Answer:
DU = 86
Step-by-step explanation:
Properties of a rectangle,
- Opposite sides are equal in measure.
- Diagonals of a rectangle are equal.
- Diagonals bisect each other.
In the given rectangle QUAD,
Diagonals AQ and DU bisect each other at P.
AQ = DU
2(QP) = DU [Since, AQ = 2(PQ)]
2(2x + 7) = 5x - 4
4x + 14 = 5x - 4
5x - 4x = 14 + 4
x = 18
Since, DU = 5x - 4
DU = 5(18) - 4
= 90 - 4
= 86
Therefore, measure of DU = 86 units
The possible digits could be 0, 1, 2, 3, or 4 as they would cause the entire number to round down instead of up.
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Answer:
Step-by-step explanation:
we know that
The sum of interior angles in a triangle must be equal to 180 degrees
so
solve for x
