Solve the system of equations and enter the solution as an ordered pair. 2x - 5y = -6 8x + 3y = 68
1 answer:
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If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:
You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.
This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.
AREA
The formula for the area of a rectangle is:
So we can plug our dimensions into the formula:
So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.
PERIMETER
The formula for the perimeter of a rectangle is:
We can plug our dimensions into the formula:
So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.
Answer:
- The graph of this line i.e.
should be BELOW the DOTTED line as
involves < symbol.
- The graph of this line i.e.
should be ABOVE the DOTTED line as it involves > symbol.
- The correct graph for line 1 and line 2 is shown in attached figure.
Step-by-step explanation:
- If the inequality involves < or >, then the graph of the equation involves a dotted line.
- If the inequality involves ≤ or ≥, then the graph of the equation involves a solid line.
<em>Considering the line 1</em>
Solving line 1
As involves < symbol, so the graph of this line should be BELOW the DOTTED line.
But, as you can see that there is an error in the graph. As the graph of is being shown ABOVE the SOLID line.
Therefore, the graph of this line i.e. should be BELOW the DOTTED line as it involves < symbol.
<em>Considering the line 2</em>
As involves > symbol, so the graph of this line should be ABOVE the DOTTED line.
But, as you can see that there is an error in the graph. As the graph of is being shown ABOVE the SOLID line.
Therefore, the graph of this line i.e. should be ABOVE the DOTTED line as it involves > symbol.
The <em>correct graph</em> for line 1 i.e. and line 2 i.e.
is shown in <em>attached figure</em>.
From the attached graph, it is shown that only (5, -2) satisfies the both inequalities. So, (5, -2) is the correct solution for the given inequalities.
<em>Solution Verification:</em>
<u><em>Putting (5, -2) in line 1 and line 2</em></u>
For line 1:
2x - 3y > 12 ⇒ 2(5) - 3(-2) > 12 ⇒ 10 + 6 > 12 ⇒ 16 > 12 which is true.
For line 2:
y > -2x + 5 ⇒ -2 > -2(5) + 5 ⇒ -2 > -10 + 5 ⇒ -2 > -5 which is true.
So, (5, -2) is IN the solution for line 1 and line 2
<em><u>Putting (-1, -1) in line 1 and line 2</u></em>
For line 1:
2x - 3y > 12 ⇒ 2(-1) - 3(-1) > 12 ⇒ -2 + 3 > 12 ⇒ 1 > 12 which is false.
For line 2:
y > -2x + 5 ⇒ -1 > -2(-1) + 5 ⇒ -1 > 2 + 5 ⇒ -1 > 7 which is false.
So, (-1, -1) is NOT in the solution for line 1 and line 2
<em><u>Putting (0, 5) in line 1 and line 2</u></em>
For line 1:
2x - 3y > 12 ⇒ 2(0) - 3(5) > 12 ⇒ 0 - 15 > 12 ⇒ -15 > 12 which is false.
For line 2:
y > -2x + 5 ⇒ 5 > -2(0) + 5 ⇒ 5 > 0 + 5 ⇒ 5 > 5 which is false.
So, (0, 5) is NOT in the solution for line 1 and line 2
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<em>Keywords: inequality, solution, graph, dotted line, solid line</em>
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