Three numbers are in the ratio 6:3:1, and the sum of these numbers is 420. If the first number is reduced by 50%, and the second number is increased by 42, and the sum of the numbers remain the same, find the resulting ratio of the numbers .

Answers

Answer 1

Answer: $x:y:z\ \ \ \Leftrightarrow\ \ \ 6:3:1\n \n (x)/(z) =(6)/(1)\ \ \ \Rightarrow\ \ \ x=6z\ \ \ \ \ \ \ and\ \ \ \ \ \ \ (y)/(z) =(3)/(1)\ \ \ \Rightarrow\ \ \ y=3z\n \nx+y+z=420\ \ \ \Rightarrow\ \ \ 6z+3z+z=420\ \ \ \ \Rightarrow\ \ \ \ 10z=420\ /:10\n \nz=42\ \ \ \Rightarrow\ \ \ \ x=6\cdot42=252\ \ \ \ and\ \ \ \ y=3\cdot42=126\n \n \na=x-50\%x=50\%x= (1)/(2) \cdot252=126=3\cdot42\n \nb=y+42=126+42=168=4\cdot42\n \nc=420-126-168=126=3\cdot42\n \na:b:c\ \ \ \Leftrightarrow\ \ \ 3:4:3$

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Solve Equation
log (x-9) = 1 - log x

Answers

$\log (x-9) = 1 - \log x \n D:x-9>0 \wedge x>0\n D: x>9 \wedge x>0\n D:x>9\n \log(x-9)+\log x=1\n \log x(x-9)=1\n 10^1=x^2-9x\n x^2-9x-10=0\n x^2+x-10x-10=0\n x(x+1)-10(x+1)=0\n (x-10)(x+1)=0\n x=10 \vee x=-1\n -1\not \in D \Rightarrow x=10$

What is a property of irrational numbers?A. Can be written as a fraction
B. Non-repeating
C. Can be written as a ratio
D. Terminating

Answers

. an irrational number is any real number that cannot be expressed as a ratio of intergers.irrational numbers cannot be represented as terminating or repeating decimals.

your answer is a:

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