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Mathematics

1 answer:

aleksley [76]2 years ago

3 0

7. 233
8. 4
9. 6
10. 5
11. 4
12. 7
13. 7

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Given: f(x)=x^2, g(x)=x+6, h(x)=7<br><br>Find h{g[f(x)]}

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Step-by-step explanation:

$f(x)=x^2,\ g(x)=x+6,\ h(x)=7\\\\h(x)=7\ \text{It's the constant function. Therefore}\ h\{g[f(x)]\}=7$

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Jenna's class brought in 40 pieces of fruit for a celebration and 32 pieces of fruit were eaten. What percentage of the fruit wa

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Answer:

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Step-by-step explanation:

40 pieces total

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Show that if x and y may both be written as the sum of the squares of two rational integers, then their product xy may also be w

Georgia [21]

Answer:

See proof below

Step-by-step explanation:

One way to solve this problem is to "add a zero" to complete the required squares in the expression of xy.

Let $x=m^2+n^2$ and $y=l^2+k^2$ with $m,n,l,k\in \mathbb{Z}$ . Multiplying the two equations with the distributive law and reordering the result with the commutative law, we get $xy=(m^2+n^2)(l^2+k^2)=m^2l^2+m^2k^2+n^2l^2+n^2k^2=n^2l^2+m^2k^2+m^2l^2+n^2k^2$

Now, note that $0=2lkmn-2lkmn=2nkml-2nlmk$ by the commutativity of rational integers. Add this convenient zero the the previous equation to obtain $xy=n^2l^2-2nlmk+m^2k^2+m^2l^2+2nkml+n^2k^2=(nl-mk)^2+(ml+nk)^2$ , thus xy is the sum of the squares of $nl-mk,ml+nk\in \mathbb{Z}$ .