1. f(x) = 9x² + 6x - 8
f(x) = (3x - 2)(3x + 4)
When (3x - 2) = 0, then x = 2/3
When (3x + 4) = 0, then x = -4/3
Answer: The zeros are two divided by three and negative four divided by three.
2. f(x) = 9x³ - 45x² + 36x
f(x) = 9x(x² - 5x + 4)
= 9x(x - 1)(x - 4)
When 9x = 0, then x = 0
When (x-1) = 0, then x = 1
When (x-4) = 0, then x = 4
Answer: 0, 1 and 4
3. f(x) = 4(x+7)²(x-7)³
When (x+7)² = 0, then x = -7 (twice)
When (x-7)³ = 0, then x = 7 (thrice)
Answer: 7, multiplicity 2; -7 multiplicity 3
4. The zeros of f(x) are √5, -√5, -7
The factors of f(x) are (x-√5)(x+√5)(x+7)
Note that (x-√5)(x+√5) = x² - (√5)² = x² - 5
f(x) = (x²-5)(x+7)
= x³ + 7x² - 5x - 35
Answer: f(x) = x³ + 7x² - 5x - 35
5. Expand (2x + 4)³
From Pascal's Triangle, the coefficients are 1 3 3 1
Therefore
(2x + 4)³ = 1(2x)³(4)⁰ + 3(2x)²(4)¹ + 3(2x)¹(4)² + 1(2x)⁰(4)³
= 8x³ + 48x² + 96x + 64
Answer: 8x³ + 48x² + 96x + 64
From x=1 to x=5
x=1 is starting time
x=time
y=mx+b
m=slope
b=yintercept
slope=(y2-y1)/(x2-x1)
for points (x1,y1) and (x2,y2)
(1,52000) and (5,116000)
slope=(116000-52000)/(5-1)=64000/4=16000
y=16000x+b
find b
(1,52000)
52000=16000(1)+b
52000=16000+b
minus 16000 from both sides
36000=b
the equation is
y=16000x+36000
at 12 years, x=12
y=16000(x)+36000
y=16000(12)+36000
y=192000+36000
y=228000
sales at year 12 is $228,000
Answer:
The team can be formed in 756 different ways
Step-by-step explanation:
This is a combination problem since we are to select a set of people from a group. Combination has to do with selection.
for example, if r number of object is to be selected from a pool of n objects, this can be done in nCr number of ways.
Now If A company has 7 male and 9 female employees, and needs to nominate 2 men and 2 women for the company bowling team, then this can be done in the following way;
7C2 * 9C2 = 21*36
= 756
The team can be formed in 756 different ways
The possible problems of using graphs to find roots are:
- Having complex roots.
- Having irrational roots.
<h3>How to find the roots of a quadratic function with a graph?</h3>
First, the roots of a quadratic function are the values of x such that:
a*x^2 + b*x + c = 0
To find the roots using a graph, we need to see at which values of x does the graph of the parabola intercepts the horizontal axis.
<h3>What are the possible problems with this method?</h3>
There are two, the first one is having irrational roots, in that case, an analytical or numerical approach will give us a better estimation of the roots. Finding irrational values by looking at the intercepts of the graph can be really hard, so in these cases using the graph to find the roots is not the best option.
The other problem is if we <u>don't have real roots</u>, this means that the graph never does intercept the horizontal axis. In these cases, we have complex roots, that only can be obtained if we solve the problem analytically.
If you want to learn more about quadratic functions, you can read:
brainly.com/question/7784687
X^2-3x-10. You solve it by foiling. I attached a photo explaining how to do it.
