Answer:
x = 1
Step-by-step explanation:
4x-5=y
4x-5= -1
4x = -1+5
4x=4
x=1
2x-y=3
2x-(-1)=3
2x+1=3
2x= 3-1
2x= 2
x=1
since the two answers for x are the same therefore:
x = 1
Answer:
it increases by 125 for each ton of sugar being transported
Step-by-step explanation:
750-875= 125
Answer:
x=2
Vertex (2,-8)
Intercepts: 2 ±2/3 sqrt(6)
Because the parabola opens upwards, it has a minimum at the vertex
Domain: all real numbers
Range: y>= -8
Step-by-step explanation:
y= 3x^2 -12x+4
To find the axis of symmetry, we use the formula
h= -b/2a where ax^2 +bx+c
h = -(-12)/2*3 = 12/6=2
The axis of symmetry is x=2
The x coordinate of the vertex is at the axis of symmetry. To find the y coordinate, substitute x into the equation
y= 3(2)^2 -12(2) +4
y = 3*4-24+4
= 12-24+4
= -8
The vertex is at (2,-8)
We can use the quadratic formula to find the x intercepts
x = -b ±sqrt(b^2-4ac)
-----------------------
2a
= 12 ± sqrt(12^2 - 4*3*4)
---------------------------------
2*3
= 12± sqrt(144-48)
----------------------
6
= 12±sqrt(96)
---------------
6
=2 ±1/6 * 4sqrt(6)
= 2 ±2/3 sqrt(6)
Because the parabola opens upwards, it has a minimum at the vertex.
The domain is the values that x can take.
X can be all real numbers
The range is the values that y can take. Since there is a minimum, y must be greater than that minimum
Range: y>= -8
Answer:
see explanation
Step-by-step explanation:
The inverse of a matrix A =
is
=
![\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5C%5C%5Cend%7Barray%7D%5Cright%5D)
If ad - bc = 0 then the matrix has no inverse
A = ![\left[\begin{array}{ccc}11&-5\\3&-1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11%26-5%5C%5C3%26-1%5C%5C%5Cend%7Barray%7D%5Cright%5D)
ad - bc = (11 × - 1) - (- 5 × 3) = - 11 - (- 15) = - 11 + 15 = 4 , then
=
= ![\left[\begin{array}{ccc}-0.25&0.75\\-1.25&2.75\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-0.25%260.75%5C%5C-1.25%262.75%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
738 miles
Step-by-step explanation:
324 miles = 18 gallons
18 miles = 1 gallon
738 miles = 41 gallons