<span>
4. The x-coordinate of the solution is 9.</span><span>
5. The y-coordinate of the solution is −8 .</span><span>
6.The ordered pair that is the solution to the system lies in Quadrant IV .</span><span>
Proof:
Solve the following system:
{4 x + 3 y = 12 | (equation 1)
{2 x + 3 y = -6 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{4 x + 3 y = 12 | (equation 1)
{0 x+(3 y)/2 = -12 | (equation 2)
Multiply equation 2 by 2/3:
{4 x + 3 y = 12 | (equation 1)
{0 x+y = -8 | (equation 2)
Subtract 3 × (equation 2) from equation 1:
{4 x+0 y = 36 | (equation 1)
{0 x+y = -8 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 9 | (equation 1)
{0 x+y = -8 | (equation 2)
Collect results:
Answer: {x = 9 , y = -8</span>
Answer:
y = (x - 3)² + 1
Step-by-step explanation:
the equation of a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (3, 1 ) , then
y = a(x - 3)² + 1
to find a substitute (1, 5 ) into the equatiuon
5 = a(1 - 3)² + 1 ( subtract 1 from both sides )
4 = a(- 2)² = 4a ( divide both sides by 4 )
1 = a
then equation of quadratic function is
y = (x - 3)² + 1
I would say the graph, only because it is doing run/rise not rise/run
Answer:
<A
Step-by-step explanation:
The side BC is opposite an angle
The angle that is opposite BC is Angle A
<h3>
Answer: Choice D) 22.5</h3>
========================================
Explanation:
x = length of BC
AC = AB+BC
AC = 6 + x
CE = CD+DE
CE = 22+8
CE = 30
Triangles ACE and BCD are similar triangles (can be proven by the AA similarity theorem due to the fact that AE || BD)
Therefore the corresponding sides are proportional letting us set up the proportion below
AC/BC = CE/CD
(6+x)/x = 30/22 .... substitution
22(6+x) = 30x ... cross multiply
132+22x = 30x
132 = 30x-22x ..... subtract 22x from both sides
132 = 8x
8x = 132
x = 132/8 .... divide both sides by 8
x = 16.5
Now use this to find the length of AC
AC = 6+x
AC = 6+16.5
AC = 22.5