Let f(x)=2x-3 and g(x)= -x^2-1 find ( g o f) (x)

Answers

Answer 1

Answer: $f(x)=2x-3\ \ \ and\ \ \ g(x)= -x^2-1\n\n( g \circ f) (x)=g\bigg(f(x)\bigg)=g\bigg(2x-3\bigg)=-(2x-3)^2-1=\n\n=-(4x^2-12x+9)-1=-4x^2+12x-9-1=-4x^2+12x-10$

Answer 2

Answer: $g \circ f=-(2x-3)^2-1=-(4x^2-12x+9)-1=\n =-4x^2+12x-9-1=-4x^2+12x-10\n$

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Find the 6th term in the expanded form of the equation (2x+y)^9

Answers

$T_r={n \choose r-1}a^(n-(r-1))b^(r-1)\n T_6={9 \choose 6-1}(2x)^(9-(6-1))y^(6-1)\n T_6={9 \choose 5}(2x)^4y^(5)\n T_6=(9!)/(5!4!)16x^4y^(5)\n T_6=(6\cdot7\cdot8\cdot9)/(2\cdot3\cdot4)16x^4y^(5)\n T_6=7\cdot2\cdot9\cdot16x^4y^(5)\n T_6=2016x^4y^5$

$Use\ the\ Pascal's\ Triangle\ (look\ at\ the\ picture)\n\n6-th\ term\ of\ (2x+y)^9\ is\n\n 126(2x)^4y^5=126*16x^4y^5=2016x^4y^5$

If anyone understands proofs, could you walk me through this? I really don't get them. Any help would be appreciated!

Answers

Just a note before I get started: The specific theorem/postulate/definition will be given in quotes. Everything else will be explanation of why we will use itLets get started :D
b. We can use the "definition of a square" because it states that it a square, every side is congruent. We can use this because we already know that the shape is a square due to a.

c. We can use "definition of a square" again for the same reason as b.

e. We know that the hypotenuses (hypoteni?) of both triangles are congruent, and they both share a side, so we can use the "Hypotenuse Leg Theorem"

f. Because we know that the triangles are congruent, we can use the "Base Angle Theorem" to say that the angles are congruent.

h. Because they share the same side, we can use the "Linear Pair Theorem" to say that they are supplementary angles

Hope this helped! Sorry if its a bit late. :D

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms.

The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.The bigger square is x+3 on all 3 sides.
The smaller square is x on every side.

Answers

Given:
Big square: side length = x + 3
Small square: side length = x

Area of a square = a² where a represents the side length.

Area of big square = (x+3)²
A = (x+3)(x+3)
A = x(x+3) + 3(x+3)
A = x² + 3x + 3x + 9
A = x² + 6x + 9

Area of small square = x²

Total Area = Area of Big square + Area of Small square
Total Area = x² + 6x + 9 + x²
Total Area = 2x² + 6x + 9

What is 12.48 in simplest form?

Answers

312/25 is the simplest way to describe that.

: Ram lived in a small village. When he left for a college in a city, the population of his village was 840. When he came back, the , population had grown by 5%. What was the nopulation he found?