1. first parabola is up, so a are going to be positive
y = a(x-r)(x-s),
roots -7,-3, so we can write y=a(x+7)(x+3) [1]
we can take point (-5,-2), substitute into equation [1], and find value of a
-2=a(-5+7)(-5+3)
-2=a*2*(-2)
a=1/2
so first parabola has an equation
y=1/2(x+7)(x+3)
2. second parabola
y=a(x-r)(x-s) roots are 2 and 4 so we ca write
y=a(x-2)(x-4) take point (3,4) and substitute into this equation
4 =a(3-2)(3-4)
4=-a
a=-4, and it will look down
y=-4(x-2)(x-4)
Answer:
8 is the probablitiy
Step-by-step explanation:
4+5=9 -1 = 8
Answer:
Z(-0.2, 2.2).
Step-by-step explanation:
We will use section formula when a point, say P, divides any segment ,say AB, internally in the ratio m:n.
![[x=\frac{mx_2+nx_1}{m+n}, y= \frac{my_2+ny_1}{m+n}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2C%20y%3D%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
We have been given the points of segment XY as X at (-2,1) and Y at (4,5) and ratio is 3:7.

Upon substituting coordinates of our given points in section formula we will get,
![[x=\frac{(3*4)+(7*-2)}{3+7}, y= \frac{3*5+7*1}{3+7}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B%283%2A4%29%2B%287%2A-2%29%7D%7B3%2B7%7D%2C%20y%3D%20%5Cfrac%7B3%2A5%2B7%2A1%7D%7B3%2B7%7D%5D)
![[x=\frac{12-14}{10}, y= \frac{15+7}{10}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B12-14%7D%7B10%7D%2C%20y%3D%20%5Cfrac%7B15%2B7%7D%7B10%7D%5D)
![[x=\frac{-2}{10}, y= \frac{22}{10}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B-2%7D%7B10%7D%2C%20y%3D%20%5Cfrac%7B22%7D%7B10%7D%5D)
![[x=-0.2, y= 2.2]](https://tex.z-dn.net/?f=%5Bx%3D-0.2%2C%20y%3D%202.2%5D)
Therefore, coordinates of point Z will be (-0.2, 2.2).
Answer:
The numerator is 57 ⇒ B
The denominator is 78 ⇒ B
The value of the fraction is 73.1% ⇒ A
Step-by-step explanation:
Let us solve it step by step
∵ The loan is 12 month
∵ The numerator is after 6 month
- Put n = 1 in each bracket
∴ The numerator = {(1 + 11) + (1 + 10) + (1 + 9) + (1 + 8) + (1 + 7) + (1 + 6)}
∴ The numerator = {12 + 11 + 10 + 9 + 8 + 7}
∴ The numerator = {57}
The numerator is 57
∵ The denominator = {(n) + (n + 1) + (n + 2) + .......... + (n + 11)}
- Do the same as the numerator put n = 1
∴ The denominator = {1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12}
∴ The denominator = {78}
The denominator is 78
Now find the value of the fraction
∵ The fraction = 
∴ Its value = 0.730769230
- Multiply it by 100%
∴ Its value = 0.730769230 × 100% = 73.0769230%
- Round it to the nearest tenth
∴ Its value = 73.1%
The value of the fraction is 73.1%