Think about this. What do the numbers in a coordinate stand for? They stand for X and Y. If you're trying to figure out what the X is, wouldn't you be solving for x? And didn't they just give you an equation? ;) First off, do you see how the "Y" value is given to you in the coordinate? All you have to do is substitute that 3 in for the "y" in the equation! 3=2x+5. Hey.... that looks like a simple equation! First, you need to subtract 5 from the other side of the equation. Now you're left with 2x=-2. Divide both sides by 2, and you get that x=-1. Now, just substitute that "x' value into the coordinate, and your answer should come out to be (-1, 3). :D
Answer: Question #1 The height of the tree is about 18 feet.
To solve this problem, you have to write a proportion using the similar triangles that are drawn. The height of the tree matches the height of the person and the shadows match.
Therefore, we can write and solve the following equation:
x/15 = 5.5/4.5
82.5 = 4.5x
x = 18.33
Answer:
<em>Any width less than 3 feet</em>
Step-by-step explanation:
<u>Inequalities</u>
The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:
A = L.W
The first condition can be written as follows:
LW < 18
The length should be 3 feet longer than the width, thus:
L = W + 3
Substituting in the inequality:
(W + 3)W < 18
Operating and rearranging:
Factoring:
(W-3)(W+6)<0
Since W must be positive, the only restriction comes from:
W - 3 < 0
Or, equivalently:
W < 3
Since:
L = W + 3
W = L - 3
This means:
L - 3 < 3
L < 6
The width should be less than 3 feet and therefore the length will be less than 6 feet.
If the measures are whole numbers, the possible dimensions of the garden plot are:
W = 1 ft, L = 4 ft
W = 2 ft, L = 5 ft
Another solution would be (for non-integer numbers):
W = 2.5 ft, L = 5.5 ft
There are infinitely many possible combinations for W and L as real numbers.
It was stated in the problem that a given volume of a is inversely proportional with the pressure of the system. It means that the as the volume increases, the pressure would decrease and as the volume decreases, the pressure would increase. We would express it as:
V α 1/P
To change it to an equality, we introduce a proportionality constant, k. We do as follows:
V = k/P
So, to determine what is asked, we need to first calculate for the value of k.
V = k/P
At V = 160 m^3 P = 108 cmHg
160 = k / (108)
k = 17280
Thus, at P = 87 cmHg
V = 17280 / 87
V = 198.62 m^3
