Most quadratic functions(which is what you have there, to a degree of 2) are solved using factoring and the zero product law. If you can not factor then you have to use the quadratic formula or graph it. However this one can be factored.
It's pretty simple to just factor it by inspection but I use the chart method, if you know decomposition that works as well.
Factoring gives us,
Then you set each factor to 0 and solve for x,
And the second one,
The solutions to this equation are
x = -1/2, 3
Answer:
The equation of the required line is y = x + 5
Step-by-step explanation:
The equation of the given line is y = x - 2
The required line = A line parallel to the given line
The point through which the required line passes = (-3, 2)
The general form of the equation of a straight line, is y = m·x + c
Where;
m = The slope of the line
By comparison, the slope of the given line, m = 1
When two lines are parallel, their slope are equal
Therefore, the slope of the required line = m = 1
The equation of the required line in point and slope form is therefore;
y - 2 = x - (-3) = x + 3
∴y = x + 3 + 2 = x + 5
The equation of the required line is therefore;
y = x + 5.
Answer: he must work for at least 26.32 hours
Step-by-step explanation:
Let x represent the number of hours that Hayden works as a life guard.
Hayden earns $9.50 per hour as a lifeguard. This means that the amount that he earns for working for x hours would be
9.5x
He earns a bonus of $50.00 for taking a training course. If he takes this bonus cost, the amount that he would earn for working for x hours is
9.5x + 50
Therefore, the number of hours that he must work to earn at least $300.00 would be
9.5x + 50 ≥ 300
9.5x ≥ 300 - 50
9.5x ≥ 250
x ≥ 250/9.5
x ≥ 26.32
Answer:
A, B, C, D
Step-by-step explanation:
(A) Checking the Equal Variance Assumption, the appropriate technique to use is:
- The ANOVA (Analysis of Variance) F test
- Plot residuals against fitted values
(B) Checking the Normal Assumption, the appropriate techniques to use are:
- Test for Kurtosis & Skewness
- Kolmogorov-Smirnov Test
- Q-Q Plots (the graphical method) also known as Quantile Plot
- Do not use a histogram; it is not advisable
(C) Checking for Model Misspecification, the appropriate techniques to use are:
- The Ramsey Regression Specification Error Test; also called RESET
- The Davidson & MacKinnon J. Test
(D) Checking for dependent errors, the appropriate technique to use is:
- Plot residuals against time variables
To answer the question, you have to multiply $25,200 by 1/4 (portion allocated/ alloted for the tax -
$25,200 * 1/4 = 25,200/4 (then divide 25,200 by 4)
= $6,300
Therefore, the family spent $6,300 for taxes from their annual income of $25,200.
