Answer:
x = 7
Step by step explanation:
<em>minus</em><em> </em><em>x</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em>
6 = x -1
<em>add</em><em> </em><em>1</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em>
<em>x</em><em> </em><em>=</em><em> </em><em>7</em>
Okay, so, to find out if an equation has one solution, an infinite number of solutions, or no solutions, we must first solve the equation:
(a) 6x + 4x - 6 = 24 + 9x
First, combine the like-terms on both sides of the equal sign:
10x - 6 = 24 + 9x
Now, we need to get the numbers with the variable 'x,' on the same side, by subtracting, in this case:
10x - 6 = 24 + 9x
-9x. -9x
______________
X - 6 = 24
Now, we do the opposite of subtraction, and add 6 to both sides:
X - 6 = 24
+6 +6
_________
X = 30
So, this particular equation has one solution.
(a). One solution
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(b) 25 - 4x = 15 - 3x + 10 - x
Okay, so again, we combine the like-terms, on the same side of the equal sign:
25 - 4x = 25 - 2x
Now, we get the 2 numbers with the variable 'x,' to the same side of the equal sign:
25 - 4x = 25 - 2x
+ 2x + 2x
________________
25 - 2x = 25
Next, we do the opposite of addition, and, subtract 25 on each side:
25 - 2x = 25
-25 -25
___________
-2x = 0
Finally, because we can't divide 0 by -2, this tells us that this has an infinite number of solutions.
(b) An infinite number of solutions.
__________________________________________________
(c) 4x + 8 = 2x + 7 + 2x - 20
Again, we combine the like-terms, on the same side as the equal sign:
4x + 8 = 4x - 13
Now, we get the 'x' variables on the same side, again, and, we do that by doing the opposite of addition, which, is subtraction:
4x + 8 = 4x - 13
-4x -4x
______________
8 = -13
Finally, because there is no longer an 'x' or variable, we know that this equation has no solution.
(c) No Solution
_________________________________
I hope this helps!
9514 1404 393
Answer:
168 cubic inches
Step-by-step explanation:
The formula for the volume of a pyramid is ...
V = (1/3)Bh
where B is the area of the base, and h is the height.
The base is a rectangle, whose are is given by the formula ...
A = LW
A = (8 in)(7 in) = 56 in²
Then the pyramid volume is ...
V = (1/3)(56 in²)(9 in) = 168 in³
The volume of the pyramid is 168 cubic inches.
