Answers:
16. 6-x= 10
move +6 to the other side
sign changes from +6 to -6
6-6-x= 10-6
-x= 4
Mutiply both sides by -1
(-1)(-x)= (-1)(4)
x= -4
17. 4a+3= -9
move +3 to the other side
sign changes from +3 to -3
4a+3-3= -9-3
4a= -12
divide both sides by 4
4a/4= -12/4
a= -3
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Answer:
- 0 < x < 4
- (- ∞ < x < 0) ∪ (4 < x < ∞)
- x ∈ {0, 4}
Step-by-step explanation:
1. The solution is the set of x-values for which the graph is above the x-axis, where y = 0. Those x-values are in the interval (0, 4).
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2. The solution is the set of x-values for which the graph is below the x-axis. Those x-values are in either of the two intervals (-∞, 0) or (4, ∞).
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3. The x-intercepts of the graph are x=0 or x=4.
Answer:
Line A
Step-by-step explanation:
Line A has a constant of proportionality (slope) of 4.
Multiply both sides of the second equation by 100 to get rid of the decimals:
0.05<em>n</em> + 0.10<em>d</em> = 1.50
==> 5<em>n</em> + 10<em>d</em> = 150
Multiply both sides of the first equation by -5:
<em>n</em> + <em>d</em> = 21
==> -5<em>n</em> - 5<em>d</em> = -105
Add the two equations together:
(5<em>n</em> + 10<em>d</em>) + (-5<em>n</em> - 5<em>d</em>) = 150 + (-105)
Notice that the terms containing <em>n</em> get eliminated and we can solve for <em>d</em> :
(5<em>n</em> - 5<em>n</em>) + (10<em>d</em> - 5<em>d</em>) = 150 - 105
5<em>d</em> = 45
<em>d</em> = 45/5 = 9
Plug this into either original equation to solve for <em>n</em>. Doing this with the first equation is easiest:
<em>n</em> + 9 = 21
<em>n</em> = 21 - 9 = 12
So Donna used 12 nickels and 9 dimes.
