Answer:
Option C
The student's conclusion is correct because the solution to the system of equations
and
is ![(5,6)](https://tex.z-dn.net/?f=%285%2C6%29)
Step-by-step explanation:
Let
x------> the cost of each burger
y-----> the cost of each sandwich
we know that
-----> equation A
----> equation B
Solve the system of equations
Multiply the equation B by ![-2](https://tex.z-dn.net/?f=-2)
----->
------> equation C
Adds equation A and equation C
![3x+2y=27 \\-4x-2y=-32\\ ----------\\ 3x-4x=27-32\\ -x=-5\\x=5](https://tex.z-dn.net/?f=3x%2B2y%3D27%20%5C%5C-4x-2y%3D-32%5C%5C%20----------%5C%5C%203x-4x%3D27-32%5C%5C%20-x%3D-5%5C%5Cx%3D5)
Substitute the value of x in the equation B
![2(5)+y=16](https://tex.z-dn.net/?f=2%285%29%2By%3D16)
![10+y=16](https://tex.z-dn.net/?f=10%2By%3D16)
![y=6](https://tex.z-dn.net/?f=y%3D6)
The solution of the system of equations is the point ![(5,6)](https://tex.z-dn.net/?f=%285%2C6%29)
so
The price of each burger is ![\$5](https://tex.z-dn.net/?f=%5C%245)
The price of each sandwich is ![\$6](https://tex.z-dn.net/?f=%5C%246)
Note the order of the letters:
A C E G
M N P R
You read it like this:
A ≅ M
C ≅ N
CE ≅ NP
AG ≅ MR
... and so on
In the following choices:
CE ≅ NP is the true statement
Answer: I think its B
Step-by-step explanation: My friend answered it.
The sides of the triangle are given as 1, x, and x².
The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.
Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.
Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.
Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.
Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.