Which expression(s) have positive values? Choose

Mathematics

1 answer:

OLEGan [10]3 years ago

5 0

9514 1404 393

Answer:

2. -(-73) is positive

Step-by-step explanation:

It's not too difficult, but you can get wrapped around the axle. Here are the rules:

the opposite of a positive number is a negative number
the opposite of a negative number is a positive number

That is, turning a number to its opposite is just changing its sign.

If you layer these rules, you find ...

the opposite of (the opposite of a positive number) is a positive number

The first rule tells you the statement in parentheses is a negative number, and the second rule tell you its opposite is a positive number.

That is, a double opposite gets you back where you started. In short, any even number of minus signs cancel each other.

The numbers you have listed here* are ...

-730 (negative)
-(-73) = 73 (positive)
-75 (negative)
-(-(-701)) = -701 (negative)

_____

* We say "listed here" because we're seeing mismatched parentheses and brackets, so we know something is missing. We're going by the signs and numbers that we do see. YMMV

You might be interested in

X^5 + 243 divided by x+3

ch4aika [34]

-3   | 1   0   0   0   0   243 $\longleftarrow$ coefficients of the polynomial you're dividing
.     |                                   $\longleftarrow$ drop down the leading coefficient
- - - - - - - - - - - - - - - - - - -
.     | 1

On the left side of the frame, we write -3 because we're dividing by $x+3=x-(-3)$ . (The algorithm is followed for division of a polynomial by a factor of $x-c$ .) Since we're dividing a degree 5 polynomial by a degree 1 polynomial, we expect to get a degree 4 polynomial.

-3   | 1   0   0   0   0   243
.     |      -3                         $\longleftarrow$ multiply -3 by 1, write in next column, add to 0
- - - - - - - - - - - - - - - - - - -
.     | 1 -3

Repeat step for the remaining columns.

-3   | 1   0   0   0   0   243
.     |      -3   9
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9

-3   | 1   0   0      0   0   243
.     |      -3   9   -27
- - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27

-3   | 1   0   0      0 0   243
.     |      -3   9   -27   81
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81

-3   | 1   0   0      0 0 243
.     |      -3   9   -27   81 -243
- - - - - - - - - - - - - - - - - - - - -
.     | 1 -3   9   -27   81       0

which translates to

$\dfrac{x^5+243}{x+3}=x^4-3x^3+9x^2-27x+81$

So the bottom row of the frame gives the coefficients of each term in the quotient by descending order. Since the last coefficient is 0, this means the remainder upon division vanishes, i.e. $x^5+243$ is exactly divisible by $x+3$ .

- - -

Another way to get the same result is to use a well-known result: for $a+b\neq0$ ,

$a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)\implies\dfrac{a^5+b^5}{a+b}=a^4-a^3b+a^2b^2-ab^3+b^4$

and in this case $a=x$ and $b=3$

3 0

4 years ago

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

Paha777 [63]

Answer:

the second one

Step-by-step explanation:

trust me i've done this before

5 0

3 years ago

I need help with question a and b

DaniilM [7]

Solving for part A

$f(x) = x^{2} \;\;and\;\; g(x) = \frac{1}{x^{3}} \\\\f(g(x)) = (\frac{1}{x^{3}})^{2} =\frac{1}{x^{6}}$

Domain of composition: x ≠ 0 i.e. Domain is the set of "Real numbers excluding number 0".

Solving for part B

$f(x) = \frac{x}{x-2}\;\;and\;\;g(x) =\frac{3}{x} \\\\f(g(x))=\frac{\frac{3}{x}}{\frac{3}{x}-2}=\frac{\frac{3}{x}}{\frac{3-2x}{x}} =\frac{3}{3-2x}\\\\ Domain:\;3-2x\neq 0 \;\;OR\;\;x\neq \frac{3}{2}$