Hey There!!
The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).
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Answer:
The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,
μ
=
mass of string
length of string
=
m
l
.
In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass
(
Δ
m
)
of a small length of string
(
Δ
x
)
is
Δ
m
=
μ
Δ
x
.
For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is
μ
=
0.06
kg
2.00
m
=
0.03
kg
m
.
If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is
Δ
m
=
μ
Δ
x
=
(
0.03
kg
m
)
0.001
m
=
3.00
×
10
−
5
kg
.
The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.
Answer:
1.75 ounces per bag.
Step-by-step explanation:
First, we add the ounces all together and we get 45.5 ounces of trail mix. If we divide that by 26 bags, we will get 1.75 ounces per bag. I hope this helps. If someone else answers, can you give me brainliest? I really need it. Thanks!
The coefficient of x in the equation of the given line, 3, is its slope. The slope of the perpendicular line is the negatve reciprocal of that, -1/3. You now have the slope and a point on the perpendicular line, so you can write its equation using the point-slope form:
y = m(x -x₁) +y₁
where m is the slope and (x₁, y₁) is the point.
An equation for your perpendicular line is
y = (-1/3)(x -(-1)) -3
y = (-1/3)x -10/3
The slope-intercept form of the equation of the perpendicular line is ...
y = (-1/3)x -10/3