TODAY'S PROBLEMS
Heritage team DO THIS 10 minutes! Go!
Friendly Hills - (check out the answers)
1. Simplify 3(x+4) - 2(8+x) + 10 - x(x+3)
2. How many centimeters are in the sum of 115mm and 20 cm and 1m?
3. In Canada the speed limits are in Km/hr. If six tenths of a mile is one kilometer, what speed is 90 km /hr in miles per hour?
4. Write the absolute value inequality for 3 ≤ x ≤ 9
5. Find x :
ANSWERS
1. 3(x+4) - 2(8+x) + 10 - x(x+3)
3x+12 + -16 +
-2x + 10 + -
x2 +
-3x
Combine the bold terms above to get
-
x2 - 2x + (12 + -16 + 10)
Then add to simplify
-
x2 -2x + 6
2.
Convert all to cm.
11.5 cm + 20 cm + 100 cm
Simplify to 131.5 cm
3. 90 km/hr x .6mi/km (since .6mi = 1 km I'm really just multiplying by one!)
With a km in the numerator and a km in the denominator, they cancel out.
90 x .6 mi/h = 54 mi/h or 54 mph So when the speed limit in Canada says 90, that's in Km/hr and means 54 mph.
4. Draw the inequality on a number line:
|--|--|--
|--|--|--|--|--|--|
0 1 2 3 4 5 6 7 8 9
Absolute value can be thought of as "distance". You see that the midpoint is 6, so this graph shows all the numbers within a distance of 3 from 6. Hence: |x-6| ≤ 3 (or |6-x| ≤ 3)
Let's check: 3, 6 and 9 should be true. 2 and 10 should be false . Yep!
5. The straight line angle composed of 2x + 90
o + 3x +18
o must = 180
o
Combine like terms: 5x +108
o= 180
o
Subtract 108
o from both sides:
5x = 72
o
Divide both sides by 5: x = 14.4
o
FRIENDLY HILLS
Frank Sullivan |
6 |
39.7 |
Cyrus Martin Risch |
2 |
19.0 |
Noelle Wang |
4 |
17.5 |
Oscar Halverson |
4 |
17.0 |
Naomi Spande |
2 |
12.3 |
Nick Wendt |
0 |
11.7 |
Oslo Martin Risch |
0 |
9.0 |
Lydia Houge |
4 |
7.3 |
Dain Dolan |
0 |
6.0 |
Aiden Lee |
|
5.0 |
Nicholas Reisig |
0 |
4.0 |
Aidan Dolan |
0 |
3.0 |
Lily Pince |
|
1.0 |
Emma Stevenson |
2 |
0.7 |
Sophia Schomer |
|
0.0 |
Jake Lancaster |
? |
0.0 |
HERITAGE
Aiden
Jacobs |
28.7 |
Anthony Rocke |
24.7 |
Abbey Dzurilla |
24.3 |
Steve Nickson |
18.3 |
Cullen Sander |
11.0 |
Skylar Janssen |
8.7 |
Ben Nickson |
4.5 |
Angel Hernandez |
2.0 |