Answer:
.
Step-by-step explanation:
Given information:
According to the Pythagoras theorem,
Using Pythagoras theorem, we get
Taking square root on both sides.
Hence, the expression of the hypotenuse is
.
Answer:
(x, y) = (0, 1/2) or (1, 3)
Step-by-step explanation:
The first equation factors as ...
x(3x -y) = 0
This has solutions x=0 and y=3x.
__
<u>x = 0</u>
Using this in the second equation gives ...
2y -0 = 1
y = 1/2
(x, y) = (0, 1/2) is a solution
__
<u>y = 3x</u>
Using the expression for y in the second equation, we get ...
2(3x) -5x = 1
x = 1 . . . . . . . . . simplify
y = 3x = 3 . . . . using x=1 in the first equation
(x, y) = (1, 3) is a solution
_____
Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be <em>anything</em>. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.
Given
jacinta buys 4 pounds of turkey and 2 pounds of ham & pays a total of $30, turkey costs $1.50 less per pound than the ham.
find out the combined cost of 1 pound of turkey and 1 pound of ham
To proof
As given in the question
jacinta buys 4 pounds of turkey and 2 pounds of ham
total pay by jacinta = $30
let us assume that the price of the ham = x
as given in the question
turkey costs $1.50 less per pound than the ham
turkey costs becomes = x - 1.50
then the equation becomes
30 = 4 (x - 1.50) + 2x
30 = 4x + 2x - 6
36 = 6x
x = 6
thus
ham cost per pound = $6
turkey cost per pound = 6 - 1.50
= $ 4.5
Now find out
cost of 1 pound of turkey + 1 pound of ham = $ 6 + $ 4.5
= $ 10.5
Hence proved
The given equation is
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm