Answer: n = - 6
Step-by-step explanation:
Given (x + h) is a factor of a polynomial f(x) then f(- h) = 0
Here
f(x) = x³ + 2x² - 5x + n and (x + 3) is a factor then f(- 3) = 0 , that is
f(- 3) = (- 3)³ + 2(- 3)² - 5(- 3) + n = 0 , so
- 27 + 2(9) + 15 + n = 0
- 27 + 18 + 15 + n = 0
6 + n = 0 ( subtract 6 from both sides )
n = - 6
Answer: A
Explanation: The sum of the multiplicities must be .
n
.
Starting from the left, the first zero occurs at =−3.
x
=
−3.
The graph touches the x-axis, so the multiplicity of the zero must be even. The zero of −3
−3
has multiplicity 2.
2.
The next zero occurs at =−1.
x
=
−1.
The graph looks almost linear at this point. This is a single zero of multiplicity 1.
The last zero occurs at =4.
x
=
4.
The graph crosses the x-axis, so the multiplicity of the zero must be odd. We know that the multiplicity is likely 3 and that the sum of the multiplicities is likely 6.
The mathematical functions (equations) are matched to their graph line respectively as follows:
- y = 960 - 78x: purple straight line.
- y = 8·3^x: violet line curve that slopes to the left.
- y = 960·(1/2)^x: green line curve that slopes to the right.
<h3>What is a linear function?</h3>
A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. Mathematically, a linear function is given by this equation:
y = mx ± c.
<h3>What is an exponential function?</h3>
An exponential function can be defined as a type of mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = keˣ
Next, we would match each of the mathematical functions (equations) to their graph line respectively as follows:
- y = 960 - 78x: purple straight line.
- y = 8·3^x: violet line curve that slopes to the left.
- y = 960·(1/2)^x: green line curve that slopes to the right.
Read more on graphs here: brainly.com/question/24298987
#SPJ1
Answer:
The Probability of strictly increasing or decreasing order is 20/216
Step-by-step explanation:
First Die 1 2 3 4 5 6
Second Die 1 2 3 4 5 6
Third Die 1 2 3 4 5 6
Total number of outcomes= 6*6*6= 216
Possible outcomes of increasing order
1,2,3-----1,2,6 (4)
1,3,4------1,3,6 (3)
1,4,5------1,4,6 (2)
1,5,6 (1)
2,3,4—-2,4,6 (3)
2,4,5—-2,4,6 (2)
2,5,6 (1)
3,4,5—-3,4,6 (2)
3,5,6 (1)
4,5,6 (1)
Total number of possible moves of increasing order= 4+3+2+1+3+2+1+2+1+1= 20
Probability of strictly increasing order is 20/216
Similarly Probability of strictly decreasing order is calculated which is also equal to 20/216
