Ask a New Question
Menu

Jacqueline has two part-time jobs. She earns $15 per hour, l , working as a lab assistant, and $12 per hour, s , working as a cashier. This is modeled by 15l+12s . Evaluate for l=5 and s=7 to find how much money Jacqueline will earn at her two jobs this week.

11 answers

To find out how much money Jacqueline will earn at her two jobs this week, we can use the expression \( 15l + 12s \).

Given:

  • \( l = 5 \) (hours worked as a lab assistant)
  • \( s = 7 \) (hours worked as a cashier)

Now we can substitute the values into the expression:

\[ 15l + 12s = 15(5) + 12(7) \]

Calculating each part:

  1. \( 15(5) = 75 \)
  2. \( 12(7) = 84 \)

Now combine the results:

\[ 75 + 84 = 159 \]

Thus, Jacqueline will earn $159 this week at her two jobs.

Simplify  5a−8c+b+3c−9a+6b .

To simplify the expression \(5a - 8c + b + 3c - 9a + 6b\), we can combine like terms.

Let's group the terms by their variables:

  • Terms with \(a\): \(5a - 9a\)
  • Terms with \(b\): \(b + 6b\)
  • Terms with \(c\): \(-8c + 3c\)

Now, simplify each group:

  1. \(5a - 9a = -4a\)
  2. \(b + 6b = 7b\)
  3. \(-8c + 3c = -5c\)

Now combine these results:

\[ -4a + 7b - 5c \]

So, the simplified expression is:

\[ \boxed{-4a + 7b - 5c} \]

Simplify  −3/4r + 3 − 5/6r − 6 .

To simplify the expression \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\), we will first combine like terms.

  1. Combine the constant terms: \[ 3 - 6 = -3 \]

  2. Combine the \(r\) terms: \[ -\frac{3}{4}r - \frac{5}{6}r \] To combine these, we need a common denominator. The least common multiple of 4 and 6 is 12.

    • Convert \(-\frac{3}{4}r\) to a fraction with a denominator of 12: \[ -\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r \]

    • Convert \(-\frac{5}{6}r\) to a fraction with a denominator of 12: \[ -\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2}r = -\frac{10}{12}r \]

    Now combine the two \(r\) terms: \[ -\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r \]

  3. Putting it all together: \[ -\frac{19}{12}r - 3 \]

Thus, the simplified expression is:

\[ \boxed{-\frac{19}{12}r - 3} \]

But how is 3-6= -3

I apologize for any confusion; let’s clarify that step.

When we subtract \(6\) from \(3\):

\[ 3 - 6 = -3 \]

This means that if you have \(3\) and then take away \(6\), you are left with \(-3\), which indicates a debt or being below zero.

To recap the entire simplification of \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\):

  1. Combine the constant terms: \[ 3 - 6 = -3 \]

  2. Combine the \(r\) terms: \[ -\frac{3}{4}r - \frac{5}{6}r \] To combine these, we convert them to a common denominator:

    • \(-\frac{3}{4}r = -\frac{9}{12}r\)
    • \(-\frac{5}{6}r = -\frac{10}{12}r\)

    Thus, \[ -\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r \]

  3. Combining everything gives: \[ -\frac{19}{12}r - 3 \]

So the final simplified expression is:

\[ \boxed{-\frac{19}{12}r - 3} \]

Thank you for your understanding! If you have any more questions or need further clarification, feel free to ask!

Expand 8(3p+2).

To expand the expression \(8(3p + 2)\), you distribute the \(8\) to both terms inside the parentheses:

\[ 8(3p) + 8(2) \]

Now, calculate each term:

  1. \(8 \cdot 3p = 24p\)
  2. \(8 \cdot 2 = 16\)

Now combine the results:

\[ 24p + 16 \]

So, the expanded expression is:

\[ \boxed{24p + 16} \]

Expand −4(6a−5)

To expand the expression \(-4(6a - 5)\), you distribute the \(-4\) to both terms inside the parentheses:

\[ -4(6a) + (-4)(-5) \]

Now, calculate each term:

  1. \(-4 \times 6a = -24a\)
  2. \(-4 \times -5 = 20\)

Now combine the results:

\[ -24a + 20 \]

So, the expanded expression is:

\[ \boxed{-24a + 20} \]