Answer:
B. .32
Step-by-step explanation:
I think its B .32
Answer:
A
Step-by-step explanation:
Reflection: in the line y=−1
The image of triangle △RST after the glide reflection, which involves a translation of (x, y) → (x - 3, y) followed by a reflection in the line y = -1, is △R'S'T' with vertices R'(1, -2), S'(4, -5), and T'(3, -6).
To graph triangle △RST with vertices R(4, 1), S(7, 3), and T(6, 4), and its image after the glide reflection, we'll follow these steps:
Start by plotting the original triangle △RST using the given vertices:
R(4, 1)
S(7, 3)
T(6, 4)
Now, let's apply the translation to every vertex of the triangle.
The translation (x, y) → (x - 3, y) shifts each point 3 units to the left (in the negative x-direction).
Apply this translation to each vertex:
R' = (4 - 3, 1) = (1, 1)
S' = (7 - 3, 3) = (4, 3)
T' = (6 - 3, 4) = (3, 4)
Next, we'll apply the reflection in the line y = -1 to the translated vertices. The reflection in this line flips each point across the line.
To do this, we'll calculate the distance between each point and the line y = -1 and then move the same distance in the opposite direction.
R'' is reflected across the line y = -1 to (1, -2).
S'' is reflected across the line y = -1 to (4, -5).
T'' is reflected across the line y = -1 to (3, -6).
Now, we have the vertices of the image triangle △R'S'T'.
You can plot these points on the same graph as the original triangle to visualize the glide reflection transformation.
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Answer:
Step-by-step explanation:
Points R(4,1) S(7,3) T(6,4) after translation
R(4-3, 1) S(7-3, 3) T(6-3, 4)
R'(1, 1) S'(4, 3) T'(3, 4)
Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection
R''(1, -3) S''(4, -5) T''(3, -6)
Answer:
The answer is "20".
Step-by-step explanation:
It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.
The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7
Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.
In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.
Put the values in the data set into increasing order:
−10, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9
The minimum (the smallest number) is −10
and the maximum (the largest number) is 9.
Find the median,
The median is the middle number
The median is = 4.
Find Q1 and Q3.
Q1 = 2, Q3 = 7
Range = max−min = 9−(−1) = 19
Interquartile range = Q3−Q1 = 7−2 = 5.
Thus,
The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7
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The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.
The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.
The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.
We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.
Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.
Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.
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Measurement of Angle LOK = 82 degrees.
Solve for x.
Answer:
x = 14
Step-by-step explanation:
<LOJ = 3x
<KOJ = (2x + 12)°
<LOK = 82°
m<LOJ + m<KOJ = m<LOK (angle addition postulate)
3x + 2x + 12 = 82 (substitution)
5x + 12 = 82
5x = 82 - 12 (Subtraction property of equality)
5x = 70
x = 70/5 (division property of equality)
x = 14