Solve the following system: 3x + 2y = 7 -4.5x - 3y = -10.5
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
Let
x----> the length of the rectangular garden
y---> the width of the rectangular garden
we know that
The perimeter of the rectangle is equal to
we have
so
simplify
------> equation A
Remember that the area of rectangle is equal to
----> equation B
substitute equation A in equation B
----> this is a vertical parabola open downward
The vertex is a maximum
The y-coordinate of the vertex is the maximum area
The x-coordinate of the vertex is the length side of the rectangle that maximize the area
using a graphing tool
The vertex is the point
see the attached figure
so
Find the value of y
The garden is a square
the area is equal to
----> is equal to the y-coordinate of the vertex is correct
Answer:
3.) 0.894
Step-by-step explanation:
✔️First, find BD using Pythagorean Theorem:
BD² = BC² - DC²
BC = 17.89
DC = 16
Plug in the values
BD² = 17.89² - 16²
BD² = 64.0521
BD = √64.0521
BD = 8.0 (nearest tenth)
✔️Next, find AD using the right triangle altitude theorem:
BD = √(AD*DC)
Plug in the values into the equation
8 = √(AD*16)
Square both sides
8² = AD*16
64 = AD*16
Divide both sides by 16
4 = AD
AD = 4
✔️Find AB using Pythagorean Theorem:
AB = √(BD² + AD²)
AB = √(8² + 4²)
AB = √(64 + 16)
AB = √(80)
AB = 8.9 (nearest tenth)
✔️Find sin x using trigonometric ratio formula:
Reference angle = x
Opposite side = BD = 8
Hypotenuse = AB = 8.944
Thus:
(nearest thousandth)