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:
This is the alternate exterior angle theorem
Step-by-step explanation:
This is because angle 2 and angle 7 are in the <u>outer</u> part of each side of opposite lines
Answer:
If the number is x, then the equation is;
x-m = 5 + n
Step-by-step explanation:
Here, we want to write the given statement in algebraic form
What number exceeds m by five more than n
Let the number be x
x-m = n + 5
Value of x is 35°
Step-by-step explanation:
- Step 1: Since the line segment is a perpendicular bisector, the angle formed is equal to 90° and two triangles are also formed.
Find x using the property of triangles that sum of angles of a triangle is 180°
⇒ x° + 55° + 90° = 180°
⇒ x° + 145° = 180°
∴ x = 180 - 145 = 35°
The pentagon does not belong because it has 5 sides while the other 3 shapes have only 4 sides.
