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Questions in mathematics

📝 Answered - Solve $\log _5(2 x)-\log _{\frac{1}{5}}(x)=\log _{25}(x+4)$ graphically.

📝 Answered - Fill in the blanks to make the following statements true. a. (-45) x 16 = _ x (-45) b. 79 x (0 - 60) = (_ x 0) - (79 x _) c. -34 x 1 = 1 x _ d. -1 x (_ x 56) = (-1 x 0) x _ e. 99 x (-71) = _ x 99

📝 Answered - 2. Fill in the blanks. a. 1 crore = ______ million b. 1 million = ______ lakh c. 100 thousand = 1 ______ d. 1000 thousand = 1 ______ 3. Look at the number 78,93,245. a. Number of ones in 78,93,245 = 78,93,245 ones b. Number of tens = 789324 tens c. Number of hundreds = 78932 d. Number of thousands = ______ e. Number of lakhs = ______

📝 Answered - A student finishes the first half of an exam in [tex]$\frac{2}{3}$[/tex] the time it takes him to finish the second half. If the entire exam takes him an hour, how many minutes does he spend on the first half of the exam? (A) 20 (B) 24 (C) 27

📝 Answered - If [tex]s(x)=2-x^2[/tex] and [tex]t(x)=3 x[/tex], which value is equivalent to [tex](s \circ t)(-7)[/tex]? A. -439 B. -141 C. 153 D. 443

📝 Answered - Which exponential function has an initial value of $2$? $f(x)=2\left(3^x\right)$ $f(x)=3\left(2^x\right)$ | x | f ( x ) | | --- | ------- | | -2 | $\frac{1}{8}$ | | -1 | $\frac{1}{4}$ |

📝 Answered - If [tex]log_{10} 8 = 0.9031[/tex], find the value of [tex]4 \times log_{10} 16[/tex].

📝 Answered - The arithmetic sequence $1,3,5,7,9, \ldots$ represents the set of odd natural numbers. What is the explicit rule for the sequence? $I_k=1 \checkmark+(k-1) 2$ What is the 200th odd natural number? $a_{200}=\square$

📝 Answered - Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through $(-5,-5)$ and $(5,7)$ Type the point-slope form of the equation of the line. $\square$ (Use integers or simplified fractions for any numbers in the equation.)

📝 Answered - Melissa collected the data in the table. | x | Given | Predicted | Residual | |---|---|---|---| | 1 | 2 | 1 | 1 | | 2 | 3 | 4 | -1 | | 3 | 8 | 7 | 1 | | 4 | 9 | 10 | ? | When x=4, what is the residual? A. -3 B. -1 C. 1 D. 3