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Questions in mathematics

[Jawaban] Consider the equation [tex]$0.3 \cdot e^{3 x}=27$[/tex]. Solve the equation for [tex]$x$[/tex]. Express the solution as a logarithm in base-e. [tex]$x=$[/tex] Approximate the value of [tex]$x$[/tex]. Round your answer to the nearest thousandth. [tex]$x \approx$[/tex]

[Jawaban] Work out $\frac{5}{6} \times \frac{7}{3}$. Give your answer as a fraction in its simplest form.

[Jawaban] $\sqrt{75 t^{11} u^3}$ Assume that all variables represent positive real numbers.

[Jawaban] (U15) A is the point $(-3, -2)$ and B is $(4, 3)$. 1. Find the midpoint of the line segment AB. 2. Complete the table for $y = 7 + 4x - 3x^2$ for the interval $-3 \leq x \leq 3$. | x | -3 | -2 | -1 | 0 | 0.5 | 1 | 1.5 | 2.5 | 3 | | --- | ----- | -- | -- | --- | --- | --- | --- | --- | --- | | y | -32 | | | 7.5 | 8.5 | | 1 | 1 | 8 | 3. Using 2 cm as 1 unit on the x-axis and 1 cm as 1 unit on the y-axis, draw the graph of y for the given intervals.

[Jawaban] 10 Case-based Questions A. Students of Winkee Wee school visit a plant nursery with their class teachers. In the nursery, they see that the plants are kept in rows where the number of plants in each row follows a pattern. Based on the above information, answer the following questions. (i) There are 3 plants in the first row, 6 in the second row, and 9 plants in the third row. If the same pattern is followed, how many plants will be in the ninth row? (a) 18 (b) 27 (c) 36 (d) 9 (ii) How many total plants would be there in the 25th row? (a) 50 (b) 65 (c) 75 (d) 100 B. Bob, the builder, is building a museum made of glass. He starts the construction by placing 1 glass block in the first row, 4 glass blocks in the second row, 9 glass blocks in the third row, and so on. Based on the above information, answer the following questions. (i) If Bob continues the same pattern, then how many glass blocks will be in the 7th row? (a) 18 (b) 27 (c) 36 (d) 49 (ii) How many glass blocks are needed to construct the 9th row? (a) 64 (b) 81 (c) 100 (d) 121 C. A group of friends is counting the number of stars they see each night. On the first night, they see 5 stars. Each subsequent night, they see 2 more stars than the previous night. (i) How many stars will they see on the 4th night? (a) 11 (b) 14 (c) 15 (d) 16 (ii) If this pattern continues, how many stars will they see on the 10th night? (a) 20 (b) 21 (c) 24 (d) 23

[Jawaban] Solve the equation. $-9x + 1 = -x + 17$

[Jawaban] [tex]\frac{1}{2} \div \frac{3}{4}[/tex]

[Jawaban] If [tex]$f(x)=x-2$[/tex], which of the following is the inverse of [tex]$f(x)$[/tex]? A. [tex]$f^{-1}(x)=2-x$[/tex] B. [tex]$f^{-1}(x)=2 x$[/tex] C. [tex]$f^{-1}(x)=x-2$[/tex] D. [tex]$f^{-1}(x)=x+2$[/tex]

[Jawaban] Which equation represents a circle with a center at $(2,-8)$ and a radius of $11$? A. $(x-8)^2+(y+2)^2=11$ B. $(x-2)^2+(y+8)^2=121$ C. $(x+2)^2+(y-8)^2=11$ D. $(x+8)^2+(y-2)^2=121

[Jawaban] The first equation in the system models the height, $h$, of a falling volleyball as a function of time, $t$. The second equation models the height, $h$, of the hands of a player jumping up to spike the ball as a function of time, $t$. Which statement describes the situation modeled by this system? $\left\{\begin{array}{l} h=14-16 t^2 \\ h=7+24 t-16 t^2 \end{array}\right.$ A. The volleyball is 7 feet above the ground at the instant the player begins her jump. B. The volleyball is 14 feet above the ground at the instant the player begins her jump. C. The volleyball is 16 feet above the ground at the instant the player begins her jump. D. The volleyball is 24 feet above the ground at the instant the player begins her jump.