Math Problem Statement
Solution
Let's go through each question visible in the image:
-
Q7: "What is each angle size in a triple junction?"
Answer: 120°.
A triple junction occurs when three angles meet at a point. Since the sum of angles around a point is 360°, dividing that by 3 gives 120° per angle. -
Q8: "6 - 5/8 = 5.375"
This is a subtraction of a fraction from a whole number. The result, 5.375, is correct. Converting 5/8 to decimal gives 0.625, and subtracting from 6 results in 5.375. -
Q9: "Find 400% of $40."
Answer: $160.
400% of a number is 4 times the original number. So, . -
Q10: "A quadrilateral with two pairs of congruent adjacent sides is called a kite."
Answer: Kite.
A kite is defined as a quadrilateral with two distinct pairs of adjacent sides that are congruent. -
Q11: "The volume of a coffee tin 10 cm deep and 20 cm in diameter is ______ cm³."
To calculate the volume of a cylindrical object:
Volume = π × r² × h, where r is the radius and h is the height.
Here, the diameter is 20 cm, so the radius is 10 cm. The height (depth) is 10 cm.
Volume = cm³. -
Q12: "Is a triangle with sides of 3, 4, and 5 a Pythagorean triple?"
Answer: Yes.
A Pythagorean triple consists of three positive integers that satisfy the equation . For sides 3, 4, and 5:
, so the triangle is a Pythagorean triple. -
Q13: "Two sisters share an inheritance of $1 million dollars by a ratio of 2:3. How much does each sister inherit?"
The total ratio parts are .
The first sister receives , and the second sister receives .
Would you like further details or explanations on any of these answers?
Here are 5 related questions to expand your knowledge:
- How do you calculate the interior angles of polygons based on the number of sides?
- What is the relationship between percentages and fractions in real-world applications?
- What are the properties of different types of quadrilaterals, such as rectangles, rhombuses, and kites?
- How can the Pythagorean theorem be applied in three-dimensional geometry?
- How can ratios be used to solve real-world problems involving sharing or dividing quantities?
Tip: When calculating volumes of 3D shapes like cylinders, always double-check your units to ensure consistency (e.g., cm for both height and radius).
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Math Problem Analysis
Mathematical Concepts
Geometry
Percentage calculations
Pythagorean Theorem
Ratios
Formulas
Volume of a cylinder: V = πr²h
Percentage calculation: (percentage / 100) * amount
Pythagorean triple: a² + b² = c²
Ratio-based division
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 7-9
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