m = -9!
Proof:
![6=-\frac{2}{3}m\\\\[Multiply by 3 to cancel the fraction, the result is]\\\\6(3)=-2m\\18=-2m\\\\[Now divide by -2 to get your answer]\\\\m = -9](https://tex.z-dn.net/?f=6%3D-%5Cfrac%7B2%7D%7B3%7Dm%5C%5C%5C%5C%5BMultiply%20by%203%20to%20cancel%20the%20fraction%2C%20the%20result%20is%5D%5C%5C%5C%5C6%283%29%3D-2m%5C%5C18%3D-2m%5C%5C%5C%5C%5BNow%20divide%20by%20-2%20to%20get%20your%20answer%5D%5C%5C%5C%5Cm%20%3D%20-9)
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Let's do this step by step:
Our objective is to find out x.
First, we have to take the '-3' to the right side, and put it next to the 11. When we do this its operation reverses, so it becomes 11 + 3, which is 14.
So we have 9x > 2x + 14.
Then we do the same to the numbers with X, but this time we take the number from the right side to the left. So 2x to the left (reversed) becomes 9x-2x which is 7x.
So 7x > 14
Now let's simplify, 14/7 = 2
so x = 2
Answer:
The answer is below
Step-by-step explanation:
1) The number of rooms Joe company needs is 50. Let the number of rooms needed be n, this can be represented by the inequality:
n ≥ 50
Joe has already reserved 16 rooms, therefore the number of additional rooms needed to be reserved = 50 - 16 = 34 rooms. At least 34 rooms have to be reserved, if B is the number of additional blocks that Joe reserves, the inequality is:
B ≥ 34
2) Each block contains 8 rooms therefore the minimum number of block (a) needed to be reserved = 34/8 = 4.25 = 5 to the next whole number. Therefore the minimum number of blocks needed is given as:
a ≥ 5
Since each block cost $900, let c represent the minimum amount of money needed, therefore the least amount of money needed is given as:
c = $900(5) = $4500
c ≥ $4500
Answer:
The height of the lamp post is 15 feet ⇒ 1st answer
Step-by-step explanation:
The ladder , the lamp post and the ground formed a right triangle, the length of the ladder is its hypotenuse (l), the height of the lamp post (h) and the horizontal distance on the ground between the base of the ladder and the base of the lamp post (d) are the legs of the triangle
By using Pythagoras Theorem ⇒ <em>the square of the hypotenuse is equal to the sum of the squares of the other two legs</em>
∵ l² = h² + d²
∵ The length of the ladder is 25 feet
∴ l = 25
∵ The ladder is placed 20 feet from the lamp post
- That means the distance between the base of the ladder and
the base of the lamp post on the ground
∴ d = 20
- Substitute the values of l and d in the Pythagoras formula
∵ (25)² = h² + (20)²
∴ 625 = h² + 400
- Subtract 400 from both sides
∴ 225 = h²
- Take √ for both sides
∴ 15 = h
∴ The height of the lamp post is 15 feet
