What is the equation of the line that passes through the point (8,-8)(8,−8) and has a slope of -1/4?
1 answer:
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The answer is, 
I'm about to basically type up a report on explaining this answer so bear with me :P
<em>Step 1.)</em> Factor
using Polynomial Division.
Just a basic rundown of what polynomial division is. When using polynomial division for this problem we find all the factors of our constant, 84, and then see which one, when substituted for x, makes the expression equal zero. After we find our variable that makes the problem equal zero, we divide it into our original expression. Here's how it's done:
These are our factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
strating from one and plugging in these numbers, the first one we come upon that works is 4. So, now we will divide. below is a picture of what it should look like.
After we divide, we get an answer of
<em>Step 2.)</em> split into two terms
To do that we multiply the coefficient of the first term (2) by the constant (-21)
So:
Now we ask "which two numbers add up to equal 11, but multiply to equal -42". Those two numbers are 14 and -3.
Now we basically split 11x as the sum of 14 and -3. So now our problem should look like this:
<span><span>
</span></span><em>Step 3.)</em> Factor out the common terms in the first two terms, then the last two like this:
From this:
To this:
<em>Step 4.)</em> Factor the term (x + 7) out of the parenthesis
After we do that, we are left with our problem looking like this:
The last thing we do is set each parenthesis equal to zero and work it out to find our zeros.
That gives us our answer of our zeros being
Thank you for our question! I hope this helped! Have an amazing day! :D
I'm about to basically type up a report on explaining this answer so bear with me :P
<em>Step 1.)</em> Factor
Just a basic rundown of what polynomial division is. When using polynomial division for this problem we find all the factors of our constant, 84, and then see which one, when substituted for x, makes the expression equal zero. After we find our variable that makes the problem equal zero, we divide it into our original expression. Here's how it's done:
These are our factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
strating from one and plugging in these numbers, the first one we come upon that works is 4. So, now we will divide. below is a picture of what it should look like.
After we divide, we get an answer of
<em>Step 2.)</em> split
To do that we multiply the coefficient of the first term (2) by the constant (-21)
So:
Now we ask "which two numbers add up to equal 11, but multiply to equal -42". Those two numbers are 14 and -3.
Now we basically split 11x as the sum of 14 and -3. So now our problem should look like this:
<span><span>
</span></span><em>Step 3.)</em> Factor out the common terms in the first two terms, then the last two like this:
From this:
To this:
<em>Step 4.)</em> Factor the term (x + 7) out of the parenthesis
After we do that, we are left with our problem looking like this:
The last thing we do is set each parenthesis equal to zero and work it out to find our zeros.
That gives us our answer of our zeros being
Thank you for our question! I hope this helped! Have an amazing day! :D
Answer: D)
Step-by-step explanation:
From the given table we can see that this is not representing a linear function as the rate of change is not constant.
So it can be exponential growth function , where A is the initial amount , b is the multiplicative rate of growth and n is the time period in weeks.
Now here at n=1 , f(n)=8
Therefore, A=8
Now, for n=2
By substitute the values of A and b in the above equation, we get the equation
Therefore, the function best shows the relationship between n and f(n) is
, where n is the number of weeks.
Answer:
There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).
Step-by-step explanation:
The question is incomplete:
<em>"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."</em>
This is a hypothesis test for the difference between proportions.
The claim is that the proportions are not equal.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample 1, of size n1=1000 has a proportion of p1=0.031.
The sample 2, of size n2=1200 has a proportion of p2=0.018.
The difference between proportions is (p1-p2)=0.013.
The pooled proportion, needed to calculate the standard error, is:
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the z-statistic as:
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportions are not equal.