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2 years ago

-(4x+6)<2(5x+9)+2x write the solution for interval notation

Mathematics

1 answer:

Ludmilka [50]2 years ago

3 0

Answer:

$(-1.5,\infty)$

Step-by-step explanation:

-(4x+6)<2(5x+9)+2x

Distribute:

-4x-6<10x+18+2x

Combine like terms on either side:

-4x-6<12x+18

We want to now gather variable terms on one side of the inequality and constants (terms without variables) on the opposing side.

Add 4x on both sides:

-6<16x+18

Subtract 18 on both sides:

-24<16x

Divide both sides by 16:

-24/16<x

This implies:

x>-24/16

Reduce:

x>-3/2

x>-1.5

So in an interval notation this is $(-1.5,\infty)$ .

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

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2 years ago

You have $40 to spend on n gallons of gas that costs $3.25 per gallon.

Citrus2011 [14]

Answer:

You can buy 12 gallons of gas.

Step-by-step explanation:

I took 40 and 3.25, then divided them.

I got a very large ugly decimal. When simplified it is 12.

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2 years ago

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Replace the variable

with

in the expression.

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)

(

)

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Simplify the result.

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The

value at

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Replace the variable

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Its D

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2 years ago