Answer:
Inequalities are,
y ≥ 4x + 2
y ≥ 2
Step-by-step explanation:
Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).
Let the equation of this line is,
y = mx + b
Slope of the line = 
m = 
m = 4
Y-intercept 'b' = -2
Equation of the line will be,
y = 4x - 2
Since shaded area is on the left side of this solid line so the inequality representing this region will be,
y ≥ 4x - 2
Another line is a solid blue line parallel to the x-axis.
Shaded region (blue) above the line will be represented by,
y ≥ 2
Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.
1) Road Trip: Let’s say two friends are meeting at a playground. Mary is already at the park but her friend Bob needs to get there taking the shortest path possible. Bob has two way he can go - he can follow the roads getting to the park - first heading south 3 miles, then heading west four miles. The total distance covered following the roads will be 7 miles. The other way he can get there is by cutting through some open fields and walk directly to the park. If we apply Pythagoras's theorem to calculate the distance you will get:
(3)<span>2 </span>+ (4)2 =
9 + 16 = C2
√25 = C
5 Miles. = C
Walking through the field will be 2 miles shorter than walking along the roads. .
2) Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of Pythagoras' theorem to complete their work. The painter needs to determine how tall a ladder needs to be in order to safely place the base away from the wall so it won't tip over. In this case the ladder itself will be the hypotenuse. Take for example a painter who has to paint a wall which is about 3 m high. The painter has to put the base of the ladder 2 m away from the wall to ensure it won't tip. What will be the length of the ladder required by the painter to complete his work? You can calculate it using Pythagoras' theorem:
(5)<span>2 </span>+ (2)2 =
25 + 4 = C2
√100 = C
5.3 m. = C
Thus, the painter will need a ladder about 5 meters high.
3) Buying a Suitcase: Mr. Harry wants to purchase a suitcase. The shopkeeper tells Mr. Harry that he has a 30 inch of suitcase available at present and the height of the suitcase is 18 inches. Calculate the actual length of the suitcase for Mr. Harry using Pythagoras' theorem. It is calculated this way:
(18)<span>2 </span>+ (b)2 = (30)2
324 + b2 = 900
B2 = 900 – 324
b= √576
= 24 inches
Answer:
5/2
Step-by-step explanation:
5/2
5x - 3y = -11 (×2)
2x - 6y = -14 (x5)
10x - 6y = -22
10x - 30y = -70
---------------------- -
24y = 48
y = 2
Answer:
Step-by-step explanation:
integer=8
negative fraction=1/2
positive fraction=1/9
negative decimal=0.4
positive decimal=0.8
