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Yakvenalex [24]
3 years ago
10

Simplify 36n^7p^5 over 9n^4p

Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0
2(exponent2)n(exponent11)p(exponent6)
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Given the system<br><br> y &gt; -2<br><br> x + y &lt; 4
katen-ka-za [31]

1. Points that lie on the intersection area of the inequalities are solutions.

For example (0,2), (-4,4), (2,-1), (-8,0) and all others which lie in this area.

2 Not solutions are points that are on the lines (because we have signs > and <, not ≤ and ≥), or on the areas that are not intercepted. For example, (6,2), (2,2), (2,-4),(-6,-2).

7 0
3 years ago
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)
Gekata [30.6K]

Answer:

The solution of the system of linear equations is x=3, y=4, z=1

Step-by-step explanation:

We have the system of linear equations:

2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]

the variable matrix is

\left[\begin{array}{c}x&y&z\end{array}\right]

and the constant matrix is

\left[\begin{array}{c}12&-2&13\end{array}\right]

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

  • multiply the 1st row by 1/2

\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]

  • add -1 times the 1st row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]

  • add -3 times the 1st row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]

  • multiply the 2nd row by -2/7

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]

  • add 7/2 times the 2nd row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]

  • multiply the 3rd row by 1/3

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]

  • add 12/7 times the 3rd row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add 3 times the 3rd row to the 1st row

\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add -3/2 times the 2nd row to the 1st row

\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]

From the reduced row echelon form we have that

x=3\\y=4\\z=1

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0
3 years ago
What is the answer for 2b+5=15.
vfiekz [6]
I believe b equals 5, which would make 2x5 +5, making it 15.
4 0
3 years ago
Read 2 more answers
Nora's paper airplane flew 9 1/6 feet. That was 2 3/4 feet farther than Max's plane flew. Write and solve an equation to show ho
stepan [7]

Answer:

Max's paper airplane flew \frac{77}{12} feet or 6\frac{5}{12} feet.

Step-by-step explanation:

As Nora's paper airplane flew 9 1/6 feet

i.e.

9\frac{1}{6}=\frac{55}{6}

Nora's paper was farther than Max's plane flew by = 2 3/4 feet

i.e.

2\frac{3}{4}=\frac{11}{4}

Thus the equation to show how far Max's paper airplane flew is:

\:\:9\frac{1}{6}-2\frac{3}{4}

=\frac{55}{6}-\frac{11}{4}

\mathrm{Least\:Common\:Multiplier\:of\:}6,\:4:\quad 12

\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}

=\frac{110}{12}-\frac{33}{12}

\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}

=\frac{110-33}{12}

\mathrm{Subtract\:the\:numbers:}\:110-33=77

=\frac{77}{12}

=6\frac{5}{12}

Therefore, Max's paper airplane flew \frac{77}{12} feet or 6\frac{5}{12} feet.

6 0
3 years ago
A gourment shop wants to mix coffe beans that cost $3.00 per pound with coffe beans that cost $4.25 per pound to create 25 pound
guajiro [1.7K]
If the gourmet shopkeeper mix 15 pounds of coffee beans which costs 3.0$ per pound with 10 pounds of coffee beans costing 4.25$ per pound.
The mixture of 25 pounds will cost 3.5$ per pound.

It can be found using 
3*x + 4.25*(25 -x) = 25*3.50

4 0
2 years ago
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