9514 1404 393
Answer:
- x=2 (work is correct)
- x=4
- x=44
- x=4
- x=any number
- impossible; no such number
Step-by-step explanation:
1. The equation is ...
3x +5 = 11
3x = 11 -5 = 6
x = 6/3 = 2 . . . . matches the work shown
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2. The equation is ...
(x +2)·5 = 30
x +2 = 30/5 = 6
x = 6 -2 = 4
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3. The equation is ...
(x/2) +2 = 24 . . . . matches the work shown
x/2 = 24 -2 = 22
x = 22·2 = 44
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4. The equation is ...
2x +8 = x +12
2x = x + 12 -8 = x +4
2x -x = x -x +4
x = 4
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5. The equation is ...
2x +4 -x -3 = x +1
x +1 = x +1 . . . . . true for any value of x
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6. The equation is ...
(3x +6) -2x = x +3
x +6 = x +3 . . . . . not true for any number
_____
<em>Additional comment</em>
The work shown is correct. You find x by writing and solving an appropriate equation. To solve the equation, undo the steps that are done to x. Undo addition by adding the opposite. Undo multiplication by diving by the multiplier. It often helps to collect terms before you start the "undo" steps.
For x on both sides of the equation (as in problems 4–6), you can subtract the term with the lowest coefficient. (Of course, you must subtract it from both sides of the equation.) In problem 5, if you do that, you get 1=1, which is true for any value of x. In problem 6, if you do that, you get 6=3, a false equation, indicating no value of x will make it true.
Answer:
Under 800 square feet of carpet to be cleaned: $0.53 per square foot
800 - 1,500 square feet: $0.49 per square foot
Over 1,500 square feet: $0.42 per square foot
Stairs (standard size): $4.16 each stair
<span>y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start.
Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed.
x=8
y=2*8+3
y=19</span>
Because these triangles are congruent, then angle a is the same degree measure as angle x; angle b is the same as y; and angle c is the same as z. We also know that, because of the Triangle Angle-sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. So for us that means that a+b+c(which is also z) = 180. 50 + 2x + 40 + 4x + 8 = 180. Combining like terms we have 6x + 98 = 180. Subbtracting 98 from both sides gives us 6x = 82 and x = 13 2/3
Answer: OPTION D.
Step-by-step explanation:
You can observe in the graph that represents f(x) that this function intersects the x-axis at the point (1,0). Then:
We know that a function intersects the x-axis when 
.
We can observe the table that represents the function g(x). When the value of "y" is 0 (
), the value of "x" is -1 (
). Therefore, the x-intercept of f(x) is greater that the x-intercept of g(x).
You can observe in the graph that represents f(x) that this function intersects the y-axis at the point (0,-1). Then:
We know that a function intersects the y-axis when 
. In the table that represents the function g(x), we can see that, when the value of "x" is 0 (), the value of "y" is 1 (
). Therefore, the y-intercept of g(x) is greater that the y-intercept of f(x).
