The answer is 7/5. I attached the work below.
Step 1) Draw a dashed line through the points (0,6) and (4,7). These two points are on the line y = (1/4)x+6. To find those points, you plug in x = 0 to get y = 6. Similarly, plug in x = 4 to get y = 7. The dashed line indicates that none of the points on this line are part of the solution set.
Step 2) Draw a dashed line through (0,-1) and (1,1). These two points are on the line y = 2x-1. They are found in a similar fashion as done in step 1.
Step 3) Shade the region that is above both dashed lines. We shade above because of the "greater than" sign. This is shown in the attached image I am providing below. The red shaded region represents all of the possible points that are the solution set. Once again, any point on the dashed line is not in the solution set.
Answer:
The solution of the equations are -6 and 1
Step-by-step explanation:
* <em>Lets explain how to solve the problem</em>
- We want to find the solution of the equation (x + 2) (x + 3) = 12
- <em>At first lets use the Foil method to multiply the two brackets</em>
(x + 2) (x + 3) = (x)(x) + (x)(3) + (2)(x) + (2)(3)
(x + 2) (x + 3) = x² + 3x + 2x + 6 ⇒ add the like term
(x + 2) (x + 3) = x² + 5x + 6
∵ (x + 2) (x + 3) = 12
∴ x² + 5x + 6 = 12
- Subtract 12 from both sides
∴ x² + 5x - 6 = 0
- <em>Factorize the left hand side</em>
∵ x² = (x)(x)
∵ -6 = 6 × -1
∵ 6x + -1x = 5x
∴ (x + 6)(x - 1) = 0
- <em>Lets use the zero product property </em>
∵ (x + 6)(x - 1) = 0
∴ x + 6 = 0 ⇒ <em>OR</em> ⇒ x - 1 = 0
∵ x + 6 = 0
- Subtract 6 from both sides
∴ x = -6
∵ x - 1 = 0
- Add 1 to both sides
∴ x = 1
∴ The solution of the equations are -6 and 1
(a)7x4=28
2x2=4
28-4=24
24-1=23 points
(b)20/4=7 correct answers