Answer: OPTION D.
Step-by-step explanation:
The rate of change of a linear function is also known as "Slope".
The slope can be calculated with the following formula:
Choose two points on the function "R" graphed:
You can say that:
Substituting values into the formula, you get:
Choose two point from the table that models the function "S":
You can say that:
Substituting values into the formula, you get:
Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".
The rate of change of a linear equation (first degree) is equivalent to the slope of a line. Slope is described as the vertical movement (rise) of the line over its horizontal counterpart (run). In determining the rate of change or slope (m) given 1 data point (x',y'), point-slope form is applicable. Point-slope form is: (y-y') = m (x-x'). Substitute the given point (-5,-1) in the equation. By substitution, [y-(-1)] = m [x-(-5)]. Re-arranging the equation, the rate of change or slope is, m = (y+1)/(x+5).
Answer:
45 and 135
Step-by-step explanation:
If angles, with measurements a and b, are supplementary, then a and b have sum 180 degrees.
So we have the following equation so far:
a+b=180
Now we also have that one angle has a measurement that is 1/3 the value of the one.
So we also have 3a=b which means we are letting the angle whose measurement be a have 1/3 the value of b.
So lets plug the second equation into first giving us:
a+3a=180
Add like terms:
4a=180
Divide both sides by 4:
a=180/4
a=45
So b=3a=3(45)=135.
So the angles in question have measurement s 45 and 135.
The formula for the Binomial Theorem with a power 6 is as:
Thus, if we plug in 20 for x and 5 for y, our first term itself will be 
which is much greater than 256 and thus it will not make any sense to use 
to approximate 256 using the binomial theorem.
Also, it will not make any sense to use 
as that has no power and we know that Binomial Theorem makes use of Power. Anyway, 
.
Our best bet here would be to use the equation with power 8:
and have 
and 
which will give us
Answer:
The answer is 5 students taking English and Math but not History
Step-by-step explanation:
The total students are 28 which are divided into 5 possible groups with no students taking either English only or History only:
- Taking Math only
- Taking English and Math but not History
- Taking Math and History but not English
- Taking English and History but not Math
- Taking triple subjects
The number of students in group 3 is 6. Hence, the total number in group 1, 2, 4 and 5 is: 28 - 6 = 22
Also, the number of students in group 4 is five times the number in group 5, therefore: group 2 + group 5 = 6 times group 5
Additionally, the number of students in group 1 equals that in group 2.
Hence, the equation is: 6 x group 5 + 2 x group 2 = 22 => group 2 = 11 - 3 x group 5 => group 2 = 5 because group 5 is an even number and non-zero, it must be 2.
