Solve this system of equations.2x + 6y = −6,
4x − 3y = −12
what is the solution system of equations?

The average rate of change will be negative 7 / 3.

How to find the average rate of change of something?

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

Average rate = (y₂ - y₁) / (x₂ - x₁)

The exponential function is given below.

f(x) = (0.5)ˣ - 6

Then the average rate of change will be

Average rate = [f(0) - f(-3)] / [0 - (-3)]

Average rate = [(0.5⁰ - 6) - (0.5⁻³ - 6)] / 3

Average rate = [1 - 6 - 8 + 6] / 3

Average rate = - 7 / 3

More about the average rate of change link is given below.

brainly.com/question/23715190

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I hope that this helps :) :) :)

Answer:

It would be the...

Step-by-step explanation:

Average rate of change = -1/3

Answer:

Option A is right

Step-by-step explanation:

The graph represents the results of a survey where 400 people were asked to identify the preferred TV channcel.

Of those the data collected gave

WKOD 13%

WANR 22%

WCLM 24%

WWCN 41%

Ratio of people who preferred WANR to those who preferred WCLM

= 22%/24%

=11:12

Hence answer is 11:12

Answer: it’s option C: No, the points are in a linear pattern

Step-by-step explanation:

Took on edge

Final answer:

To determine if the line of best fit is appropriate for the data, plot the residuals on a graph and examine the pattern. In this case, the residual plot does not show a linear or curved pattern, indicating that the line of best fit is not appropriate for the data.

Explanation:

The residual plot shows the difference between the observed Y-values and the predicted Y-values. To plot the residuals, subtract the predicted Y-values from the observed Y-values for each corresponding X-value. Then plot the resulting points on a graph. In this case, the points are:

(1, 0.86), (2, -0.25), (3, -1.66), (4, -2.34), (5,-4.1).

To determine if the line of best fit is appropriate for the data, we need to examine the pattern of the residual plot. If the points have no pattern or are evenly distributed about the x-axis, it indicates that the line of best fit is appropriate. In this case, the points do not exhibit a linear or curved pattern, and they are not evenly distributed about the x-axis. Therefore, the residual plot does not show that the line of best fit is appropriate for the data.

Hence, the correct answer is: C. No the points are in a linear pattern.

Answer:

Step-by-step explanation:

Given:

• p = log 2
• q = log 3

To find :

• log 162 in terms of p and q.

Solution:

In order to find the logarithm of 162 in terms of p and q, we can use the properties of logarithms.

We can start by expressing 162 as a product of prime factors:

Now, we can use the properties of logarithms to simplify this expression:

Since log(ab) = log(a) + log(b), we can split this into separate logarithms:

Now, we can use the fact that q = log 3:

Using the property, we get:

Now, substitute the values of p and q:

So, the logarithm of 162 in termsof p and q is:

Answer:

log 162 = 6p + 2q

Step-by-step explanation:

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.

We can write 162 as follows:

```

162 = 2^6 * 3^2

```

Therefore,

```

log 162 = log (2^6 * 3^2)

```

Using the logarithmic properties of addition and multiplication, we can simplify this to:

```

log 162 = 6 * log 2 + 2 * log 3

```

Finally, substituting p = log 2 and q = log 3, we get the following expression:

```

log 162 = 6p + 2q

```

Therefore, log 162 can be written as **6p + 2q** in terms of p and q.

Okay, let's break this down step-by-step:

* log 162 = log (2^4 * 3^2)   (by prime factorization)

* log (2^4 * 3^2) = 4log2 + 2log3  (by properties of logarithms)  

* Let p = log 2 and q = log 3

* Substituting:

* log 162 = 4p + 2q

Therefore, log 162 can be written as 4p + 2q, where p = log 2 and q = log 3.

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To express log 162 in terms of p (log 2) and q (log 3), you can use logarithm properties, particularly the change of base formula. The change of base formula states that:

log_b(a) = log_c(a) / log_c(b)

In your case, you want to find log 162:

log 162 = log 2^1 * 3^4

Now, we can use the change of base formula with base 10 (or any other base):

log 162 = (log 2^1 * 3^4) / (log 10)

Since log 10 is simply 1 (logarithm of 10 to any base is 1), we can simplify further:

log 162 = (log 2^1 * 3^4) / 1

Now, apply the properties of logarithms to split the logarithm of a product into a sum of logarithms:

log 162 = (log 2^1) + (log 3^4)

Now, we can replace log 2 with p and log 3 with q:

log 162 = p + (4q)

So, log 162 in terms of p and q is:

log 162 = p + 4q

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.