5a^2 -25b^2..Factorise fully
2 answers:
→ Given equation : 5a² – 25b²
Apply formula for this : a²–b² = (a+b) (a-b)
5a² - 25b² = 5 • (a² - 5b²)
Factoring: a²- 5b²
Theory : A difference of two perfect squares, A² - B² can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 5 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
You might be interested in
Part 1: You can simplify to
Presumably, the sequence starts at <em>n</em> = 1. It's easy to see that the sequence is strictly decreasing, since larger values of <em>n</em> make either fraction smaller.
(a) So, the sequence is bounded above by its first value,
(b) And because both fractions in converge to 0, while remaining positive for any natural number <em>n</em>, the sequence is bounded below by 0,
(c) Finally, is bounded above and below, so it is a bounded sequence.
Part 2: Yes, is monotonic and strictly decreasing.
Part 3:
(a) I assume the choices are between convergent and divergent. Any monotonic and bounded sequence is convergent.
(b) Since is decreasing and bounded below by 0, its limit as <em>n</em> goes to infinity is 0.
Part 4:
(a) We have
and the (-1)ⁿ makes this limit alternate between -10 and 10. So the sequence is bounded but clearly not monotonic, and hence divergent.
(b) Taking the limit gives
so the sequence is unbounded and divergent. It should also be easy to see or establish that the sequence is strictly increasing and thus monotonic.
For the next three, I'm guessing the options here are something to the effect of "does", "may", or "does not".
(c) may : the sequence in (a) demonstrates that a bounded sequence need not converge
(d) does not : a monotonic sequence has to be bounded in order to converge, otherwise it grows to ± infinity.
(e) does : this is true and is known as the monotone convergence theorem.
Answer:
perimeter = 56 m
area= 196 m^2
Step-by-step explanation:
perimeter = 4 x sides = 4 x 35(2/5) = 4 x 14 = 56 m
area= sides^2 = (35 x = 14^2 = 196 m^2
Answer:
a)
b)
c) For this case we can use the slope from the linear model to answer this question, the 0.95 on this case represent the increase in the hourly pay rate per each year of experience, for example if we have one year of experience the pay rate increase 0.95. So then the answer for this case is 0.95.
Step-by-step explanation:
Assuming the following question: "The scatter plot shows the number of years of experience, x, and the hourly pay rate, y, for each of 25 cashiers in Ohio. x represent the number of years of experience and y the hourly pay rate. The line adusted is: y=0.95x+7.95, to answer the questions below. Give exact answers, not rounded approximations. "
(a) What is the predicted hourly pay rate for a cashier with 7 years of experience?
For this case we can use the lineal model given:
And we can replace x =7 years and we got:
(b) What is the predicted hourly pay rate for a cashier who doesn't have any experience?
For this case we just need to replace in the linear model x=0 since that means no experience and we got:
(c) For an increase of one year of experience, what is the predicted increase in the hourly pay rate?"
For this case we can use the slope from the linear model to answer this question, the 0.95 on this case represent the increase in the hourly pay rate per each year of experience, for example if we have one year of experience the pay rate increase 0.95. So then the answer for this case is 0.95.