How can you tell if an expression factors as (a + b)(a

Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper i

stiks02 [169]

Based on the calculations, we have the following:

The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is equal to 36 square inches.
The area of the parallelogram is equal to 60 square inches.
The altitude of the parallelogram is equal to 6.51 square inches.

<u>Given the following data:</u>

Dimension of paper = 12-inch by 8-inch.

<h3>How to calculate the paper's area.</h3>

Mathematically, the area of the paper is given by this formula:

$Area = length \times breadth\\\\Area = 12 \times 8$

Area = 96 square inches.

<u>For the four (4) right triangles:</u>

Dimension 1 = 2 inches by 9 inches.

Dimension 2 = 3 inches by 6 inches.

Therefore, the combined area of the triangle cutouts is given by:

$A_2= (2 \times \frac{1}{2} \times 2 \times 9) + 2 \times \frac{1}{2} \times 3 \times 6\\\\A_2=18+18\\\\A_2=36\;in^2$

<h3>The area of the parallelogram.</h3>

This would be determined by subtracting the area of the four (4) right triangles from the areas of the paper as follows:

$P = A_p -A_2\\\\P=96-36$

P = 60 square inches.

<h3>The altitude of the parallelogram.</h3>

$P = base \times altitude\\\\Altitude =\frac{P}{base} \\\\Altitude =\frac{60}{9.22}$

Altitude = 6.51 square inches.

Read more on parallelogram here: brainly.com/question/4459854

<u>Complete Question:</u>

A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches.

8 0

2 years ago

Read 2 more answers

Assuming ideal solution behavior, how many liters of hcl gas, measured at 30. 0 °c and 745 torr, are required to prepare 1. 25 l

Nostrana [21]

The volume of HCl gas required to prepare the solution is 101.54 L

<h3>How to determine the mole of HCl </h3>

Volume of solution = 1.25 L
Molarity = 3.20 M
Mole of HCl =?

Mole = Molarity x Volume

Mole of HCl = 3.2 × 1.25

Mole of HCl = 4 moles

<h3>How to determine the volume of HCl </h3>

Number of mole (n) = 4 moles
Temperature (T) = 30 °C = 30 + 273 = 303 K
Pressure (P) = 745 torr = 745 / 760 = 0.98 atm
Gas constant (R) = 0.0821 atm.L/Kmol

Volume =?

Using the ideal gas equation, the volume of the HCl gas can be obtained as follow:

PV = nRT

Divide both side by P

V = nRT / P

V = (4 × 0.0821 × 303) / 0.98

V = 101.54 L

Learn more about ideal gas equation:

brainly.com/question/4147359

3 0

2 years ago

A(t)=(t−k)(t−3)(t−6)(t+3) Given that a(2)=0 , what is the absolute value of the product of the zeros of a?

Ugo [173]

So using a(2)=0 we can first solve for k by substituting t for 2
0 = (2-k)(2-3)(2-6)(2+3)
0 = (2-k)(-1)(-4)(5)
0 = (2-k)20
0 = 40 - 20k
-40 = -20k
k = 2

The next step would be to find all the 0s of a.
0 = (t-2)(t-3)(t-6)(t+3)
T = 2,3,6,-3

Then we find the product
2x3x6x-3 = -108

Since the problem asks for the absolute value, the answer is positive 108

6 0

3 years ago

How do animals affect us?

kodGreya [7K]

They provide food for us animal fur helps keep us warm and cats and dogs keep us company

5 0

3 years ago

You want to arrange digits 0 to 9 such that 1 and 2.

Roman55 [17]

Answer:

huh?

Explanation:

4 0

3 years ago

How can you tell if an expression factors as (a + b)(a - b)?