Question

for 11-14, evaluate each expression for the given value of the variable(s).

1. 3d - 4

d = 1.2

1. 0.5f - 2.3g

f = 12, g = 2

1. \\(\frac{2}{3}p + 3\\)

p = \\(\frac{3}{5}\\)

1. 34 + \\(\frac{4}{9}w\\)

w = \\(\frac{1}{2}\\)

Explanation:

Problem 11: Evaluate \( 3d - 4 \) when \( d = 1.2 \)

Step 1: Substitute \( d = 1.2 \) into the expression

We replace \( d \) with \( 1.2 \) in \( 3d - 4 \), so we get \( 3\times1.2 - 4 \).

Step 2: Calculate the multiplication

First, calculate \( 3\times1.2 \). \( 3\times1.2 = 3.6 \).

Step 3: Calculate the subtraction

Now subtract 4 from 3.6: \( 3.6 - 4 = -0.4 \).

Step 1: Substitute \( f = 12 \) and \( g = 2 \) into the expression

We replace \( f \) with \( 12 \) and \( g \) with \( 2 \) in \( 0.5f - 2.3g \), so we get \( 0.5\times12 - 2.3\times2 \).

Step 2: Calculate the multiplications

First, calculate \( 0.5\times12 = 6 \) and \( 2.3\times2 = 4.6 \).

Step 3: Calculate the subtraction

Now subtract 4.6 from 6: \( 6 - 4.6 = 1.4 \).

Step 1: Substitute \( p = \frac{3}{5} \) into the expression

We replace \( p \) with \( \frac{3}{5} \) in \( \frac{2}{3}p + 3 \), so we get \( \frac{2}{3}\times\frac{3}{5} + 3 \).

Step 2: Calculate the multiplication

First, calculate \( \frac{2}{3}\times\frac{3}{5} \). The 3s cancel out, so we get \( \frac{2}{5} \).

Step 3: Calculate the addition

Now add 3 to \( \frac{2}{5} \). \( 3 + \frac{2}{5} = 3\frac{2}{5} = \frac{17}{5} = 3.4 \).

Answer:

\( -0.4 \)

Problem 12: Evaluate \( 0.5f - 2.3g \) when \( f = 12 \) and \( g = 2 \)