There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
Answer:
x=12
Step-by-step explanation:
The right side is a right triangle
The base is 1/2 of the bottom or 5
The height is x and the hypotenuse is 13
We can use the Pythagorean theorem
a^2 +b^2 = c^2
5^2 +x^2=13^2
25+x^2 = 169
Subtract 25 from each side
25-25+x^2 = 169-26
x^2 =144
Take the square root of each side
sqrt(x^2) = sqrt(144)
x= 12
Answer:
did you forget a picture?
Step-by-step explanation:
Answer:
Demand
Step-by-step explanation:
Supply is what the stores have and demand is what the customers want
Answer: x = 9.0
Step-by-step explanation:
From the given right angle triangle,
the hypotenuse of the right angle triangle is x
With m∠39 as the reference angle,
the adjacent side of the right angle triangle is 7
The unknown side represents the opposite side of the right angle triangle.
To determine x, we would apply
the cosine trigonometric ratio which is expressed as
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 39 = 7/x
x = 7/cos 39 = 7/0.777
x = 9.0 to the nearest tenth
