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rjkz [21]
3 years ago
8

You have three consecutive odd integers. Four times the smallest decreased by 5 is the same as the largest increased by 12. What

is the smallest of the integers?
Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

Answer:

The smallest of the integers is 7

Step-by-step explanation:

Let the integers be x, y and z

From the question, the integers are consecutive odd integers.

Hence,

If the smallest of the integers is x and the largest is z, then we can write that,

x + 2 = y and

y + 2 = z

Then, x + 2 + 2 = z

∴ x + 4 = z ....... (1)

From the question, four times the smallest decreased by 5 is the same as the largest increased by 12, that is

4x -5 = z + 12 ....... (2)

Put the value of z = x + 4 in equation (1) into equation (2),

We then get

4x - 5 = x + 4 + 12

4x - x = 4 + 12 + 5

3x = 21

x = 7

Hence, the smallest of the integers is 7

The other integers are 9 and 11 ( y= 9 and z = 11)

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Owen solves the equation below and his steps are shown. When he plugged his solution back into the original equation, he did not
Usimov [2.4K]

Answer:

THE FIRST STEP in which he made an error is step 4, instead of subtracting 2x from either side of the equation, he is to add 2x to either side of the equation.

The correct value of x is 3.6

Step-by-step explanation:

To solve the given equation, we will follow the steps below;

3 (x-4) = -4 - 2 (x-5)

step 1 : open the parentheses

That is,   3x - 12 = -4 - 2x  + 10

Step 2 : simplify, that is, yo can add the or subtract like terms

hence

3x - 12 = -2x -4 + 10

step 3 :

3x - 12 = -2x + 6

step 4 : Add 2x to both-side of the equations in order to nullify the 2x on the right-hand side of the equation

3x + 2x - 12  = -2x + 2x + 6

step 5:

5x - 12  = 6

step 6:  Add 12 to both-side of the equation

5x - 12 + 12  = 6 + 12

step 7

5x  = 18

Step 8: divide both-side of the equation by   5

5x/5 = 18/5

step 9:

x =3.6

THE FIRST STEP in which he made an error is step 4, instead of subtracting 2x from either side of the equation, he is to add 2x to either side of the equation.

That is why he got the wrong answer.

4 0
3 years ago
In ΔRST, r = 210 inches, t = 550 inches and ∠T=166°. Find all possible values of ∠R, to the nearest degree.
valkas [14]

Answer:

m(∠R) = 5°

Step-by-step explanation:

By applying sine rule in the given triangle RST.

\frac{\text{sin}(\angle R)}{ST}= \frac{\text{sin}(\angle T)}{SR}

\frac{\text{sin}(\angle R)}{r}= \frac{\text{sin}(\angle T)}{t}

\frac{\text{sin}(\angle R)}{210}= \frac{\text{sin}(166)}{550}

sin(∠R) = \frac{210\times \text{sin}(166)}{550}

           = 0.09237

m(∠R) = \text{sin}^{-1}(0.09237)

           = 5.3°

           ≈ 5°

4 0
3 years ago
Eric Kweeder can paint a wall in
pentagon [3]
The answer of the question is 12minutes
4 0
3 years ago
Read 2 more answers
When solving negative one over five (x − 25) = 7, what is the correct sequence of operations?
Stels [109]

Answer:

Multiply each side by −5, add 25 to each side

Step-by-step explanation:

-1/5(x-25) = 7

Multiply each side by -5/1 to clear the fraction

-5/1* -1/5(x-25) = 7*-5/1

x-25 = -35

Then add 25 to each side

x-25+25 = -35+25

x = -10

3 0
2 years ago
1
serg [7]

Answer:

35 by 40

Step-by-step explanation:

4 0
3 years ago
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