Answer:
(5, 2 ) and (- 1, 8 )
Step-by-step explanation:
Given the equations
y = - x + 7 → (1)
y = 0.5(x - 3)²
= 0.5(x² - 6x + 9)
y = 0.5x² - 3x + 4.5 → (2)
Substitute y = - x + 7 into (2)
- x + 7 = 0.5x² - 3x + 4.5 ( subtract - x + 7 from both sides )
0 = 0.5x² - 2x - 2.5 ( multiply through by 2 ) , then
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = -(- 1) + 7 = 1 + 7 = 8 ⇒ (- 1, 8 )
Answer:
The principal amount necessary to fund is $573.31
Step-by-step explanation:
Given as :
The quarterly withdrawal amount = A = $850
The time period for withdrawals = t = 9 years
The rate of interest = r = 4.4% compounded quarterly
Let The principal amount necessary to fund = $p
Now, <u>From Compound Interest</u>
Amount = Principal × 
Or, $850 = p × 
Or, $850 = p × 
Or, $850 = p × 
Or, $850 = p × 1.4826
∴ p = 
i.e p = $573.31
So,The principal amount necessary to fund = p = $573.31
Hence, The principal amount necessary to fund is $573.31 Answer
Answer: y=-x-8
Step-by-step explanation:
x-int: (-8, 0)
y-int: (0, -8)
m=(y2-y1)/(x2-x1)
m=(-8-0)/(0-(-8))
m=-8/(0+8)
m=-8/8
m=-1
y=mx+b
y=-x+b
-8=-0+b
b=-8
y=-x-8
The answer is b.18 because there are a total of 630 teachers needed and 630-612=18
Answer: the answer is d
Step-by-step explanation:
