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2 years ago

14

If your income is $27 a month, the price of pizza is $5 and the price of a video is $4, how many pizzas will you buy and how

many videos will you rent each month?

1 answer:

mixas84 [53]2 years ago

8 0

27-4=23-4=19-5=14-4=10-5=5-5 ( 3 pizzas and 3 videos)

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What is the area of this figure?<br><br> A. 102<br> B. 132<br> C. 168<br> D. 340

matrenka [14]

The total area of the figure is the area of the square plus the area of the rectangle plus the area of the triangle.
area of the square: (6)*(6)=36cm^2
area of the rectangle: (7)*(6)=42cm^2
area of the triangle: (1/2)*(8)*(6)=24cm^2
total area
At=36+42+24=102cm^2

8 0

2 years ago

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

1 year ago

Find the product. y4 · y5

Alexandra [31]

I would assume this to be equal to y⁴ ₓ y⁵

= y⁴ ⁺ ⁵, By law of indices.

= y⁹

I hope this helped.

8 0

2 years ago

Given that x = 3, y = -2 and z = 0, calculate the value of each of the following algebraic expressions: 2x + y. Answer quick ple

icang [17]

2 times 3+(-2)
6-2
4. Is the cord answer

4 0

2 years ago

According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, 62% of graduate

egoroff_w [7]

Answer:

$\frac{31}{50}$

Step-by-step explanation:

percentage of graduates with loan = 62%

total sample = 50

Number of student in the sample with student loan

= (percentage of graduates with loan) x (total sample)

= 62% x 50

= 31

Proportion of student in the sample with student loan = $\frac{31}{50}$

4 0

2 years ago