Answer: fourth option
Explanation:1) the pair x = 3 f(x) = 0, leads you to probe this:
f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0
=> A [4^2] = - C
A[16] = - C
if A = 1/4
16 / 4 = 4 => C = - 4
That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4
2) Now you verify the images for that function for all the x-values of the table:
x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check
x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check
x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.
Therefore, you have proved that the answer is the fourth option.
Answer:
Step-by-step explanation:
5x + 9y = -11
3x + 9y = -3
5x + 9y = -11
-3x - 9y = 3
2x = -8
x = -4
-12 + 9y = -3
9y = 9
y = 1
(-4, 1)
Answer is C
Answer:
8/25 is the simplest form
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.
The factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).
<h2>Polynomial</h2>
Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Given
5x³ + 20x³ + 2x +8 is a polynomial.
<h3>To find </h3>
The factor of the polynomial.
<h3>How to find the factor of the polynomial?</h3>
5x³ + 20x³ + 2x +8 is a polynomial.
Take common, we get
5x²(x + 4) + 2(x + 4)
(5x² + 2) (x + 4)
[(x√5)² - (i√2)](x + 4)
(√5x - i√2)(√5x + i√2)(x + 4)
Thus, the factor of the polynomial is (√5x - i√2)(√5x + i√2)(x + 4).
More about the polynomial link is given below.
brainly.com/question/17822016