- Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
![\:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}](https://tex.z-dn.net/?f=%20%5C%3A%E2%9D%8F%20%5C%3A%20%20%20%5C%3A%20%5CLARGE%7B%5Crm%7B%7B%7B%5Ccolor%7Borange%7D%7B6%20%7Bx%20%7D%5E%7B2%7D%20%20%5C%3A%20%20%2B%20%20%5C%3A%207x%20%5C%3A%20%20-%203%7D%7D%7D%7D%7D)
- Factorize the equation by breaking down the middle term.
![\large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3](https://tex.z-dn.net/?f=%20%5Clarge%20%20%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A%206%20%7Bx%20%7D%5E%7B2%7D%20%20%5C%3A%20%20%2B%20%20%5C%3A%207x%20%5C%3A%20%20-%203)
- Let’s identify two factors such that their sum is 7 and the product is -18.
Sum of two factors = 7 = 9 - 2
Product of these two factors = 9 × (-2) = 18
- Now, split the middle term.
![\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3](https://tex.z-dn.net/?f=%5Clarge%20%20%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A6%20%7Bx%7D%5E%7B2%7D%20%5C%3A%20%20%20%2B%20%5C%3A%209x%20%5C%3A%20%20-%20%20%5C%3A%202x%20%5C%3A%20-%20%20%5C%3A%203)
- Take the common terms and simplify.
![\: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)](https://tex.z-dn.net/?f=%20%20%5C%3A%20%20%5C%5C%20%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A3x%282x%20%5C%3A%20%20%2B%20%20%5C%3A%203%29%5C%3A%20-1%282x%20%5C%3A%20%20%2B%20%5C%3A%203%29)
![\\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0](https://tex.z-dn.net/?f=%20%5C%5C%20%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A%283x%20%5C%3A%20%20-%20%20%5C%3A1%20%29%20%5Cquad%20%5C%3A%20%282x%20%5C%3A%20%20%2B%20%20%5C%3A%203%29%20%5C%3A%20%20%3D%20%20%5C%3A%200)
Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.
- Solving these two linear factors, we get
![\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2} \\](https://tex.z-dn.net/?f=%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3Ax%20%5C%3A%20%3D%20%20%5C%3A%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5C%3A%20%20%5C%3A%20%2C%20%20%5C%3A%20%20%5C%3A%20%5Cfrac%7B%20-%203%7D%7B2%7D%20%20%5C%5C%20)
Answer:
1,3,5,15,25 and 75 :)
Step-by-step explanation:
Answer: 480 ft
Step-by-step explanation:
We can use Similarity of Triangles.
| lighthouse
60 ft | ruler
|___________ 3 in |__
x 2 ft
3 inches = 0.25 ft
60/0.25 = x/2
0.25x = 120
x = 120/0.25
x = 480 ft
1. You can call
to the cost of each one of Tanya's items and
to the cost of each one of Tony's items.
2. Based on the information given in the problem and knowing that both paid the same amount of money, you can write the following expression:
![5(x-1.25)=4x](https://tex.z-dn.net/?f=5%28x-1.25%29%3D4x)
3. You must solve for
:
4. The total amount of money that Tanya and Tony paid was:
dollars
5. Therefore, the amount of money that Tony paid for each item was:
dollars
The answer is: The individual cost of each Tanya's items is
dollars and the individual cost of each Tony's items is
dollars.
Answer:
A, D, C, F, B, G
Step-by-step explanation: