Answer:
68
Step-by-step explanation:
40+28
Here we have to convert 423 yards into feet.
first let us find the basic relation between yard and feet
1 yard =3 foot
so applying this to our question we get,
423 yard =423*3 foot = 1269 feet
Answer 423 yards =1269 feet
Answer:
7.2
Step-by-step explanation:
the original is 40 and discount is 28% so $40-28%
Answer:
y = -4x² + 32x - 48
Step-by-step explanation:
The standard form of a quadratic equation is
y = ax² + bx + c
We must find the equation that passes through the points:
(2, 0), (6,0), and (3, 12)
We can substitute these values and get three equations in three unknowns.
0 = a(2²) + b(2) + c
0 = a(6²) + b(6) + c
12 = a(3²) + b(3) + c
We can simplify these to get the system of equations:
(1) 0 = 4a + 2b + c
(2) 0 = 36a + 6b + c
(3) 12 = 9a + 3b + c
Eliminate c from equations (1) and (2). Subtract (1) from (2).
(4) 0 = 32a + 4b
Eliminate c from equations (2) and (3). Subtract (3) from (2).
(5) -12 = 27a - 3b
Simplify equations (4) and (5).
(6) 0 = 8a + b
(7) -4 = 9a - b
Eliminate b by adding equations (6) and (7).
(8) a = -4
Substitute (4) into (6).
0 = -32 + b
(9) b = 32
Substitute a and b into (1)
0 = 4(-4) + 2(32) + c
0 = -16 + 64 + c
0 = 48 + c
c = -48
The coefficients are
a= -4, b = 32, c = -48
The quadratic equation is
y = -4x² + 32x - 48
The diagram below shows the graph of your quadratic equation and the three points through which it passes.
Let's say we placed dominoes close together such that they only fell over one way: to the right hand side. Let's call the dominoes A and B.
Domino A is to the left of domino B. If we push over domino A, then it will hit domino B to cause it to fall over as well. We have a mini chain reaction of sorts. The fall of A triggers the fall of B, but not the other way around.
For this problem, we can think of domino A as "Jillian gets a raise" and domino B as "she will buy a new car". The raise causes her to get a new car, but not vice versa.
Since we're told in the last sentence she definitely got the raise, this must mean she will definitely get the new car.
In terms of symbols, the law of detachment is stated as
- If P, then Q
- P is true
- Therefore Q is true
Side note: some books might use the term "modus ponens" instead of "law of detachment". They're the same thing.
