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Phantasy [73]
2 years ago
14

8. A novel has 14 times as many pages as a short story. The combined number

Mathematics
1 answer:
alekssr [168]2 years ago
4 0

Answer:

The short story have 26 pages

The novel's pages is  364

Step-by-step explanation:

Step one:

given data

let the short story have x pages

so that the novel's pages will be 14x

the combined pages for novel and short story is =390 pages

Required

the individual number of pages

14x+x=390

15x=390

divide both sides by 15

x=26

the short story have 26 pages

the novel's pages will be 14(26)= 364

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The slope of a line perpendicular to the

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<h3>How to find the slope of a line?</h3>

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The two rectangular prisms are similar. What is the volume of the larger rectangular prism?
Brums [2.3K]

The question is missing the figure which is attached below.

Answer:

1620 cm³

Step-by-step explanation:

Given:

The two prisms are similar.

Volume of the smaller prism (V₁) = 60 cm³

Length of the smaller prism (l₁) = 5 cm

Length of the larger prism (l₂) = 15 cm

Now, we know that, for similar figures, the dimensions of the figure are in proportion to each other. Therefore,

\frac{l_2}{l_1}=\frac{b_2}{b_1}=\frac{h_2}{h_1}=k(constant)\\\\Where,\\b_1,b_2\to\ widths\ of smaller\ and\ larger\ prisms\ respectively\\\\h_1,h_2\to\ heights\ of\ smaller\ and\ larger\ prisms\ respectively

\frac{l_2}{l_1}=\frac{15\ cm}{5\ cm}=3\\\\\therefore\ k=3

This means that, the smaller figure is dilated by a scale factor of 3.

Hence, l_2=3l_1,b_2=3b_1,h_2=3h_1

Volume of smaller prism is given as:

V_1=l_1b_1h_1\\\\l_1b_1h_1=60\ cm^3

Volume of larger prism is given as;

V_2=l_2b_2h_2\\\\V_2=3l_1\times 3b_1\times 3h_1\\\\V_2=27(l_1 b_1h_1)\\\\V_2=27\times 60=1620\ cm^3\ \ \ \ [\because\ l_1b_1h_1=60\ cm^3]

Therefore, the volume of the larger rectangular prism is 1620 cm³.

4 0
2 years ago
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