5x - 3y = 11 ⇒ 5x - 3y = 11 ⇒ 5x - 3y = 11
x - 2y = 2 ⇒ -5(x - 3y) = 2 ⇒ <u>-5x + 15y = 2</u>
<u>12y</u> = <u>13</u>
12 12
y = 1 1/12
5x - 3(1 1/12) = 11
5x - 3 1/4 = 11
<u> +3 1/4 +3 1/4</u>
<u> 5x</u> = <u>14 1/4</u>
5 5
x = 2 17/20
(x, y) = (2 17/20, 1 1/12)
Answer:
The area of the circle is 50.24 mm
²
Step-by-step explanation:
To solve this exercise we need to use the area formula of a circle:
a = area
r = radius = 4mm
π = pi = 3.14
a = π * r²
a = 3.14 * (4mm
)²
a = 3.14 * 16mm
²
a = 50.24 mm
²
The area of the circle is 50.24 mm
²
Answer:
Step-by-step explanation:
Let's solve 2x^2 = -X^2 - 5x - 1. Consolidate all terms on the left side and write 0 on the right side:
3x^2 + 5x + 1 = 0. This is a quadratic equation. Let's solve it for x using the quadratic formula:
a = 3, b = 5, c = 1, and so the discriminant is b^2 - 4ac = 5^2 - 4(3)(1) = 13. Because the discriminant is positive, we know that there are two distinct, real roots; the graphs of y = 2x^2 and y = x^2 - 5x - 1 intersect in two places whose x-coordinates are the real roots mentioned above.
Answer A is not correct as stated, but would be correct if we were to replace "the y-coordinates" with "the x-coordinates."
Answer C would be correct if and only if we write y = x^2 - 5x - 1.
Answer:
20
Step-by-step explanation:
Using the rule of radicals
× 
⇔ 
Given
× 
= 
= 
= 20
