Answer:
Road C is 1.5 mi east of Road A
Step-by-step explanation:
we know that
Road B is 4.6 mi east of Road A
Road C is 3.1 mi west of Road B
so
Road C is between Road A and Road B
AB=4.6 miles
CB=3.1 miles
AB=AC+CB
Solve for AC
AC=AB-CB
AC=4.6-3.1=1.5 miles
therefore
Road C is 1.5 mi east of Road A
Answer:
See explanation
Step-by-step explanation:
1. R is the set of all integers with absolute value less than 10, thus
![R=\{a\in \mathbb{Z}\ :\ |a|](https://tex.z-dn.net/?f=R%3D%5C%7Ba%5Cin%20%5Cmathbb%7BZ%7D%5C%20%3A%5C%20%7Ca%7C%3C10%20%5C%7D%3D%5C%5C%20%5C%5C%3D%5C%7B-9%2C%5C%20-8%2C%5C%20-7%2C%5C%20-6%2C%5C%20-5%2C%5C%20-4%2C%5C%20-3%2C%5C%20-2%2C%5C%20-1%2C%5C%200%2C%5C%201%2C%5C%202%2C%5C%203%2C%5C%204%2C%5C%205%2C%5C%206%2C%5C%207%2C%5C%208%2C%5C%209%5C%7D)
2. A is its subset containing all natural numbers less than 10, thus
![A\subset R\\ \\A=\{b\in \mathbb{N}\ :\ b](https://tex.z-dn.net/?f=A%5Csubset%20R%5C%5C%20%5C%5CA%3D%5C%7Bb%5Cin%20%5Cmathbb%7BN%7D%5C%20%3A%5C%20b%3C10%5C%7D%3D%5C%7B1%2C%5C%202%2C%5C%203%2C%5C%204%2C%5C%205%2C%5C%206%2C%5C%207%2C%5C%208%2C%5C%209%5C%7D)
3. B is the set of all integer solutions of inequality 2x+5<9 that are less than 10 by absolute value (and therefore, it is also a subset of R). First, solve the inequality:
![2x+5](https://tex.z-dn.net/?f=2x%2B5%3C9%5C%5C%20%5C%5C2x%3C9-5%5C%5C%20%5C%5C2x%3C4%5C%5C%20%5C%5Cx%3C2)
Thus,
![B\subset R\\ \\B=\{c\in \mathbb{Z}\ :\ 2c+5](https://tex.z-dn.net/?f=B%5Csubset%20R%5C%5C%20%5C%5CB%3D%5C%7Bc%5Cin%20%5Cmathbb%7BZ%7D%5C%20%3A%5C%202c%2B5%3C9%2C%5C%20%7Cc%7C%3C10%5C%7D%3D%5C%7Bc%5Cin%20%5Cmathbb%7BZ%7D%5C%20%3A%5C%20c%3C2%2C%5C%20%7Cc%7C%3C10%5C%7D%3D%5C%5C%20%5C%5C%3D%5C%7B-9%2C%5C%20-8%2C%5C%20-7%2C%5C%20-6%2C%5C%20-5%2C%5C%20-4%2C%5C%20-3%2C%5C%20-2%2C%5C%20-1%2C%5C%200%2C%5C%201%5C%7D)
See the diagram in attached diagram.
Note that
![A\cup B=R\\ \\A\cap B=\{1\}.](https://tex.z-dn.net/?f=A%5Ccup%20B%3DR%5C%5C%20%5C%5CA%5Ccap%20B%3D%5C%7B1%5C%7D.)
Answer:
![r(s(3))=7](https://tex.z-dn.net/?f=r%28s%283%29%29%3D7)
Step-by-step explanation:
we have
![r(x)=x^{2} +2x-1](https://tex.z-dn.net/?f=r%28x%29%3Dx%5E%7B2%7D%20%2B2x-1)
![s(x)=x-1](https://tex.z-dn.net/?f=s%28x%29%3Dx-1)
we know that
The function composition is equal to
(r ∘ s )(x) = r(s(x))
In the function r(x) substitute the variable x by the function s(x)
so
![r(s(x))=(x-1)^{2} +2(x-1)-1](https://tex.z-dn.net/?f=r%28s%28x%29%29%3D%28x-1%29%5E%7B2%7D%20%2B2%28x-1%29-1)
For x=3
substitute the value of x=3 in the function composition
![r(s(3))=(3-1)^{2} +2(3-1)-1](https://tex.z-dn.net/?f=r%28s%283%29%29%3D%283-1%29%5E%7B2%7D%20%2B2%283-1%29-1)
![r(s(3))=(2)^{2} +2(2)-1](https://tex.z-dn.net/?f=r%28s%283%29%29%3D%282%29%5E%7B2%7D%20%2B2%282%29-1)
![r(s(3))=4+4-1](https://tex.z-dn.net/?f=r%28s%283%29%29%3D4%2B4-1)
![r(s(3))=7](https://tex.z-dn.net/?f=r%28s%283%29%29%3D7)
Hi!
First make the denominators the same.
![\frac{8}{20} + \frac{10}{20} = ?](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B20%7D%20%2B%20%20%5Cfrac%7B10%7D%7B20%7D%20%3D%20%3F)
Add the numerators
![\frac{8}{20} + \frac{10}{20} = \frac{18}{20}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B20%7D%20%2B%20%20%5Cfrac%7B10%7D%7B20%7D%20%3D%20%5Cfrac%7B18%7D%7B20%7D)
Simplify to get your answer
The answer is
![\frac{9}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B10%7D%20)
Hope this helps! :)
Answer:
6 2/3 minutes
Step-by-step explanation:
Amare runs 1/10 mile in 2/3 minutes
Therefore his speed in miles per minutes clean be calculated as follows
= 1/10, the denominator here is 10
= 10 × 2/3
= 20/3
= 6 2/3 minutes