Q: How much is 3 to the power of 4?

Answer: 81 Explanation: To calculate \(3^4\), multiply 3 by itself four times: \[ 3 \times 3 \times 3 \times 3 = 81 \]

Q: What is 3 to the 3rd power?

Answer: 27 Explanation: To calculate \(3\) to the 3rd power, you multiply \(3\) by itself three times: \[ 3 \times 3 \times 3 = 9 \times 3 = 27 \]

Q: Triangle 1 has an angle that measures 34° and an angle that measures 48°. Triangle 2 has an angle that measures 34° and an angle that measures a°, where a ≠ 48. Based on the information, Jennifer claims that triangle 1 and triangle 2 cannot be similar. What value of a, in degrees, will refute Jennifer's claim?

Answer: \( a = 98^\circ \) Explanation: For two triangles to be similar, they must have the same angles. Triangle 1 has angles of \(34^\circ\), \(48^\circ\), and \(98^\circ\) (since the sum of angles in a triangle is \(180^\circ\)). Triangle 2 has angles \(34^\circ\), \(a^\circ\), and another angle. To refute Jennifer's claim, \(a\) must be \(98^\circ\) to match the third angle of Triangle 1. Steps: Sum of Angles in a Triangle: The sum of the angles in any triangle is \(180^\circ\). Calculate Third Angle of Triangle 1: \[ 180^\circ - 34^\circ - 48^\circ = 98^\circ \] So, the angles of Triangle 1 are \(34^\circ\), \(48^\circ\), and \(98^\circ\). Determine Condition for Similarity: Triangle 2 has an angle of \(34^\circ\) and \(a^\circ\). For similarity, the third angle must be \(180^\circ - 34^\circ - a^\circ\). Set Condition for Similarity: To be similar, Triangle 2 must have angles \(34^\circ\), \(a^\circ\), and the third angle that matches Triangle 1's \(98^\circ\). Therefore, \(a = 98^\circ\). Thus, setting \(a = 98^\circ\) will make Triangle 2 similar to Triangle 1, refuting Jennifer's claim.

Q: Acute Angles Write the following function in terms of its cofunction. Assume that all angles in which an unknown appears are acute angles. sin (θ + 25°) ___ sin (θ + 25°) = cos 65 (Simplify your answer. Do not include the degree symbol in your answer.)

Answer: \( \cos(65^\circ - \theta) \) Explanation: The problem involves expressing the sine function in terms of its cofunction, cosine. The cofunction identity for sine and cosine states that \(\sin(90^\circ - x) = \cos(x)\). We need to express \(\sin(\theta + 25^\circ)\) using this identity. Steps: Identify the Cofunction Identity: The cofunction identity for sine is \(\sin(90^\circ - x) = \cos(x)\). Rewrite the Expression: We have \(\sin(\theta + 25^\circ)\). To use the cofunction identity, we need to express this in the form \(\sin(90^\circ - x)\). Set up the Equation: Let \(x = 90^\circ - (\theta + 25^\circ)\). Simplify: \[ x = 90^\circ - \theta - 25^\circ = 65^\circ - \theta \] Apply the Cofunction Identity: Using \(\sin(90^\circ - x) = \cos(x)\), we have: \[ \sin(\theta + 25^\circ) = \cos(65^\circ - \theta) \] Therefore, \(\sin(\theta + 25^\circ)\) is expressed as \(\cos(65^\circ - \theta)\).

Q: Write the name of the period that has the digits 913.

Answer: Thousands Explanation: In the context of place value in the decimal number system, each group of three digits is referred to as a "period." The periods are named from right to left as units, thousands, millions, etc. The digits 913 fall in the thousands period. Steps: Identify the Place Value System: The decimal system is organized in groups of three digits, each called a period. Determine the Period Name: The first period from the right is the units (or ones) period. The second period is the thousands period. The third period is the millions period, and so on. Locate the Digits 913: Since 913 is typically placed in the second group from the right in a larger number, it belongs to the thousands period. Thus, the name of the period that has the digits 913 is the thousands period.

Question

How many Acres in a Square Mile?

Accepted Answer

Answer: 640 acres

Explanation: A square mile is a unit of area commonly used in the United States. One square mile is equivalent to 640 acres. This conversion is based on the definition that an acre is a measure of land area in the imperial system, and there are 640 acres in one square mile.