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3 years ago

7

Jenny used 15 centimeters of tape to wrap 5 presents. How much tape will Jenny need in all if she has to wrap 10 presents? Assum

e the relationship is directly proportional.

1 answer:

Scorpion4ik [409]3 years ago

7 0

Answer:

30

Step-by-step explanation:

15cm for 5

5 x 2=10

15 x 2 = 30

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If logb2=x and logb3=y, evaluate the following in terms of x and y:

Alja [10]

$log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x$

<em><u>Solution:</u></em>

Given that,

$log_b2 = x\\\\log_b3 = y --------(i)$

<em><u>Use the following log rules</u></em>

Rule 1: $log_b(ac) = log_ba + log_bc$

Rule 2: $log_b\frac{a}{c} = log_ba - log_bc$

Rule 3: $log_ba^c = clog_ba$

$a) log_b{162}$

Break 162 down to primes:

$162 = 2^1 \times 3^4$

$log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y$

Thus we get,

$log_b162 = x + 4y$

Next

$b) log_b 324$

Break 324 down to primes:

$324 = 2^2 \times 3^4$

$log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y$

Next

$c) log_b\frac{8}{9}$

By rule 2

$log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} = 3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} = 3x - 2y$

Next

$d) \frac{log_b27}{log_b16}$

By rule 2

$\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} = 3y - 4x$

Thus the given are evaluated in terms of x and y

3 0

3 years ago

What is the solution to the inequality 14y−14≥14?

makkiz [27]

14y > 0 is the answer

6 0

3 years ago

Read 2 more answers

Please help hurry!!!!! This is due in a couple of minutes!!!!

kumpel [21]

Answer:

200 in.

Step-by-step explanation:

1250/75=5000/300=50/3 simplification

50*12=600 conversion to inches

600/3=200 simplification

5 0

3 years ago

Sam watched 10 cars drive past

Sunny_sXe [5.5K]

Answer:

3/5

Step-by-step explanation:

6 white cars out of 10 cars would be written as 6/10.

You then would simplify this fraction to 3/5.

So your answer is 6/10 or 3/5.

8 0

3 years ago

What are the solutions of the equation x6 – 9x3 + 8 = 0? Use u substitution to solve.

Natalka [10]

X6 – 9x3 + 8 = 0
let u = x^3
u^2 - 9u + 8 = 0
(u-8)(u-1) = 0
u = 1,8
back substitute
1 = x^3
8 = x^3

<span>x = 1 , 2</span>

4 0

3 years ago