What is 3/5 of $40 restaurant bill

Crackers were on sale 2 for 5.50. I bought three packs, How much did I spend?

MrRissso [65]

Answer:

6.75

Step-by-step explanation:

2 crackers=5.50

1 cracker=5.50÷2

=2.25

3 crackers=2.25×3

=6.75

8 0

2 years ago

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Use matrices to solve the system of equations if possible. Use Gaussian elimination with back substitution or gauss Jordan elimi

CaHeK987 [17]

In matrix form, the system is given by

$\begin{bmatrix} -1 & 1 & -1 \\ 2 & -1 & 1 \\ 3 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -20 \\ 29 \\ 29 \end{bmatrix}$

I'll use G-J elimination. Consider the augmented matrix

$\left[ \begin{array}{ccc|c} -1 & 1 & -1 & -20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right]$

• Multiply through row 1 by -1.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right]$

• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 5 & -2 & -31 \end{array} \right]$

• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 3 & 24 \end{array} \right]$

• Multiply row 3 by 1/3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right]$

• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right]$

• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).

$\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right]$

Then the solution to the system is

$\boxed{x=9, y=-3, z=8}$

If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix

$\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right]$

The third row tells us that $z=8$ . Then in the second row,

$y-z = -11 \implies y=-11 + 8 = -3$

and in the first row,

$x-y+z=20 \implies x=20 + (-3) - 8 = 9$

5 0

2 years ago

Use the zeros and the labeled point to write the quadratic function

Anarel [89]

Answer:

y = 2x2 - 10x + 12

Step-by-step explanation:

5 0

2 years ago

If VT=2,what is the length of PT?

marusya05 [52]

Step-by-step explanation:

$\underline{ \underline{ \text{Given : }}}$

Perpendicular ( P ) = VT = 2
Base ( b ) = PT
$\theta = \tt{60 \degree}$

$\underline{ \underline{ \text{Solution}}} :$

$\tt{ \tan(60 \degree) = \frac{perpendicualar}{base}}$

⟶ $\tt{ \sqrt{3} = \frac{2}{PT}}$

⟶ $\tt{ \sqrt{3} \: PT= 2}$

⟶ $\tt{PT = \frac{2}{ \sqrt{3}} }$

⟶ $\tt{PT= \boxed{\tt{ \frac{2 \sqrt{3} }{{3} }}}}$

Hope I helped ! ♡

Have a wonderful day / night ! ツ

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6 0

3 years ago

You work at a craft store that sells paint kits. The kits have 4 thin paintbrushes for every 6 thick brushes. What is

liq [111]

Answer:2:3

Step-by-step explanation:

if you were to simplify the ratio just like you would a fraction you would get 2:3

6 0

3 years ago

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