For this case we have the following inequality:

We multiply both sides of the equation by -1.
By doing this, change the symbol of the inequality.
We have then:

From here, we clear the value of x.
We have then:
Answer:
The solution set is:
{x | x R, x < -12}
Please find diagram attached
Answer and explanation:
Perpendicular lines are lines that meet at 90 degrees/ right angle.
The question seems to be incomplete but I will explain what perpendicular lines are in the context of lines lll and mmm, with some assumptions about the lines.
Assume that line III is 30mm long and line mmm is 25mm long, we say that line III is perpendicular to line mmm if line III meets line mmm at 90 degrees as we see in the diagram attached.
Given:
The line passing through (-2,5) and (2,p) has a gradient of
.
To find:
The value of p.
Solution:
If a line passes through two points, then the slope of the line is:

The line passing through (-2,5) and (2,p). So, the slope of the line is:



It is given that the gradient or slope of the line is
.

On cross multiplication, we get




Divide both sides by 2.

Therefore, the value of p is 3.
Answer:
1:5 or you can write 1/5 or 1 to 5
Step-by-step explanation:
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
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Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%