Answer:
(x + 5)(2x + 1)
Step-by-step explanation:
Given
2x² + 11x + 5
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 5 = + 10 and sum = + 11
The factors are + 10 and + 1
Use these factors to split the x- term
2x² + 10x + x + 5 ( factor the first/second and third/fourth terms )
= 2x(x + 5) + 1 (x + 5) ← factor out (x + 5 from each term
= (x + 5)(2x + 1) ← in factored form
{ solution is attached below}
Answer:
Step-by-step explanation:
The table shows a set of x and y values, thus showing a set of points we can use to find the equation.
1) First, find the slope by using two points and substituting their x and y values into the slope formula, 
. I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:
Thus, the slope is 
.
2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.
3) Finally, write an equation in slope-intercept form, or 
format. Substitute the 
and 
for real values.
The represents the slope of the equation, so substitute it for . The represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:
(a) From the histogram, you can see that there are 2 students with scores between 50 and 60; 3 between 60 and 70; 7 between 70 and 80; 9 between 80 and 90; and 1 between 90 and 100. So there are a total of 2 + 3 + 7 + 9 + 1 = 22 students.
(b) This is entirely up to whoever constructed the histogram to begin with... It's ambiguous as to which of the groups contains students with a score of exactly 60 - are they placed in the 50-60 group, or in the 60-70 group?
On the other hand, if a student gets a score of 100, then they would certainly be put in the 90-100 group. So for the sake of consistency, you should probably assume that the groups are assigned as follows:
50 ≤ score ≤ 60 ==> 50-60
60 < score ≤ 70 ==> 60-70
70 < score ≤ 80 ==> 70-80
80 < score ≤ 90 ==> 80-90
90 < score ≤ 100 ==> 90-100
Then a student who scored a 60 should be added to the 50-60 category.
