∠1 and ∠2 are supplementary // given∠3 and ∠4 are supplementary // given∠1 ≅ ∠3 // given m∠1 + m∠2 = 180° // definition of supplementary anglesm∠3 + m∠4 = 180° // definition of supplementary angles m∠1 + m∠2 = m∠3 + m∠4 // transitive property of equality m∠1 = m∠3 // definition of congruent angles m∠1 + m∠2 = m∠1 + m∠4 // substitution property of equality (replaced m∠3 with m∠1) m∠2 = m∠4 // subtraction property of equality (subtracted m∠1 from both sides) ∠2 ≅ ∠4 // definition of congruent angles
Answer:
Guitarist wtote 25 songs
Drummer wrote 10 songs
Step-by-step explanation:
G: number of guitarist songs
D: number of Drummer songs
We have:
G=3D - 5 (The guitarist wrote 5 fewer than three times the number of songs that the drummer wrote)
G+D=35 (They wrote a total of 35 songs)
That is the meaning of each equation.
Now we have to solve these system of equations:
G=3D-5
G+D=35
Using the substitution method:
(3D-5)+D=35
4D=35+5
4D+40
D=10
Thus: G=35-10
G=25
Answer:
Proven
Step-by-step explanation:
We prove the polynomial with factorization. We must first simplify the expression before we can factorize:
4 is the common number and we can take it out of the expression:
We can factorize further with the x term being zero. For this to be true we must have -2x and 2x to cancel out and therefore the expression is proven:
The area of the rectangular roof (both sides of the roof) = 1,360 ft²
Cost to cover both sides = $1,020
<h3>What is the Area of a Rectangle?</h3>
The area of a rectangle = (length)(width)
- Length of one side of the roof = 40 ft
- Width of one side of the roof = √(15² + 8²) = 17
Area of both sides of the roof = 2(area of rectangle) = 2(40×17) = 1,360 ft²
Cost to cover both sides = 1,360 × 0.75 = $1,020
Learn more about the area of a rectangle on:
brainly.com/question/1884491
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