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Questions in mathematics

[Jawaban] Using the definition of the derivative, find $f^{\prime}(x)$. Then find $f^{\prime}(1), f^{\prime}(2)$, and $f^{\prime}(3)$ when the derivative exists. $f(x)=-x^2+2 x-2$ $f^{\prime}(x)=$ $\square$ (Type an expression using $x$ as the variable.) Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. $f(1)=$ $\square$ (Type an integer or a simplified fraction.) B. The derivative does not exist. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. $f^{\prime}(2)=$ $\square$ (Type an integer or a simplified fraction.) B. The derivative does not exist. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. A. $f^{\prime}(3)=$ $\square$ (Type an integer or a simplified fraction.) B. The derivative does not exist.

[Jawaban] Select the correct answer. What is this expression in simplified form? $\frac{\sqrt{6}}{\sqrt{23}}$ A. $\frac{\sqrt{138}}{\sqrt{23}}$ B. $\frac{\sqrt{14}}{21}$ C. $\frac{\sqrt{138}}{23}$ D. $\frac{14 \sqrt{3}}{7}$

[Jawaban] Graph this function: [tex]f(x)=x^2-4 x-5[/tex] Step 1: Identify [tex]a[/tex] and [tex]b[/tex]. [tex]a=[/tex] $\square$ [tex]b=[/tex] $\square$ Check

[Jawaban] Evaluate the expression. [tex]$4! \cdot 3!$[/tex]

[Jawaban] Mrs. Hwang is taking her vehicle to the shop to have the gas tank expanded by 10 gallons. Now, it costs her $42.56 to fill the tank. Once the new tank is in, it will cost her $72.96. How large is her tank now? A. 20 gallons B. 16 gallons C. 18 gallons D. 14 gallons

[Jawaban] The line $y = x$ is transformed into the line $y=\frac{x}{4}+2$. Fill in the blanks to describe the slope and $y$-intercept of the new line. The slope is $\square$, and the line is shifted $\square$. flatter steeper

[Jawaban] What is the value of $a$ in the equation $3a + b = 54$, when $b = 9$?

[Jawaban] Which of the following is true? A. 8 multiplied by 4 is equal to 4 divided by [tex]$8 (8 \times 4 = 4 \div 8)$[/tex] B. 8 multiplied by 4 is equal to 4 multiplied by [tex]$8 (8 \times 4 = 4 \times 8)$[/tex] C. 8 divided by 4 is equal to 4 multiplied by [tex]$8 (8 \div 4 = 4 \times 8)$[/tex] D. 8 divided by 4 is equal to 4 divided by [tex]$8 (8 \div 4 = 4 \div 8)$[/tex]

[Jawaban] A right triangle has one angle that measures [tex]$23^{\circ}$[/tex]. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle [tex]$=\frac{1}{2} b h$[/tex] A. 68.7 [tex]$cm^2$[/tex] B. 161.8 [tex]$cm^2$[/tex] C. 381.3 [tex]$cm^2$[/tex] D. 450.0 [tex]$cm^2$[/tex]

[Jawaban] sin 30° and cos 30° = 2 A. True B. False