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3 years ago

This year the winner of the new york marathon ran the 8 kilometer event in 24 mins. What is the runners unit rate

Mathematics

1 answer:

Nataliya [291]3 years ago

6 0

3km / 1 min because 24/8 =3

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Use the table to find the ratio. Enter the ratio as a fraction in simplest form. 9 white socks. 6 black socks. 7 blue socks. 2 b

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Answer:

Step-by-step explanation:

i did the test ty hope it helps and give brainly and a thanks and 5star please :D you and you will get a A on that test or homework. IT really works

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3 years ago

Solve for r 4r + 8 = 7.2 + 5r

sineoko [7]

Answer: r=0.8

Step-by-step explanation:

4r + 8 = 7.2 + 5r

8=7.2+r

8-7.2=r

0.8=r

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3 years ago

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If f(x) = 2x-7 and g(x)= x2-5, find g[f(5)]

Georgia [21]

Answer:

4x-12

Step-by-step explanation:

2x-5[2x-7(5)}=2x+2x-7-5

4x-12

negative integers are added to each other

4 0

3 years ago

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150 inches = ___ feet ___ inches ( please help asap )

PIT_PIT [208]

There are 12 inches in a foot, so divide 1590 by twelve. It equals 12.5. That is 12 feet and 5 inches!

3 0

3 years ago

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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):

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

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

Thus $\frac{r}{\bar{r}}=1$ . From this, $r=\bar{r}$ . A complex number is real if and only if it is equal to its conjugate, therefore r is real.

3 0

3 years ago