Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
Answer:
The inequality is equivalent to x(x+2)(x−3)>0 , with the additional conditions that x≠0 and x≠3 .
Since x(x+2)(x−3) only changes signs when crossing −2 , 0 and 3 , from the fact that the evaluating the polynomial at 4 yields 24 , we see that the polynomial is
positive over (3,∞)
negative over (0,3)
positive over (−2,0)
negative over (−∞,−2)
Thus the solution set for your inequality is (−2,0)∪(3,∞) .
Step-by-step explanation:
hi Rakesh here is your answer :)
#shadow
Good morning ☕️
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Answer:
4
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Step-by-step explanation:
Just solve the equation 5-√x = 3
So, let’s solve it:
5-√x = 3 ⇔ 5-3=√x ⇔ √x = 2 ⇔ x=4
Then ?=4
:)
Answer:
y = 10x + 6.
Step-by-step explanation:
y = mx + c
Here the slope m = 10 and c = 6 ( the y-intercept)
It's 6 because the point (0, 6) lies on the y-axis (where x = 0).
Answer:
£312
Step-by-step explanation:
Amount spent on 60 jumpers = £120
80% of the jumpers :
0.8 * 60 = 48 jumpers
Sales price for 80% = £8 each
Total = £8 * 48 = £384
The remain at an half price offer :
Half price = £8 / 2 = £4
£4 * (60 - 48)
£4 * 12 = £48
Total sales revenue = £(48 + 384) = £432
Total profit made :
Total sales revenue - purchase price
£432 - £120
= £312
