The coefficient in this term is x^0
Answer:
x =
, x = ![\frac{13}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B2%7D)
Step-by-step explanation:
Given
4x² - 16x = 16x - 39 ( subtract 16x - 39 from both sides )
4x² - 32x + 39 = 0
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term, that is
product = 4 × 39 = 156 and sum = - 32
The factors are - 26 and - 6
Use these factors to split the x- term
4x² - 26x - 6x + 39 = 0 ( factor the first/second and third/fourth terms )
2x(2x - 13) - 3(2x - 13) = 0 ← factor out (2x - 13) from each term
(2x - 13)(2x - 3) = 0
Equate each factor to zero and solve for x
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
2x - 13 = 0 ⇒ 2x = 13 ⇒ x = ![\frac{13}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B2%7D)
Answer: width- 60
Length- 120
Step-by-step explanation:
The slope is -2/3 and the y-intercept is 2. It should look something like this. Let me know if you need more of an explanation.
Answer:
![\huge\boxed{(-5,\ -1)}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%28-5%2C%5C%20-1%29%7D)
Step-by-step explanation:
![\text{The vertex form of a quadratic equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{where}\ (h,\ k)\ \text{is a vertex},\ \text{and}\ h=\dfrac{-b}{2a},\ k=f(h).](https://tex.z-dn.net/?f=%5Ctext%7BThe%20vertex%20form%20of%20a%20quadratic%20equation%7D%5C%20y%3Dax%5E2%2Bbx%2Bc%3A%5C%5C%5C%5Cy%3Da%28x-h%29%5E2%2Bk%5C%5C%5C%5C%5Ctext%7Bwhere%7D%5C%20%28h%2C%5C%20k%29%5C%20%5Ctext%7Bis%20a%20vertex%7D%2C%5C%20%5Ctext%7Band%7D%5C%20h%3D%5Cdfrac%7B-b%7D%7B2a%7D%2C%5C%20k%3Df%28h%29.)
![\text{We have}\ y=x^2+10x+24\to a=1,\ b=10,\ c=24.\\\\\text{Substitute:}\\\\h=\dfrac{-10}{2(1)}=\dfrac{-10}{2}=-5\\\\k=f(-5)\to\text{put}\ x=-5\ \text{to the equation}:\\\\k=(-5)^2+10(-5)+24=25-50+24=-1\\\\\text{The vertex}:\ (-5,\ -1)](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%7D%5C%20y%3Dx%5E2%2B10x%2B24%5Cto%20a%3D1%2C%5C%20b%3D10%2C%5C%20c%3D24.%5C%5C%5C%5C%5Ctext%7BSubstitute%3A%7D%5C%5C%5C%5Ch%3D%5Cdfrac%7B-10%7D%7B2%281%29%7D%3D%5Cdfrac%7B-10%7D%7B2%7D%3D-5%5C%5C%5C%5Ck%3Df%28-5%29%5Cto%5Ctext%7Bput%7D%5C%20x%3D-5%5C%20%5Ctext%7Bto%20the%20equation%7D%3A%5C%5C%5C%5Ck%3D%28-5%29%5E2%2B10%28-5%29%2B24%3D25-50%2B24%3D-1%5C%5C%5C%5C%5Ctext%7BThe%20vertex%7D%3A%5C%20%28-5%2C%5C%20-1%29)