MATHEMATICS HIGH SCHOOL

An open box is to be made from a rectangular piece of tin by cutting 3-inch squares out of the corners and folding up the sides. The length of the piece of tin is twice the width. The volume of the box will be 60 cubic inches. Find the dimensions of the original rectangular piece of tin

Answers

Answer 1

Answer:

Answer:

Width of the Rectangular Tin=8 inch

Length of the Rectangular Tin= 16 inch

Step-by-step explanation:

Let the Width of the Rectangle=W

The length of the piece of tin is twice the width, Length = 2W

Since Squares of 3 inch are cut from all four corners of the rectangle

Length of the box = 2W-(3+3)=(2W-6) inches

Breadth of the Box = W-(3+3)=(W-6) inches

Height = 3 inches

Volume of the box = 60 cubic inches

Now, Volume of a cuboid=lbh

3(2W-6)(W-6)=60

Divide both sides by 3

(2W-6)(W-6)=20

Expanding the brackets

$(2W-6)(W-6)=20\n2W^2-12W-6W+36=20\n2W^2-18W+36-20=0\n2W^2-18W+16=0$

Factorizing

$2W^2-16W-2W+16=0\n2W(W-8)-2(W-8)=0\n(W-8)(2W-2)=0\nW-8=0 , 2W-2=0\nW=8, 1$

Since the Width cannot be less than 6,

Width of the Rectangular Tin=8 inch

Length= 2 X 8 = 16 inch

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the width of a rectangle is 33 centimeters. the perimeter is atleast 776 centimeters. write and solve an inequality to find the possible lengths of the rectangle

A bar graph in which the bars are arranged in frequency order is
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It is a histogram because they are by frequency.

When you graph an inequality, you used a closed dot when you use which
symbols?

Answers

You should only use a closed dot for the symbols ≤ and ≥.

When you should use a closed dot?

There are two types of dots used when graphing inequalities, closed and open.

We use closed dots when the value where the dot is, is a solution.
We use open dots when the velue where the dot is, is not a solution.

So, for exampe in:

x > 3.

We would put an open dot at 3, because the value x = 3 is not a solution, but all the values at the right of the 3 are solutions.

In the other hand, for:

x ≥ 3

Now 3 is in fact a solution, so here we should use a closed dot.

Then, answering the question.

"When you graph an inequality, you used a closed dot when you use which symbols?"

The ≤ and ≥ symbols.

If you want to learn more about inequalities, you can read:

brainly.com/question/11234618

You use a closed dot with the greater than or less than with the line under the symbol or the greater than or equal to or the less than or equal to symbols. The line indicates a closed dot.

Select the correct answer.The function f(x) is given by the table of values.

x 1 2 3 4
f(x) 1 8 27 64
If f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?

x 5 6 7 8
g(x) 5 12 31 68

x 1 2 3 4
g(x) 5 12 31 68

x 5 6 7 8
g(x) 1 8 27 64

x 1 2 3 4
g(x) 4 32 108 256

Answers

The solution is Option B.

x = { 1 , 2 , 3 , 4 }

g(x) = { 5 , 12 , 31 , 68 }

The function g ( x ) = x³ + 4

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

when x = 1

f ( x ) = 1

when x = 2

f ( x ) = 8

when x = 3

f ( x ) = 27

when x = 4

f ( x ) = 64

So , the equation will be y = x³ be equation (1)

Now , f(x) is shifted 4 units up to obtain g(x)

So , Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

when x = 1

g ( x ) = 1 + 4 = 5

when x = 2

g ( x ) = 8 + 4 = 12

when x = 3

g ( x ) = 27 + 4 = 31

when x = 4

g ( x ) = 64 + 4 = 68

Therefore , the function is g ( x ) = x³ + 4

Hence , the function is g ( x ) = x³ + 4

To learn more about transformation of a function click :

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#SPJ2

Answer:

The second answer is correct.

Step-by-step explanation:

So g(x) = f(x) + 4

If f(x) = 1, 8, 27, and 64 then g(x) = 5, 12, 31, and 68.

What is the remainder when (2x3 + 4x2 – 32x + 18) ÷ (x + 3) ?2

12

96

110

Answers

For the answer to the question above,

Let f(x)=2x3 + 4x2 − 32x +1 8

The remainder when f(x) is divided by (x−a) is f(a).

So when divide by (x + 3 ) = (x − (−3)) the remainder is:

f(−3) = 2(−27) + 4(9)− 32 (−3) +18=−54 +3 6 + 96 + 18 =96Yes, the remainder is 96I hope my answer helped you

96 because if you use synthetic or long division the remainder will be 96

Is relation t a function? Is the inverse of relation t a function? Relation t:

x; 0 , 2 , 4 , 6
y; -10 , -1 , 4 , 8

Relation t is not a function. The inverse of relation t is not a function.

Relation t is a function. The inverse of relation t is a function.

Relation t is a function. The inverse of relation t is not a function.

Relation t is not a function. The inverse of relation t is a function.

Answers

A set of points can be classified as a function using the vertical test rule which tells that a function should pass a vertical test such that no to points lie on the same vertical line. This means no two points should have the same x. In this case, the set of points project a function as well as its inverse. Hence the answer is B.

PLEASE ANSWER QUICKLY! I WILL GIVE BRAINLIEST. What is 5/6 of 1/2?

A. 5/12
B. 6/12
C. 5/8
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