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lys-0071 [83]
3 years ago
14

Recall the shipping box scenario from the Introduction. As an employee of a sporting goods company, you need to order shipping b

oxes for bike helmets. Each helmet is packaged in a box that is n inches wide, n inches long, and 8 inches tall. The shipping box you order should accommodate the boxed helmets along with some packing material that will take up an extra 2 inches of space along the width and 4 inches of space along the length. The height of the shipping box should be the same as the helmet box. The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Mathematics
1 answer:
7nadin3 [17]3 years ago
8 0

Answer:

The dimensions of the helmet box are as follows

Width is 9 inches

Length is 9 inches

Height is 8 inches

The dimensions of the shipping box ordered are as follows;

Width is 11 inches

Length is 13 inches

Height is 8 inches

Step-by-step explanation:

8(n + 2)(n + 4) = 1144

8·n² + 48·n + 64 = 1144

8·n² + 48·n - 1080 = 0

8×(n - 9)×(n + 15) = 0

∴ n = 9 or -15 inches

The dimensions of the helmet box are as follows

Width = 9 in.

Length = 9 in.

Height = 8 in.

The dimensions of the shipping box ordered are as follows;

Width = 9 + 2 = 11 in.

Length = 9 + 4 = 13 in.

Height = 8 in.

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notsponge [240]

Answer:

2 batches of orange water = 6 tablespoon of yellow water and 2 tablespoon of red water

4 batches of orange water = 12 tablespoon of yellow water and 4 tablespoon of red water

Step-by-step explanation:

1 batch

Yellow water = 3 teaspoons

Red water = 1 teaspoons

Yellow water : Red water = 3 : 1

2 batches of orange water

Multiply the ratios by 2

Yellow water : Red water

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2 batches of orange water = 6 tablespoon of yellow water and 2 tablespoon of red water

4 batches of orange water

Multiply the ratios by 4

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= (3 : 1) * 4

= 12 : 4

4 batches of orange water = 12 tablespoon of yellow water and 4 tablespoon of red water

4 0
3 years ago
f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2
iren2701 [21]

Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4,\infty)

g(x)=2x^2+8x+6=2(x^2+4x+3)

g(x)=0

2(x^2+4x+3)=0

x^2+4x+3=0

x^2+3x+x+3=0

x(x+3)+1(x+3)=0

(x+1)(x+3)=0

x+1=0\implies x=-1

x+3=0\implies x=-3

Therefore, x-intercept of g(x) at (-1,0) and (-3,0).

Substitute x=-2

g(-2)=2(-2)^2+8(-2)+6=8-16+6=-2

g(x)=2(x^2+4x)+6

g(x)=2(x^2+2\times x\times 2+4-4)+6=2(x^2+2\times x\times 2+4)-8+6

g(x)=2(x+2)^2-2

By comparing with the equation of parabola

y=a(x-h)^2+k

Where vertex=(h,k)

We get vertex of g(x)=(-2,-2)

Range of g(x)=[-2,\infty)

Zeroes of f and g are same .

But range of f and g are different.

Range of f contains -3 and -4 but range of g does not contain -3 and -4.

f and g are both quadratic functions.

3 0
3 years ago
8. what is the graph of the inequality in the coordinate plane? <br><br> y&lt;-2
LekaFEV [45]
1) Draw the coordinate plane

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3) The solution (graph of the inequality y < - 2) is all the area below the line y = - 2.
4 0
3 years ago
What’s the equation for g(x)
taurus [48]

Answer:

g(4)=10

Step-by-step explanation:

4 0
3 years ago
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account
Yuki888 [10]
Formula for amount for compound interest:

Amount, A =  P(1 + r/100)^n

Where r is rate, P is principal, and n is the number of years.

P = 2000, r = 5, n = t years.

A = 2000( 1 + 5/100)^t

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A = 2000(1.05)^t

A(t) = 2000(1.05)^t

None in the option look like the answer we have.

Except you didn't type the last option correctly.    

5 0
4 years ago
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