HELP PLEASE DUE IN 3 MINUTES

Your hair is growing at 1 inch per month. You got your hair cut to 4 inches in length. Write and equation that gives the length

Korvikt [17]

Answer:

Your hair grows 2 to 4 inches in 4 months, 4 to 6 inches in 9 months, and 6 to 8 inches in a year. Though this is how the usual growth cycle works, it also depends on seasonal changes, hair and scalp health, medications, hormonal changes, and diet among other factors.

Step-by-step explanation:

7 0

2 years ago

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat

NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

35x = -0.05(x² - 800x + 160000) + 9492

35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

35x = -0.05x² +40x - 8000 + 9492

35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

$x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492} }{2X0.05} = \frac{5 +/- \sqrt{25 + 298.4} }{0.1} = \frac{5 +/- \sqrt{323.4} }{0.1}\\= \frac{5 +/- 17.983 }{0.1}\\= \frac{5 - 17.983 }{0.1} or \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or \frac{22.983 }{0.1}\\= -129.83 or 229.83$

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0

3 years ago

Read 2 more answers

If (x - h) = 4 and (y - k) = 3, what is the radius of the circle above?

I am Lyosha [343]

(x-h)²+(y-k)²=r² is the equation of a circle with radius of r

so if x-h=4 and y-k=3 then

4²+3²=r²
16+9=r²
25=r²
sqrt both sides
5=r
radius is 5 units

5 0

2 years ago

5 7/10 x 6 1/9 simplify

Softa [21]

Answer:

34 5/6

Step-by-step explanation:

Convert the mixed numbers into improper fractions:

57/10 × 55/9

We can reduce these fractions by using the greatest common factor, 3

19/2 × 11/3

Multiply

19/2 × 11/3 = 209/6

Convert to mixed number

209/6 = 34 5/6

4 0

2 years ago

A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The near

Serga [27]

Answer:

T.C ( 1.1007 ) = T.C_min = $2252

Step-by-step explanation:

Given:

- Cost of electricity construction over water C_w = $250 / mile

- Cost of electricity construction over ground C_w = $150 / mile

- The distance from hotel island = 3.5 miles

- The distance from beach to power source = 10 miles

Find:

Find the least expensive price for which you can bill the job

Solution:

- This problem requires cost optimization. So we need to develop a cost function as follows

Total Cost = C_w*(distance from island to x) + C_g*( distance from x to power)

- Now calculate the relevant distances using Pythagoras theorem:

Distance from island to x = sqrt ( x^2 + 3.5^2 )

Distance from x to power station = 10 - x

- Input the distances in the cost function:

T.C ( x ) = C_w*sqrt ( x^2 + 3.5^2 ) + C_g*(10 - x )

- Input the relevant rates:

T.C ( x ) = 250*sqrt ( x^2 + 3.5^2 ) + 150*(10 - x )

- Simplify:

T.C ( x ) = 250*sqrt ( x^2 + 12.25 ) + 1500 - 150x

- Next, we will optimize the cost to minimum. We need the distance x that would give us the minimum cost. To minimize the function, set its derivative with respect to x equals to zero.

T.C' ( x ) = 500*x*( x^2 + 12.25 )^( -0.5 ) - 150

- Set the derivative to zero and solve for x:

sqrt ( x^2 + 12.25 ) = 10x/3

Squaring both sides:

9*x^2 + 110.25 = 100*x^2

Simplify and solve:

x = sqrt (110.25 / 91) = 1.1007 miles

- The cost function is minimized at x = 1.1007 miles. We will input this back into our function and evaluate the minimum cost as follows:

T.C ( 1.1007 ) = 250*sqrt ( 1.1007^2 + 12.25 ) + 1500 - 150*1.1007

T.C ( 1.1007 ) = T.C_min = $2252

- So the minimum cost associated with this plan is $2252.

6 0

2 years ago