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3 years ago

Insert 5 G.Ms between 3 and 192

Mathematics

1 answer:

never [62]3 years ago

7 0

Answer:

6, 12, 24, 48 and 96.

Step-by-step explanation:

We look for a geometric sequence with first term = 3:

nth term= a1 r^(n-1)

3 r^(n-1) = 192

r^(n-1) = 192 / 3 = 64

2 ^ 6 = 64 so r = 2.

Series is 3 ,6, 12, 24, 48, 96, 192.

So 5 geometric means would be 6, 12, 24, 48 and 96.

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Solve the following equation. Remember to check for extraneous solutions 1/(x-6) + (x/(x-2)) = (4/(x²-8x+12)).

xxMikexx [17]

Answer:

-1, 2, 6

Step-by-step explanation:

We have to solve the equation as follows: 1/(x-6) + (x/(x-2)) = (4/(x²-8x+12)).

Now, we have, $\frac{1}{x-6} +\frac{x}{x-2} = \frac{4}{x^{2}-8x+12 }$

⇒ $\frac{(x-2)+x(x-6)}{(x-2)(x-6)} = \frac{4}{x^{2}-8x+12 }$

⇒ $\frac{x-2+x^{2}-6x }{(x-2)(x-6)} =\frac{4}{(x-2)(x-6)}$

⇒ $\frac{(x-2)(x-6)}{x^{2}-5x-2 }=\frac{(x-2)(x-6)}{4}$

⇒ $(x-2)(x-6)[\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0$

⇒ $(x-2)(x-6) =0$ or, $[\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0$

If, (x-2)(x-6) =0, then x=2 or x=6

If, $[\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0$ , then $x^{2} -5x-2=4$

and (x-6)(x+1) =0

Therefore, x=6 or -1

So the solutions for x are -1, 2 6. (Answer)

4 0

3 years ago

In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement ∠PRQ ≅ ___ A. ∠SRT B. ∠RST C. ∠STR D. ∠T

Oduvanchick [21]

The complete statement is ∠PRQ ≅ <u>∠SRT</u>. The correction option is A. ∠SRT

<h3>Similar triangles </h3>

From the question, we are to complete the given statement

From the given information,

We have that ΔPQR ≅ ΔSTR

This means ΔPQR is congruent to ΔSTR

Then,

∠PQR ≅ ∠STR

∠PRQ ≅ ∠SRT

∠QPR ≅ ∠TSR

Hence, the complete statement is ∠PRQ ≅ <u>∠SRT</u>. The correction option is A. ∠SRT

Learn more on Congruent Triangles here: brainly.com/question/28032367

#SPJ1

4 0

2 years ago

A professor wants to award prizes for 1st, 2nd, 3rd, 4th and 5th in the class of 30. In how many ways can the prizes be awarded

aniked [119]

Answer:

$Selection = 17100720\ ways$

Step-by-step explanation:

Given

$Students = 30$

$Positions = 5$ i.e. first to fifth

Required

Determine number of selection

1st position = Any of the 30 students

2nd position = Any of the 29 students

3rd position = Any of the 28 students

4th position = Any of the 27 students

5th position = Any of the 26 students

Number of selection is then calculated as:

$Selection = 30 * 29 * 28 * 27 * 26$

$Selection = 17100720\ ways$

8 0

3 years ago

Write an equation in slope-intercept form for the line with slope -2 and y-intercept 5.

Nana76 [90]

Answer:

y = -2x + 5

Step-by-step explanation:

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3 years ago

What is the value of y?<br><br> Enter your answer, as an exact value, in the box.

mylen [45]

Answer:

y/2 = tan(60) => y = 2 tan(60) = 2sqrt(3) = 3.464

Step-by-step explanation:

5 0

3 years ago

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Insert 5 G.Ms between 3 and 192​

Insert 5 G.Ms between 3 and 192