Answer:
The solution is
. Fourth option
Explanation:
Solve for x:
![2x^2+3x-7=x^2+5x+39](https://tex.z-dn.net/?f=2x%5E2%2B3x-7%3Dx%5E2%2B5x%2B39)
Move all the terms from the right to the left side of the equation, a zero in the right side:
![2x^2+3x-7-x^2-5x-39=0](https://tex.z-dn.net/?f=2x%5E2%2B3x-7-x%5E2-5x-39%3D0)
Join all like terms:
![x^2-2x-46=0](https://tex.z-dn.net/?f=x%5E2-2x-46%3D0)
The general form of the quadratic equation is:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
Solve the quadratic equation by using the formula:
![\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
In our equation: a=1, b=-2, c=-46
Substituting into the formula:
![\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-%28-2%29%5Cpm%20%5Csqrt%7B%28-2%29%5E2-4%281%29%28-46%29%7D%7D%7B2%281%29%7D)
![\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B4%2B184%7D%7D%7B2%7D)
![\displaystyle x=\frac{2\pm \sqrt{188}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B188%7D%7D%7B2%7D)
Since 188=4*47
![\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B4%2A47%7D%7D%7B2%7D)
Take the square root of 4:
![\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B2%5Cpm%202%5Csqrt%7B47%7D%7D%7B2%7D)
Divide by 2:
![\displaystyle x=1\pm \sqrt{47}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D1%5Cpm%20%5Csqrt%7B47%7D)
First option: Incorrect. The answer does not match
Second option: Incorrect. The answer does not match
Third option: Incorrect. The answer does not match
Fourth option: Correct. The answer matches exactly this option
Supply is the amount of product a seller is able to make
4:1 means for every four soccer player there is 1 volleyball player
that means there are four times the number of soccer players than volleyball players
Answer:
um what?
Step-by-step explanation:
I don't understand this
Step-by-step explanation:
1. Perimeter = 2 ( 5+4) = <u>18 cm</u>
Area = 5 × 4 = <u>20 cm^2</u>
2. Perimeter = 2 (5+5) = <u>20 cm</u>
Area = 5 × 5 = <u>25 cm^2</u>
3. Cups of seed needed per sq. meter = Area of the rectangle backyard
= 6 × 7
= <u>42 </u><u>cups</u><u> </u><u>of</u><u> </u><u>seed</u>
4. Feet of fence needed = Perimeter of the Square garden
= 2(8+8)
<u>= 32 feet</u>
5. Perimeter of rectangular quilt = 2 (4+6) feet
= <u>20 feet</u>
6. Area of the room = 9 feet × 8 feet
= <u>72 feet^2</u>