4/3n=2 Solve for n Also, show work

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two

Oliga [24]

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of the rectangle is equal to

$A=x*y$

The area of the two congruent right triangles is equal to the area of the rectangle

$A=2*44=88\ in^{2}$

so

$88=x*y$ -------> equation A

$y=x-3$ -----> equation B

Substitute equation B in equation A

$x*[x-3]=88$

$x^{2} -3x-88=0$ --------> equation that can be used to solve for the length of the rectangle

Using a graph tool-------> solve the quadratic equation

see the attached figure

The solution is

$x=11\ in$ -----> the length of the rectangle

Find the value of y

$88=11*y$

$y=8\ in$ ----> the width of the rectangle

Statements

case A) The area of the rectangle is $88$ square inches

The statement is True

See the procedure

Case B) The equation $x*[x-3]=44$ can be used to solve for the dimensions of the triangle

The statement is False

Because, the equation $x*[x-3]=88$ can be used to solve for the dimensions of the triangle

case C) The equation $x^{2} -3x-88=0$ can be used to solve for the length of the rectangle

The statement is True

see the procedure

case D)The triangle has a base of $11$ inches and a height of $8$ inches

The statement is True

Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle

case E) The rectangle has a width of $4$ inches

The statement is False

See the procedure

8 0

3 years ago

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Circle C has radius of 10 cm. Each of points B and D is on the midpoint of the radius. Find the area of the shaded region.

olya-2409 [2.1K]

Simple :)
Area of shaded part = are of 1/4 circle - area of both triangles.
Are of circle = pie r^2 so 100x3.14 = 314 cm2.
Area of triangle AOB= area of triangleDOE = bh/2= 5x10/2= 25 each
However, the traingles share a common area which is quad DOB(I)
Lets take traingle AOE, whose are is bh/2=10x10/2=50cm2.
50-area of triangle A(I)E= 50-(

7 0

3 years ago

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A salesman earns 20% commission on all merchandise that he sells. Last month he sold $700 worth of merchandise. How much commiss

Neko [114]

Answer:

140$

Step-by-step explanation:

You can use the three rule step.

20% ?

-------=------------

100%. 700$

Then u go 20 x 700 divided by 100 which gives you the 20% in $

6 0

3 years ago

B. Interpretation Answer the following. 1. Focus What are the four characteristics of the Plains Indians' lives?

kirill [66]

The normally had small extended families.
They were a hunter-gatherer community
Sioux and Cheyenne tribes hunted buffalo
They were nomadic and almost completely dependent on buffalo

4 0

3 years ago

The owner of ProPhone has charted the company's marginal revenue and marginal cost for its latest line of smartphones, the Blaze

steposvetlana [31]

Profit is total revenue minus total cost. So, the profit for each row of data is:
Quantity | Profit
0 | 30 (loss)
1 | 30
2 | 160
3 | 190
4 | 260
5 | 300
6 | 310
7 | 290

The company has to produce 6 quantities to maximize profit.

5 0

3 years ago

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