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Simplify the expression.

−1/2(−6x+3)

(1 point)
Responses

−3x−3
negative 3 x minus 3

−3x+3/2
negative 3 x plus 3 halves

3x+3
3 x plus 3

3x−3/2

11 answers

To simplify the expression \(-\frac{1}{2}(-6x + 3)\), we can distribute \(-\frac{1}{2}\) to both terms inside the parentheses:

\[ -\frac{1}{2}(-6x) + \left(-\frac{1}{2}(3)\right) \]

Calculating each term:

  1. \(-\frac{1}{2}(-6x) = 3x\)
  2. \(-\frac{1}{2}(3) = -\frac{3}{2}\)

Putting it all together, we have:

\[ 3x - \frac{3}{2} \]

Thus, the simplified expression is:

\[ \boxed{3x - \frac{3}{2}} \]

Evaluate the expression when w = 2 and y = 5.

10(3w−2y)


(1 point)
Responses

4
4

-40
-40

120
120

-4
-4

To evaluate the expression \(10(3w - 2y)\) when \(w = 2\) and \(y = 5\), we first substitute the values of \(w\) and \(y\) into the expression.

  1. Substitute \(w = 2\) and \(y = 5\): \[ 10(3(2) - 2(5)) \]

  2. Calculate inside the parentheses: \[ 3(2) = 6 \] \[ 2(5) = 10 \] Now substitute these results back into the expression: \[ 10(6 - 10) \]

  3. Simplify further: \[ 6 - 10 = -4 \] So now we have: \[ 10(-4) \]

  4. Finally, multiply: \[ 10 \times -4 = -40 \]

Therefore, the evaluated expression is: \[ \boxed{-40} \]

Evaluate the expression when c = - 1 and d = 15.

c−d/−2


(1 point)
Responses

7
7

-7
-7

-8
-8

8

To evaluate the expression \(\frac{c - d}{-2}\) when \(c = -1\) and \(d = 15\), we will first substitute the values of \(c\) and \(d\) into the expression.

  1. Substitute \(c = -1\) and \(d = 15\): \[ \frac{-1 - 15}{-2} \]

  2. Calculate the numerator: \[ -1 - 15 = -16 \] Now the expression becomes: \[ \frac{-16}{-2} \]

  3. Simplify the fraction: \[ \frac{-16}{-2} = 8 \]

Thus, the evaluated expression is: \[ \boxed{8} \]

Manny has two part-time jobs. She earns $21 per hour (a) working as an aerobics instructor, and $12.50 per hour (d) working at the donut shop. Her earnings are represented by the expression 21a+12.50d
. How much money will she earn working 4 hours as an aerobics instructor and 8 hours at the donut shop?(1 point)
Responses

$134
$134

$218
$218

$33.50
$33.50

$184

To find out how much money Manny will earn working 4 hours as an aerobics instructor and 8 hours at the donut shop, we can use the expression \(21a + 12.50d\), where \(a\) is the number of hours worked as an aerobics instructor and \(d\) is the number of hours worked at the donut shop.

  1. Substitute \(a = 4\) (hours as an aerobics instructor) and \(d = 8\) (hours at the donut shop): \[ 21(4) + 12.50(8) \]

  2. Calculate the earnings from each job:

    • For the aerobics instructor: \[ 21 \times 4 = 84 \]
    • For the donut shop: \[ 12.50 \times 8 = 100 \]

  3. Add the two amounts to find the total earnings: \[ 84 + 100 = 184 \]

Therefore, Manny will earn $184.

So the answer is: \[ \boxed{184} \]

Simplify.

11−9(−2x−3)


(1 point)
Responses

−4x−6
negative 4 x minus 6

18x−38
18 x minus 38

−4x+6
negative 4 x plus 6

18x+38

To simplify the expression \(11 - 9(-2x - 3)\), we'll follow the order of operations and distribute appropriately.

  1. Start by distributing \(-9\) to both terms inside the parentheses: \[ 11 - 9(-2x) - 9(-3) \]

  2. Calculate each term:

    • \(-9(-2x) = 18x\)
    • \(-9(-3) = 27\)

  3. Now substitute these results back into the expression: \[ 11 + 18x + 27 \]

  4. Combine like terms:

    • Combine the constants: \(11 + 27 = 38\)

Finally, we have: \[ 18x + 38 \]

Thus, the simplified expression is: \[ \boxed{18x + 38} \]

Factor this expression completely.

35x−40


(1 point)
Responses

7(5x+8)
7 times open paren 5 x plus 8 close paren

7(5x−8)
7 times open paren 5 x minus 8 close paren

5(7x+8)
5 times open paren 7 x plus 8 close paren

5(7x−8)

To factor the expression \(35x - 40\) completely, we first need to find the greatest common factor (GCF) of the two terms \(35x\) and \(-40\).

  1. Identify the coefficients: The coefficients are \(35\) and \(40\). The GCF of \(35\) and \(40\) is \(5\).

  2. Factor out the GCF: \[ 35x - 40 = 5(7x - 8) \]

Thus, the completely factored expression is: \[ \boxed{5(7x - 8)} \]