at least 4 different angles are present
Answer:
c = 12.5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Identify</u>
Leg <em>a</em> = 7.5
Leg <em>b</em> = 10
Hypotenuse <em>c</em> = <em>c</em>
<em />
<u>Step 2: Solve for </u><em><u>c</u></em>
- Substitute in variables [Pythagorean Theorem]: 7.5² + 10² = c²
- Rewrite: c² = 7.5² + 10²
- Evaluate exponents: c² = 56.25 + 100
- Add: c² = 156.25
- [Equality Property] Square root both sides: c = 12.5
Answer:
First number = 33, Second number = -19
Step-by-step explanation:
We can use F to represent the first number and S to represent the second number.
Our two equations then are F + S = 14 and 2F + 3S = 9
We can use substitution:

This is the answer and method is above
Answer:
(d) m∠AEB = m∠ADB
Step-by-step explanation:
The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.
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<h3>applicable relations</h3>
Several relations are involved here.
- The measures of the arcs of a circle total 360°
- A diameter cuts a circle into two congruent semicircles
- The measure of an inscribed angle is half the measure of the arc it intercepts
<h3>application</h3>
In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)
If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.
The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.
m∠AEB = m∠ADB
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<em>Additional comment</em>
Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.