If x= 1/2-√3 , prove that x³-2x²-7x+5=3

Answers

Answer 1

Answer: $x=(1)/(2)-\sqrt3\n\nx^3-2x^2-7x+5=3\n\n((1)/(2)-\sqrt3)^3-2((1)/(2)-\sqrt3)^2-7((1)/(2)-\sqrt3)+5\n\n=((1)/(2))^3-3\cdot((1)/(2))^2\cdto\sqrt3+3\cdot(1)/(2)\cdot(\sqrt3)^2-(\sqrt3)^3-...\n\n...-2[((1)/(2))^2-2\cdot(1)/(2)\cdot\sqrt3+(\sqrt3)^2]-(7)/(2)+7\sqrt3+5$

$=(1)/(8)-(3\sqrt3)/(4)+(9)/(2)-3\sqrt3-2((1)/(4)-\sqrt3+3)-(7)/(2)+7\sqrt3+5\n\n=(1)/(8)+(9)/(2)-(1)/(2)-6-(7)/(2)+5-(3)/(4)\sqrt3-3\sqrt3+2\sqrt3+7\sqrt3\n\n=(1)/(8)+(1)/(2)-1+5(1)/(4)\sqrt3=(1)/(8)-(1)/(2)+5(1)/(4)\sqrt3=(1)/(8)-(4)/(8)+5(1)/(4)\sqrt3\n\n=-(3)/(8)+5(1)/(4)\sqrt3\neq3$

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Which fraction is the largest? 3/4 ,4/5, 7/8, or 5/4? and why?

Answers

5/4 because if you simplify it, it's 1 1/4 and with the '1' it makes it greater than the rest

The largest is 5/4 because the LCD of this fraction is the smallest one of the group we have

Elmer has a collection of 300 fossils. Of these, 21 percent are fossilized snail shells.

Answers

In order to figure out the number of fossilized snail shell, multiply 21% by 300. first change 21% into a decimal, in order to do that, move the percent symbol two spaces to the left, and replace the "%" symbol to a decimal. 0.21 X 300= 63
so 21% of 300 is 63

What is 7 multiplied by 230

Answers

7 multiplied by 230
7 × 230
2
230
× 7
--------
1610

7 × 230 = 1610

10.44 is 14.4% of what number?

Answers

Cross multiplication.

10.44 14.4%
______ = ______ = 10.44*100/14.4x = 1044/ 14.4 = 72.5
x 100%

The answer for that is .. 17?

Match the sequence (term) with the correct type of sequence (definition).Match Term Definition
128, 32, 8, 2, ... A) Arithmetic, common difference is 5
1, 3, 9, 27, ... B) Arithmetic, common difference is -3
5, 10, 15, 20, ... C) Geometric, common ratio is 0.25
20, 17, 14, 11, ... D) Geometric, common ratio is 3

Answers

The correct answer among all the other choices is 20, 17, 14, 11, ... D) Geometric, common ratio is 3. This is the sequence (term) with the correct type of sequence (definition) among the examples given. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help.

Which function has an inverse function a) f(x)=|x-4|+1 (b) f(x)=25x^2+70x+49 (c) x^4 (d) x+3÷7

Answers

Answer:

$f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Step-by-step explanation:

Property of inverse function:

The function should be bijective function ( one-to-one and onto)

Option A) f(x)=|x-4|+1

It is absolute function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [1,∞)

False ( Inverse not possible )

Option B) $f(x)=25x^2+70x+49$

It is quadratic function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option C) $f(x)=x^4$

It is polynomial function with even degree. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option D) $f(x)=(x+3)/(7)$

It is linear function. one-to-one and onto

Domain: All real (-∞,∞)

Range: All real (-∞,∞)

True ( Inverse possible )

Inverse of $f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Hence, The function inverse function $f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Answer: Hello there!

A function only can have an inverse if the function is injective and surjective (and continuous):

Then we need to see; if f(x1) = f(x2) = y, and x1 is different from x2, then f(x) has not an inverse:

a) f(x) = Ix - 4I + 1

for example, f(0) = I-4I + 1 = 5

and f(8) = I8 -4I + 1 = 4 + 1 = 5

then f(x) does not have an inverse

b) f(x) = 25x^2 + 70x + 49

This is a cuadratic function, wich is graphed as a arc going up or down, wich means that there are two values of x that give the same value for f(x), then this function has not inverse. (this will be the case for all even powers)

c) f(x) = x^4

Again, an even power. But let's probe it:

f(1) = 1^4 = 1

f(-1) = (-1)^4 = 1

f(x) does not have an inverse:

d) f(x) = x + 3/7

Ok, here we have a linear equation, wich means that is injective and surjective.

The inverse of this function can be g(x) = x - 3/7

proof:

f(g(x)) = f( x - 3/7) = (x - 3/7) + 3/7 = x

then f and g are inverses of each other.

(if in this case f(x) = (x + 3)/7 = x/7 + 3/7 is also a linear equation, so it is injective and surjective (and continuous), wich implies that has an inverse)

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