# A small company that manufactures snowboards uses the relation below to model its profit. In the model,represents the number of snowboards in thousands, and P represents the profit in ten thousands of dollars.What is the maximum profit the company can earn? How many snowboards must it produce to earn thismaximum profit?a. Factor P =4x2 + 32x + 336 to find the roots.b. Find the axis of symmetry then use it to find the vertex.c. Therefore, we need to see snowboards to make a maximum profit of

a)   x₁ = 14

x₂ = - 6

b) x = 4

c) P(max ) = 4000000 \$

Step-by-step explanation:

To find the axis of symmetry we solve the equation

a) -4x² + 32x + 336 = 0

4x²  - 32x  - 336  = 0       or    x² - 8x - 84 = 0

x₁,₂ = [ -b ± √b² -4ac ]/2a

x₁,₂ = [ 8  ±√(64) + 336 ]/2

x₁,₂ = [ 8  ± √400 ]/2

x₁,₂ =( 8 ± 20 )/2

x₁  = 14

x₂ = -6

a) Axis of symmetry must go through the middle point between the roots

x = 4 is the axis of symmetry

c) P = -4x² + 32x + 336

Taking derivatives on both sides of the equation we get

P´(x) = - 8x + 32  ⇒  P´(x) = 0     - 8x + 32

x = 32/8

x = 4    Company has to sell  4 ( 4000 snowboard)

to get  a profit :

P = - 4*(4)² + 32*(4) + 336

P(max) = -64  + 128 + 336

P(max) = 400           or  400* 10000 =  4000000

## Related Questions

Which statement is true? Step by step.

The correct answer is A.  The probability of randomly selecting a daisy from Bouquet S is less than the probability of randomly selecting a daisy from bouquet T.

Step-by-step explanation:

We are told that Bouquet S contains 30 flowers and 13 of those flowers are daisies.   Therefore, the probability of selecting a daisy from Bouquet S can be modeled by:

13/30, which is greater than 1/3 but less than 1/2

We are also told that Bouquet T contains 13 flowers and 13 daises.  From this information, we can conclude that all of the flowers in Bouquet T are daises, or the probability can be modeled by:

13/13 = 1

Therefore, because the probability of selecting a daisy from Bouquet S is 13/30 and the probability of selecting a daisy from Bouquet T is 1, we can conclude that, as option A states, the probability of selecting a daisy from Bouquet S is less than the probability of selecting a daisy from Bouquet T.

Hope this helps!

I believe the answer is A.

Step-by-step explanation:

If there are 13 daises per bouquet, that means one bouquet is all daises. The other bouquet has 30 flowers. 30-13 is 17 which means there are 17 other flowers rather than daises. 17 is greater than 13 by 4 which is not that  much. Therefore I think the answer is letter A.

(2x+3)(x+1) simplified

Would love the solution worked out also thank you

(2x + 3) (x + 1)

2x² + 3x + 2x + 3

2x² + 5x + 3

Step 1

Step 2

Which set of ordered pairs could represent the same function as y = x2 ?A (1, 1), (2, 4), (3,6)
B (1,1),(3,9), (7,49)
© (1,2), (4,16), (8, 64)
D (4,8), (5, 25), (6,36)

B (1, 1),(3, 9), (7, 49)

Step-by-step explanation:

Given function:

• y = x²

Let's verify which set of pairs are same with the given function:

A....................

• (1, 1) - yes
• (2, 4) - yes
• (3, 6)  - no, 6≠ 3²

B....................

• (1, 1) - yes
• (3, 9) - yes
• (7, 49)  - yes

C....................

• (1, 2)- no, 2≠ 1²
• (4, 16) - yes
• (8, 64)  - yes

D....................

• (4, 8) - no, 8 ≠ 4²
• (5, 25) - yes
• (6, 36) - yes

9s − 5 s = 8 knnnkjbkbbhjhghuj

9*8=72

72-5=67

The final answer is 67.

Thank you

What two numbers have a least common multiple of 40 and a greatest common factor of 2?

2 and 40
Common factors
40={1,2,4,5,8,10,20,40}
2 = {1,2}

Greatest common factor =2

Common multiples
40={40,80,...}
2 = {2,4,6,8,10,...,40,42,...}

Least common multiple= 40

Find the equation for the line that passes through the points ( 1 , 1 ) and ( − 5 , 6 ) . Give your answer in point-slope form. You do not need to simplify.

Step-by-step explanation:

The equation of the line passing through (1,1) and (-5,6) is y - 1 = -5/6(x - 1).

### Explanation:

To find the equation for the line passing through the points (1, 1) and (-5, 6) in point-slope form, we need to calculate the slope and use one of the given points. The slope, denoted by 'm', can be calculated as the change in y divided by the change in x. Substituting the values (1, 1) and (-5, 6) into the slope formula, we get m = (6 - 1) / (-5 - 1) = 5 / -6 = -5/6. Using the point-slope form, y - y1 = m(x - x1), we can substitute the slope and one of the given points to obtain the equation of the line.

Using the point (1, 1), we substitute x1 = 1 and y1 = 1 into the equation. This gives us y - 1 = -5/6(x - 1).

Therefore, the equation of the line that passes through the points (1, 1) and (-5, 6) in point-slope form is y - 1 = -5/6(x - 1).