Sarah went to an electronics store, purchased 3 cds and 5 dvds, and spent $137. michelle went to the same store, bought 2 cds and 7 dvds, and spent $161. how much does each cd sell for at the store? . a) $13 . b)$14 . c)$18 . d) $19 .

b) $14

Step-by-step explanation:

Let x be the cost of each CD and y be the cost of each DVD,

Since, 3 CDs and 5 DVDs cost $ 137,

⇒ 3x + 5y = 137 -------(1),

Also, 2 CDS and 7 DVDs cost $ 161,

⇒ 2x + 7y = 161 --------(2),

7 × equation (1) - 5 × equation (2)   ( ∵ we need the value of x so we have to eliminate y for this LCM(7,5) = 35 )

We get,

21x - 10x = 959 - 805

11x = 154

⇒ x = = 14

Hence, the cost of each CD is $ 14,

Option 'b' is correct.

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!

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.