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polet [3.4K]
4 years ago
15

Rewrite y = 3x in function notation.

Mathematics
1 answer:
Alborosie4 years ago
4 0
Function notation replaces the 'y' with a letter, usually 'f' and then puts the variable in parenthesis.

f(x) = 3x

Other equivalent examples would be:
g(x) = 3x
f(z) = 3z
h(a) = 3a

All of these represent the same function, just written in different forms of function notation. The variable can be represented as any letter and the function name can be different letters as well.
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8(x/4)>4 solve the inequality
Hoochie [10]

ANSWER


x>2

<u>EXPLANATION</u>

We have the inequality


8(\frac{x}{4})>4


We can cancel directly to get;


2(\frac{x}{1})>4


\Rightarrow 2x>4



We now divide both sides by 2,


\Rightarrow x>\frac{4}{2}



x>2


See graph in attachment

3 0
3 years ago
If:
PSYCHO15rus [73]

Take some trinomial expansions to find some useful expressions and their values.

• 2nd degree expansion

x + y + z = 7 \\\\ \implies (x+y+z)^2 = x^2+y^2+z^2+2(xy+xz+yz) = 7^2 \\\\ \implies xy+xz+yz = \dfrac{49-33}2 = 8

• 3rd degree expansion

x+y+z=7 \implies (x+y+z)^3 = 7^3 \\\\ \implies \\ 243 = x^3+y^3+z^3+3(x^2y+x^2z+xy^2+y^2z+xz^2+yz^2) + 6xyz \\\\ \implies \\ x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 + 2xyz = \dfrac{343 - 145}3 = 66

• 4th degree expansion

x+y+z=7 \implies (x+y+z)^4 = 7^4 \\\\ \implies \\ 2401 = x^4+y^4+z^4+4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~+ 6(x^2y^2+x^2z^2+y^2z^2) + 12(x^2yz+xy^2z+xyz^2) \\\\ \implies \\\\ x^4+y^4+z^4 = 2401 - 4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~~~~~~~~~~~- 6(x^2y^2+x^2z^2+y^2z^2) - 12(x^2yz+xy^2z+xyz^2)

Simplify:

x^3y+x^3z+xy^3+y^3z+xz^3+yz^3 \\\\ ~~~~ = x^2 (xy+xz) + y^2 (xy+yz) + z^2 (xz + yz) \\\\ ~~~~ = x^2 (xy+xz+yz) + y^2 (xy+xz+yz) + z^2 (xy + xz + yz) - (x^2yz + xy^2z + xyz^2) \\\\ ~~~~ = (x^2+y^2+z^2) (xy+xz+yz) - xyz (x+y+z) \\\\ ~~~~ = 264 - 7xyz

x^2y^2+x^2z^2+y^2z^2 \\\\ ~~~~ = xy\cdot xy + xz \cdot xz + yz \cdot yz \\\\ ~~~~ = xy(xy+xz+yz) + xz(xy+xz+yz) + yz(xy+xz+yz) - 2(x^2yz+xy^2z+xyz^2) \\\\ ~~~~ = (xy+xz+yz)^2 - 2xyz(x+y+z) \\\\ ~~~~ = 64 - 14xyz

x^2yz+xy^2z+xyz^2 = xyz (x + y + z) = 7xyz

Then the equation we got from the 4th degree expansion reduces to

x^4+y^4+z^4 = 2401 - 4(264-7xyz) - 6(64-14xyz) - 12(7xyz) \\\\ ~~~~~~~~~~~~~~~~~= 961 + 28xyz

and all we need now is the value of xyz.

In the 3rd degree expansion, we have

x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 \\\\ ~~~~ = x(xy + xz) + y(xy + yz) + z(xz + yz) \\\\ ~~~~ = x(xy+xz+yz) + y(xy+xz+yz) + z(xy+xz+yz) - 3xyz \\\\ ~~~~ = (x+y+z)(xy+xz+yz) - 3xyz \\\\ ~~~~ = 56 - 3xyz \\\\ \implies (56 - 3xyz) + 2xyz = 66 \\\\ \implies xyz = -10

So, we end up with

x^4+y^4+z^4 = 961 - 280 = \boxed{681}

4 0
1 year ago
Which of the following equations is quadratic?
Dominik [7]

Answer:

C

Step-by-step explanation:

hope this helps.

6 0
3 years ago
Which bedt describes the solutions to 4-7?
Snowcat [4.5K]

Answer:

4-7

this gives us answer of -4

hope it helps

4 0
3 years ago
Brooke found the equation of the line passing through the points (–7, 25) and (–4, 13) in slope-intercept form as follows.
Arturiano [62]

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cut-off point with the y axis

m = \frac {y2-y1} {x2-x1}

We have the following points:

(x1, y1): (- 7,25)\\(x2, y2): (- 4,13)

Substituting the values:m = \frac {13-25} {- 4 - (- 7)} = \frac {-12} {- 4 + 7} = \frac {-12} {3} = - 4

Thus, the line is of the form:

y = -4x + b

We substitute one of the points and find "b":

13 = -4 (-4) + b\\13 = 16 + b\\b = 13-16 = -3

Finally we have to:

y = -4x-3

Answer:

The equation es y = -4x-3

6 0
3 years ago
Read 2 more answers
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