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
Learn more at:
brainly.com/question/19491153
brainly.com/question/24299265
brainly.com/question/28038287
#SPJ9
Answer: x=0 or x= -5/6
Step-by-step explanation: x=((−2)(3))(x2)−4x
Answer:
He has written about 100 times as many words.
Step-by-step explanation:
In order to find this, we first need to find the number that he has written this month. In order to do so, we need to subtract the previous month from the current total.
12,580 - 125 = 12,455
Now that we have that number, we can divide it by the previous month to see how many times more words he wrote in the second month.
12,455/125 = 99.64 times more, or rounded, about 100 times more.
Answer:
No. X's above 2: 1
Above 3: 1
Above 4: 3
Above 5: 3
Step-by-step explanation:
Drawing a line plot of a data set means that you record the number of times that particular value shows up in the set. 2 on the line plot would only have 1 'X' placed above it because there is only one 2 in the data set:
5, 5, 4, 3, 2, 5, 4, 4
3 would also have 1 'X' above it because there is also only one 3 in the data set:
5, 5, 4, 3, 2, 5, 4, 4
Similarly, 4 and 5 would both have three 'X's because there are three 4's and three 5's in the data set:
4's: 5, 5, 4, 3, 2, 5, 4, 4
5's: 5, 5, 4, 3, 2, 5, 4, 4
Hope this helped!
The equations that express the relationship between the side lengths of the triangles are
<h3>Pythagorean triple</h3>
From the question, we are to write an equation that expresses the relationship between the side lengths of each triangle
From the Pythagorean theorem,
In a right triangle, the square of the longest side (hypotenuse) equals sum of squares of the other two sides
That is,
c² = a² + b²
Where c is the longest side (hypotenuse)
a and b are the other two sides
The equation is
10² = 6² + 8²
- For
The equation is
- For
The equation is
- For
The equation is
- For
The equation is
Hence, the equations that express the relationship between the side lengths of the triangles are
Learn more on Pythagorean triple here: brainly.com/question/3223211
#SPJ1