Simplify (-2x3)2 · y · y9. A) -4x6y8 B) -4x4y8 C) 4x6y10 D) -4x4y10

A bag is filled with green and blue marbles. There are 125 marbles in the bag. If there are 29 more green

ValentinkaMS [17]

Answer:

89 green marbles and 46 blue marbles

Step-by-step explanation:

3 0

2 years ago

The sum of three consecutive even numbers is 552. What is the 1st number?

wariber [46]

Answer:

Let 2n = the first of three consecutive even numbers, where n is an integer.

Let 2n + 2 = the second of three consecutive even numbers, and

Let 2n + 4 = the third of three consecutive even numbers.

We're given that "sum of three consecutive even numbers is 552." We can translate this English sentence mathematically into the following equation to be solved for n:

2n + (2n + 2) + (2n + 4) = 552

Removing the parentheses, we have:

2n + 2n + 2 + 2n + 4 = 552

Now, by the Commutative Law of Addition, i.e., a + b = b + a, we have on the left side of the equation:

2n + 2n + 2n + 2 + 4 = 552

Now, collecting like-terms on the left, we get:

6n + 6 = 552

To solve for the variable n, We now begin isolating n on the left side by subtracting 6 from both sides as follows:

6n + 6 - 6 = 552 - 6

6n + 0 = 546

6n = 546

Now, divide both sides by 6 to finally solve for n:

(6n)/6 = 546/6

(6/6)n = 546/6

(1)n = 91

n = 91

Therefore, the first of three consecutive even numbers, 2n, is:

2n = 2(91)

= 182

The second of three consecutive even numbers is:

2n + 2 = 2(91) + 2

= 182 + 2

= 184

The third of three consecutive even numbers is:

2n + 4 = 2(91) + 4

= 182 + 4

= 186

CHECK:

2n + (2n + 2) + (2n + 4) = 552

182 + 184 + 186 = 552

552 = 552

Therefore, the desired and first of three consecutive even numbers is indeed 2n = 182.

7 0

2 years ago

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Use Gauss-Jordan elimination to solve the following linear system.

marysya [2.9K]

Just put the coefients in to a matrix

1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14

$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\-2&2&-3|-14\end{array}\right]$
mulstiply 2nd row by -1 and add to 3rd
$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&2&0|-6\end{array}\right]$
divde last row by 2
$\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]$
multiply 2rd row by 6 and add to top one
$\left[\begin{array}{ccc}1&0&-3|-14\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]$
multiply 1st row by -1 and add to 2nd
$\left[\begin{array}{ccc}1&0&-3|-14\\-3&0&0|6\\0&1&0|-3\end{array}\right]$
divide 2nd row by -3
$\left[\begin{array}{ccc}1&0&-3|-14\\1&0&0|-2\\0&1&0|-3\end{array}\right]$
mulstiply 2nd row by -1 and add to 1st row
$\left[\begin{array}{ccc}0&0&-3|-12\\1&0&0|-2\\0&1&0|-3\end{array}\right]$
divide 1st row by -3
$\left[\begin{array}{ccc}0&0&1|4\\1&0&0|-2\\0&1&0|-3\end{array}\right]$

rerange
$\left[\begin{array}{ccc}1&0&0|-2\\0&1&0|-3\\0&0&1| 4\end{array}\right]$

x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)

B is answer

7 0

3 years ago

Part 2 of the other question and obvi the ones that are crossed out, you do not have to do.

zavuch27 [327]

Answer:

19)51.06

22)-3.08

25) 19.25 cost per visit.

Step-by-step explanation:

7 0

2 years ago

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The volume of a rectangular prism can be found with the formula V = lwh

kipiarov [429]

The height of the prism is 12 feet.

5 0

3 years ago