Hello here is a solution
look graph :
the curve : color blue
the first tangent : y = 0.13x +1.87 color Pink
the second tangent : y = 1.88 x +0.14 color green
Answer:
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
Step-by-step explanation:
Given,
CGPA = 2.75
Credit hours = 105
Last semester GPA = 4
Last semester credit hours = 15
CGPA =
credit hours * gpa
in our case, it would be:
CGPA = ![\frac{(2.75*105)+(4*15}{105+15}](https://tex.z-dn.net/?f=%5Cfrac%7B%282.75%2A105%29%2B%284%2A15%7D%7B105%2B15%7D)
=> ![\frac{(288.75)+(60)}{120}](https://tex.z-dn.net/?f=%5Cfrac%7B%28288.75%29%2B%2860%29%7D%7B120%7D)
=> ![\frac{348.75}{120}](https://tex.z-dn.net/?f=%5Cfrac%7B348.75%7D%7B120%7D)
=> 2.90
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
The number of students in Mr. Boggs’s homeroom is equal to b. Add the total number of students in each class and set it equal to 90.
90 = b + 1.5(b + 2) + 15 + (2b – 9)
Use the Distributive Property, and collect like terms. 90 = b + 1.5b + 3 + 15 + 2b – 9
90 = 4.5b + 9
Answer:
not sure man... goodluck tho
Answer:
Step-by-step explanation:
Our equations are
![y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\](https://tex.z-dn.net/?f=y%20%3D%20-3x%5E2%20%2B%20x%20%2B%2012%5C%5Cy%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5Cy%20%3D%20x%5E2%20%2B%207x%20-%2011%5C%5Cy%20%3D%20-x%5E2%20-%208x%20-%2016%5C%5C)
Let us understand the term Discriminant of a quadratic equation and its properties
Discriminant is denoted by D and its formula is
![D=b^2-4ac\\](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%5C%5C)
Where
a= the coefficient of the ![x^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D)
b= the coefficient of ![x](https://tex.z-dn.net/?f=x)
c = constant term
Properties of D: If D
i) D=0 , One real root
ii) D>0 , Two real roots
iii) D<0 , no real root
Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .
Let us start with
![y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\](https://tex.z-dn.net/?f=y%20%3D%20-3x%5E2%20%2B%20x%20%2B%2012%5C%5Ca%3D-3%20%2C%20b%20%3D1%20%2C%20c%20%3D12%5C%5CD%3D1%5E2-4%2A%28-3%29%2A%2812%29%5C%5CD%3D1%2B144%5C%5CD%3D145%5C%5CD%3E0%20%5C%5C)
Hence we have two real roots for this equation.
![y = 2x^2 - 6x + 5\\](https://tex.z-dn.net/?f=y%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5C)
![y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D](https://tex.z-dn.net/?f=y%20%3D%202x%5E2%20-%206x%20%2B%205%5C%5Ca%3D2%2Cb%3D-6%2Cc%3D5%5C%5CD%3D%28-6%29%5E2-4%2A2%2A5%5C%5CD%3D36-40%5C%5CD%3D-4%5C%5CD%3C0%5C%5C)
Hence we do not have any real root for this quadratic
![y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\](https://tex.z-dn.net/?f=y%20%3D%20x%5E2%20%2B%207x%20-%2011%5C%5Ca%3D1%2Cb%3D7%2C-11%5C%5CD%3D7%5E2-4%2A1%2A%28-11%29%5C%5CD%3D49%2B44%5C%5CD%3D93%5C%5C)
Hence D>0 and thus we have two real roots for this equation.
![y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20-%208x%20-%2016%5C%5Ca%3D-1%2Cb%3D-8%2Cc%3D-16%5C%5CD%3D%28-8%29%5E2-4%2A%28-1%29%2A%28-16%29%5C%5CD%3D64-64%5C%5CD%3D0%5C%5C)
Hence we have one real root to this quadratic equation.