1/2(x)=16 please explain the steps ty <3
1 answer:
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Let's carry this math sentence over to its natural, "shapey" element. We're going to look at each term not as an ordinary number, but as <em>the area of some shape</em>.
x² (read as "x <em>squared"</em>) can be seen as the area of a square with side lengths of x. 2x can similarly be seen as the area of a <em>rectangle </em>with a length of x and a width of 2. (Picture 1)
What's our question actually asking, though? Something about <em>perfect squares</em>. More specifically, we're looking for something to add on that'll <em>make this thing a perfect square</em>. We're trying to find a missing piece we can slot in to make a square, in other words. Problem is, our shapes don't look much like a square if we put them together right now. We need to do a little cutting and gluing first.
First, we're gonna cut the 2x rectangle lengthwise, getting two rectangles with an area of x, a length of 1, and a width of x. Next, we're going to attach them to the x² square, creating this shape that looks, strangely, like a square with a little bit missing from it (picture 2). What we're trying to do is <em>complete this square, </em>to find the area of that little missing chunk.
As it turns out, we have all the information we need for this. Notice that, using the lengths of the x rectangles, we can find that the square's dimensions are 1 x 1, which means that its area is 1 x 1 = 1.
If we tack this new area on to our original expression, we've "completed the square!" We now have a perfect square with side lengths of (x + 1) and an area of (x + 1)² (picture 3).
So, our final expression is x² + 2x + 1, and the missing constant - the area of the "missing square" we had to find to complete our larger one - is 1.
Answer:
x ≥ 2
0 ≤ 20 (not quite sure if the question is right)
Step-by-step explanation:
x+18 ≥ 8x+4
x - 8x ≥ 4 - 18
-7x ≥ -14
x ≥
x ≥ 2
________________
15x-15 ≤ 15x+5
15x - 15x ≤ 5 + 15
0 ≤ 20
(I don't think this is the right question...cuz theres a 0)
Answer:
48. or
51. or
54. or
57. or
Step-by-step explanation:
48.
-There are two equations:
Equation 1:
or
Equation 2:
Solving equation 1:
(Inequality sign changed, because of dividing by a negative number)
-Solving equation 2:
(Inequality sign changed, because of dividing by a negative number)
-Answers:
or
51.
-There are two equations:
Equation 1:
or
Equation 2:
-Solving equation 1:
-Solving equation 2:
Answers:
or
54.
-There are two equations:
Equation 1:
or
Equation 2:
-Solving equation 1:
-Solving equation 2:
-Answers:
or
57.
-There are two equations:
Equation 1:
or
Equation 2:
-Solving equation 1:
Solving equation 2:
Answers:
or
And we are finished.
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