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3 years ago

Determine the integer value of n that satisfies the the equation. 4^n=16 3^n=1/81

Mathematics

1 answer:

tresset_1 [31]3 years ago

7 0

Answer:

Step-by-step explanation:

$4^{n} = 16 \\\\4^{n} = 4^2\\\\$

n = 2

$3^{n} =\frac{1}{81}\\\\ = \frac{1}{3^{4}}\\\\3^{n} = 3^{-4}$

n = -4

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Consider the line y = 9x-5.

goldenfox [79]

Answer:

$4 \times {4}^{ - 5 \times 4}$

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3 years ago

Five times the sum of a number and 27 is greater than or equal to six times the sum of that num

stepladder [879]

Question:

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26.

What is the solution set of this problem?

Answer:

$x \leq -21$

Step-by-step explanation:

Given

<em>Represent the number with x</em>

So:

$5 * (x + 27) \geq 6 * (x + 26)$

Required

Determine the solution set

$5 * (x + 27) \geq 6 * (x + 26)$

Open Both Brackets

$5 * x + 5 * 27 \geq 6 *x + 6 * 26$

$5x + 135 \geq 6x + 156$

Collect Like Terms

$5x - 6x \geq 156-135$

$- x \geq 21$

Multiply both sides by -1

$x \leq -21$

Hence, the solution set is $x \leq -21$

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3 years ago

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Archy [21]

Answer:

$2\frac{1}{2}\ liters$

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

$1\frac{1}{5}=\frac{1*5+1}{5}=\frac{6}{5}$

step 2

Using proportion

$\frac{3}{(6/5)}\frac{liters}{doors} =\frac{x}{1}\frac{liters}{door}\\ \\x=3/(6/5)\\ \\x=15/6\ liters$

step 3

Convert to mixed number

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3 years ago

the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age

max2010maxim [7]

We have,

$a:b=3:6,a+b=96$

Introduce variable $x$ such that $a=3x,b=6x$

The sum $a+b=96$ is therefore $9x=96\implies x=10.\overline{6}$

So,

$a=3\cdot10.\overline{6}=\boxed{32}$ (sadia's age)

$b=6\cdot10.\overline{6}=\boxed{64}$ (father's age)

Hope this helps :)

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3 years ago

Show that 6^3-1 is divisible by 5 using our identities

Doss [256]

Answer:

Step-by-step explanation:

a³-b³=(a-b)(a²+ab+b²)

6³-1=6³-1³=(6-1)(6²+6*1+1²)=5×43

so 6³-1 is divisible by 5.

8 0

3 years ago

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