1. This must be greater than or equal to 0 (there can't be any negatives!)
8 - .5t ≥ 0.
8 ≥ .5t
t ≤ 16
D.
2. 4(2x-1) = 2x + 35
8x - 4 = 2x + 35
6x = 39
x = 6.5
H.
3. c = .8(x-15) = .8x-12
A.
4. m = number of marble cupcakes
s = number of strawberry shortcake cupcakes
6m + 8.5s = 391
m = 1/2s
6(.5s)+8.5s = 391
11.5s = 391
s = 34
m = 17
F.
5. B
6. Use substitution
2x + 3x = 10
5x = 10
x = 2
7. (sorry I'm not sure!)
8. G
9. L = number of balls
B = number of bats
L + B = 100
B = 100 - L
4.5L+20B = 822
4.5L + 20(100-L) = 822
4.5L -20L + 2000 = 822
1178 = 15.5L
L = 76
10. J
Okay so basically an integer is just a whole number that isn’t a fraction. Comparing integers is basically comparing whole numbers. For example, comparing the numbers 2 and 34 would be 2<34 and that’s comparing them to each other! :)
Answer:
a) 13, 10, 16
Step-by-step explanation:
The usual form of the triangle inequality requires the sum of the two shortest sides exceed the longest side (a+b>c). The only choice for which this is true is ...
10 + 13 > 16 . . . . choice A
_____
<em>Comment on the triangle inequality</em>
Some authors also allow the sum to equal the longest side (a+b≥c). In that case, choice B (1+2=3) is also an answer. This "triangle" would look like a line segment of length 3. It has zero area.
Answers:
A) 
C) 
Step-by-step explanation:
<u>Part 1:</u>
We have the followig equation:
Calculating the least common multiple (l.c.m) in the denominator in the left side of the equation, being l.c.m=15:
Solving for the left part of the equation:
Operating with cross product:
Applying the distributive property:
Isolating 
:
Dividing numerator and denominator by 11:
Hence, the correct option is A
<u>Part 2:</u>
We have the followig equation:
Operating with cross product:
Isolating 
:
Hence, the correct option is C
