Answer:
x = 18
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
- Subtract Property of Equality
Step-by-step explanation:
<u>Step 1: Define</u>
2x + 4y = 24
y = -3
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in <em>y</em>: 2x + 4(-3) = 24
- Multiply: 2x - 12 = 24
- Isolate <em>x</em> term: 2x = 36
- Isolate <em>x</em>: x = 18
Answer:
- 1. First blank: <u>∠ACB ≅ ∠E'C'D'</u>
- 2. Second blank: <u>translate point E' to point A</u>
Therefore, the answer is the third <em>option:∠ACB ≅ ∠E'C'D'; translate point D' to point B</em>
Explanation:
<u>1. First blank: ∠ACB ≅ ∠E'C'D'</u>
Since segment AC is perpendicular to segment BD (given) and the point C is their intersection point, when you reflect triangle ECD over the segment AC, you get:
- the image of segment CD will be the segment C'D'
- the segment C'D' overlaps the segment BC
- the angle ACB is the same angle E'C'D' (the right angle)
Hence: ∠ACB ≅ ∠E'C'D'
So far, you have established one pair of congruent angles.
<u>2. Second blank: translate point D' to point B</u>
You need to establish that other pair of angles are congruent.
Then, translate the triangle D'C'E' moving point D' to point B, which will show that angles ABC and E'D'C' are congruents.
Hence, you have proved a second pair of angles are congruent.
The AA (angle-angle) similarity postulate assures that two angles are similar if two pair of angles are congruent (because the third pair has to be congruent necessarily).
So let's see here...
6:00 A.M. temperature is 33°F.
12:00 P.M temperature increased by 10°F making it 43°F.
3:00 P.M. temperature increased by another 12°F making it 55°F.
At 10:00 P.M it would decrease by 15°F making it 40°F.
The temperature would need to fall (or decrease) by 7°F to reach the original temperature of 33°F
Hope this helped!
Answer:
112 hours
Step-by-step explanation:
1 week = 7 days
2 weeks = 14 days
= 14 × 8
= 112 hours
The general form is x^2 + y^2 = r^2 where r = the radius of the circle. The radius is 15 so the equation is x^2 + y^2 = 15^2. That is x^2 + y^2 = 225.J
