Question

in 1 - 3, use the properties of operations to multiply the expressions.

1. (10.3y)(4y)
2. 2x(5 - 0.4x)
3. (t + t)(4.9t)
4. what is the area of this rectangle?

the area of the rectangle is

1. which expression is equivalent to (4.5j + 6)(-2.3j)?

Explanation:

Step1: Multiply coefficients and variables for (10.3y)(4y)

$(10.3\times4)y^{1 + 1}=41.2y^{2}$

Step2: Use distributive property for 2x(5 - 0.4x)

$2x\times5-2x\times0.4x = 10x-0.8x^{2}$

Step3: Simplify (t + t)(4.9t)

First, t + t = 2t. Then, $(2t)(4.9t)=(2\times4.9)t^{1 + 1}=9.8t^{2}$

Step4: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$. Here, $l = 20.1b$ and $w = 14b$, so $A=(20.1b)\times(14b)=(20.1\times14)b^{2}=281.4b^{2}\text{ ft}^2$

Step5: Expand (4.5j + 6)(-2.3j)

Using distributive property: $(4.5j)\times(-2.3j)+6\times(-2.3j)=-10.35j^{2}-13.8j$

Answer:

1. $41.2y^{2}$
2. $10x - 0.8x^{2}$
3. $9.8t^{2}$
4. $281.4b^{2}\text{ ft}^2$
5. B. $-10.35j^{2}-13.8j$