Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?3.48 × 42.37 = 147.4476
23.2 × 8.8 = 20.416
0.39 × 7.2 = 28.08
43.72 × 9.2 = 4,022.24

Let

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

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

we know that

The area of the rectangle is equal to

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

so

-------> equation A

-----> equation B

Substitute equation B in equation A

--------> 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

-----> the length of the rectangle

Find the value of y

 ----> the width of the rectangle

Statements

case A) The area of the rectangle is square inches

The statement is True

See the procedure

Case B) The equation   can be used to solve for the dimensions of the triangle

The statement is False

Because, the equation can be used to solve for the dimensions of the triangle

case C) The equation 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 inches and a height of 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 inches

The statement is False

See the procedure

The correct statements are:

• The area of the rectangle is 88 square inches.
• The equation x^2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
• The triangle has a base of 11 inches and a height of 8 inches.

What are the dimensions of the rectangle?

When a rectangle is split diagonally, two right triangles are formed.

The area of a triangle = 1/2 x base x height

44 = 1/2 × (x - 3) × x

Where x represents the length

In order to determine the value of x, take the following steps:

Multiply both sides of the equation by 2: 88 = x² - 3x

x² - 3x - 88 = 0

Use the factorisation method to find x: (x² + 8x) (-11x - 88x)

x(x + 8) -11(x + 8)

x + 8 = 0

x = -8

x - 11 = 0

x = 11

Width = 11 - 3 = 8

Area of the rectangle = length x width

11 x 8 = 88 square inches.

To learn more about how to determine the area of a triangle, please check: brainly.com/question/9329354

Answer:

x = 11 or x = -4

Step-by-step explanation:

x² - 7x - 34 = 10

Subtract 10 from both sides.

x² - 7x - 44 = 10

Factor the trinominal. We need 2 numbers whose product is -44 and whose sum is -7. They are -11 and 4.

(x - 11)(x + 4) = 0

x - 11 = 0  or  x + 4 = 9

x = 11 or x = -4

Answer:

37.2

Step-by-step explanation:

when you turn the small triangle LMN to its right angle to cover the right angle of KLM, you find that they are similar triangles.

therefore the corresponding side lengths are at the same ratio.

LM/KM = MN/LN

LM = 24

MN = 13

we can get LN via Pythagoras of the small triangle

LN² + MN² = LM²

LN² + 13² = 24²

LN² = 24² - 13² = 576 - 169 = 407

LN = sqrt(407) = 20.174241

now back to our main problem

24/KM = 13/sqrt(407)

24×sqrt(407)/13 = KM = 37.2

Answer:

(x − 4)(x − 2)(x + 1)

Step-by-step explanation:

Answer:

18

Step-by-step explanation: