Math Problem Statement

T

The original question submitted by the user as text.

Solution

Sure, let's go through the questions one by one:

31. Inequalities

a) Form two simple inequalities:

Let xx be the number of women.

  • More than 30: x>30x > 30
  • Less than 37: x<37x < 37

b) Form a compound inequality:

Combine both: 30<x<3730 < x < 37

c) Represent the compound inequality on a number line:

Draw a number line and shade the region between 30 and 37, with open circles on 30 and 37 to indicate they are not included.

32. Ladder Problem

Given:

  • Ladder length: 6.5 m
  • Distance from tree base: 6 m

Use the Pythagorean theorem to find the height hh:

36 + h^2 = 42.25\\ h^2 = 42.25 - 36 = 6.25 \\ h = \sqrt{6.25} = 2.5$$ The height at which the ladder touches the tree is 2.5 meters. ### 33. Area of Grazing Area The area is a trapezium. Calculate each shape's area and add them: 1. Rectangle area = $$160 \times 60 = 9600$$ m² 2. Triangle area (base = 60, height = height given from apex): $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 60 \times \text{height}$$ 3. Convert to hectares (1 hectare = 10,000 m²). ### 34. Tile Problem a) **Calculate the area of each rhombus tile:** Given diagonals are 16 cm and 12 cm. The area $$A$$ of a rhombus is given by: $$A = \frac{1}{2} \times d_1 \times d_2$$ $$A = \frac{1}{2} \times 16 \times 12 = 96 \, \text{cm}^2$$ Let me know if you'd like any more details or help!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inequalities
Pythagorean Theorem
Area of Shapes
Geometry

Formulas

Inequality: x > 30, x < 37
Pythagorean Theorem: a^2 + b^2 = c^2
Area of a rhombus: A = (1/2) * d1 * d2
Area of a triangle: Area = (1/2) * base * height

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 7-9

Related Recommendation

Pythagorean Theorem and Area Calculations for Trapezoid and Rhombus

Solving Geometry Problems: Triangles, Rectangles, and Circles

Solving Inequalities, Triangle Area, and Simplifying Algebraic Expressions

Solving Geometry Problems: Triangle Area, Pythagoras Theorem, and Rectangle Area

Geometry Problems: Angles and Areas Explained