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sergij07 [2.7K]
3 years ago
15

A collection of animals including both birds and beasts has 43 heads and 120 feet how many based are there in the collection

Mathematics
1 answer:
DaniilM [7]3 years ago
8 0

Step-by-step explanation:

x = number of birds

y = number of beasts

x + y = 43 (as each of these creatures had only 1 head).

2x + 4y = 120 (birds have 2 feet, beasts 4 feet).

x + 2y = 60 (divided both sides by 2)

so, second equation minus the first equation is

(x-x) + (2y-y) = 60-43

y = 17

x + y = 43

x + 17 = 43

x = 26

so, there are 17 beasts and 26 birds.

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What is the similarity ratio of ΔABC to ΔDEF?<br> Tri ABC: AC=4 CB=5<br> Tri DEF: DF= 2
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The similarity ratio of ΔABC to ΔDEF = 2 : 1.

Solution:

The image attached below.

Given  ΔABC to ΔDEF are similar.

To find the ratio of similarity triangle ABC and triangle DEF.

In ΔABC: AC = 4 and CB = 5

In ΔDEF: DF = 2, EF = ?

Let us first find the length of EF.

We know that, If two triangles are similar, then the corresponding sides are proportional.

⇒ \frac{AC}{DF} =\frac{BC}{EF}

⇒ \frac{4}{2} =\frac{5}{EF}

⇒ 4EF=5\times2

⇒ EF=\frac{5\times 2}{4}

⇒ EF=\frac{5}{2}

Ratio of ΔABC to ΔDEF = \frac{AC}{DF} =\frac{4}{2}=\frac{2}{1}

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Step-by-step explanation:

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The given data are:

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s = 7.7

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The given values are:

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Substituing values:

(\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816})

(29.7532, 170.9093)

The interval for variance is: 29.7532 ≤ \sigma^{2} ≤ 170.9093

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