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Gelneren [198K]
2 years ago
10

How much must be added to each of the three numbers 1, 11, and 23 so that together they form a geometric progression?

Mathematics
1 answer:
Sliva [168]2 years ago
5 0

Answer:

49

Step-by-step explanation:

Let x be unknown number which should be added to numbers 1, 11, 23 to get geometric progression. Then numbers 1 + x, 11 + x, 23 + x are first three terms of geometric progression.

Hence,

b_1=1+x\\ \\b_2=11+x\\ \\b_3=23+x

and

b_2=b_1\cdot q\Rightarrow 11+x=(1+x)q\\ \\b_3=b_2\cdot q\Rightarrow 23+x=(11+x)q

Express q:

q=\dfrac{11+x}{1+x}=\dfrac{23+x}{11+x}

Solve this equation. Cross multiply:

(11+x)^2=(1+x)(23+x)\\ \\121+22x+x^2=23+x+23x+x^2\\ \\121+22x=23+24x\\ \\22x-24x=23-121\\ \\-2x=-98\\ \\2x=98\\ \\x=49

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3 years ago
Find the slope of the line that passes through (4, 5) and (6,4)
Dahasolnce [82]

Answer:

-1/2

Step-by-step explanation:

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2 years ago
1: In order to solve the inequality -1/4 x > 8, which of the following steps must be done?
pogonyaev

Answer:

Step-by-step explanation:

-1/4x>8

x>8/(-1/4)

x>(8/1)(-4/1)

x>-32/1

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--------------------------

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3 0
3 years ago
a rectangle has an area that is represented by 9x²-4. the length of the rectangle is 3x-2. what is the width?
PSYCHO15rus [73]

Step-by-step explanation:

the area is

length × width

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to find width we could do a real polynomial division or simply recognize the fact that

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and we see that in our area calculation we are missing the (a + b) factor.

so, width = (3x + 2)

but if you want the division :

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-----------------

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Answer:

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