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bezimeni [28]
3 years ago
9

F(x) = 4x + 7, g(x) = 3x^2 Find (f + g)(x)

Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0
For the functions f(x) = 4x + 7 and g(x) = -9x + 11, find f(g(0)). For the functions f(x) = 3x2 - 7 and g(x) = -3x2 + 4, find f(g(2)). (Do NOT put commas in large numbers.)
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Really need help with this pls help!!
worty [1.4K]

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.

5 0
3 years ago
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Phillip wanted to leave a 15% tip. Phillip's bill is $42.00. How much should he leave for a tip?
Amiraneli [1.4K]

Answer: Double the tax so that hes not a jerc

Step-by-step explanation:

8 0
2 years ago
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Look at the rectangle and the square:
Rudiy27

Answer:

bla bla bla bla bla bla

6 0
3 years ago
4. The manager of a furniture store bought 25 vases at a total cost of
Kamila [148]

The answer is D. 25

All that was need to be done was to divide

5 0
2 years ago
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Solve for x: <br><br> -4x +8 = 42<br><br> x =
vladimir1956 [14]
The answer for x is -8.5
4 0
3 years ago
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