Answer:
(, 3)
Step-by-step explanation:
Given the 2 equations
2x + 5y = 16 → (1)
10x - 3y = - 4 → (2)
Multiplying (1) by - 5 and adding to (2) will eliminate the term in x
- 10x - 25y = - 80 → (3)
Add (2) and (3) term by term
(10x - 10x) + (- 3y - 25y) = (- 4- 80) ← simplify
- 28y = - 84 ( divide both sides by - 28 )
y = 3
Substitute y = 3 into (1) or (2) for corresponding value of x
(1) : 2x + 15 = 16 ( subtract 15 from both sides )
2x = 1 ( divide both sides by 2 )
x =
Solution is (, 3 )
Answer:
y = 2/3x +4
Step-by-step explanation:
The y intercept is where the line crosses the y axis
y intercept =4
We can find the slope using two points on the line
(0,4) and (3,6)
m = (y2-y1)/(x2-x1)
= (6-4)/(3-0)
= 2/3
The equation of a line in slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 2/3x +4
Using the equilateral triangles, the hexagon shaped design will use 6 triangles.
Solve first for the area of the triangle using the formula.
Area of the triangle= sqrt3/4s^2
= 6.93 cm^2
Total area of the hexagon = 6 x area of the triangle
= 41.57 cm^2
Hi there!
We can calculate dy/dx using implicit differentiation:
xy + y² = 6
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx) + 2y(dy/dx) = 0
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6
-y + y² = 6
y² - y - 6 = 0
(y - 3)(y + 2) = 0
Thus, y = -2 and 3.
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.