Question

For each diagram below, write and solve an equation for x .

Answer 1

To solve the linear equations, operations such as division are used to isolate y. The equations yield lines with varying slopes and y-intercepts. For the exponential functions, a understanding of their graphs' shapes helps in sketching them.

Step-by-step explanation:

The student's question requires solving linear equations and understanding how to sketch graphs of exponential functions. For the equation 7 y = 6x + 8, solving for y would involve dividing both sides by 7 to obtain y = (6/7)x + 8/7. If we take 4y = 8, we can solve for y by dividing both sides by 4 to get y = 2. Furthermore, rearranging the equation y + 7 = 3x to solve for y gives us y = 3x - 7. For the exponential equations, such as y = e^x and y = e^(-x), these are not linear equations but can be sketched using their known properties: e^x increases rapidly as x becomes positive, and e^(-x) decreases rapidly as x becomes positive.

Answer 2

x = 100 , x = 3

Step-by-step explanation:

(a)

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the angles and equate to 540

x + x + 125 + 125 + 90 = 540 , that is

2x + 340 = 540 ( subtract 340 from both sides )

2x = 200 ( divide both sides by 2 )

x = 100

(b)

the 2 given angles are alternate exterior angles and are congruent , then

6x + 18 = 2x + 30 ( subtract 2x from both sides )

4x + 18 = 30 ( subtract 18 from both sides )

4x = 12 ( divide both sides by 4 )

x = 3