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STALIN [3.7K]
3 years ago
14

it takes 4 cups of suger to bake a cake and 2 cups of suger to make a tray of cookies. Mary has a total of 15 cups of sugar to b

ake x cakes and y trays of cookies.
Mathematics
1 answer:
Stolb23 [73]3 years ago
7 0
She can make two cakes and 3 trays of cookies 
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Find the unit rate: $9.60 for 4 pounds. and how whould you solve it
ad-work [718]
To find the unit rate of any two numbers you divide:
9.60 divided by 4 = 2.4

Unit rate = $2.40

Hope I helped! :)
6 0
2 years ago
4. CSC X COS X - 2 cos x = 0
Alisiya [41]

Answer:

infinitely many answers, any odd integer n times π/2

ex. π/2, 3π/2, 5π/2

Step-by-step explanation:

we know that cos (π/2) or cos(3π/2) is 0

if one factor is 0, the product is zero, so we will not care about csc(x).

x is any odd integer n times π/2

3 0
3 years ago
A child throws a ball with a speed of 5 feet per second at an angle of 73 degrees with the horizontal. Express the vector descri
maxonik [38]

Answer:

  v = 5cos(73°)i +5sin(73°)j

Step-by-step explanation:

The components of the velocity vector are ...

  horizontal (i direction): 5·cos(73°)

  vertical (j direction): 5·sin(73°)

Then the velocity vector is the sum of these component vectors:

  v = 5cos(73°)i +5sin(73°)j

3 0
2 years ago
What is the answer for each sentence
Harman [31]

Answer:

1. surface area, 2. volume. 3. surface area, 4. volume

Step-by-step explanation:

The stain means it's just the surface of the box, and not what can go in it.

the question is asking how many shoe boxes can fit IN

5 0
2 years ago
Use Gaussian elimination to write each system in triangular form
Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

  1. Swapping two rows
  2. Multiplying a row by a nonzero number
  3. Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]

For this matrix we need to perform the following row operations:

  • R_2 - 1 R_1 \rightarrow R_2 (multiply 1 row by 1 and subtract it from 2 row)
  • R_3 + 1 R_1 \rightarrow R_3 (multiply 1 row by 1 and add it to 3 row)
  • R_4 - 1 R_1 \rightarrow R_4 (multiply 1 row by 1 and subtract it from 4 row)
  • R_2 \leftrightarrow R_3 (interchange the 2 and 3 rows)
  • R_2 / 2 \rightarrow R_2 (divide the 2 row by 2)
  • R_1 - 1 R_2 \rightarrow R_1 (multiply 2 row by 1 and subtract it from 1 row)
  • R_4 - 1 R_2 \rightarrow R_4 (multiply 2 row by 1 and subtract it from 4 row)
  • R_3 \cdot ( -1) \rightarrow R_3 (multiply the 3 row by -1)
  • R_2 - 1 R_3 \rightarrow R_2 (multiply 3 row by 1 and subtract it from 2 row)
  • R_4 + 3 R_3 \rightarrow R_4 (multiply 3 row by 3 and add it to 4 row)
  • R_4 / 4.5 \rightarrow R_4 (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5  \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 &  2 \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right]

If you later perform the following operations you can find the solution to the system.

  • R_1 + 0.5 R_4 \rightarrow R_1 (multiply 4 row by 0.5 and add it to 1 row)
  • R_2 + 0.5 R_4 \rightarrow R_2 (multiply 4 row by 0.5 and add it to 2 row)
  • R_3 - 2 R_4 \rightarrow R_3(multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9}  \\0 & 1 & 0 & 0 &   -\frac{1}{9}\\0 & 0 & 1 & 0 &  \frac{4}{9} \\0 & 0 & 0 & 1 &  \frac{7}{9}\end{array}\right]

Thus, the solution is:

x =  -\frac{1}{9}, y= -\frac{1}{9}, z= \frac{4}{9} and w = \frac{7}{9}

7 0
3 years ago
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