A student's grades in the three tests in College Algebra are 85, 60, and 69. a) How many points does the student need on the final to average 74? b) Find part (a), assuming that the final carries double the weight. a) The student must score on the final. (Type an integer or a decimal.) b) The student must score on the final, assuming that the final carries double the weight. (Type an integer or a decimal.) A company manufactures shaving sets for $ each

(a) The student need 82 points on the final to average 74.

(b) The student must score 41 points on the final, assuming that the final carries double the weight.

Step-by-step explanation:

We are given that a student's grades in the three tests in College Algebra are 85, 60, and 69.

As we know that the formula for calculating the average of numbers is given by;

          Average (Mean)  =  

(a) Let the points student need on the final test to average 74 be ''.

So, Average of all four test  =  

Hence, the student needs 82 points on the final to average 74.

(b) It is given that the final carries double the weight, this means that let the points student need on the final test to average 74 be ''.

So, Average of all four test  =  

                        = 41

Hence, the student must score on the final 41 points, assuming that the final carries double the weight.

x = 23.78

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!