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GuDViN [60]
3 years ago
5

find three consecutive odd integers such that the sum of the smallest number and middle number is 27 less than 3 times the large

st number​
Mathematics
1 answer:
katrin2010 [14]3 years ago
7 0

A generic odd number can be written as

2k+1,\quad k \in \mathbb{Z}

Since there is an odd number every two numbers, three consecutive odd numbers will be

2k+1,\quad 2k+3,\quad 2k+5

Now let's make up the equations: the sum of the first two is

(2k+1)+(2k+3)

And 27 less than 3 times the largest is

3(2k+5)-27

These two must be the same, so we have

(2k+1)+(2k+3)=3(2k+5)-27 \iff 4k+4 = 6k+30-27 \iff 4k+4=6k+3

Subtracting 4k and 3 from both sides gives

1=2k \iff k=\dfrac{1}{2}

Which means that the problem has no solution.

To confirm this hypothesis, we can observe that, on the left hand side, we have the sum of two odd numbers, which is even

On the right hand side, we have an odd number, multiplied by 3 (still odd), take away 27 (still odd).

So, the left hand side is even, and the right hand side is odd. They can't be the same number.

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3x+6=30 i need some help
goldenfox [79]

Answer:

24

Step-by-step explanation:

3x+6=30

Get the co-efficient by itself

3x +6=30

     -6.   -6

3x=24

Divide by 3 on both sides

24/3

x =8

4 0
3 years ago
Read 2 more answers
Select the two expressions that equivalent to 4 + w + 12w
Korvikt [17]

Answer:

A and C :)

Have an amazing day!!

Please rate and mark brainliest!!

4 0
2 years ago
Note: Figure is not drawn to scale. If m1 + m2 = 134°, what is m3? A. 138° B. 49° C. 46° D. 136°
NemiM [27]

Answer:

Measure of angle 3: C (46 degrees)

Step-by-step explanation:

As there is no attachment, I will assume the question is in reference to a triangle. Knowing that a triangle contains 3 angles the answer can be retrieved through simple steps:

m∠1 + m∠2 + m∠3 = 180 degrees, by Sum of Angles in Triangle Theorem, <em>thus;</em>

Through substitution + algebra:

134 + m∠3 = 180,

m∠3 = 46 degrees

8 0
3 years ago
A survey of 9th and 10th graders was conducted to see which type of pet they
Studentka2010 [4]

Answer:

D 9/26

Step-by-step explanation:

Out of the 10th graders there are 104 total responses.  Knowing we only need data from 10th graders we can ignore everything else.  36/104 10th graders like cats and if you divide that by 4 you'll get the only possible answer of 9/26.  D 9/26 10th graders like cats.

6 0
3 years ago
Read 2 more answers
Jean and Sarah are buying tubs of ice cream. 2 scoops of ice cream are twice the price of 1 scoop of ice cream. Jean buys 4 tubs
liberstina [14]

Answer:

The answer is below

Step-by-step explanation:

Let x represent the cost of 1 scoop of ice cream. Since the cost of 2 scoops of ice cream are twice the price of 1 scoop of ice cream, therefore the cost of 2 scoops of ice cream = 2x

Jean buys 4 tubs with 2 scoops in them and 2 tubs with 1 scoop each. Therefore the money spent by Jean is:

Money spent by Jean = 4(2x) + 2(x) = 8x + 2x = 10x

Sarah buys 2 tubs of 2 scoops and 4 tubs of 1 scoop. The money spent by Sarah is:

Money spent by Sarah = 2(2x) + 4(x) = 4x + 4x = 8x

Sarah spends 2.50 € less than Jean. Therefore:

Money spent by Sarah = Money spent by Jean - 2.5

8x = 10x - 2.5

2x = 2.5

x = €1.25

Therefore the cost of 1 scoop of ice cream is €1.25, the cost of 2 scoops of ice cream is €2.50.

Money spent by Jean = 10x = 10(1.25) = €12.5

Money spent by Sarah = 8x = 8(1.25) = €10

3 0
2 years ago
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