MATHEMATICS HIGH SCHOOL

Dixie packaging co has contracted to manufacture a box with no top that is to be made by removing squares of width x from the corners of a 15-in by 60-in piece of cardboard.a) Write a function for the VOLUME of the box as a function of x.

b) Determine x so that the volume of the box is at least 450 cubic inches.

c) Determine x so that the volume of the box is maximum.

Answers

Answer 1

Answer:

The volume of the box as a function of x V(x) = x ( 60 -2x )( 15-2x )

The volume of the box as a function of x inches 0.55 inches ≤ x ≤ 6.79

The volume of the box is maximum x ≥ 6.79 inches

Given ,

The box with no top that is to be made by removing squares of width x

The corners of a 15-in by 60-in piece of cardboard.

Volume can be represented by this function below

V(x) = x ( 60 -2x )( 15-2x )

Where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width

The volume of the box as a function of x is V(x) = x ( 60 -2x )( 15-2x )

To determine x so that,

The volume of the box ≥ 450 inches

V(x) = x ( 60 -2x )( 15-2x )

The volume of the box is at least 450 cubic inches.0.55 inches ≤ x ≤ 6.79 inches

The value of x for which volume of the box is maximum will be x ≥ 6.79 inches.

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Answer 2

Answer:

Answer:

a) V(x) = x ( 60 -2x )( 15-2x )

b) 0.55 inches ≤ x ≤ 6.79 inches

c) x ≥ 6.79 inches

Step-by-step explanation:

Given data:

No top, cardboard dimensions ; 15-in by 60-in

a) A function for the volume of the box as a function of x the Volume can be represented by this function below

= V(x) = x ( 60 -2x )( 15-2x )

where : x = height , ( 60 - 2x ) = length , ( 15 -2x ) = width

b) determine x so that the volume of the box ≥ 450 inches

450 = x( 60 - 2x ) ( 15 -2x ) ( solving the equation )

0.55 inches ≤ x ≤ 6.79 inches

c ) The value of x for which volume of the box is maximum

will be x ≥ 6.79 inches

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What value or values of x satisfy 2|x+5.3|=4.2a. x can only equal –3.2.
b. x can only equal 7.4.
c. x can equal –3.2 or –7.4.
d. x can equal –3.2 or 7.4.

Answers

we have

$2\left|x+5.3\right|=4.2$

Step 1

Find the first solution (case positive)

$2(x+5.3)=4.2$

Eliminate the parenthesis left side

$2x+10.6=4.2$

Subtract $10.6$ both sides

$2x=4.2-10.6$

$2x=-6.4$

Divide by $2$ both sides

$x=-3.2$

Step 2

Find the second solution (case negative)

$2[-(x+5.3)]=4.2$

Eliminate the parenthesis left side

$-2x-10.6=4.2$

Adds $10.6$ both sides

$-2x=4.2+10.6$

$-2x=14.8$

Divide by $-2$ both sides

$x=-7.4$

therefore

the answer is the option C

x can equal –3.2 or –7.4

We have, /x+5.3/ = 2.1;
Then, x + 5.3 = 2.1 or x + 5.3 = -2.1;
x = 2.1 - 5.3; x = -3.2;
x = -2.1-5.3; x = -7.4;
The correct answer is c.

Choose the correct simplification of the expression (−2x + 8y)(9x − 3y).−18x2 + 78xy − 24y2
18x2 + 78xy − 24y2
−18x2 − 78xy + 24y2
−18x2 + 72xy − 24y2

Answers

For these kinds of expressions use FOIL (first, outside, inside, last).

-2x • 9x = -18x^2
-2x • -3y = 6xy
8y • 9x = 72 xy
8y • -3y = -24y^2

Now combine them all:

-18x^2 + 78xy - 24y^2

Answer:

The answer is A I just took the test

Step-by-step explanation:

Who procrastinates to study✋

Answers

Hi There! :)

Who procrastinates to study

ME!!!!

3(5 − 2x) = −2(6 – 3x) − 10x

Answers

3(5-2x) = -2(6-3x)-10x
15-6x = -12+6x-10x
15-6x = -12-4x
-2x = -27
x = 27/2

I think the answer is 27/2

Add an explanation on how to get the right answer and I will give out Brainliest

Answers

Answer:

=439.04 ft^2

Step-by-step explanation:

First find the area of the total rectangle

A = l*w

40*16 =640 ft^2

We have 2 semi circles with diameter 16

That equals 1 circle with diameter 16

The radius is d/2 = 16/2 =8

The area of a circle is

A = pi r^2

A = (3.14) (8)^2

=200.96

Subtract the unshaded area from the total area

640-200.96=439.04

Solve the proportion. 10/a =15/30
a. 2
b. 5
c. 20
d. 10

Answers

multiply the denominators by 30a.
300=15a
a=20
so the correct answer is C

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