Answer:
The y-intercept is 3 aka. (0,3)
Step-by-step explanation:
The slope is 1 (since (6-4)/(3-1)=2/2=1)
y=1x+b
4=1+b
3=b
Upon a slight rearrangement this problem gets a lot simpler to see.
x^3-x+2x^2-2=0 now factor 1st and 2nd pair of terms...
x(x^2-1)+2(x^2-1)=0
(x+2)(x^2-1)=0 now the second factor is a "difference of square" of the form:
(a^2-b^2) which always factors to (a+b)(a-b), in this case:
(x+2)(x+1)(x-1)=0
So g(x) has three real zero when x={-2, -1, 1}
Given that a company budgeted 5 1/4 hours to complete a project, determine how much time they spent on research if they spent 1/3 of the total budget.
First, convert the budget from hours into minutes.
5 1/4 hours = 315 minutes
1 hour = 60 min
1/4 hour = 15 min
60 x 5 = 300
300 + 15 = 315
Then, divide the minutes by 3 or multiply it by 1/3.
315 / 3 = 105
315 x 1/3 = 105
Lastly convert to a mixed number.
1 3/4 hour
Thus, the company plans to spend 1 3/4 hours or 1 hour and 45 minutes on research.
I'm assuming this is a yearly interest.
2500*.04=100
7500*.05=375
so that would be $475 earned from interest
d) You have a <u>difference of squares</u>:
49y² - 9 = (7y)² - 3²
Recall the identity,
a² - b² = (a - b) (a + b)
So,
49y² - 9 = (7y - 3) (7y + 3)
e) Pull out the common factor 3 from each term:
3x² - 3x - 90 = 3 (x² - x - 30)
Now use the <u>sum-product method</u>. Notice that we can write 30 = 5 • 6, and 5 - 6 = 1, so
3x² - 3x - 90 = 3 (x + 5) (x - 6)
f) Same as in (e), use the <u>sum-product method</u>. Notice that 42 = 7 • 6, and -7 - 6 = -13, so
x² - 13x + 42 = (x - 7) (x - 6)
