Solve the exponential equation. Express the solution set in terms of natural logarithms.
= -1
Fill in the blank(s) with the appropriate word(s).
{ln (-1 + sqrt(2))}
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Solve the problem.A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, whereas the semicircle is of tinted glass that transmits only one-fifth as much light per unit area as clear glass does. The total perimeter is fixed. Find the proportions of the window that will admit the most light. Neglect the thickness of the frame.
A. 
= 
B. 
= 
C. 
= 
D. 
= 
Provide an appropriate response.Solve the following equation: 
= 
Fill in the blank(s) with the appropriate word(s).
Solve the equation. First simplify the expression by combining like terms.-6b + 7 + 4b = -3b + 12
A. { -12 } B. { -7 } C. { 12 } D. { 5 }
Translate the sentence into an equation. If needed, use x to represent "a number."Seven added to twice a number equals -23.
A. 2x - 23 = 7 B. 2(x + 7) = -23 C. 2x + 23 = 7 D. 2x + 7 = -23