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2 years ago

Complete the proof that △FGH isn't similar to △JIH

Mathematics

2 answers:

Sedaia [141]2 years ago

6 0

Answer:

step 2: (FH)/(JH)=5/6

step 3: (GH)/(IH)=(FH)/(JH)

Step-by-step explanation:

this is right

Taya2010 [7]2 years ago

3 0

Answer:

one looks bigger the other one

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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

15=3(2x+4)-3 prove x=1

kherson [118]

Answer:

X=1

Step-by-step explanation:

6x+12-3=15

6x+9=15

6x+9-9=15-9

6x=6

X=1

4 0

3 years ago

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It takes Dan 32 minutes to complete 2 pages of math homework. At this rate, how many pages does he complete in 200 minutes?

Anna [14]

He can complete about 6 pages of math homework.
you first do 200 divided by 32 and you get 6.25. So therefore Dan can complete 6 pages in 200 minutes.

7 0

2 years ago

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The ducks at the Duck Pond game are numbered 1 through 31 with a 32nd one bearing the Big Prize

neonofarm [45]

Answer: 96 games

Step-by-step explanation:

32 total possibilities

3 people

32*3= 96

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2 years ago

- A contractor plans to build a rectangular office complex. The floor area on the first floor of the

Neko [114]

Answer:

Width = 30

Step-by-step explanation:

Area = 18x * 10y = 180xy

Length = 6xy

Width = ?

Since the shape of the office complex is a rectangle,

Area of a rectangle = length × width

180xy = 6xy × width

Width = 180xy / 6xy

Width = 30

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2 years ago