Linear Systems
Using elimination, solve for x and y (Round to the nearest decimal)
2y+2x= 18
5y-x=-3
y= 1
x = 8
USE ELIMINATION
An air traffic controller is coordinating the schedules of two aircraft expected to land within a 15-minute timeframe. The paths of the aircraft are described by the equations 3x−5y=20 and 72=3x+15y. Should the controller change the path?
y= 2.6
x=11
Yes, they are good and do not need to change
A man climbed on top of a giant box near a house. He spots his friend's house, Joeyat an angle of depression of 20. The giant box is 50 m tall. What is the distance from the bottom of the box and the house?
The distance is 137.37
A man is blindfolded and walks on a triangle-shaped tight rope. He walks 5 metres, turns left, and steps 4 metres, then goes up 5 metres. What are the angles of the triangle?
A= 66
B=66
C=47
You have a rectangular pan of cookie dough with a width of 18" and a height of 10". You have one circular cookie cutter with a radius of 2". After you cut out as many as you can, what is the surface area of the remaining dough?
Approximately 80 inches
Solve for x and y using substitution (Round to nearest decimal)
y= 2x-2
8x+3y= 9
x= 1.5
y= -1
Anna wants to sell an almond mix with cranberries. Almonds cost $15/kg and cranberries cost $5/kg. How much would it cost to create a mixture of 100/kg to sell for $12/kg? USE SUBSITITION.
There is 50 kg of both almonds and cranberries
A ladder is leaning against a wall. The distance between the ladder and the wall is 4 metres and the ladder is 2 metres away from the wall. What is the angle of the ladder and the ground?
63.43
Mark has a triangle-shaped garden named DEF but he wants to know the angle D. He knows
d= 6cm
e= 3cm
f= 4cm.
D= 117.28
A train is travelling at a constant speed of 22km/h. It is heading 100 km east and 50 km north in a straight line. How long will it take for the train to arrive?
Around 5 hours
x=2.4
y=0.4
GRAPH
1 aircraft ascends at y=2x+3 and another goes descending at y=-2x+5 When will they collide?
They would collide (0.5,4)
Nathan is flying a kite. The string is 100m and she notices that the string forms a 70-degree angle with the ground. Mark is on the other side and sees the kite at an angle of elevation of 30 degrees. How far is Mark from Allison?
Mark is 196.96 metres away
You have a triangle-shaped cake marked ABC. AB is 10 cm long and AC is 8 cm. Angle C is 50 degrees. Solve the other angles.
B= 37.79
A=92
Find the midpoint for
A= (-2,6) and B= (-4,7)
(-3, 6.5)
Use any solution:
y= 2/3x+9
3y+x=12
x= -7.5
y= 6.5
Use any solution.
You are a waiter. You are serving 2 dinners; a chicken dinner costs $20 and a fish dinner costs $18. Two 100 have been ordered in advance, and the total cheque is $3800. Create the linear systems and determine how many of each dinner was ordered.
There are 100 chicken and fish meals ordered
Bob the taxi driver sets off one morning from his company's yard at which he keeps his taxi. This yard is 10 km west of his home. He first heads 20km east and 5km south. He picks someone up and travels halfway back. He heads 15.2 km north and 4km east to drop off his passenger before heading back to the yard. What is the area of the semi-circular region he was in during his route?
Approximately 333km^2