17 - 5(2x - 9) = -(-6x + 10) + 4
On the right side of the equation, there is a negative sign infront of the parentheses. This means that you are multiplying the parentheses by -1.
17 - 5(2x - 9) = (6x -10) + 4
The 6x is positive because a negative times a negative is positive. The 10 is negative because a negative times a positive is a negative. Now, combine the like terms on the right side of the equation by adding -10 and 4 together.
17 - 5(2x - 9) = 6x - 6
Now that you have simplified the right side of the equation, move to the left side. Start with multiplying 5 times (2x - 9) using the distributive property.
17 - (10x - 45) = 6x - 6
After that, combine the like terms by subtracting -45 from 17. Because you would be doing 17 - -45, you would change all signs because when you subtract with negatives, you have to change the signs. Due to the change of the signs, you are just adding 17 and 45 together.
62 + 10x = 6x - 6
Now, you need to get the x's on one side and the whole numbers on the other side. Begin by subtracting 6x from both sides.
62 + 10x = 6x - 6
-6x -6x
62 + 4x = -6
Now, subtract 62 from negative 6. Remember to change the signs. You will end up with -6 + -62.
4x = -68
Finally, divide both sides by 4.
<u>4x</u> = <u>-68
</u>4 4
x = 17
Final Answer: x = -17
2:1 because it decreases my half which is the same as saying 2/1
Mean (μ) = 11.5 feet
Standard deviation (σ) = 1.7 feet
First we need to find the z-score for less than 13.5 feet.
The formula of z-score is : z = (X - μ)/σ
Here X= 13.5, so z = 
z = 
= 1.18
P(X < 13.5) = P(z< 1.18) =P(z< (1.1 + .08)) = 0.8810 (from z-score table)
P(X< 13.5) = 88.1% (for making percentage from decimal, we need to multiply by 100)
So, the probability that a randomly selected tree is less than 13.5 feet tall = 88.1%
Answer:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Step-by-step explanation:
Geometrically speaking, the area of a rectangle (
), in square centimeters, is described by following expression:
(1)
Where:
- Width, in centimeters.
- Height, in centimeters.
By Differential Calculus, we find an expression for the rate of change of the area of the rectangle (
), in square centimeters per second:
(2)
Where:
- Rate of change of the width of the rectangle, in centimeters per second.
- Rate of change of the length of the rectangle, in centimeters per second.
If we know that 
, 
, 
and 
, then the rate of change of the area of the rectangle is:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
3 tons would be greater than 3,000 pounds
1 ton= 2,000 pounds
3 tons=6,000 pounds
