Answer: Telescopes use lenses or mirrors to collect and focus waves from the electromagnetic spectrum, including visible light, allowing us to look at celestial objects. By studying the electromagnetic waves given off by objects such as stars, galaxies, and black holes, astronomers can better understand the universe.
Step-by-step explanation:
It is not reasonable that she has 1/2 of her homework to do. She did 3/6 (1/2) at home. She actually has 1/6 of her homework left to do.
Let Peter's hit be x and Alice's runs be y.
x = 2(y - 6) . . . (1)
x + y = 18 . . . (2)
Putting (1) into (2) gives,
2y - 12 + y = 18
3y = 18 + 12 = 30
y = 30/3 = 10
x = 2(10 - 6) = 2(4) = 8
Therefore, Peter hit 8 home runs and Alice hit 10 home runs.
Answer:
Step-by-step explanation:
If y varies directly with x, it is:
Constant is -2, it means k= -2
Answer: x = 4 and x = -3/2
Procedure:
1) Given: 2x^2 - 5x - 12 = 0
2) Multiply both sides by : 2(2x^2) - 2(5x) - 2(12) = 0
3) Rearrange: (2x)^2 -5(2x) - 24 = 0
4) Notice that the common factor is (2x)
5) Set the parenthesis with the common factor inside:
(2x ) (2x ) =0
6) The first sign is the same sign of the second term of the trinomial, which is negative, the second sign is the product of the signs of the second and the third terms of the polynomial, which is (-)*(-) = + (positive)
(2x - )(2x + ) = 0
7) find two numbers that sum up - 5x and its product is -24.
- 8 + 3 = - 5
(-8)(+3) = -24
=> the numbers in the factors are -8 and +3
(2x - 8) (2x + 3) = 0
That is the factored equation. Now you can solve
8) a) 2x - 8 = 0 => 2x = 8 => x = 8/2 => x = 4
b) 2x + 3 = 0 => 2x = - 3 => x = - 3/2
Answer: the two solutions are x = 4 and x = -3/2
