Answer:
8/3 km
Step-by-step explanation:
we can represent the given information on a table:
Kilometers time (hours)
2/5 ⇔ 1 1/2
and since we want to know how many kilometers (x) will be paved on 10 hours:
Kilometers time (hours)
2/5 ⇔ 1 1/2
x ⇔ 10
The relationship these 3 numbers have can be described by using the <u>rule of three,</u> which is to multiply the cross quantities on the table (2/5 by 10) and then divide by the remaining amount (1 1/2):
x =
÷ ![1\frac{1}{2}](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D)
x =
÷ ![1\frac{1}{2}](https://tex.z-dn.net/?f=1%5Cfrac%7B1%7D%7B2%7D)
we use
x =
÷ ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
and we make the division:
x =
÷
= ![\frac{20*2}{5*3}=\frac{40}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B20%2A2%7D%7B5%2A3%7D%3D%5Cfrac%7B40%7D%7B15%7D)
we simplify the fraction by dividing the numerator and denominator both by 5, and we get the result:
x = ![\frac{8}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D)
thus, in 10 hours the crew will pave 8/3 km. Which is about 2.66 km.
Distance formula : d = sqrt (x2 - x1)^2 + (y2 - y1)^2
(11,4)(10,5)
d = sqrt (10 - 11)^2 + (5 - 4)^2
d = sqrt (-1^2) + (1^2)
d = sqrt (1 + 1)
d = sqrt 2
d = 1.41 <===
3x - 5y = 18 over
-10x + 5y = 10
Add them because the 5y's have the right symbols for us to add
-7x = 28
Divide
x = -4
Now you can plug in -4 for x in one equation, I would use the first equation!
3(-4) - 5y = 18
-12 - 5y = 18
Add 12
-5y = 30
Divide
y = -6
Your solutions are going to be:
x = -4
y = -6
To check your work plug x and y into one equation:
3(-4) - 5(-6) = 18
-12 + 30 = 18
18 = 18
Since 18 does equal 18 you know that your solution's work!
Answer:
![\frac{x-5}{5x+4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-5%7D%7B5x%2B4%7D)
Step-by-step explanation:
Given
× ![\frac{x^2-3x-10}{5x^2+6x-8}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2-3x-10%7D%7B5x%5E2%2B6x-8%7D)
Factorise numerator/ denominator of both fractions
=
× ![\frac{(x-5)(x+2)}{(5x-4)(x+2)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-5%29%28x%2B2%29%7D%7B%285x-4%29%28x%2B2%29%7D)
Cancel common factors on numerator/ denominator of both fractions
=
× ![\frac{x-5}{5x-4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-5%7D%7B5x-4%7D)
Cancel the common factor 5x - 4 on numerator/ denominator, leaving
= ![\frac{x-5}{5x+4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-5%7D%7B5x%2B4%7D)