The required system of inequalities is:
-2x + 3y > 15
y + 3x ≥ -4
y + 11x ≥ 6
In the given graph:
The dotted line represents the equation:
-2x + 3y = 15 → line 1.
The line towards the left of the shaded region represents the equation:
y + 3x = -4 → line 2.
The line towards the right of the shaded region represents the equation:
y + 11x = 6 → line 3.
Let's take a point in the shaded region and use the equations of the line to determine the inequality.
Consider the point (-2, 6) and substitute these values in the equations of all three lines.
Line 1:
LHS of line 1 = -2x + 3y = -2(-2) + 3(6) = 4 + 18 = 22
RHS of line 2 = 15.
Therefore, LHS > RHS.
⇒The required inequality is -2x + 3y > 15. It is a strict inequality since the equation of the line is not included in the shaded region.
Line 2:
LHS of line 2 = y + 3x = 6 +3(-2) = 6 - 6 = 0
RHS of line 2 = -4
Therefore, LHS > RHS.
⇒The required inequality is y + 3x ≥ -4. The "Equal to" symbol is used because the equation of the line is included in the shaded region.
Line 3:
LHS of line 3 = y + 11x = 6 + 11(-2) = 6 - 22 = -16
RHS of line 3 = 6
Therefore, LHS < RHS.
⇒The required inequality is y + 11x ≥ 6. The "Equal to" symbol is used because the equation of the line is included in the shaded region.
Therefore, the required system of inequalities is:
-2x + 3y > 15
y + 3x ≥ -4
y + 11x ≥ 6
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When you divide a negative bumber with a negative the result will be positive :
-525 ÷ (-125) = 4.2
<h3>
Answer: Trapezoid</h3>
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Explanation:
There are two ways to do this problem.
Method 1 involves listing out the terms until we reach the seventh one.
- square
- hexagon
- trapezoid
- triangle
- square
- hexagon
- trapezoid
- triangle
We see that the trapezoid is term 7.
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Method 2 is faster and the one I recommend.
Since the pattern repeats every 4 items, this means we divide by 4 and look at the remainder. Ignore the quotient entirely.
7/4 = 1 remainder 3
The remainder 3 means that the answer is found in term 3, which is the trapezoid.
Answer:
62.5 miles per hour
Step-by-step explanation:
Given data
distance= 125m
time= 2 hours
We know that
speed= distance/time
Subsitute
Speed= 125/2
speed= 62.5 miles per hour
