Answer:
The area (A) of a triangle varies jointly as its ba
se (b) and height (h). If its base is 8 inches and i
ts height is 7 inches, it has an area of 28 square
inches. Find the base if its height is 5 inches an
5
d its area is 16 square inches.
Formulate the equation of variation.
Step-by-step explanation:
Step-by-step explanation:
Absolute value of a number gives the positive quantity of the number.
For instance,
From this example, therefore we know that
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In this question,
1) Striangle = 1/2 * (12-8) * 4 = 1/2 * 4 * 4 = 8 km^2
2) Srectangle = 4 * 8 = 32 km^2
3) Sfigure = 8 + 32 = 40 km^2
Number C
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 ( , )