Add the linear expressions: 2n + 6 and 6n -2

Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut

Slav-nsk [51]

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let <em>l</em> represent the length of the box and let <em>w</em> represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, <em>h</em>, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

4 0

3 years ago

Find the number of ways you can arrange (a) all of the letters and (b) two of the letters in the word TRY. a. The number of ways

Phantasy [73]

Answer:

a) 6 ways

b) 6 ways

Step-by-step explanation:

a) for all of the letters

for the first letter, we have 3 options

for the second, we have 2 options

for the third, we have 1 option

So the number of options will be;

3 * 2 * 1 = 6

b) for the first, we have 3 options, for the second, we have 2 options

so the number of options will be 3 * 2 = 6 options

8 0

2 years ago

You leave an 22% tip on a $54 bill. How much did you pay?

notka56 [123]

Answer:

You will pay $65.88 in total

Step-by-step explanation:

Bill amount: $54
Tip: 22% = $54 * 0.22 = $11.88

Sum up: $54 + $11.88 = $65.88

6 0

2 years ago

Name the pair of opposite rays with endpoint N.

Elza [17]

Answer:

<h2>Possible Answers: NA and NX or NM and NC.</h2>

Step-by-step explanation:

PLS MARK ME BRAINLEIEST AND FLW ME

3 0

3 years ago

Graph the solution set of this inequality: 5x − 4y > 20.

Yanka [14]

Answer:

Step-by-step explanation:

Solve the inequality 5x − 4y > 20 for y, as follows: Subtract 5x from both sides, obtaining:

-4y > 20 - 5x;

Then divide all terms by -4:

y < -5 +(5/4)x, where the direction of the inequality sign has been reversed because of division by a negative quantity.

Temporarily replace the < symbol with = obtaining y = -5 +(5/4)x. Now choose at least three x values and find the corresponding y values. For example:

x y = -5 +(5/4)x

0 -5

4 0

-8 -15

Now plot these three points (0, -5), (4, 0) and (-8, -15). Draw a dashed line through them. Because of the < symbol in y < -5 +(5/4)x, shade the area underneath the dashed line.

3 0

3 years ago