What is the expression that is equivalent to 6(3z-2)?

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.

slava [35]

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

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

Factorizing

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

Since the Width cannot be less than 6,

Width of the Rectangular Tin=8 inch

Length= 2 X 8 = 16 inch

5 0

3 years ago

Hey everyone i need your help again what's 3(11x + 5) = 279

VikaD [51]

Answer:

x = 8

Step-by-step explanation:

We can use PEMDAS to solve algebraic equations:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

First, we have parentheses in this equation, so distribute

3(11x) + 3(5) = 279

Next, because there are no exponents, multiply

33x + 15 = 279

To isolate x, subtract 15 from both sides

33x + 15 - 15 = 279 - 15

33x = 264

Then divide both sides by 33

x = 8

3 0

3 years ago

If 4(x/y + 1) = 10, what is the value of y in terms of x?<br> Plz explain

lora16 [44]

Answer:

x=1.5y

Step-by-step explanation:

4(x/y+1)=10

x/y+1=10/4

x/y+1=2.5

x/y=2.5-1

x/y=1.5

x=1.5y

7 0

4 years ago

A person on a moving sidewalk 21 feet in 7 senconds the moving sidewalk has a lenght of 180 feet. How long will it take to move

aliina [53]

Answer:

He will take 60 seconds to move from one end of the sidewalk to other.

Step-by-step explanation:

Given:

A person on a moving sidewalk,

21 feet in 7 seconds

Then 180 feet

To Find:

Total time =?

Solution:

Speed:

Speed is defined as the rate of distance covered in per unit time.

It is given as

$\textrm{Speed }=\dfrac{\textrm{Distance}}{Time}$

Substituting the given values we get

$\textrm{Speed }=\dfrac{21}{7}=3\ m/s$

Now, With this speed if he walk 180 feet then the time is

$\textrm{Time}=\dfrac{\textrm{Distance}}{Speed}$

Substituting Speed and Distance we get

$\textrm{Time}=\dfrac{180}{3}=60\\\\Time=60\ s$

He will take 60 seconds to move from one end of the sidewalk to other.

5 0

3 years ago

If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Natasha_Volkova [10]

The correct answers are:
1) sin(x) = $\frac{ \sqrt{3} }{2}$
2) tan(x) = $\sqrt{3}$

Explanation:
Given:
$cos(x) = \frac{1}{2}$

Step 1:
Since, according to the Trigonometric identity:
$sin^2(x) + cos^2(x) = 1$ -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
$sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x) = \frac{3}{4}$

Step 3:
Take square-root on both sides:
$\sqrt{sin^2(x)} = \sqrt{\frac{3}{4}}$

sin(x) = $\frac{ \sqrt{3} }{2}$

Now to find the tan(x), we would use the following formula:

tan(x) = $\frac{sin(x)}{cos(x)}$ --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = $\frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }$

Hence tan(x) = $\sqrt{3}$

6 0

3 years ago

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