Answer:
Step-by-step explanation:
Yes, the irrational number stays irrational.
Make the assumption that this statement is false and that a rational and an irrational can produce a rational. x is irrational. Assume that a, b, c, and d are all integers. If you like, they can be relatively prime to each other.
a/b + x = c/d Subtract a/b from both sides.
x = c/d - a/b Now put the 2 fractions over a common denominator.
x = (c*b - d*a)/(b*d) Investigate what you have.
b*d are two integers multiplied together. multiplication of integers is closed (the answer will be an integer).
cb and da are also integers. subtracted integers are also closed under subtraction.
But
Here's the kicker. An irrational number is one that cannot be expressed as a fraction. Sqrt(2) for example cannot be shown to be rational. There is no fraction that equals sqrt(2)
So our proof is "bogus." It cannot work. An irrational number excludes the possibility of being able to be represented by a fraction by definition.
Answer:
all i know is that its not alternate exterior angles theorem
Step-by-step explanation:
so sorry, i wish i could help more!
2(17)+4
2* 17=34
34+4=38
So it equals 38
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!
Answer: E. (126 + 10.5x) square feet
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The length of a living room is 12 feet and its width is 10 1/2 feet. If the length of the room is being expanded by x feet, then the new length would be (12 + x) feet
Therefore, an expression to represent the new area of the living room in square feet would be
10.5(12 + x)
The expanded form of the expression would be
(126 + 10.5x) square feet