The dimensions in the given should have the same unit in order for us to do mathematical operations with them. 3.5 km when converted to meters become 3500 m. The problem asked for the tiger's displacement, that is the distance from his starting point to his final position. This is equal to 1,250 m subtracted from 3500 m. Thus, the answer is 2250 meters.
Answer:
answer in comment
Step-by-step explanation:
So, we have to find the slope of the line. We are given two points, so we can use those:
(x1,y1) = (-4,6)
(x2,y2) = (1,2)
m = (y2-y1)/(x2-x1) = (2-6)/(1--4) = (2-6)/(1+4) = -4/5
Also, we know that point-slope is of the form:
(y-y1) = m*(x-x1)
It doesn't matter which point you use, though, you can also use:
(y-y2) = m*(x-x2)
So we can plug the variables into the equation and get:
(y-2) = -4/5*(x-1)
OR
(y-6) = -4/5*(x+4)
9514 1404 393
Answer:
a) $540 cost to paint
b) 72000 liters to fill
Step-by-step explanation:
Relevant formulas are ...
P = 2(L +W) . . . . perimeter of a rectangle of length L and width W
A = LW . . . . . . area of a rectangle of length L and width W
V = LWH . . . volume of a cuboid of length L, width W, and height H
__
a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.
A = PH + LW = 2(L +W)H +LW
A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²
At $6 per square meter, the cost of painting the pool is ...
($6 /m²)(90 m²) = $540 . . . . cost to paint the pool
__
b) The volume in liters is best figured using the dimensions in decimeters.
V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L
72000 liters will be needed to fill the pool.
y = 3(x + 4)^2 + 31
Step-by-step explanation:
We can convert the given quadratic equation into its vertex form by completing the square:
y = 3x^2 + 24x + 43
= 3(x^2 + 8x) + 43
= 3(x^2 + 8x + 4) + 31
= 3(x + 4)^2 + 31
This is the vertex form of the given quadratic equation with (-4, 31) as its vertex
<em>Presuming you mean y = -2x^2 - 8x - 13</em>
Firstly, put the x terms in parentheses and factor out -2:
![y=-2(x^2+4x)-13](https://tex.z-dn.net/?f=%20y%3D-2%28x%5E2%2B4x%29-13%20)
Next, we want to make what's inside those parentheses a perfect square. To do this, divide the x coefficient by 2 and square that result. In this case, that result is 4. Add 4 to the inside of the parentheses, and add 8 to the outside of the parentheses to balance it out. (Since when foiled, 4 x -2 = -8)
![y=-2(x^2+4x+4)-13+8\\y=-2(x^2+4x+4)-5](https://tex.z-dn.net/?f=%20y%3D-2%28x%5E2%2B4x%2B4%29-13%2B8%5C%5Cy%3D-2%28x%5E2%2B4x%2B4%29-5%20)
Next, factor what's inside the parentheses, and <u>your final answer will be
</u>