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3 years ago

12x+7<-11 AND 5x-8=>40

Mathematics

2 answers:

Sladkaya [172]3 years ago

6 0

12x + 7 < -11

12x < -18

x < -1.5

5x - 8 => 40

5x => 48

x => 9.6

Andreyy893 years ago

5 0

Answer:

The values of x = [-1.5, -∞) and [9.6, ∞)

Step-by-step explanation:

Here we have to solve the given system of inequalities.

12x + 7 ≤ -11 and 5x - 8 ≥ 40

Here we have to solve for x. Let's take the first inequality and solve for x.

12x + 7 ≤ -11

Subtracting 7 from both sides,

12x + 7 - 7 ≤ -11 - 7

12x ≤ -18

Dividing both sides by 12, we get

x ≤ $\frac{-18}{12}$

We can simplify this fraction.

x $\leq \frac{-3}{2}$

x $\leq -1.5$

Now let's solve the second inequality.

5x - 8 ≥ 40

Add 8 on both sides,

5x - 8 + 8 ≥ 40 + 8

5x ≥ 48

Dividing both sides by 5, we get

x ≥ $\frac{48}{5}$

x ≥ 9.6

So, solving those inequalities, we get

x ≤ -1.5 and x ≥ 9.6

This means, the values of x = [-1.5, -∞) and [9.6, ∞)

Let's draw the solution in a number line.

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Step-by-step explanation:

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3 years ago

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1 year ago

Which pairs of points would result in a line with a rate of change of 2:1? Select all that apply.

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Answer:

Options A, C, D are true.

Step-by-step explanation:

We have to choose the pair of points from that given in the attached file which will result in a line with a rate of change i.e. slope of 2:1 i.e. 2.

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Then the slope of the joining line is $\frac{-7-(-11)}{-2-(-4)} =2$

B. The points are (5,6) and (-5,12).

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Then the slope of the joining line is $\frac{-11-(-3)}{-4-0} =2$

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7 0

3 years ago

<img src="https://tex.z-dn.net/?f=if%20%5C%3A%20%28%20%5Cfrac%7B3%7D%7B4%7D%20%29%5E%7B6%7D%20%20%5Ctimes%20%28%20%5Cfrac%7B16%7

zhenek [66]

Answer:

Step-by-step explanation:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}$

$\frac{3^6}{4^6} \cdot \frac{16^5}{9^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{(4^2)^5}{(3^2)^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{4^{10}}{3^{10}}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{3^{10}} \cdot \frac{4^{10}}{4^6}=\frac{4^{x+2}}{3^{x+2}}$

$3^{-4} \cdot 4^{4}=4^{x+2}3^{-(x+2)}$

This implies

x+2=4

and

-(x+2)=-4.

x+2=4 implies x=2 since subtract 2 on both sides gives us x=2.

Solving -(x+2)=-4 should give us the same value.

Multiply both sides by -1:

x+2=4

It is the same equation as the other.

You will get x=2 either way.

Let's check:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{2+2}$

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{4}$

Put both sides into your calculator and see if you get the same thing on both sides:

Left hand side gives 256/81.

Right hand side gives 256/81.

Both side are indeed the same for x=2.

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3 years ago