What are the solutions to the system of equations? x2 + y2 = 5 y = 2x.
2 answers:
Answer:
(1, 2) and (- 1, - 2)
Step-by-step explanation:
Given the 2 equations
x² + y² = 5 → (1)
y = 2x → (2)
Substitute y = 2x into (1)
x² + (2x)² = 5, that is
x² + 4x² = 5
5x² = 5 ( divide both sides by 5 )
x² = 1 ( take the square root of both sides )
x = ± = ± 1
Substitute these values into (2) for corresponding values of y
x = 1 → y = 2(1) = 2 ⇒ (1, 2)
x = - 1 → y = 2(- 1) = - 2 ⇒ (- 1, - 2)
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Answer:
240 miles
Step-by-step explanation:
Given that:
Charges offered by Prestige car rentals for renting a midsize vehicle:
Fixed charges = $47
Per mile charges for renting a midsize vehicle = $0.07
Charges offered by Gateway Auto for renting a midsize vehicle:
Fixed charges = $35
Per mile charges for renting a midsize vehicle = $0.12
To find:
Number of miles for which both the companies charge the same price?
Solution:
Let the number of miles for which both the companies will charge the same price = miles
Charges for one mile by Prestige car rentals = $0.07
Charges for miles by Prestige car rentals = $0.07
Total charges by Prestige Car rentals = $47 + $0.07
Charges for one mile by Gateway Auto = $0.12
Charges for miles by Gateway Auto = $0.12
Total charges by Gateway Auto = $35 + $0.12
As per question statement, the charges are same:
Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A = × leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 = × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 = × 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse =
∴ hypotenuse =
∵ The simplest form of = 2
∴ The length of the hypotenuse = 2 inches