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\( \begin{array}{ll} & \text { Solve for } x: \\ 2.1 & (x-5)(x+3)=0 \\ 2.2 & 2^{x-1}=10-2^{x+1} \\ 2.3 & 5^{3 x-6}=125 \\ 2.4 & \frac{x^{2}-3}{2}=x\end{array} \)
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Suppose you invest \( \$ 190 \) a month for 6 years into an account earning \( 9 \% \) compounded monthly. After 6 years, you leave the money, without making additional deposits, in the account for another 29 years. How much will you have in the end?. Question Help: Video 1
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\( 22 \quad \frac { 1 } { 4 } x - \frac { 5 } { 2 } = - 2 \)
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Integrate: \( \int 5 x \sqrt{x-2} d x \)
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In this exercise, lines m and n are parallel. Find the measure of each numbered angle.
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Integrate \( \int_{-2}^{2} 24(6 x-3)^{3} d x \) Answer \( =\square \)
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D) A student claimed that the largest integer of \( k \) for which the graph \( y=2 x^{2}-3 x+k-1 \) meets the \( x \)-axis is 2 . Verify this statement.
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3.1.2 The number pattern is quadratic and \( T_{4}=2+5 y \). 3.2 In a linear number pattern, the \( 19^{\text {th }} \) term is 40 and the \( 7^{\text {th }} \) term is 16 . Thus, determine the first two terms.
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10. A girl swims 400 m in still water and then returns to the initial point (from where she started) in 20 minutes. Determine the speed of the girl. 11. A man is running at a speed of \( 3 \mathrm{~m} / \mathrm{s} \) and covers some distance in 15 sec . Find the time taken by his pet dog to cover the same distance at a speed of \( 10 \mathrm{~m} / \mathrm{s} \).
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Evaluate the integral by making the given substitution. \( \int \sec (4 x) \tan (4 x) d x, \quad u=4 x \) \( +C \)
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