Four feet less than twice its width? what does this mean? can i get the formula and steps?

Let's get a feel for what information we need for this problem. We ultimately want to find the dimensions of the mural. What we know are

Let's see how this information can help us through the different parts of the problem.

A good place to start is with naming our variables so we can start to put together equations. Let's call our length l and our width w. We're told that l is "four feet less than twice" w, or symbolically:

l = 2w - 4

Any time we have to use an l, we're now able to substitute the expression 2w - 4 instead.

Again, let's start with giving our function a name. If we call the area of the mural A, we use the abbreviation A(w) to mean "A as a function of w," or "A of w" for short.

We know that the area A of a rectangle is normally just its length times its width - A = lw - but sense we want this function as a function of w alone, we can replace l with the expression 2w - 4 from earlier to give us

A(w) = (2w - 4)w = 2w² - 4w

We're finally ready to tackle this problem's main question. Our function from the last section tells us what the area of the mural is entirely in terms of w, and the first section tells us how to find l if we already know w. Going back to one of the first bullet points, we also know that the area of the mural is 70 ft², so we can say that we want to know what w is when A(w) = 70, or equivalently, when

2w² - 4w = 70

To solve for w, we can first divide away a 2 on either side, leaving us with

w² - 2w = 35

or equivalently,

w(w - 2) = 35

The only value w can be to make this true is 7, since 7(7 - 2) = 7(5) = 35, so we know that the width must be 7 ft. The area is 70 ft², so the length of the mural must be 10 ft., since 7 x 10 = 70.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

37 = ending with 7

unit's digit in the cube..3

56 = ending with 6

unit's digit in the cube..2

133 = ending with

unit's digit in the cube..7

hope it : ( : )