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3 years ago

15 points

Mathematics

1 answer:

Alika [10]3 years ago

4 0

Answer:

July 2

Step-by-step explanation:

June has 30 days total.

2 weeks is 7(2) or 14 days

18 + 14 = 32

July 2nd would be the correct option because the 2 extra days that come from 32 would go into July. Hope this helps :)

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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 n :

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

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

5 0

3 years ago

A science fair poster is a rectangle 3 feet long and 2 feet wide. What is the area of the poster in square inches? Be sure to in

vredina [299]

Area = length · width
Area = 3ft · 2ft
Area = 6ft²

hope this helps!

5 0

3 years ago

Are 6 exponent 3 and -x exponent 3 alike

amid [387]

Answer:

Step-by-step explanation:

6^3 = 216

(-x)^3 = - x^3.

5 0

3 years ago

Anyone feel like answering this page for me

LUCKY_DIMON [66]

1.7x+35
2.5w-20
3.-5m+25
4.18-9a
5.2y+6
6.-2x-14
7.35m-21
8.6n+24
9.-12c-48
10.-8k-10
11.2-k
12.4-28p
13.18r-63
14.-5k-4

4 0

3 years ago

Triangle ABC has A(-3,6),B(2,1), and C(9,5) what the length of side AB? What the length BC what the length AC and what ABC

vovikov84 [41]

Answer:

AB = 5√2

AC = √145

BC = √65

Step-by-step explanation:

Using the formula for calculating the distance between two points

D = √(x2-x1)²+(y2-y1)²

For AB A(-3,6),B(2,1),

AB = √(2+3)²+(1-6)²

AB = √(5)²+(-5)²

AB = √25+25

AB = √50

AB = 5√2

For AC A(-3,6) and C(9,5)

AC = √(9+3)²+(5-6)²

AC = √(12)²+(-1)²

AC = √144+1

AC = √145

For BC B(2,1), and C(9,5)

BC = √(9-2)²+(5-1)²

BC = √(7)²+(4)²

BC = √49+16

BC = √65

Since All the sides are difference, hence triangle ABC is a scalene triangle

8 0

2 years ago