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Which pair of expressions is equivalent using the Associative Property of Multiplication?

RUDIKE [14]

Answer:

Step-by-step explanation:

In the associative property of multiplication, the product of the multiplication of 3 or more numbers is the same irrespective of how they are grouped. This means that irrespective of the bracket or which number comes first, the product will always be the same.

From the given scenarios, the pair of expressions that are equivalent using the Associative Property of Multiplication are

B 6(4a ⋅ 2) = (4a ⋅ 2) ⋅ 6

C 6(4a ⋅ 2) = 6 ⋅ 4a ⋅ 2

D6(4a ⋅ 2) = (6 ⋅ 4a) ⋅ 2

The results are the same irrespective of the arrangement of the numbers.

3 0

2 years ago

A factory produces some batteries daily. 7/8 of the batteries are packaged immediately. 2/3 of the

frozen [14]

Answer:

$\frac{1}{24}$

Step-by-step explanation:

Let the total number of batteries produced daily be represented by x.

7/8 of the batteries are packaged immediately.

So the total number of packaged batteries = $\frac{7x}{8}$

Remaining batteries = $x-\frac{7x}{8}$

= $\frac{x}{8}$

Two third of the remaining batteries are sent to charity.

So the total number of batteries sent to charity= $\frac{2}{3} * \frac{x}{8}$

= $\frac{x}{12}$

Remaining batteries are faulty.

So the total number of faulty batteries = $\frac{x}{8} - \frac{x}{12}$

= $\frac{3x - 2x}{24}$

= $\frac{x}{24}$

So the faction of batteries which are faulty =

= $\frac{x}{24} \div x$

= $\frac{1}{24}$

3 0

2 years ago

Solve the system by graphing. Write the solution as an ordered pair. y = 1/3x + 2 y = –x – 2

Dima020 [189]

ANSWER

The solution is where the two graphs intersect, which is
$(-3,1).$

EXPLANATION

The given system of equations are
$y = \frac{1}{3} x + 2$
and

$y = - x - 2$

We need to graph the two equations.

Let us graph

$y = \frac{1}{3} x + 2$
first.

We need at least two points.

You can choose any appropriate value for x and solve for y. Choosing zero makes our working easier. So let us plot the intercepts.

When
$x = 0$

$\Rightarrow \: y = \frac{1}{3} (0) + 2$

$\Rightarrow y = 0 + 2$

$\Rightarrow y = 2$

So this gives us the ordered pair,

$(0,2)$

When
$y = 0$
we get,

$0= \frac{1}{3} x + 2$

$\Rightarrow \: - 2 = \frac{1}{3} x$

$\Rightarrow \: - 2 \times 3= x$

$\Rightarrow \: -6= x$
This also gives the ordered pair

$(-6,0).$

We plot these two points and draw a straight line through them to obtain the blue graph in the attachment.

For the second line

$y = - x - 2$

We again find the intercepts and plot them.

When
$x = 0$

$y = - 0 - 2$

$\Rightarrow \: y = - 2$

This gives the ordered pair

$(0,-2)$

Also, when
$y = 0$

then we have,

$0 = - x - 2$

$2 = - x$

$x = - 2$

Then we again have the ordered pair,

$(-2,0)$

We plot these two points on the same graph sheet to obtain the red graph above.

The intersection of the two lines is
$(-3,1)$

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