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2 years ago

Please help me. 2 (a + 4) =

Mathematics

2 answers:

Oksana_A [137]2 years ago

8 0

You distribute 2to a which gives you 2a then you distribute 2 to 4 which gives you 8
so your answer would be 2a+8

vitfil [10]2 years ago

7 0

Answer:

2a+8

Step-by-step explanation:

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

Alja [10]

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

Solution:

Given that,

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

Use the following log rules

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,

$log_b162 = x + 4y$

$b) log_b 324$

Break 324 down to primes:

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

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

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

By rule 2

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

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

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

2 years ago

Identify the slope and y-intercept of the graph of the equation.

Aleksandr [31]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Someone Explain to me how 5. Is valid ???

vichka [17]

This is valid through the law of syllogism. If you swap lines 1 and 2, then you'll have this argument:

If I step on a beehive, then I will get stung.

If I get stung by a bee, then it will hurt.

Therefore, if I step on a beehive, then it will hurt

------------------

So it's like connecting a chain together. Point A (stepping on the hive), leads to point B (getting stung), which leads to point C (getting hurt). We can take a shortcut to bypass point B to jump from A to C in one step. Check out the attached image for a visual of what I'm referring to.