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goldenfox [79]
2 years ago
14

Use the associative property to simplify 3(4x).

Mathematics
2 answers:
jolli1 [7]2 years ago
6 0
Using the associative property
A ( Bx + C ) = ABx + AC
3 ( 4x + 0 ) = 12x + 0
= 12x
vivado [14]2 years ago
4 0

Step-by-step explanation:

3(4x)=12x

Hope it helps?!

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Consider the following sets of matrices: M2(R) is the set of all 2 x 2 real matrices; GL2(R) is the subset of M2(R) with non-zer
defon

Answer:

Step-by-step explanation:

REcall the following definition of induced operation.

Let * be a binary operation over a set S and H a subset of S. If for every a,b elements in H it happens that a*b is also in H, then the binary operation that is obtained by restricting * to H is called the induced operation.

So, according to this definition, we must show that given two matrices of the specific subset, the product is also in the subset.

For this problem, recall this property of the determinant. Given A,B matrices in Mn(R) then det(AB) = det(A)*det(B).

Case SL2(R):

Let A,B matrices in SL2(R). Then, det(A) and det(B) is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)\neq 0.

So AB is also in SL2(R).

Case GL2(R):

Let A,B matrices in GL2(R). Then, det(A)= det(B)=1 is different from zero. So

\text{det(AB)} = \text{det}(A)\text{det}(B)=1\cdot 1 = 1.

So AB is also in GL2(R).

With these, we have proved that the matrix multiplication over SL2(R) and GL2(R) is an induced operation from the matrix multiplication over M2(R).

7 0
3 years ago
An assembly line produces 2 toasters per minute. It is 2:00pm and the line has finished 560 out of its goal of 900 for the day.
LenaWriter [7]

Answer:

I won't stop the line for a half hour break.

Step-by-step explanation:

<u>Proportions</u>

One quantity A is said to be proportional to other B if A can always be obtained by multiplying or dividing B by any constant number. Numbers {4,8,12} are proportional to {2,4,6} because they can be computed as twice their value

.

There is a situation described in the problem where we need to know if there will be enough time to produce the 900 toasters (the goal for the day) when the assembly line is stopped by half an hour.

Actual time: 2:00 pm

Final time: 5:00 pm

Rate of production: 2 toasters/minute

Actual production: 560 toasters

Updated goal: 900-560 = 340 toasters  

Those 340 toasters must be produced in the remaining 3 hours (180 minutes) of work. If the assembly line stops for half an hour (30 minutes), there will be only 150 minutes to finish the goal production. At a rate of 2 toasters/minute, there will be 2*150 = 300 toasters produced. But we need to produce 340 more toasters, so that break cannot be granted or we'll be 40 toasters under goal.

It the line keeps producing for 180 minutes, it would produce 2*180 = 360 toasters, 20 more than the goal.

Note: The maximum break time that can be granted is 20/2 = 10 minutes

4 0
3 years ago
This question is really hard for me.Please answer.
GarryVolchara [31]
The correct answer is 13
4 0
3 years ago
Evaluate the expression \dfrac{5\cdot x^3}{x^2} x 2 5⋅x 3 ​ start fraction, 5, dot, x, cubed, divided by, x, squared, end fracti
Fantom [35]

Answer:

10

Step-by-step explanation:

Given the expression:

(5 * x³) / x² ; for x = 2

Simplifying (5 * x³) / x²

5 * x^(3-2)

5 * x^1

= 5x

For x = 2

5x = 5*2 = 10

8 0
2 years ago
Can someone please help me
Y_Kistochka [10]
The answer is 280 degrees.
8 0
1 year ago
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