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qwelly [4]
2 years ago
9

Five double-digit numbers We have five consecutive positive double-digit integers. If we swap places on the numbers in the large

st number, the sum of the five numbers increases by 1 more than the mean of the original numbers. What is the lowest number?
Mathematics
1 answer:
barxatty [35]2 years ago
3 0

Answer:

  • 33

Step-by-step explanation:

<u>Let the numbers are:</u>

  • x, x + 1, x + 2, x + 3 and x + 4
  • Their sum is 5x + 10
  • Their mean is (5x + 10)/2 = x + 2

If we swap the digits on the largest number, the sum increases by 1 more than x + 2

<u>We are looking for the number x + 4 = ab such that:</u>

  • ba - ab = ab - 2 + 1
  • ba = 2ab - 1
  • 10b + a = 2(10a + b) - 1
  • 10b + a = 20a + 2b - 1
  • 8b = 19a - 1
  • 19a = 8b + 1

<u>By trial method we get the solution:</u>

  • a = 3, b = 7

<u>Since x + 4 = 37, the lowest number is:</u>

  • x = 37 - 4 = 33

<u>Lets verify:</u>

  • 33, 34, 35, 36, 37

<u>The sum is:</u>

  • 5*33 + 10 = 175

<u>The mean is:</u>

  • 35

<u>Change the largest number tp 73 and find the sum again:</u>

  • 175 + (73 - 37) = 175 + 36 = 175 + 35 + 1

The sum has increased by 1 more than 35

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PLEASE HELP!! Ill mark the brainliest!!!!
ira [324]

Answer:

x = 5√2

y = 5√6

z = 5√3

ΔABC ~ ΔBDC ~ ΔADB

Step-by-step explanation:

ΔABC, ΔBDC, and ΔADB are all similar triangles to each other.

By definition of similar triangles, the corresponding sides have the same ratios.

CD from ΔBDC corresponds to BD from ΔADB, and BD from ΔBDC corresponds to AD from ΔADB. So:

CD / BD = BD / AD

10 / x = x / 5

x² = 50

x = 5√2

Since ΔBDC is right, we can use the Pythagorean Theorem to solve for y:

CD² + BD² = BC²

10² + (5√2)² = y²

y² = 100 + 50 = 150

y = 5√6

Again, since ΔΔABD is right, we can use the Pythagorean Theorem to solve for z:

AD² + BD² = AB²

5² + (5√2)² = z²

z² = 25 + 50 = 75

z = 5√3

3 0
3 years ago
Read 2 more answers
If carlos did some work and got 3x + 2x - 6 = 24 what mistake did he make
Makovka662 [10]

Carlos made the mistake that he did not combine like terms (3 x and 2 x) properly and did not use addition property of equality.

<u>Step-by-step explanation:</u>

Carlos did the work as 3 x + 2 x - 6 = 24

We need to find his mistake that he made in above given.

Here, he did not add the like terms (3 x and 2 x)

             3 x + 2 x = 5 x

Therefore, his work should be

             5 x  - 6 = 24

Also, he did not use addition property of equality. It means the equation remains same even though the same number gets added on both sides. It would be

                          5 x  - 6 = 24

                                 + 6 = + 6

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

                           5 x = 30

Dividing 30 by 5, we get answer as '6'. Hence,

                            x=\frac{30}{5} = 6

So, stated the above two are the mistakes found in carlos work.

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3 years ago
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jolli1 [7]
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Step-by-step explanation:

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Step-by-step explanation:

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