Step-by-step explanation:
3(x+3)=12
3x+9=12
3x=12-9
3x=3
x=1
1. Given
2. Definition of Supplementary Angles
3. First Substitution
4. Subtraction property of Equality
5. Second Substitution
6. Exterior Side in Opposite Rays
7. If corresponding angles are equal, then lines are parallel
Answer:
The product of a non-zero rational number and an irrational number is irrational.
Answer:
D. domain: (-infinity, infinity); range: [1, infinity)
Step-by-step explanation:
The domain is the values that x can take
The domain is (-infinity, infinity)
The range is the values that y can take
absolute value is 0 or greater
cos x is from -1 to 1
The minimum value is when x=0
The smallest value is 1 and the largest is infinity
The correct answer is: [D]: " 7.2 units" .
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Explanation:
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Use the Pythagorean theorem:
a² + b² = c² ;
in which: "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle); and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle; We wish to solve for "c" ;
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6² + 4² = c² ; Solve for "c" ;
↔ c² = 6² + 4² ;
= (6*6) + (4*4) ;
= 36 + 16 ;
= 52 ;
c² = 52 ;
Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ;
√(c²) = √52 ;
c = √52 ;
At this point, we know the 7² = 49 ; 8² = 64 ; so, the answer is somewhere between "7" and "8" ; yet closer to "7" ; so among the answer choices given;
The correct answer is: [D]: " 7.2 units" .
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However, let use a calculator:
c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
which corresponds to:
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Answer choice: [C]: " 7.2 units" .
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