Linear Systems
Solve the following system of linear equations:
2x+3y=16
4x−y=9
x = 3.07 and y = 3.28
Factor the quadratic expression x2−5x+6.
x2−5x+6=(x−2)(x−3)
Solve the quadratic equation x2−4=0.
x = 2 or x = -2
In a right triangle, one of the angles is 30∘ and the hypotenuse is 10 units long. Find the length of the side opposite the 30∘ angle.
opposite=10×2/1=5
Find the distance between the points A(2,3) and B(5,7).
d=5
Solve the following system of linear equations:
3x−2y=5
x+4y=11
x = 3 and y = 2
Solve the quadratic equation x2+4x−21=0.
x=−7 or x=3
Solve the quadratic equation 2x2−3x=0.
So, the solutions are x=0 and x=3/2
In a right triangle, the side opposite the angle θ is 4 units and the hypotenuse is 5 units. Find θ.
θ≈53.13∘
Find the midpoint of the line segment joining the points C(−1,4) and D(3,−2).
M=(1,1)
Solve the following system of linear equations:
5x+2y=20
3x−4y=−6
x = 2.62 y = 3.45
Rewrite the quadratic expression x2+6x+5 in the form of (x+p)2+q.
(x+3)2−4
Solve the quadratic equation x2+6x+5=0 by completing the square.
so, x = -1 or -5
In a right triangle, the lengths of the legs are 6 units and 8 units. Find the length of the hypotenuse.
c=10
Find the equation of the line passing through the points E(1,2) and F(4,8).
m=2
x+y=5
2x−y=1
x = 2 y = 3
Solve the quadratic equation 3x2−2x−8=0 using the quadratic formula.
x=2 and x=−3/4
Solve the quadratic equation 3x2+x−4=0 using the quadratic formula.
x = 1 and x=−3/4.
n a right triangle, one of the angles is 45∘ and the side adjacent to this angle is 7 units long. Find the length of the side opposite the 45∘ angle.
opposite=7
Find the point of intersection of the lines y=2x+3y and y=−x+1y.
So, the point of intersection is (−3/2,3/5).
Solve the following system of linear equations:
2x+3y−z=7
4x−y+2z=5
x+y+z=4
x = 1, y = 2 and z = 1
A rectangular garden has an area of 48 square meters. The length is 2 meters more than twice the width. Find the dimensions of the garden.
The length is 2w+2=2(4)+2=10
The product of two consecutive positive integers is 182. Find the integers.
So, the integers are 13 and 14.
A ladder is leaning against a wall. The ladder is 15 meters long and makes an angle of 60∘ with the ground. How high up the wall does the ladder reach?
So, the ladder reaches 7.5 meters up the wall.
Find the equation of the circle with center (3,−2) and radius 5.
The equation of the circle is (x−3)2+(y+2)2=25.