A piece of string is 112 inches long. Isabel wants to cut it into 2 pieces so that one piece is three times as long as the other. How long is each piece?

Answers

Answer 1

Answer: you have to divide 112 by 2 which is 56 then multiply it by three and you get 168

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An engineer scale model shows a building that is 3 inches tall. If the scale is 1 inch = 600 feet, how tall is the actual building in feet ?

Answers

The actual height of building is 1800 feet.

Step-by-step explanation:

Given,

Height of building in model = 3 inches

Scale used by engineer;

1 inch = 600 feet

Therefore;

Actual height of building = Height in model * Scale used

Actual height of building = 3 * 600

Actual height of building = 1800 feet

The actual height of building is 1800 feet.

70 POINTS! ∆ABC is reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x to form ∆A′B′C′.The coordinates of vertex A′ are ____.
The coordinates of vertex B′ are ____ .
The coordinates of vertex C′ are ____.

Answers

Answer:

A'(1, 1); B'(3, 2); C'(1, 2)

Step-by-step explanation:

The original points are A(1,1 ), B(2, 3) and C(2, 1).

Reflecting the triangle across the x-axis will negate every y-coordinate; this maps

(1, 1)→(1, -1); (2, 3)→(2, -3); (2, 1)→(2, -1)

Rotating the figure 90° clockwise about the origin switches the x- and y-coordinates and negates the x-coordinate; this maps

(1, -1)→(-1 -1); (2, -3)→(-3, -2); (2, -1)→(-1, -2)

Reflecting across the line y=x will negate both the x- and y-coordinates; this maps

(-1, -1)→(1, 1); (-3, -2)→(3, 2); (-1, -2)→(1, 2)

Final answer:

To find the coordinates of ∆ABC after reflection across the x-axis, rotation by 90°, and reflection across y = x, we would apply these transformations to each point. Initially reflected across x-axis results in (x, -y), the 90° rotation gives (-y, x), and final reflection over y = x gives (x, -y). To find A′B′C′ we would need original coordinates, but general rule follows this pattern.

Explanation:

In this mathematics problem, we will find the coordinates for vertex A′, B′, and C′ of ∆A′B′C′. Given a triangle ∆ABC reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = x, we need the original coordinates of A, B, and C to find A′B′C′. However, if we take a generic point (x, y), we can assume the following:

The reflection about the x-axis would turn it into (x, -y).
The 90° clockwise rotation about the origin would give the new coordinates (-y, x).
Finally, the reflection over the line y = x would change (-y, x) to (x, -y).

Assuming these transformations, we can find the final coordinates for A′, B′, and C′.