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2 years ago

What is the additive inverse of 22? 1. 22 2. -22 3. -(-|-22|) 4. -(-(-(-22)))

Mathematics

2 answers:

Mashutka [201]2 years ago

6 0

Answer:

the additive inverse of 22 is -22

Gennadij [26K]2 years ago

5 0

Answer:the additive inverse of 22 is -22

Step-by-step explanation:

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Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a law

NARA [144]

Answer:

Slope of this line is given by:

Aaron’s rate for mowing lawns is 0.5 acres per hour

Step-by-step explanation:

It is given that time is tracked by Aaron related to x coordinate.

and the area of land mowed in acres is related to y coordinate.

Two of his points are given as:

(3, 1.5) and (5,2.5)

We know that the coordinates are represented in the form of (x,y)

i.e. first coordinate represents x coordinate and

second coordinate represents y coordinate.

So, it can be observed that:

$x_1=3, y_1=1.5\\x_2=5, y_2=2.5$

Change in x coordinate = $x_2-x_1=5-3 = 2$

i.e. total time taken is 2 hours.

Change in y coordinate = $y_2-y_1=2.5-1.5 = 1$

i.e. total land mowed taken is 1 acre.

In other words, it takes 2 hours for Aaron to mow 1 acre of land.

So, "option 1) It takes Aaron about 1 hour to mow 2 acres." is incorrect.

Rate of mowing lawn is the land mowed by Aaron in 1 hour.

Land mowed in 2 hours = 1 acre

Land mowed in 1 hours = $\frac{1}{2}$ acre i.e. 0.5 acre

Also, slope of a line is given as:

$m = \dfrac{y_2-y_1}{x_2-x_1}$

Here $y_2 - y_1 = 1$

$x_2 - x_1 = 2$

As per formula:

$m = \dfrac{1}{2} = 0.5$

So, option 2) Aaron’s rate for mowing lawns is 0.5 acres per hour.

6 0

2 years ago

Read 2 more answers

19. A girl has four skirts and six blouses. How many different skirt-blouse combiNtions can she wear?

cupoosta [38]

4 combinations of skirt blouses

7 0

1 year ago

Which of the following functions are homomorphisms?

Vikentia [17]

Part A:

Given $f:Z \rightarrow Z,$ defined by $f(x)=-x$

$f(x+y)=-(x+y)=-x-y \\ \\ f(x)+f(y)=-x+(-y)=-x-y$

but

$f(xy)=-xy \\ \\ f(x)\cdot f(y)=-x\cdot-y=xy$

Since, f(xy) ≠ f(x)f(y)

Therefore, the function is not a homomorphism.

Part B:

Given $f:Z_2 \rightarrow Z_2,$ defined by $f(x)=-x$

Note that in $Z_2$ , -1 = 1 and f(0) = 0 and f(1) = -1 = 1, so we can also use the formular $f(x)=x$

$f(x+y)=x+y \\ \\ f(x)+f(y)=x+y$

and

$f(xy)=xy \\ \\ f(x)\cdot f(y)=xy$

Therefore, the function is a homomorphism.

Part C:

Given $g:Q\rightarrow Q$ , defined by $g(x)= \frac{1}{x^2+1}$

$g(x+y)= \frac{1}{(x+y)^2+1} = \frac{1}{x^2+2xy+y^2+1} \\ \\ g(x)+g(y)= \frac{1}{x^2+1} + \frac{1}{y^2+1} = \frac{y^2+1+x^2+1}{(x^2+1)(y^2+1)} = \frac{x^2+y^2+2}{x^2y^2+x^2+y^2+1}$

Since, f(x+y) ≠ f(x) + f(y), therefore, the function is not a homomorphism.

Part D:

Given $h:R\rightarrow M(R)$ , defined by $h(a)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)$

$h(a+b)= \left(\begin{array}{cc}-(a+b)&0\\a+b&0\end{array}\right)= \left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right) \\ \\ h(a)+h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)+ \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)=\left(\begin{array}{cc}-a-b&0\\a+b&0\end{array}\right)$

but

$h(ab)= \left(\begin{array}{cc}-ab&0\\ab&0\end{array}\right) \\ \\ h(a)\cdot h(b)= \left(\begin{array}{cc}-a&0\\a&0\end{array}\right)\cdot \left(\begin{array}{cc}-b&0\\b&0\end{array}\right)= \left(\begin{array}{cc}ab&0\\-ab&0\end{array}\right)$

Since, h(ab) ≠ h(a)h(b), therefore, the funtion is not a homomorphism.

Part E:

Given $f:Z_{12}\rightarrow Z_4$ , defined by $\left([x_{12}]\right)=[x_4]$ , where $[u_n]$ denotes the lass of the integer $u$ in $Z_n$ .

Then, for any $[a_{12}],[b_{12}]\in Z_{12}$ , we have

$f\left([a_{12}]+[b_{12}]\right)=f\left([a+b]_{12}\right) \\ \\ =[a+b]_4=[a]_4+[b]_4=f\left([a]_{12}\right)+f\left([b]_{12}\right)$

and

$f\left([a_{12}][b_{12}]\right)=f\left([ab]_{12}\right) \\ \\ =[ab]_4=[a]_4[b]_4=f\left([a]_{12}\right)f\left([b]_{12}\right)$

Therefore, the function is a homomorphism.

7 0

2 years ago

a spinner is divided into four equal sections labled pink blue purple and gold. if the spinner is spun 50 times. how many times

I am Lyosha [343]

Answer:

1/4 of the times

Step-by-step explanation:

because there are 4 sections, that means that there is a 1/4 probability.

4 0

2 years ago

Simplify completely****

andreyandreev [35.5K]