Ethan writes the ratio x8=y16 to help him reduce the size of a two-dimensional shape. If the new value of y is 3 units, what will be the value of x ?
To find the value of x when y is 3 units, we can use the ratio x8=y16.
First, we can simplify the ratio by dividing both sides by 8 to get x=y2.
Then, we substitute y=3 into the equation to find x:
x = 3/2
x = 1.5
Therefore, the value of x when y is 3 units will be 1.5 units.
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph?(1 point)
Responses
1.5 inches by 1 inch
1.5 inches by 1 inch
1 inch by 0.5 inches
1 inch by 0.5 inches
12 inches by 8 inches
12 inches by 8 inches
2 inches by 1 inch
To find a smaller scale drawing of the original printed photograph, we need to reduce the dimensions proportionally. The original dimensions are 6 inches by 4 inches.
A smaller scale drawing could be represented by a ratio where both dimensions are multiplied by the same factor.
For example, if we reduce the dimensions by a factor of 2, we would get 3 inches by 2 inches, which is smaller than the original size.
Let's check each option with that in mind:
1.5 inches by 1 inch:
Original dimensions multiplied by 0.25
6 inches x 0.25 = 1.5 inches
4 inches x 0.25 = 1 inch
1 inch by 0.5 inches:
Original dimensions multiplied by 0.1667 (rounded)
6 inches x 0.1667 = 1 inch
4 inches x 0.1667 = 0.6668 inches, not quite 0.5 inches
12 inches by 8 inches:
Original dimensions multiplied by 2
6 inches x 2 = 12 inches
4 inches x 2 = 8 inches
2 inches by 1 inch:
Original dimensions multiplied by 0.3333 (rounded)
6 inches x 0.3333 = 2 inches
4 inches x 0.3333 = 1.3332 inches, not 1 inch
Therefore, the dimensions that represent a smaller scale drawing of the original printed photograph are 1.5 inches by 1 inch.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
To find the area of the scale drawing of the triangle, we need to consider that the area of a triangle is calculated using the formula:
Area = 0.5 * base * height
For the original triangle:
Base = 8 inches
Height = 5 inches
Area = 0.5 * 8 * 5
Area = 20 square inches
Now, we need to determine the scale factor between the original triangle and the scale drawing by comparing the heights:
Original height: 5 inches
Scale drawing height: 2 inches
Scale factor = Scale drawing height / Original height = 2 / 5 = 0.4
To find the area of the scale drawing, we apply the scale factor to the area of the original triangle:
Area of scale drawing = Area of original triangle * (Scale factor)^2
Area of scale drawing = 20 * (0.4)^2
Area of scale drawing = 20 * 0.16
Area of scale drawing = 3.2 square inches
Therefore, the area of Crystal's scale drawing of the triangle is 3.2 square inches.
What is the approximate circumference of a circle that has a radius of 90? Use 3.14 for π and express your answer to the tenths place.
The formula to calculate the circumference of a circle is:
Circumference = 2πr
Given that the radius (r) is 90, and π ≈ 3.14, we can substitute these values into the formula:
Circumference = 2 * 3.14 * 90
Circumference = 564.6
Therefore, the approximate circumference of a circle with a radius of 90 is 564.6 units.
i got 565.2
Let's calculate it step by step to be certain:
Circumference = 2 * π * radius
Circumference = 2 * 3.14 * 90
Circumference = 565.2
Therefore, after recalculating, the approximate circumference of a circle with a radius of 90 using π ≈ 3.14 is 565.2 units. Thank you for rechecking.