Answer:
A. Vasily is not correct. He should have rewritten the original expression as −6(−5g−7h+9) and then as 30g+42h−54.
Step-by-step explanation:
Given the expression;
![-6 (5g - 7h + 9 - 10g)](https://tex.z-dn.net/?f=%20-6%20%285g%20-%207h%20%2B%209%20-%2010g%29)
<em>Rearranging the above, we have;</em>
![-6 (5g - 10g - 7h + 9)](https://tex.z-dn.net/?f=%20-6%20%285g%20-%2010g%20-%207h%20%2B%209%29)
<em>Simplifying, we have;</em>
![-6 (-5g - 7h + 9)](https://tex.z-dn.net/?f=%20-6%20%28-5g%20-%207h%20%2B%209%29)
<em>Multiply, to open the bracket;</em>
![30g + 42h - 54](https://tex.z-dn.net/?f=%2030g%20%2B%2042h%20-%2054)
<em>Therefore, Vasily should have rewritten the original expression as −6(−5g−7h+9) and then as 30g+42h−54. </em>
Answer:
The speed of the car is 75 mph.
The speed of the truck is 56 mph.
Step-by-step explanation:
Call the speed of the truck (x) miles per hour. As per the given information, the car is (19) miles per hour faster. Thus, one can form expressions to represent the speeds of the vehicles.
car = ( x + 19 ) mph
truck = ( x ) mph
Using the formula, ( (speed) * (time) = (distance) ), one can say that the speed of the car, times the time it took plus the speed of the truck times the time will equal the distance between the two vehicles:
(( car speed )( time )) + (( truck speed )( time )) = ( distance between vehicles )
Substitute,
( ( x + 19 ) ( 8 ) ) + ( ( x ) ( 8 ) ) = 1048
Simplify,
8x + 152 + 8x = 1048
16x + 152 = 1048
-152 -152
16x = 896
/16 /16
x = 56
Add (19) to find the speed of the car:
truck speed + 19
= 56 + 19
= 75
The speed of the car is 75 mph.
The speed of the truck is 56 mph.
In this expansion there are 5 terms:
3, x, 2, y and 6
And from all of these, the fifth one is 6
Hope it helped,
BioTeacher101
ANSWER
The value of x is
![16.](https://tex.z-dn.net/?f=16.)
EXPLANATION
We want to solve the equation,
![\sqrt{x + 9} - 4 = 1](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%2B%209%7D%20%20-%204%20%3D%201)
The first step is to add 4 to both sides of the equation to obtain,
![\sqrt{x + 9} = 1 + 4](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%2B%209%7D%20%20%20%3D%201%20%2B%204)
We simplify the right hand side to obtain,
![\sqrt{x + 9} = 5](https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%2B%209%7D%20%20%3D%205)
We now square both sides of the equation to obtain,
![(\sqrt{x + 9} ) ^{2} = {5}^{2}](https://tex.z-dn.net/?f=%20%28%5Csqrt%7Bx%20%2B%209%7D%20%20%29%20%5E%7B2%7D%20%20%3D%20%20%7B5%7D%5E%7B2%7D%20)
This simplifies to
![x + 9= 25](https://tex.z-dn.net/?f=%20x%20%2B%209%3D%2025)
We solve for x to obtain,
![x = 25 - 9](https://tex.z-dn.net/?f=x%20%3D%2025%20-%209)
This implies that,