The next number in the sequence should be 333.111
Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
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 = 8 ⇒ (- 1, 8 )
Answer:
The correct option is A.
Step-by-step explanation:
According to statement a1 = 4 and r = 3. This shows that r is greater than 1.
If r is greater than 1 than it includes integers greater than 1 or equal to 1. It does not include all the real numbers because real numbers include negative numbers also.
If starting value is 4,if we put n=0, then we get 4, but if we put a negative value than we would get a number which is not a part of our sequence. Thus the correct option is All integers where n ≥ 1....
1$ = 100 cents, 1 hour = 60 minutes
$7.80/hour = (7.8*100) cents / (1*60)minutes
= 780 cents/60 minutes
= 13 cents/minute
<span>Option a</span>
I am going to do the first 2 problems and show my work that way you know how to do it yourself.
So first of all, the foil method:
(a+b) (c+d) = ac+ad+bc+bd
1. (3xy-1) (4xy+2) = (3xy*4xy) + (3xy*2) + (-1*4xy) + (-1*2)
(3xy-1) (4xy+2) = (12x^2y^2) + (6xy) + (-4xy) + (-2)
(3xy-1) (4xy+2) = (12x^2y^2) + (6xy-4xy) - 2
(3xy-1) (4xy+2) = 12x^2y^2 + 2xy - 2
2. <span>(2x-3y) (4x-y) = (2x*4x) + (2x*-y) + (-3y*4x) + (-3y*-y)
(2x-3y) (4x-y) = (8x^2) + (-2xy) + (-12xy) + (3y^2)
</span> (2x-3y) (4x-y) = 8x^2 + (-2xy-12xy) + 3y^2
(2x-3y) (4x-y) = 8x^2 - 14xy + 3y^2
I hope this helps!
