<span>6a^7-2a^7
=5a^7 ................combine like terms</span>
Answer:
12
Step-by-step explanation:
14+8=22... 6 is two less than 8 so x is two less than 14. 6+14=18
The answer is: "
y = − x − 4 " .
_________________________________________________________Explanation:_________________________________________________________Given a linear equation in "slope-intercept form" ; that is:
"
y = mx + b " ;
________________________________________________A line that is PARALLEL to the aforementioned equation has the same slope (i.e the same value for "m" ) ; and the given the [x and y coordinates of any particular point] on the parallel line; " (x₁ , y₁)" ; we can write the equation of the parallel line—in "slope-intercept format" — by using the following equation/formula:
y − y₁ = m(x − x₁<span>) ;
</span>
in which: "m = the slope"
and plug in the values for: "m" ; and "x₁" and "y₁" ;
We are given the coordinates of a particular point on the line that is parallel:
" (-4, 1) " ;
as such: x₁ = -4 ; y₁ = 1 ;
& we are given: "m = −
" .
_____________________________________________So:
→ y − y₁ = m(x − x₁) ;
→ y − 1 = −
[x − (-4) ] ;
→ y − 1 = −
(x + 4) ;
→ y − 1 = −
(x + 4) ;
Now; let us examine the "right-hand side of the equation" ;
We have: −
(x + 4) ;
__________________________________________________Note the "distributive property" of multiplication:__________________________________________a(b + c) = ab + ac ;a(b – c) = ab – ac .__________________________________________As such:
__________________________________________ −
* x + (−
* 4) ;
= −
* x + (−
*
) ;
Note: Examine the
" (−
*
) " ;
→ EACH of the 2 (TWO) "4's" cancel out to "1"s" ;
{ since: "4 ÷ 4 = 1" } ;
and we can rewrite the: "(−
*
) " ;
as: " (−
*
) " ;
Note that: "{-5 ÷ 1 = -5} ; and: "{1 ÷ 1 = 1} ;
so, rewrite the: "" (−
*
) " ;
as: "{-5 * 1}" → which equals: = " -5" ;
So:
−
* x + (−
*
) ;
= -
x + (-5) ;
= -
x − 5 ;
______________________________________________→ Now, bring down the "y −1" ; which goes on the left hand side;
→ y − 1 = -
x − 5 ;
Add "1" to EACH SIDE of the equation; to isolate "y" as a single variable on the "left-hand side" of the equation ; & to write the equation of the particular parallel line in "slope-intercept format" ;
→ y − 1 + 1 = -
x − 5 + 1 ;
_______________________________________________________to get:
_______________________________________________________→ "
y = − x − 4 " .
_______________________________________________________
The price for each instructor will be the same at 3 hours. How I determined this answer:
First off, you need to add the initial price and hourly price for each person together, so you already know how much it will cost for 1 hour, including the initial fee. Here's how you do it:
Ieda: $11.00 (hourly price) + $8.50 (initial fee) = $19.50 (for 1 hour)
Thanh: $10.50 (hourly price) + $10.00 (initial fee) = $20.50 (for 1 hour)
Now that you have the price for 1 hour including the initial fee, now you need to find the price for each hour after that. Here's how I did that:
I created a graph that looked like this:
Hours: 1 2 3
Ieda: 19.50 30.50 41.50
Thanh: 20.50 31.00 41.50
Here's how I figured out the price for each hour:
Ieda:
Hour 1 (including initial price):
$11.00 + $8.50 = $19.50
Hour 2 (excluding initial price): Only add the hourly price after Hour 1!
$19.50 + $11.00 = $30.50
Hour 3 (excluding initial price):
$30.50 + $11.00 = $41.50
Thanh:
Hour 1 (including initial price):
$10.50 + $10.00 = $20.50
Hour 2 (excluding initial price):
$20.50 + $10.50 = $31.00
Hour 3 (excluding initial price):
$31.00 + $10.50 = $41.50
So, looking at the graph, their prices are the same once each instruction reaches 3 hours. ($41.50)
I hope I was able to help you! :)