Two negative integers are 5 units apart on the number line, and their product is 126. What is the sum of the two integers?

Find the product (8/6n-4)(9n^2-4)

Leokris [45]

Answer:

4(3n+2) or 12n+8

Step-by-step explanation:

Given expression is:

$(\frac{8}{6n-4})(9n^{2}-4)$

The numerator of the fraction will be multiplied with 9n^2- 4

So, Multiplication will give us:

$=\frac{8(9n^2-4)}{6n-4}$

We can simplify the expression before multiplication.

The numerator will be broken down using the formula:

$a^2 - b^2 = (a+b)(a-b)\\So,\\= \frac{8[(3n)^2 - (2)^2]}{6n-4}\\ = \frac{8(3n-2)(3n+2)}{6n-4}$

We can take 2 as common factor from denominator

$=\frac{8(3n-2)(3n+2)}{2(3n-2)}\\After\ cutting\\= 4(3n+2)$

Hence the product is 4(3n+2) or 12n+8 ..

6 0

3 years ago

What type of model best fits the height of a tree increases by 2.5 feet each growing season

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)

This is the model that best fits the graph describing a growth of a plant

3 0

2 years ago

Chanda can bake and decorate 72 cookies in 2.5 hours. At this rate,how long will it take her to bake and decorate 108 cookies?

In-s [12.5K]

Hello there! A. 3.75 hours is your answer.

Okay, so lets start by finding the unit rate. To find the unit rate, we can use this formula: total ÷ time = unit rate.

total (72 cookies) ÷ time (2.5 hours) = unit rate. (how many cookies she can decorate and bake in an hour)

72 ÷ 2.5 = 28.8 cookies an hour

Now that we have this information, replace the 180 cookies in for the total number and use algebra to solve.

180 cookies ÷ x time = 28.8

Since 180 is a little more than 2 times 72, A would best fit since 3.75 is much closer to 2.5 than the other options. To check this, we can place 3.75 in for x in 180 ÷ x = 28.8.

180 ÷ 3.75 = 28.8.

So, this is your correct answer.

7 0

3 years ago

The equation y=9. 5x 0. 4 represents the line of best fit for the distance (in feet) that Marcella traveled over time (in second

Bas_tet [7]

The average speed of Marcella in feet per seconds is 9.5 feet per second.

<h3>How are time taken for travel, distance traveled, and the average speed are related?</h3>

We have this below shown relation between them

$\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Total time taken to travel that distance}= \dfrac{\text{Distance traveled}}{\text{Average speed} }$

For the given case, we have:

The equation $y=9.5x + 0.4$ represents the line of best fit for the distance (in feet) that Marcella traveled over time (in seconds)

The line of best fit can be taken as approximately telling about the data points ( y = distance traveled in feet, and x = time spent )

Let the initial time be 'x' with initial distance traveled 'y', then the time after one second will be (x+1), and the distance traveled be $y_1$

The value of y and $y_1$ are calculated as:

$y = 9.5x + 0.4\\y_1 = 9.5(x+1) + 0.4 = 9.5x + 9.9$

Thus, the average speed is calculated at time 'x' as:

$\text{Average speed} = \dfrac{\text{Distance traveled}}{\text{Total time taken to travel that distance}}\\\\or\\\\\text{Average speed} = \dfrac{y_1 - y}{x + 1 - x} = \dfrac{9.5x + 9.9 - 9.5x - 0.4}{1} = 9.5 \: \rm feet/sec$