I need the answer pls :)

Mathematics

1 answer:

photoshop1234 [79]3 years ago

6 0

I need the answer To what

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Hank Wants to divide 345 pieces of construction paper evenly among his 23 classmates. How many pieces will be left over?

sleet_krkn [62]

Answer:

There will be no pieces of paper left over. Each student will receive 15 pieces of paper.

Step-by-step explanation:

If you divide the 345 pieces of paper between the 23 classmates, you will end up with 15. There is no remainder or decimal, just 15, a whole number. That means that there will be no pieces of paper left over.

5 0

3 years ago

You are measuring the dimensions of the floor in your bedroom because you are planning to buy new carpet. Which unit of measure

aivan3 [116]

A) square feet
if you are measuring the room u do not use centimeters because it to small to measure and take forever to measure the room
mile are long so that won't work
inches take a long time to measure a room that would not work
so a is the answer

3 0

4 years ago

Prove that if $w,z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.

mr_godi [17]

Answer:

See proof below

Step-by-step explanation:

Let $r=\frac{w+z}{1+wz}$ . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then $x\bar{x}=|x|^2$ where $\bar{x}$ is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

$\frac{r}{\bar{r}}=\frac{w+z}{1+wz} \left(\frac{1+\bar{w}\bar{z}}{\bar{w}+\bar{z}}{\right)$

= $\frac{(w+z)(1+\bar{w}\bar{z})}{(1+wz)(\bar{w}+\bar{z})}=\frac{w+z+w\bar{w}\bar{z}+z\bar{z}\bar{w}}{\bar{w}+\bar{z}+\bar{w}wz+\bar{z}zw}=\frac{w+z+w+|w|^2\bar{z}+|z|^2\bar{w}}{\bar{w}+\bar{z}+|w|^2z+|z|^2w}=\frac{w+z+\bar{z}+\bar{w}}{\bar{w}+\bar{z}+z+w}=1$