Answer:
10.7 m
Step-by-step explanation:
Given that,
The speed of a sound wave, v = 6,420 m/s
The frequency of the wave, f = 600 Hz
We need to find the wavelength of the wave. We can find it using the below relation as follows :
So, the wavelength of the sound wave is equal to 10.7 m.
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
Equating the expressions for y gives ...
-1/4x +6 = x +1
5 = 5/4x . . . . . . . add 1/4x-1
4 = x . . . . . . . . . . multiply by 4/5
y = x +1 = 4 +1
y = 5
The solution is (x, y) = (4, 5).
9514 1404 393
Answer:
yes
Step-by-step explanation:
The figure can be shown to be a parallelogram by showing the sum of endpoints of the diagonals is the same.
A +C = B +D
(0, 6) +(0, -4) = (0, 2) = (3, 5) +(-3, -3) . . . . diagonals bisect each other
If the diagonals of a quadrilateral bisect each other, it is a parallelogram. A parallelogram with a right angle is a rectangle. So, ABCD is a rectangle.
_____
<em>Additional comment</em>
The midpoint of each diagonal is half the sum of the end point coordinates. That is, the midpoints are (0, 2)/2 = (0, 1). Since calculation of the midpoints requires both sums be divided by 2, we can tell the midpoints are the same if the sums are the same.
5 × 1. = 5
_ × _. = _
8 × 4. = 32
5/32
These are two questions and two answers:
Question 1:
<span>A
quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe
the solution(s) to the equation by just determining the radicand. Show
your work.
Answer: </span><span>The negative value of the radicand means that the equation does not have real solutions.
Explanation:
1) With radicand the statement means the disciminant of the quadratic function.
2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c
3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20
and the discriminant (radicand) is: (-15)² - 4(3)(20) = 225 - 240 = - 15.
4) The negative value of the radicand means that the equation does not have real solutions.
Question 2:
Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate
method. Show the steps of your work, and explain why you chose the
method used.
Answer: </span> two solutions x = 1 and x = - 8/3x
Explanation:
1) I choose factoring (you may use the quadratic formula if you prefer)
2) Factoring
Given: 3x² + 5x − 8 = 0
Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0
Group: (3x² - 3x) + (8x - 8) = 0
Common factors for each group: 3x(x -1) + 8(x - 1) = 0
Coomon factor x - 1: (x - 1) (3x + 8) = 0
The two solutions are for each factor equal to zero:
x - 1 = 0 ⇒ x = 1
3x + 8 = 0 ⇒ x = -8/3
Those are the two solutions. x = 1 and x = - 8/3
