Like Terms

$7x = 90 - 13$

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Make x the subject

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3 years ago

what is the slope of a line perpendicular to the line whose equation is 5x+6y=42. fully reduce your answer

oksian1 [2.3K]

Answer:

the slope of the line that is perpendicular to the given line is $\frac{6}{5}$

Step-by-step explanation:

As the slope intercept form is

$y=mx+b$

Where

m is the slope
b is the y-intercept

Considering the equation

$5x+6y=42$

$\mathrm{Slope-Intercept\:form\:of}\:5x+6y=42:\quad y=-\frac{5}{6}x+7$

$\mathrm{Slope\:of\:}-\frac{5}{6}x+7:\quad m=-\frac{5}{6}$

As we know that perpendicular lines have negative reciprocal slopes.

So,

$-\frac{1}{-\frac{5}{6}}=\frac{6}{5}$

Hence, the slope of the line that is perpendicular to the given line is $\frac{6}{5}$

Keywords: slope, slope of a line, equation

Learn more about slope of a line of the equation from brainly.com/question/13793576

#learnwithBrainly

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3 years ago

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Romashka-Z-Leto [24]

Answer:

Step-by-step explanation:

A 95% confidence level interval will have 0.52 (lower interval) & 0.68 (upper interval) which means that that if 90 individuals root for North HS then p value is 0.6 which will fall in the 95% confidence interval range.
For the option B the p value will also be same as in case A hence B is true as an alternative hypothesis.
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4 years ago

Find the constant of variation and the slope of the direct variation model<br> y=2x

djyliett [7]

A direct proportional variation, is really just a slope-intercept form of equation, except that the y-intercept is always 0, and the constant of variation "k" is the slope pretty much.

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
y=\stackrel{\stackrel{slope}{k}}{2}x\stackrel{y-intercept}{+0}\impliedby \stackrel{k}{2}\qquad \qquad \stackrel{slope}{\cfrac{2}{1}}$

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3 years ago