-144 is -1 x 2a x 3b what is the sum of a+b?

1 answer:

7 0

-144= -1×2a×3b
144=2a×3b
144= 6ab
24= ab

a,b could b any two factors that have a product of 24
For example a,b could = 6,4 or 8,3 or 24,1

Answer:
This question is tricky because it could have multiple answers: for example is a,b= 6,4 then a+b= 10, but if a,b=24+1=25. So, the answer is that the sum of a+b varies depending on which 2 factors of 24 a and b are equal to. Does this make sense?

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I am a number greater than 40,000 and less than 60,000. My ones digit and tens digit are the same. My ten-thousands digit is 1 l

jarptica [38.1K]

I am a number greater than 40,000 and less than 60,000:

40,000 < n < 60,000

This means that:

n = 10,000n₁ + 1,000n₂ + 100n₃ + 11n₄

And also:

4 ≤ n₁ < 6

0 ≤ n₂ ≤ 9

0 ≤ n₃ ≤ 9

0 ≤ n₄ ≤ 9

My ten thousands digit is 1 less than 3 times the sum of my ones digit and tens digit:

n₁ = 3*2n₄ - 1

n₁ = 6n₄ - 1

This means that:

n = 10,000*(6n₄-1) + 1,000n₂ + 100n₃ + 11n₄

n = 60,000n₄ - 10,000 + 1,000n₂ + 100n₃ + 11n₄

n = 60,011n₄ - 10,000 + 1,000n₂ + 100n₃

My thousands digit is half my hundreds digit, and the sum of those two digits is 9:

n₂ = 1/2 * n₃

n₂ + n₃ = 9

Therefore:

n₂ = 9 - n₃

Therefore:

9 - n₃ = 1/2 * n₃

9 = 1/2 * n₃ + n₃

9 = 1.5 * n₃

Therefore:

n₃ = 6

If n₃=6, n₂=3.

This means that:

n = 60,011n₄ - 10,000 + 1,000*3 + 100*6

n = 60,011n₄ - 10,000 + 3,000 + 600

n = 60,011n₄ - 6,400

Therefore:

0<n₄<2, so n₄=1.

If n₄=1:

n = 60,011 - 6,400

n = 53,611

Answer:

53,611

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3 years ago

Show work and explain with formulas:

Marina86 [1]

17 Answer: 205

Step-by-step explanation:

$\{1\dfrac{2}{3}+1\dfrac{5}{6}+2+...+8\dfrac{1}{3}\}\implies a_1=1\dfrac{2}{3},\ d=\dfrac{1}{6}\\\\\\a_n=a_1+d(n-1)\qquad solve\ for\ n\\\\8\dfrac{1}{3}=1\dfrac{2}{3}+\dfrac{1}{6}(n-1)\\\\\\\dfrac{25}{3}=\dfrac{5}{3}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{50}{6}=\dfrac{10}{6}+\dfrac{1}{6}n-\dfrac{1}{6}\\\\\\\dfrac{41}{6}=\dfrac{1}{6}n\\\\\\\dfrac{41}{6}\cdot 6=n\\\\41=n$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{41}=\dfrac{1\dfrac{2}{3}+8\dfrac{1}{3}}{2}\cdot 41\\\\\\.\quad =\dfrac{10}{2}\cdot 41\\\\\\.\quad =5\cdot 41\\\\.\quad =\large\boxed{205}$

18 Answer: 1968

Step-by-step explanation:

$a_1=-6,\ d=2,\ n=48, \quad \text{solve for }a_{48}\\\\a_{n}=a_1+d(n-1)\\\\a_{48}=-6+2(48-1)\\\\.\quad =-6+2(47)\\\\.\quad =-6+94\\\\.\quad =88$

$\text{Now use the sum formula:}\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\S_{48}=\dfrac{-6+88}{2}\cdot 48\\\\\\.\quad =\dfrac{82}{2}\cdot 48\\\\\\.\quad =41\cdot 48\\\\.\quad =\large\boxed{1968}$

19 Answer: -116

Step-by-step explanation:

$\{3, -2, -7, ...\}\\a_1=3,\ d=-5,\ n=8, \quad \text{solve for }a_{8}\\\\a_{n}=a_1+d(n-1)\\\\a_{8}=3-5(8-1)\\\\.\quad =3-5(7)\\\\.\quad =3-35\\\\.\quad =-32\\\\\text{Now use the sum formula:}\\\\S_8=\dfrac{a_1+a_8}{2}\cdot 8\\\\\\S_{8}=\dfrac{3-32}{2}\cdot 8\\\\\\.\quad =\dfrac{-29}{2}\cdot 8\\\\\\.\quad =-29\cdot 4\\\\.\quad =\large\boxed{-116}$

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3 years ago

can mrs davis and her two sisters get their hair colored for less than $100 (cost of the hair coloring is $28.95)if they include

vodomira [7]

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3 years ago

Read 2 more answers

What is the completely factored form of x^4+8x^2-9

miss Akunina [59]

Answer:

I think it is (x^2+9) x (x-1) x (x+1)

Step-by-step explanation:

(not sure if right but had a go)

7 0

3 years ago

Item 8

ludmilkaskok [199]

So, I didn't quite understand your question clearly, but I'll try my best to answer it.

So, the first question is quite simple: Did the runner have a % decrease in his time or an increase.
Well, 7:45 is minor than 5:51. So, his time decreased.

2nd question:
The percent of change. Well, first things first 7:45 has 2 different units, wich are minutes and seconds, I suppose. Same goes for 5:51.
So let's put everything in seconds. multiply both the 7 and 5 for 60(for every minute has 60 seconds.)

That means:
7*60= 420+45 = 465.
5*60=300+51=351.

Now, let's do the math itself:
465 -> 100%
351 -> x%
Is equal to about 75,5%
How much did it decrease then?
(75,5-100)%= 24,5%, approximately

8 0

3 years ago