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3 years ago

If 3 times a square of an integer is added to 1 times the integer, the result is 2

1 answer:

6 0

Let unknown integer be n.

So then your sentence would translate to 3n² + n = 2.

If you need to solve for n then we can move 2 to left side by subtract both sides by 2:

3n² + n - 2 = 0

Now you can factor:

3n² + 3n -2n - 2 = 0

3n( n + 1 ) - 2( n + 1 ) = 0

( 3n - 2 )( n + 1 ) = 0

3n - 2 = 0 OR n + 1 = 0

3n = 2 OR n = -1

n = 2/3 OR n = -1

Final answer: n = 2/3 OR n = -1

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How many eggs in 3 and a half dozen?

MariettaO [177]

42.
As
1 dozen is 12 eggs, 3 dozens of the eggs is 12×3=36.
half of a dozens is 6 so
36+6 =42

6 0

3 years ago

Read 2 more answers

12a^3b^2 +18a²b^2 – 12ab^2 Factor completely

AleksAgata [21]

The factorization of 12a^3b^2 +18a²b^2 – 12ab^2 is $6 a b^{2}(a+2)(2 a-1)$

Solution:

Given, expression is $12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}$

We have to factorize the given expression completely.

Now, take the expression

$12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}$

Taking $b^2$ as common term,

$b^{2}\left(12 a^{3}+18 a^{2}-12 a\right)$

Taking "a" as common term,

$b^{2}\left(a\left(12 a^{2}+18 a-12\right)\right)$

Taking "6" as common term,

$b^{2}\left(a\left(6\left(2 a^{2}+3 a-2\right)\right)\right)$

Splitting "3a" as "4a - a" we get,

$b^{2}\left(a\left(6\left(2 a^{2}+4 a-a-2\right)\right)\right)$

$\begin{array}{l}{b^{2}(a(6(2 a(a+2)-1(a+2))))} \\\\ {b^{2}(a(6((a+2) \times(2 a-1))))} \\\\ {6 a b^{2}(a+2)(2 a-1)}\end{array}$

Hence, the factored form of given expression is $6 a b^{2}(a+2)(2 a-1)$

4 0

3 years ago

How much would $600 invested at 8% interest compounded continuously be worth after 3 years? Round your answer to the nearest cen

eduard

Answer:

yes

Step-by-step explanation:

You just do it

5 0

3 years ago

Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t

Ilia_Sergeevich [38]

Answer: 220

Step-by-step explanation:

Children (x): $2

Teens (y): $3, $\frac{3}{4}x$

Adults: (z): $5

Quantity: x + y + z = 570 ⇒ x + $\frac{3}{4}x$ + z = 570 ⇒ 1.75x + z = 570

Cost: 2x + 3y + 5z = 1950 ⇒ 2x + 3 $(\frac{3}{4}x)$ + 5z = 1950 ⇒ 2x + 2.25x + 5z = 1950 ⇒ 4.25x + 5z = 1950

Qty: 1.75x + z = 570 → 5(1.75x + z = 570) → 8.75x + 5z = 2850

Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → -4.25x - 5z = -1950

4.50x = 900

x = 200

Teens (y): $\frac{3}{4}x$

y = $\frac{3}{4}(200)$

= $\frac{600}{4}$

= 150

Quantity: x + y + z = 570

200 + 150 + z = 570

350 + z = 570

z = 220

6 0

3 years ago

You have 420 saved for retirement. Your account earns 18% interest. How much will you be able to pull out each month, if you wan

forsale [732]

Answer:

495.6

Step-by-step explanation:

18% of 420 is 75.6. Multiply that by 63 to get 4762.8. 420 multiplied by 63 equals 26460. 26460 plus 4762.8 is 31222.8. 31222.8 divided by 63 is 495.6. So the answer is $495.60 per year.

6 0

3 years ago