Hey there!
<em>C = 0.25x + 40</em>
(a) For this part we solve for C when x = 240. Substitute 240 in for x.
C = 0.25(240) + 40
Multiply 240 by 0.25.
C = 60 + 40
Add.
C = 100
The cost is $100.
<u>Check</u>
100 = 0.25(240) + 40
100 = 60 + 40
100 = 100
(b) For this part we solve for x when C = 180. Substitute 180 for C.
180 = 0.25x + 40
Subtract 40 from each side.
140 = 0.25x
Divide each side by 0.25.
560 = x
This person drove 560 miles.
<u>Check</u>
180 = 0.25(560) + 40
180 = 140 + 40
180 = 180
(c) For this we must make an inequality with C = 150.
Since they want the cost to be <em>no more than</em> 150, we will use the ≥ symbol.
C ≥ 0.25x + 40
Substitute 150 for C. Solve for x.
150 ≥ 0.25x + 40
Subtract 40 from each side.
110 ≥ 0.25x
Divide each side by 0.25.
440 ≥ x
The max number of miles they can drive is 440.
<u>Check</u>
150 ≥ 0.25(440) + 40
150 ≥ 110 + 40
150 ≥ 150
Hope this helps!
8/10 = 0.8
Therefore, 0.8 (8/10) is put on the number line shown below.
Answer:
<em>8 C sometimes</em>
<em>9 64x^8 y^11</em>
<em>10 c 1.28r^2/ t^9</em>
Step-by-step explanation:
<u>Algebraic Operations
</u>
Some basic rules must be fresh in our minds when trying to simplify complex algebraic expressions. For example, the power rule respect to the product or quotient:
Let's face the questions at hand
8. A number is raised to a negative exponent is negative?
Following the expressions recalled above, let's pick the expression
This is a negative power resulting in a positive number
Now we pick
This time, the negative power leads to a negative result, so it doesn't matter the sign of exponent to determine the sign of the result
<em>Answer: C sometimes
</em>
9 simplify(4xy^2)^3(xy)^5
10 simplify(2t^-3)^3(0.4r)^2
Answer:
d.
Step-by-step explanation:
Left line is defined when x < 1 (x is less than 1). The point is not full and that means that x = 1 is not included.
Right line is defined when x is greater or equal to one x ≥ 1.
Options that have x < 1 and x ≥ 1 are b and d, so the answer is one of those.
Equations of the lines are in slope-intercept form y = mx + b, where m is slope and b is y-intercept.
Right line has steeper slope than left line, so the slope of right line will have bigger absolute value. That is the case with option d. (Left line has slope -1 and right one has slope -2, absolute value of right slope is bigger.)
You could also check with y-intercepts. Left line has y-intercept at y = 2 and left line is defined when x < 1. Only option d meets these conditions.
