Answer:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
= 
[2a + (n - 1)d ]
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
= [(2 × 5) + 2(n - 1) ]
= (10 + 2n - 2)
= (2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
Total = 36oz
Amount of 18% solution = x
Amount of 9% solution = 36 - x
Using the fact that (amount of solution) * (percent HCl) = amount HCl we can set up an expression for the amount HCl in a mixture of 18% and 9% solutions with a total volume of 36oz.
Amount of HCl = x*0.18 + (36 - x)*0.09
If we divide this by the amount of solution we get percent HCl, and we have a target of 10% HCl. Now we have an equation to solve,
[x*0.18 + (36 - x)*0.09]/36 = 0.1
x*0.09 + 3.24 = 3.6
.09x = 0.36
x = 4
Therefore,
4 ounces of 18% HCl solution and 32 ounces of 9% HCl solution
Check:
[(4*.18) + (.09*32)]/36 = 0.1?
0.1 = 0.1 Yes.
Answer:
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Step-by-step explanation:
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Answer: 12√2 cm
<u>Step-by-step explanation:</u>
Cube 1: V = 6³ = 216
Cube 2: V = 8³ = 512
Cube 3: <u>V = 10³ = 1000</u>
New Cube: V = 1728
1728 = s³
12 = s
So, each side of the new cube is 12 cm.
Use Pythagorean Theorem to find the length of the diagonal:
12² + 12² = diagonal²
144 + 144 = diagonal²
288 = diagonal²
√288 = diagonal
12√2 = diagonal
8x=6x+20
Btw I figures it out x=10
