x = number of minutes used, y = total cost in dollars
Plan A: y = 0.09x + 24
Plan B: y = 0.14x + 20
Equate the two right hand side (RHS) expressions and solve for x
0.14x + 20 = 0.09x + 24
0.14x - 0.09x = 24 - 20
0.05x = 4
x = 4/0.05
x = 80
The two plans will cost the same amount of money if you use up 80 minutes
Plug in x = 80 into either equation to find y
y = 0.09*x + 24
y = 0.09*80 + 24
y = 31.20
or
y = 0.14*x + 20
y = 0.14*80 + 20
y = 31.20
So both plans will cost $31.20 if you use up 80 minutes
Answer:
The correct answer to given question is option (a).
Step-by-step explanation:
Given function: f(x)= -2|x+1|
we need to put random values of x in given function to see that range of the given function f(x) is all real numbers.
when:
x=0; f(0)= -2|0+1|= -2|1|= -2
when x is positive i.e. x>0
x=1; f(1)= -2|1+1|= -2|2|= -4
x=2; f(2)= -2|2+2|= -2|4|= -8
when x is negative i.e. x<0
x= -1; f(-1)= -2|-1+1|= -2|0| =0
x=-2; f(-2)= -2|-2+1|= -2|-1|=2 (with the help of mod property |-1|=1)
hence, we saw that
when we take x>0; f(x)<0
when x<0; f(x)>0
we can conclude from above steps that the range of function f(x)= -2|x+1| is all real numbers.
There are 32 female performers in a dance recital the ratio of men to women is 3/8 How many men are in the dance recital
But we have 32 female performers in the dance recital. Hence there are 3×4=12 men in the dance recital.
Answer:
180, 180, 148, 180, 148
Step-by-step explanation:
The two rules in play here are ...
- the sum of interior angles of a triangle is 180°
- the angles of a linear pair are supplementary (they total 180°)
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The first of these rules answers the first two questions:
- interior angles total 180°
- angles 1, 3, 4 total 180°
We can subtract the measure of angle 1 from both sides of the previous equation to find the sum of the remaining two angles.
- angles 3 and 4 total 148°
The second rule answers the next question:
- angles 1 and 2 total 180°
As before, subtracting the value of angle 1 from both sides of the equation gives ...
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<em>Additional comment</em>
Of course, the subtraction property of equality comes into play, also. For some unknown, X, you have (in both cases) ...
X + 32° = 180°
X +32° -32° = 180° -32° . . . . . . subtraction property of equality
X = 148° . . . . . . . . simplify
In the first case, X is the sum of angles 3 and 4. In the second case, X is angle 2 only.
