1. How much ribbon is required to wrap once around a basketball present? Basketballs are 78 cm in diameter
2 Two cars leave the park at the same time. One travels north at a speed of 50 km/h for 2 hours. The
second car travels west at a speed of 80 km/h for 2 hours. After the 2 hours, how far apart are the two
cars? Be sure to draw a diagram illustrating this situation
3 Asmall tree is beginning to lean The owner decides to set up a tension wire to straighten the tree's
growth The owner chooses a wire which is 5 m in length to straighten the tree. The tree is 4 m high
How far must the owner secure the bottom of the wire from the base of the tree (assuming he attaches
the tension wire to the top of the tree)?

1) 244.92cm  2) 188.68 km  3) 3m

Step-by-step explanation:

1) We are finding the circumference of the basketball in this situation. C=pi(d), d=diameter, C=circumference. So, C= 3.14(78), and finally C= 244.92 cm.

2) We can begin to approach this problem by finding how far each car has traveled over 2 hours. The car heading north is going 50 km/h, so for two hours it has covered 100 kilometers. The car going west is at 80 km/h, so for two hours it has covered 160 kilometers. Now, we could draw this as a right triangle, with one leg being the north-headed car 100 km away from the start, and the other leg being the west moving car 160 km away from the start. The hypotenuse represents the distance between them. Now we use the pythagorean theorem! north car is a, west car is b. a^2+b^2=c^2. 100^2+160^2=c^2. 35600=c^2. take the square root of both sides for c=188.68. The distance between the two cars is approx 188.68 km.

3) `This situation can be represented as a right triangle. The height of the tree, 4m, is the height of the triangle, and the wire, 5m, is the hypotenuse. We are trying to find one of the legs, which represents the ground to the base of the tree. In the pythagorean theorem, we have a^2 and c^2, and just need to find b^2. Let's plug it into the equation:

4^2+b^2=5^2

16+b^2= 25

b^2=9

b=3

hope this helped it took a long time to explain it all! :)

step-by-step explanation: yes

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3