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CaHeK987 [17]
2 years ago
14

a square with an area of 25 in.^2 is plotted on a grid so that the bottom-left corner is at the origin. The side of the square a

re horizontal and vertical. A reflection over what line maps the square onto itself?
Mathematics
1 answer:
bazaltina [42]2 years ago
3 0

Answer:

Reflection about the vertical line x = 2.5 inches will map the square unto itself

Step-by-step explanation:

The given parameters are;

The area of the square = 25 in²

The orientation of the sides of the square are horizontal and vertical

Therefore, we have;

The area, A, of the square given by the following relation;

A = Side²

A = 25 in²

Therefore;

The area of the square = 25 = side²

The length of the sides of the square = √A = √25 = 5

The length of the sides of the square = 5 inches

The reflection of a figure that maps the figure unto itself is a reflection along the line of symmetry

One of the line of symmetry that divides the square into two similar halves is the vertical straight that passes half way through the horizontal side, which is the point 2.5 inches to the right on the x-axis with the coordinates (2.5, 0)

Therefore, reflection about the line x = 2.5 inches will map the square unto itself.

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The axis of symmetry of quadratic ax²+bx+c is x=-b/(2a). For the given equation, the axis of symmetry is ...

  x = -4/(2(3/2)) = -4/3

The only graph with its vertex at x=-4/3 is graph A.

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<em>Additional comment</em>

You can also make the correct choice by evaluating the equation at a couple of different values of x. Convenient ones are x= -1, or 0, or +1. The value at x=0 is the y-intercept, (0, -2), which seems to be a point on all of the graphs. The value at x=1 is 3/2+4-2 = 3.5, which looks like it is only seen on graph A.

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2 years ago
If the area of the rectangle avove is 180 spuare inches, then x =
oksano4ka [1.4K]

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

This question is incomplete, the missing diagram is uploaded along this answer below.

<h3>What is the value of x?</h3>

Area of a rectangle is expressed as; A = l × b

Given that;

  • Length of the rectangle l = 20in
  • Breadth b = x
  • Area A = 180in²

A = l × b

180in² = 20in × x

x = 180in² / 20in

x = 9in

Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.

Hence, option A is the correct answer.

Learn more about area of rectangle here: brainly.com/question/12019874

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