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Gelneren [198K]
3 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]3 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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What Number is X in this equation? <br><br> 9 - 3 ÷ 1/3 + 1 = X
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Step-by-step explanation:

Use PEMDAS to solve the equation, and you will get the answer 1 for x

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Read 2 more answers
PLEASE ANSWER + BRAINLIEST!!!
grandymaker [24]

Width is 11k^2

Length is 5k^3 + 2k^2

Look at: https://www.wyzant.com/resources/answers/392371/what_is_the_length_and_width_of_the_rectangle

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Evan earns $21.50 per hour for 25 hours and time and a half for overtime. If he worked 5 hours
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4 0
2 years ago
Can anyone explain this question to me? My teacher solved it but I didn’t understand how she did it
Amiraneli [1.4K]

Step-by-step explanation:

To find the space a figure takes, we need to find the volume. Volume of a rectangular prism can be found by multiplying the length, width, and height of the figure.

We can start with the green block. The dimensions of this figure are 6cm, 3cm, and 3cm. The 5cm at the bottom is not a dimension of the green figure. Instead, it shows the total width of both blocks. We will use this later.

Back to the first block, we will find its volume by multiplying its dimensions together.

3 · 3 · 6 = 54

So, the volume of the first block is 54 cm³.

To this, we will add the volume of the blue block. We can find its dimensions with some simple deduction.

The picture shows that the height of the figure is 4cm less than the height of the green one, 6cm.

6 - 4 = 2

The height, then, is 2cm.

The width can be found by subtracting the width of the green block from the total width of both figures, 5cm.

5 - 3 = 2

So, the width is also 2cm.

We can see that the length of the blue block is equal to that of the green one, so we know that the length is 3cm.

Now, multiply all the dimensions we have found together.

2 · 2 · 3 = 12

The volume of the blue block is 12cm³.

We have found the volumes of both figures, so now we can add them both together to find the total.

54 + 12 = 66

So, the total volume is 66cm³.

I hope this was a satisfactory explanation ^^ Good luck, mate

7 0
3 years ago
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