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3 years ago

The perimeter of the rectangle below is 64 units. Find the length of side CD.

Mathematics

1 answer:

ahrayia [7]3 years ago

4 0

Answer:

CD = 18 units

Step-by-step explanation:

Given a rectangle with length x and width y, the perimeter is:

P = 2x + 2y

Here, we note that x = AB = CD, y = AD = BC, and P = 64 units. So:

2AB + 2BC = 64

We know that AB = 3z and BC = 2z + 2; plug these in:

2 * (3z) + 2 * (2z + 2) = 64

6z + 4z + 4 = 64

10z = 60

z = 6

Now that we've solved for z, we can find AB and, hence, CD because AB = CD.

AB = 3z = 3 * 6 = 18 units

Thus, CD = 18 units, as well.

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If it takes 3 men 5 hours to dig 12 holes, how many hours does it take for 3 men to dig 84 holes?

alexgriva [62]

Answer:

Hence it will take 35hours

Step-by-step explanation:

Let the time it took to dig hole be x

Ley the number of holes be n

Using the relationship x = kn (direct relationship)

if it takes 3 men 5 hours to dig 12 holes, hence;

when x = 5, n = 12

k = x/n

k = 5/12

To get how many hours it take for 3 men to dig 84 holes, then;

when n = 84, x = ?

x = 5/12 * 84

x = 5 * 7

x = 35hours

Hence it will take 35hours

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Step-by-step explanation:

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barxatty [35]

Answer:

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3 years ago

Find an explicit rule for the nth term of the sequence.The second and fifth terms of a geometric sequence are 18 and 144, respec

vova2212 [387]

Given:

second term = 18

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$\begin{gathered} a_n\text{ = ar}^{n-1} \\ Where\text{ a is the first term} \\ r\text{ is the common ratio} \end{gathered}$

Hence, we have:

$\begin{gathered} \text{ar}^{2-1}\text{ = 18} \\ ar\text{ = 18} \\ \\ ar^{5-1}=\text{ 144} \\ ar^4\text{ =144} \end{gathered}$

Divide the expression for the fifth term by the expression for the second term:

$\begin{gathered} \frac{ar^4}{ar}\text{ = }\frac{144}{18} \\ r^3\text{ = }\frac{144}{18} \\ r\text{ = 2} \end{gathered}$

Substituting the value of r into any of the expression:

$\begin{gathered} ar\text{ = 18} \\ a\text{ }\times\text{ 2 = 18} \\ Divide\text{ both sides by 2} \\ \frac{2a}{2}\text{ =}\frac{18}{2} \\ a\text{ = 9} \end{gathered}$

Hence, the explicit rule for the sequence is:

$a_n\text{ = 9\lparen2\rparen}^{n-1}$

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Answer:

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