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4 years ago

Ten less than five times a number is less than six times the number decreased by eight

Mathematics

1 answer:

Luden [163]4 years ago

4 0

10 - 5x < 6x - 8

We can treat this inequality like a normal algebraic equation.

Add 5x to both sides

10 < 11x - 8

Add 8 to both sides

18 < 11x

Divide both sides by 11

1.64 < x

X is greater than the value 1.64.

Let's plug the number 2 into each value of x to verify.

10 - 5x < 6x - 8

10 - 5*2) < (6 * 2) - 8

10 - 10 < 12 - 8

0 < 4

It's correct.

Now let's plug 1, which is less than 1.64.

10 - 5x < 6x - 8

10 - 5 < 6 - 8

5 < -2

This is not correct, which means that our answer was correct.

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3 years ago

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A rectangle has a length of 12 mm and a width of 15 mm. Which statement best describes the change in the

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3 years ago

The 2nd, 6th, 8th terms of an A.P. form a G.P. , find the common ratio and the general term of the G.P.

melisa1 [442]

The terms of an arithmetic progression, can form consecutive terms of a geometric progression.

The common ratio is: $\mathbf{r = \frac{a + 5d}{a + d}}$
The general term of the GP is: $\mathbf{a_n = (a + d) \times (\frac{a + 5d}{a + d})^{n-1}}$

The nth term of an AP is:

$\mathbf{T_n = a + (n - 1)d}$

So, the 2nd, 6th and 8th terms of the AP are:

$\mathbf{T_2 = a + d}$

$\mathbf{T_6 = a + 5d}$

$\mathbf{T_8 = a + 7d}$

The first, second and third terms of the GP would be:

$\mathbf{a_1 = a + d}$

$\mathbf{a_2 = a + 5d}$

$\mathbf{a_3 = a + 7d}$

The common ratio (r) is calculated as:

$\mathbf{r = \frac{a_2}{a_1}}$

This gives

$\mathbf{r = \frac{a + 5d}{a + d}}$

The nth term of a GP is calculated using:

$\mathbf{a_n = a_1r^{n-1}}$

So, we have:

$\mathbf{a_n = (a + d) \times (\frac{a + 5d}{a + d})^{n-1}}$

Read more about arithmetic and geometric progressions at:

brainly.com/question/3927222

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3 years ago

the formula s=sqrt sa/6 gives the lenth of the side , s, of a cube with a surface area,SA. how much longer is the side of a cube

nasty-shy [4]

Using the given formula, replace sa with the given surface areas and solve for s:

Surface area = 1200

s = √1200/6

s = √200

s = 14.142

Surface area = 768

s = √768/6

s = √128

s = 11.313

Difference:

14.142 - 11.313 = 2.829 inches

Round answer as needed.

7 0

3 years ago

Read 2 more answers