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2 years ago

Hazel is three times as old as Joel, and in 4 years she will be twice as old as Joel. How old was Hazel when Joel was born?

Mathematics

1 answer:

zhenek [66]2 years ago

7 0

Answer:

Hazel was 3 years old when Joel was born.

Step-by-step explanation:

Let x be the present age ( in years ) of Joel,

Given,

Hazel is three times as old as Joel,

Age of Hazel = 3x,

After 4 years, age of Joel = x + 4,

And, age of Hazel = 3x + 4

According to the question,

2(x+4) = 3x + 4

by distributive property,

2x + 8 = 3x + 4

By subtraction property of equality,

2x = 3x + 4 - 8

2x = 3x - 4

Again by subtraction property of equality,

-x = -4

Divide both sides by - 1

x = 4

Thus, the present age of Joel = 4,

Also, the present age of Hazel = 12,

Difference in ages = 12 - 4 = 3,

Therefore, Hazel was 3 years old when Joel was born.

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2 years ago

The Toga Trench is at an elevation of 35,702 feet below sea level .The south sandwich Trench is at an elevation of 23,737 ft . b

Aleks04 [339]

Answer:

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Step-by-step explanation:

Given the following:

Tonga trench Elevation = 35,702 Feets

South sandwich trench elevation = 23,737 Feets

Expressing both numbers as rational numbers :

Both the Tonga trench Elevation and South sandwich trench elevation are already stated as rational numbers because all integers are rational numbers, be it expressed as a quotient or proportion of integer numbers ( that is numbers that are expressed without decimal components.

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2 years ago

A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium

frosja888 [35]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.

Since a total of 47 hats where purchased, hence:

x + y + z = 47 (1)

Also, he spent a total of $302, hence:

5.5x + 6y + 7z = 302 (2)

He purchases three times as many medium hats as small hats, hence:

y = 3x

-x + 3y = 0 (3)

Represent equations 1, 2 and 3 in matrix form gives:

$\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]$

Therefore he purchases 6 small hats, 18 medium hats and 23 large hats

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2 years ago

In mathematics, the Nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/N. So, the first harmonic number is 1, th

Andreyy89

Answer:

cl + 1/(N+1)

Step-by-step explanation:

If we assume that the Nth harmonic number is cl. Then we are assuming that 1+1/2+1/3+1/4+...+1/N=cl

And we know that the (N+1)th harmonic number can be found by doing

1+1/2+1/3+1/4+...+1/N+1/(N+1)

=cl + 1/(N+1)

The (N+1)th harmonic number is cl + 1/(N+1) given that the Nth term is cl