Answer:
Step-by-step explanation:
<u>Equation of a Polynomial</u>
Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:
Where a is the leading coefficient.
We know the three roots of the polynomial -6, -3, and 1, thus:
Since the y-intercept of the polynomial is y=90 when x=0:
90=a(0+6)(0+3)(0-1)
90=a(6)(3)(-1)=-18a
Thus
a = 90/(-18) = -5
The polynomial is:
We must write it in standard form, so we have to multiply all of the factors as follows:
Answer:
432 in.^2
Step-by-step explanation:
The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.
We use the Pythagorean theorem,
a^2 + b^2 = c^2
(24 in.)^2 + b^2 = (30 in.)^2
576 in.^2 + b^2 = 900 in.^2
b^2 = 324 in.^2
b = sqrt(324 in^2)
b = 18 in
area of rectangle = length * width
A = 24 in. * 18 in.
A = 432 in.^2
There are several ways to do this.
I'll show you two methods.
1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.
slope = m = (y2 - y1)/(x2 - x1)
Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.
Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.
Plug in values into the formula:
m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4
The slope is -1/4
2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.
Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4
As you can see we got the same slope using both methods.
Answer:
Step-by-step explanation:
What is a statistical question and what is its purpose? Be sure to include the 3 characteristics. That makes it up.
Answer- and statistical question is a question that guides research by defining the population of a given topic and that anticipates variability in the collected data. The purpose of a statistical question is it is the first step of the statistical process. The 3 characteristics of a statistical question are allows for clear responses, includes a specific population, and anticipates variability of the data.
What does it mean for data to have variability as it refers to statistical questions? Give an example.
A statistical question has more than one possible answer
Example- how many chores do you have? Some people might say 5 or 2 or even 0. It just depends on the person's family.
Well a dot diagram is like this for example,
And a histogram is this,
Dot diagram uses dots and the histogram uses bars.
When would we use them? Well that I can explain, you can use the dot diagram to see what pets people have or even to see how many people scored how many points.
A histogram can be used for a concert. There would be like on the bottom, 0-6, 7-12, and so on. The bars show how many people from what age group are joining the concert.
Explain the difference between center and shape of a data set.
The center is the median and/ or mean of the data. The spread is the range of the data. And, the shape describes the type of graph.
hope this helps give brainiest.
Answer:
140°
Step-by-step explanation:
total angle of a hexagon is 720. We know already 510°. That leaves 210°. The ratio between the two angles is 2:1, therefore angle CDE is 140° and angle DEF is 70 °
