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2 years ago

(a) Simplify the expression: (4x - 6) - (x + 5)

Mathematics

1 answer:

Liono4ka [1.6K]2 years ago

8 0

Answer:

a) 3x - 11

b) 10x + 4

Step-by-step explanation:

a) The negative sign before the (x+5) means to subtract those values. Reverse the signs. Then combine like terms:

4x –6 –x –5. 4x–x–6–5

3x –11

b) Put all the x terms together.

Put all the integers together.

Add. Adding a negative is the same as subtracting.

4x+x+5x = 10x

+6-2 = 4

Combine them:

10x + 4

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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>:

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

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

5 0

3 years ago

(2a+9b-7).(-8)=help

musickatia [10]

Answer:

(-16a)-72b+56

Step-by-step explanation:

Multiply 8 to each number

Hope this helped :)

4 0

3 years ago

Read 2 more answers

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joja [24]

Answer:

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Step-by-step explanation:

7 0

2 years ago

Write a real world problem that you would represent with the equation 4x+5=37.

umka2103 [35]

If there were 37 apples. One of your friends took 5 apples. You divided the leftover apples and gave it to your four friends. How many apples did each of the four friends get?

x=8
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3 years ago

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g100num [7]

Answer: $ 568.99

Because 18.99+22 x 225/9 = 568.99

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2 years ago