Given:
The graph of two lines.
To find:
The slope of each line and check whether they are same or different.
Solution:
If a line passes through two points, then the slope of a line is:
From the graph 1, it is clear that the line passes through the points (2,175) and (3,165). So, the slope of first line is:
The slope of first line is 10.
From the graph 2, it is clear that the line passes through the points (1,175) and (2,165). So, the slope of first line is:
The slope of second line is 10.
Therefore, the slopes of both lines are same, i.e. 10.
ANSWER
45 green bands
EXPLANATION
The ratio of red hair bands to green hair bands is
5 : 9
The total ratio is:
If there are a total of 70 hair bands,
Then the number of green bands
Simplify
Multiply
Therefore, there are 45 green bands.
Answer:
The solutions of the system of equations are (1 , -1) and ( , )
Step-by-step explanation:
The system of equations has a quadratic equation and a linear equation to solve it equate the two equations to find the values of x and then find the values of y
∵ y = 2x² - 8x + 5 ⇒ (1)
∵ y = x - 2 ⇒ (2)
- Equate (1) and (2)
∴ 2x² - 8x + 5 = x - 2
- Subtract x from both sides
∴ 2x² - 9x + 5 = - 2
- Add 2 to both sides
∴ 2x² - 9x + 7 = 0
Let us factorize it into two factors
∵ 2x² = (2x)(x)
∵ 7 = (7)(1)
- The last sign in the trinomial is (+) and the middle sign is (-)
then the two factors have (-) middle signs
∵ (2x)(1) + (x)(7) = 2x + 7x = 9x ⇒ nears and extreams
∴ The factors of 2x² - 9x + 7 are (x - 1)and (2x - 7)
∴ (x - 1)(2x - 7) = 0
Equate each factor by 0 to find x
∵ x - 1 = 0
- Add 1 to both sides
∴ x = 1
∵ 2x - 7 = 0
- Add 7 to both sides
∴ 2x = 7
- Divide both sides by 2
∴ x =
Now substitute the values of x in equation (2) to find the values of y
∵ x = 1
∴ y = 1 - 2 = -1
∵ x =
∴ y = - 2 =
∴ The solutions of the system of equations are (1 , -1) and ( , )