The region is in the first quadrant, and the axis are continuous lines, then x>=0 and y>=0
The region from x=0 to x=1 is below a dashed line that goes through the points:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(1,3)=(x2,y2)→x2=1, y2=3
We can find the equation of this line using the point-slope equation:
y-y1=m(x-x1)
m=(y2-y1)/(x2-x1)
m=(3-2)/(1-0)
m=1/1
m=1
y-2=1(x-0)
y-2=1(x)
y-2=x
y-2+2=x+2
y=x+2
The region is below this line, and the line is dashed, then the region from x=0 to x=1 is:
y<x+2 (Options A or B)
The region from x=2 to x=4 is below the line that goes through the points:
P2=(1,3)=(x2,y2)→x2=1, y2=3
P3=(4,0)=(x3,y3)→x3=4, y3=0
We can find the equation of this line using the point-slope equation:
y-y3=m(x-x3)
m=(y3-y2)/(x3-x2)
m=(0-3)/(4-1)
m=(-3)/3
m=-1
y-0=-1(x-4)
y=-x+4
The region is below this line, and the line is continuos, then the region from x=1 to x=4 is:
y<=-x+2 (Option B)
Answer: The system of inequalities would produce the region indicated on the graph is Option B
The first four equations are correct. The remaining 4 equations are incorrect. See the attached screenshot for a detailed breakdown of why the last four equations are incorrect.
Answer:
9
Step-by-step explanation:
9/9=1
27/9=3
The number of people who bought £4 tickets are 139.
<h3>How to illustrate the equation?</h3>
Let £4 tickets be x
Let £5 tickets be y.
Therefore based on the information given, this will be:
x + y = 223 ..... i
4x + 5y = 936 ..... ii
From equation i
x = 213 - y
Put this into equation ii
4x + 5y = 936
4(213 - y) + 5y = 936
852 - 4y + 5y = 936
Collect like terms
y = 84
This implies that the number of £5 tickets is 84.
Recall that x + y = 223
x + 84 = 223
x = 223 - 84
x = 139
The number of £4 tickets is 139
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Answer:The second choice is the correct one
Explanation:(2x+3)^2 + 8(2x+3) + 11 = 0
To use the u substitution, we will assume that:
2x + 3 = u
Substitute with this in the given expression, we will get:
u^2 + 8u + 11 = 0
The general form of the second degree equation is:
ax^2 + bx + c = 0
Comparing the expression we reached with the general one, we will find that:
a = 1
b = 8
c = 11
The roots can be found using the rule found in the attached picture.
This means that, for the given expression:
u = -4 ± √5
Now, we have:
u = 2x+3
This means that:
at u = -4 + √5
2x + 3 = -4 + √5
2x = -7 + √5
x = (-7 + √5) / 2
at u = -4 - √5
2x + 3 = -4 - √5
2x = -7 - √5
x = (-7 - √5) / 2
This means that, for the given expression:
x = (-7 ± √5 ) / 2
Hope this helps :)