Suppose the juice boxes go on sale for $1.79 for the eight 4.23-ounce

A box with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. The box is

MAXImum [283]

Answer:

Width is 12 inches and height is 4 inches.

Step-by-step explanation:

Let the width of the piece of cardboard be = w inches

Then length is = $w+12$ inches

As given, 4 inch squares are cut from each corner;

So, the width is = $w-8$ inches

Length is = $w+12-8=w+4$ inches

When we are folding the cut portion, that gives the height as = 4 inches

The volume is given by : length x width x height

And volume is given as 256 cubic inches

So, $256=(w+4)(w-8)(4)$

=> $256=(w^{2}-4w-32)4$

=> $64=(w^{2}-4w-32)$

=> $w^{2} -4w=96$

or $w^{2} -4w-96=0$

=> $w^{2} -12w+8w-96=0$

=> $w(w-12)+8(w-12)=0$

We get , $(w+8)=0$ ; w = -8(neglect the negative value)

$(w-12)=0$ ; w = 12 inches

And length = $12+12=24$ inches

Hence, dimensions are : L = 24 inches ; w = 12 inches and h = 4 inches

We can check by putting these values in equation : $256=(w+4)(w-8)(4)$

$256=(12+4)(12-8)(4)$

=> $256=(16)(4)(4)$

=> $256=256$

5 0

3 years ago

Evaluate the expression 7x2y, when x = 4 and y = 2. 112 224 542 718

cricket20 [7]

Answer:

224

Step-by-step explanation:

Substitute x = 4 and y = 2 into the expression and evaluate

7x²y = 7 × 4² × 2 = 7 × 16 × 2 = 7 × 32 = 224

5 0

3 years ago

Read 2 more answers

Help me find the slope please guys Im struggling

tatuchka [14]

Answer:

negative 1

Step-by-step explanation:

$\frac{y2 - y1}{x2 - x1} = m$

the 2 points: (-2,0), (-3,1)

(1-0)/(-3+2)

=-1

m=-1

brainliest please

7 0

3 years ago

Paul is three times as old as Mary and Peter is four times as old as Mary,If the sum of their ages is 64, how old are Peter,Paul

uysha [10]

Let Mary's age be x.

Paul is three times as old as Mary, so Paul's age would be 3x.

Peter is four times as old as Mary, so Peter's age would be 4x.

The sum of their ages is 64
⇒ Paul's age+ Peter's age+ Mary's age= 64
⇒ 3x+ 4x+ x= 64
⇒ 8x= 64
⇒ x= 64/8
⇒ x= 8

Paul's age is: 3x= 3*8= 24

Peter's age is: 4x= 4*8= 32

Final answer: Paul is 24 years old.
Peter is 32 years old.
Mary is 8 years old.

Hope this helps~

7 0

3 years ago

How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?

lidiya [134]

Q. How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?

Solution:

Here we are given with the sides of the triangle as 5m, 16m and 5.

As the Triangle inequality we know that

The sum of the length of the two sides should be greater than the length of the third side. But this inequality fails here.

Hence no triangle can be made.

So the correct option is None.

Q.How many triangles can be constructed with sides measuring 6 cm, 2 cm, and 7 cm?

Solution:

Here we are given with the sides of the triangle as 6m, 2m and 7m.

As the Triangle inequality we know that

The sum of the length of the two sides should be greater than the length of the third side. The given values follows the triangle inequality.

Hence one triangle can be formed.

So the correct option is one.

8 0

3 years ago