Which two equations would be most appropriately solved by using the zero product property? Select each correct answer. 4x² = 13
2 answers:
The zero product property tells us that if we multiply two quantities together and get zero, then one or both of these is equal to zero.
In symbols this means that if ab = 0 then a = 0, b = 0 or both.
This means that if we have a product equal to zero one of both of the factors (the things we are multiplying together) is equal to zero.
Of the equations given, the only one that has product (a few terms multiplied together) equal to zero is -(x-1)(x+9)=0 so this is the one that can most appropriately be solved by the zero product property.
We can re-write -(x-1)(x+9) = 0 as (-1)(x-1)(x+9) = 0 which means (x-1) or (x+9) or both equal zero. It should be clear that -1 cannot equal zero.
To solve we set x - 1 = 0 and obtain x = 1.
Next we set x + 9 = 0 and obtain x = -9
The solutions to the equation are x = -9 and x = 1.
We are, however, asked for two equations. Though none of the remaining equations has a product set equal to zero, we can re-write the equation
by factoring 3x from each term on the left-hand side. Doing so gives us 
. Now we have a product equal to zero which means that one or both of the factors on the left-hand side equals zero.
That is, 3x equals 0, or x-2 equals 0 or both do. If 3x = 0 then x = 0. If x-2=0 then x=2. As such the solution to the equation is x = 0, x = 2.
In symbols this means that if ab = 0 then a = 0, b = 0 or both.
This means that if we have a product equal to zero one of both of the factors (the things we are multiplying together) is equal to zero.
Of the equations given, the only one that has product (a few terms multiplied together) equal to zero is -(x-1)(x+9)=0 so this is the one that can most appropriately be solved by the zero product property.
We can re-write -(x-1)(x+9) = 0 as (-1)(x-1)(x+9) = 0 which means (x-1) or (x+9) or both equal zero. It should be clear that -1 cannot equal zero.
To solve we set x - 1 = 0 and obtain x = 1.
Next we set x + 9 = 0 and obtain x = -9
The solutions to the equation are x = -9 and x = 1.
We are, however, asked for two equations. Though none of the remaining equations has a product set equal to zero, we can re-write the equation
That is, 3x equals 0, or x-2 equals 0 or both do. If 3x = 0 then x = 0. If x-2=0 then x=2. As such the solution to the equation is x = 0, x = 2.
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<h3>The interest rate is 8 % if your balance on an investment of 857 dollars at the end of six years is 1268.36 dollars</h3>
<em><u>Solution:</u></em>
Given that,
Principal = $ 857
Amount = $ 1268.36
Number of years = 6
Rate of interest = ?
Simple Interest = Amount - principal
Simple Interest = 1268.36 - 857
Simple Interest = 411.36
<em><u>Use the formula,</u></em>
Thus the interest rate is 8 %
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is less than 140, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one left tailed test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is less than 140 pounds at 5% of signficance.