Number 10 I don't understand.

Solve each inequality, and then drag the correct solution graph to the inequality.

Nesterboy [21]

The correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

$4(9x-18)>3(8x+12)$

First, clear the brackets,

$36x-72>24x+36$

Then, collect like terms

$36x-24x>36+72\\12x >108$

Now divide both sides by 12

$\frac{12x}{12} > \frac{108}{12}$

∴ $x > 9$

For the second inequality

$-\frac{1}{3}(12x+6) \geq -2x +14$

First, clear the fraction by multiplying both sides by 3

$3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)$

$-1(12x+6) \geq -6x +42$

Now, open the bracket

$-12x-6 \geq -6x +42$

Collect like terms

$-6 -42\geq -6x +12x$

$-48\geq 6x$

Divide both sides by 6

$\frac{-48}{6} \geq \frac{6x}{6}$

$-8\geq x$

∴ $x\leq -8$

For the third inequality,

$1.6(x+8)\geq 38.4$

First, clear the brackets

$1.6x + 12.8\geq 38.4$

Collect likes terms

$1.6x \geq 38.4-12.8$

$1.6x \geq 25.6$

Divide both sides by 1.6

$\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}$

∴ $x \geq 16$

Let the graphs be A, B and C from left to right

The first graph (A) shows $x\leq -8$ and this matches the 2nd inequality

The second graph (B) shows $x \geq 16$ and this matches the 3rd inequality

The third graph (C) shows $x > 9$ and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

Learn more here: brainly.com/question/17448505

8 0

2 years ago

One estimate of the population of the world on January 1, 2005, is

inn [45]

Answer:

8,566,379,470 people

Step-by-step explanation:

Let's start simple. In order to find the population increase on January 1, 2006, we need to multiply 6,486,915,022 by 1.4% and add it to 6,486,915,022.

6,486,915,022*1.4% = 90,816,810.308
90,816,810.308+6,486,915,022 = 6,577,731,832.31 people on January 2006.

Note that the above two steps gives the same answer as 6,486,915,022*1.014.

So we need to do this for each year. 20 years pass between 1/1/2005 and 1/1/2025.

We need to do 6,486,915,022*1.014*1.014*1.014... 20 times.

This is equivalent to $6,486,915,022*1.014^{20}$ .

Multiplying it out gives us 8566379470.2 = 8,566,379,470 people.

4 0

3 years ago

For sin2x+cosx=0, use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation

Archy [21]

Answer:

Step-by-step explanation:

Given is a trignometric equation in x, as

$sin2x+cosx=0$

TO make it in one trig ratio, we can replace sin2x as 2sinx cosx

WE get now

$2sinxcosx+cosx=0\\$

$cosx(2sinx+1)=0\\cosx=0, sinx =-0.5\\$

Principal solution is $x=\frac{\pi}{2} , \frac{-\pi}{6}$

x = ±π/2 + 2kπ, where k is any integer or

x=±pi/6 +k pi, where k is any integer.

General solution is

4 0

2 years ago

Awnser please please

astraxan [27]

They're all d).

1) 28>24=10+14

2) Either 96/8=? or 8*?=96 describe the problem, ? being the number of chairs (the blank square in the answers). Of the two only the first appears in the options.

3) This question is ambiguous: if someone went both days, we could say the total number of people who went to the Saturday and Sunday games would be less than 3271+5844=9115. But who wrote the question likely wanted you to just do the sum between the two numbers, so of all options d is likely what they want you to choose.

6 0

2 years ago

What is the perimeter of a polygon with the vertices at (-2,1) (-2,4) (2,7) (6,4) (6,1)?

rusak2 [61]

Answer:

24

Step-by-step explanation:

3 0

3 years ago