The dilation is an enlargement and the dilation has a scale factor of 3. Therefore, options A and D are the correct answer.
From figure given below, square C has side of length 3 units.
Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
From given figure we can see the dashed figure, square has side of length 9 units.
Here we understood that the image has enlargement.
Now, scale factor = Dimensions of new image ÷ Dimensions of original image
= 9/3
= 3 units
Therefore, options A and D are the correct answer.
To learn more about the dilation visit:
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Answer:
The dilation is also an enlargement.
Step-by-step explanation:
B. 55.9%; decrease
C. 90%; decrease
D. 76.5%; increase
B : 500
C : 1.000
D : 1.010
Answer:
.88
Step-by-step explanation:
We can use this equation:
Where:
We just need to solve it for D
.88
Therefore the dimension will be 3
I hope it helps you!
Answer:
The dimension is 4
Step-by-step explanation:
Using the equation
N = R^d
Where,
N is the increase factor = 512
R is the reduce factor = 8
d is the dimension
512 = 5^d
Solving by logarithm
1log 512 = d log 5
D = log 512 ÷ log 5
= 3.87
Approximately 4
Answer:
9.12 + 9.12 = 18.24 inches
Step-by-step explanation:
Diameter = 23 inches (given)
Radius = 11.5 inches
2 Chords of length = 14 inches ( You didn't specify if the 14 inches is for both chords or for a single cord. I'll assume it's for two cords 14 and 14inches apart.
To clearly solve this, we'll make some mild assumptions.
Let the perpendicular distance of the chords from the center of the circle to represented as " x and y"
Therefore:
x^2 + 7^2 = 11.5 ^ 2
x^2 + 49 = 132.25
x^2 = 132.25 - 49
x^2 = 83.25
x = √ 83.25
x = 9.12 inches
Since the cords have thesame length (Assumed from the way the question was structured, the distance would still be thesame)
y^2 + 7^2 = 11.5 ^ 2
y^2 + 49 = 132.25
y^2 = 132.25 - 49
y^2 = 83.25
y = √ 83.25
y = 9.12 inches
Therefore, the distance will be :
9.12 + 9.12 = 18.24 inches
Have fun!
To find the distance from each chord to the center of the circle, use the Pythagorean theorem to calculate the height of the isosceles triangle formed by the chord and two radii.
To find the distance from each chord to the center of the circle, we first need to find the radius of the circle. Since the diameter is given as 23 inches, the radius would be half of that, which is 11.5 inches. Now, let's consider one of the chords. When a chord is drawn in a circle, it forms an isosceles triangle with the center and two radii. The distance from the chord to the center of the circle is the height of this isosceles triangle. Using the Pythagorean theorem, we can find the height:
d² = r² - (c/2)²
where d is the distance from the chord to the center, r is the radius, and c is the length of the chord.
Plugging in the values, we get:
d² = (11.5)² - (14/2)²
Simplifying this equation gives:
d² = 132.25 - 49
d² = 83.25
Taking the square root of both sides gives:
d ≈ √83.25 ≈ 9.12 inches
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Answer:
x = 7 cm
Step-by-step explanation:
The two triangles are similar so ...
x/(6 cm) = (42 cm)/(36 cm)
Multiplying by 6 cm, you get ...
x = (6 cm)(42 cm)/(36 cm) = (6 cm)(7/6)
x = 7 cm