Answer:
x = 1/2 or 3
Step-by-step explanation:
Compare the given equation to the standard form equation to identify the values of the variables in the formula. Then put those values in the formula and do the arithmetic.
![ax^2+bx+c=0\\\\2x^2-7x+3=0\\\\a=2;\ b=-7;\ c=3\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(3)}}{2(2)}=\dfrac{7\pm\sqrt{25}}{4}=\dfrac{7\pm 5}{4}\\\\x=\left\{\dfrac{1}{2},3\right\}](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0%5C%5C%5C%5C2x%5E2-7x%2B3%3D0%5C%5C%5C%5Ca%3D2%3B%5C%20b%3D-7%3B%5C%20c%3D3%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-7%29%5Cpm%5Csqrt%7B%28-7%29%5E2-4%282%29%283%29%7D%7D%7B2%282%29%7D%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B25%7D%7D%7B4%7D%3D%5Cdfrac%7B7%5Cpm%205%7D%7B4%7D%5C%5C%5C%5Cx%3D%5Cleft%5C%7B%5Cdfrac%7B1%7D%7B2%7D%2C3%5Cright%5C%7D)
Answer: D) (x+1)(x + 2)(x-3)
This is because the roots are x = -1, x = -2 and x = 3
Simply get all the numbers to each side to have 0 on the right side
x = -1 turns into x+1 = 0
x = -2 turns into x+2 = 0
x = 3 turns into x-3 = 0
The three factors are (x+1), (x+2) and (x-3)
Which leads to (x+1)(x+2)(x-3)
Parallelogram and rhombus are your answers
Hello!
To find the circumference you use the equation
![2 \pi r](https://tex.z-dn.net/?f=2%20%5Cpi%20r)
r is the radius
![2 \pi 56](https://tex.z-dn.net/?f=2%20%5Cpi%2056)
Put this into a calculator and you get the answer of about 351.86
The answer is about 351.86
Hope this helps!
Answer:
- The height of the other book is <em>2 3/4</em> inches.
Step-by-step explanation:
<em>From the information,we get:</em>
Two stacks of books together are = 7 1/2 inches tall.
One stack is given,that is = 4 3/4 inches.
To Find:
Solution:
Let us assume that the other height of the book be x.
Then the equation will be:
![4\cfrac{3}{4} + x = 7\cfrac{1}{2}](https://tex.z-dn.net/?f=%204%5Ccfrac%7B3%7D%7B4%7D%20%2B%20x%20%3D%20%207%5Ccfrac%7B1%7D%7B2%7D%20)
- Solve for x to get the other book's height.
Convert the mixed fractions to fractions:
![\implies \: \cfrac{19}{4 } + x = \cfrac{15}{2}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20%20%5Ccfrac%7B19%7D%7B4%20%7D%20%20%2B%20x%20%3D%20%20%5Ccfrac%7B15%7D%7B2%7D%20)
<em>Subtract 19/4 from both sides:</em>
![\implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5C%3A%20x%20%2B%20%20%5Ccfrac%7B19%7D%7B4%7D%20%20-%20%20%5Ccfrac%7B19%7D%7B4%7D%20%20%3D%20%20%5Ccfrac%7B15%7D%7B2%7D%20%20%20-%20%5Ccfrac%7B19%7D%7B4%7D%20)
![\implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}](https://tex.z-dn.net/?f=%20%20%5Cimplies%20%5C%3A%20x%20%3D%20%20%5Ccfrac%7B11%7D%7B4%7D%20%20%3D%5Cboxed%7B%202%20%5Ccfrac%7B3%7D%7B4%7D%20%20%5Crm%20%5C%3A%20inches%7D)
<u>Hence, we can conclude that:</u>
The height of the other book is 2 3/4 inches.