To determine the scale factor of the dilation, we determine the distances between the endpoints of the two lines through the equation,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting the known values.
Line Segment 1: d = √(1 - 2)² + (4 - 8)² = 4.123
Line Segment 2: d = √(18 - 14)² + (12 - 1)² = 11.70
Dividing the answers will give us 0.352
Answer: The correct answer is: [D]: "8" .
Step-by-step explanation:f y varies inversely with x; then y = k/x ; with "k" being the "constant" in this equation.
You can find the constant by substituting the values given: x = 16, f(x) = y = 2 ;
So, f(x) = y = 2 = k/16 ;
→ 2 = k / 16 ;
Solve for the constant; "k" ;
Multiply EACH SIDE of the equation by "16"
→ 16* (2) = (k / 16) * 16 ;
→ 32 = k ;
↔ k = 32 ;
As such, we can write the equation:
y = k/ x ; as:
→ y = 32/ x ;
Since we are given: "x = 4" ; Plug in that value; and solve for "y" ;
y = 32/4 = 8 .
y = 8 .
y = f(x) ;
So; f(x) = 8 ; which is: Answer choice: [D]: "8" .
Answer:
- x = 10
- B. 3/7
Step-by-step explanation:
1. (x - 2)/ 4 - (3x + 5)/7 = - 3
7(x -2) -4(3x +5) = -84 . . . . . . . multiply by 28
7x -14 -12x -20 = -84 . . . . . . . . eliminate parentheses
-5x -34 = -84 . . . . . . . . . . . . . . collect terms
-5x = -50 . . . . . . . . add 34
x = 10 . . . . . . . . . . . divide by -5
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2. 1/(1 + 1/(1 - 1/x)) = 4
1 = 4(1 +1/(1 -1/x)) . . . . multiply by the denominator
-3 = 4/(1 -1/x) . . . . . . . eliminate outer parentheses, subtract 4
-3(1 -1/x) = 4 . . . . . . . multiply by the denominator
-3 +3/x = 4 . . . . . . . . eliminate parentheses
3/x = 7 . . . . . . . . . . . add 3
x = 3/7 . . . . . . . . . . . multiply by x/7
Answer:
y=4x+9
Step-by-step explanation:
