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Rama09 [41]
3 years ago
15

Can anyone help me with number 6 & 8?

Mathematics
2 answers:
Liono4ka [1.6K]3 years ago
5 0

\bf \begin{cases} f(x)=x-3\\ g(x)=x^2+1\\ h(x)=-4x+1\\ -------&--------\\ (h\circ g\circ f)(x)=&(h\circ g(~f(x)~)\\ &h(~~g(~~f(x)~~)~~) \end{cases} \\\\\\ g(~~f(x)~~)=[f(x)]^2+1\implies g(~~f(x)~~)=[x-3]^2+1 \\\\\\ g(~~f(x)~~)=[x^2-6x+9]+1\implies \boxed{g(~~f(x)~~)=x^2-6x+10} \\\\\\ h(~~g(~~f(x)~~)~~)=-4[g(~f(x)~)]+1 \\\\\\ h(~~g(~~f(x)~~)~~)=-4[x^2-6x+10]+1 \\\\\\ h(~~g(~~f(x)~~)~~)=-4x^2+24x-40+1 \\\\\\ h(~~g(~~f(x)~~)~~)=-4x^2+24x-39

Irina-Kira [14]3 years ago
5 0

6.

So for this, since the circle is open, you are going to be replacing x in g(x) with -4x + 1. It will be solved as such:

g(h(x))=(-4x+1)^2+1\\ g(h(x))=16x^2-8x+1+1\\ g(h(x))=16x^2-8x+2

8.

So firstly, we will need to solve g(f(x)) before we can do h(g(f(x))). So replace x in g(x) with x - 3:

g(f(x))=(x-3)^2+1\\ g(f(x))=x^2-6x+9+1\\ g(f(x))=x^2-6x+10

So now that we know what g(f(x)) is, we can solve for h(g(f(x))). To do this, replace x in h(x) with x^2 - 6x + 10:

h(g(f(x)))=-4(x^2-6x+10)+1\\ h(g(f(x)))=-4x^2+24x-40+1\\ h(g(f(x)))=-4x^2+24x-39

In short, h(g(f(x))) = -4x^2 + 24x - 39.

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A) The greatest rectangular area will be the area of a square 10 m on each side, 100 m^2.

b) The new dimensions will be 11 m × 11 m.
.. The new area will be (11 m)^2 = 121 m^2.

c) The area was increased by 121 m^2 -100 m^2 = 21 m^2, or 21%.

d) Yes, and no.
.. If you increase the dimensions by 10%, the area will increase by 21%.
.. (40 m)^2 = 1600 m^2
.. (44 m)^2 = 1936 m^2 = 1.21*(1600 m^2), an increase of 21% over the original.

.. If you increase the dimensions by 1 unit, the area will increase by (2x+1) square units, where x is the side of the original. For x≠10, this is not 21 square units.
.. (41 m)^2 = 1681 m^2 = 1600 m^2 +(2*40 +1) m^2 = 1600 m^2 +81 m^2
4 0
3 years ago
You go to your locker to get some supplies. You grab 3 pens and 6 markers, then you find 2 more markers on the bottom of your lo
katen-ka-za [31]

Answer:

I think it is 3 + (6 + 2) or 11

Step-by-step explanation:

You first find 3 pens and 6 markers. Then you find 2 more markers at the bottom of your locker. The common answer I think would be 3 + (6 + 2) or If your teacher wants a whole answer, 11.

I hope this helped

I am sorry if I got it incorrect

6 0
2 years ago
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OverLord2011 [107]
The correct answer is C.
7 0
3 years ago
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Solve the compound inequality 7x > –35 and 3x ≤ 30.
docker41 [41]

Answer:

x>-5 x ≤10

Step-by-step explanation:

-35/7=-5

7x/7=x

3x/3=x

30/3=10

5 0
3 years ago
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Miguel: 500 out of 750 students have part time jobs.

500 ÷ 250 = 2
750 ÷ 250 = 3

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A) 200 out of 300 ⇒ 200/100 and 300/100 ⇒ 2:3
B) 700 out of 1100 ⇒ 700/100 and 1100/100 ⇒ 7:11
C) 800 out of 1200 ⇒ 800/400 and 1200/400 ⇒ 2:3
D) 9000 out of 1300 ⇒ 9000/100 and 1300/100 ⇒ 90:13

Among the choices, Choice B could represent Kureshi's Data because it is not proportional to the data of Miguel.

Choice D is not possible. You cannot have a result that is way beyond the scope of your population. It is impossible to get 9000 students out of only 1300 students.

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3 years ago
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