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Resources

Find derivatives of using multiple formulae

2

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1

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Rational Expressions / Equations QUIZ

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5

3

2024

8

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\frac{p^{2}-6p-27}{p^{2}-17 p+72}

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\frac{p-8}{p+3};\{9,-3\}

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\frac{9p^{2}}{p+8};\{1,-8\}

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\frac{7(p+1)}{5p+6};\left\{-\frac{6}{5}\right\}

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\frac{p+3}{p-8};\{9,8\}

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Simplify each expression.

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2

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\frac{2}{b+1}+\frac{3}{b-5}

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\frac{18 b+5-2b^{2}}{6b(b-1)}

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\frac{23 b+5-4b^{2}}{6b(b-1)}

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\frac{15 b+5-2b^{2}}{6b(b-1)}

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3

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\frac{6}{n-2}-\frac{5}{n+3}

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\frac{p-8}{p+3};\{9,-3\}

0

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\frac{p-8}{p+3};\{9,-3\}

1

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\frac{p-8}{p+3};\{9,-3\}

2

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\frac{p-8}{p+3};\{9,-3\}

3

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\frac{p-8}{p+3};\{9,-3\}

4

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4

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\frac{p-8}{p+3};\{9,-3\}

5

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5

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\frac{p-8}{p+3};\{9,-3\}

6

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\frac{p-8}{p+3};\{9,-3\}

7

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\frac{p-8}{p+3};\{9,-3\}

8

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9

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\frac{p-8}{p+3};\{9,-3\}

9

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\frac{9p^{2}}{p+8};\{1,-8\}

0

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\frac{9p^{2}}{p+8};\{1,-8\}

1

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\frac{9p^{2}}{p+8};\{1,-8\}

2

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\frac{9p^{2}}{p+8};\{1,-8\}

3

Which equation best matches the graph shown below?

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y=-0.8 x^{2}+x-6

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y=0.8 x^{2}+x-6.3

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y=0.8 x^{2}+x-6

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y=-0.8 x^{2}+x-6.3

IUPAC name of the following compound is \

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2

1

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1

2

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2

2

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1

1

11

\lim _{(x, y) \rightarrow(0,0)} \frac{y^{2} \operatorname{sen}^{2} x}{x^{4}+y^{4}}

\frac{-9r^{2}s^{6}t^{4}}{54r^{5}s^{2}t^{8}}

3

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7

7

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x^{3}+3xy+2y^{3}=17

, then in terms of

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x

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y

(dy)/(dx)=

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((x^{2}+y)/(x+2y^{2}))

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((x^{2}+y)/(x+2y))

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((x^{2}+y)/(2y^{2}))

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((x^{2}+y)/(x+y^{2}))

3

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7.7 \mathrm{pts}

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x^{3}+3 x y+2 y^{3}=17

, then in terms of

x

y, \frac{d y}{d x}=

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-\left(\frac{x^{2}+y}{x+2 y^{2}}\right)

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-\left(\frac{x^{2}+y}{x+2 y}\right)

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-\left(\frac{x^{2}+y}{2 y^{2}}\right)

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-\left(\frac{x^{2}+y}{x+y^{2}}\right)

1-x^{2}+\frac{x^{4}}{2!}-\frac{x^{6}}{3!}+\frac{x^{8}}{4!}+\cdots+(-1)^{n} \frac{x^{2 n}}{n!}+\cdots

converges to which of the following?

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\cos \left(x^{2}\right)+\sin \left(x^{2}\right)

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1+x \sin x

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\cos x

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e^{-x^{2}}

\lim _{x \rightarrow 2} \frac{x^{2}+x-6}{x-2}

\frac{\sqrt{54 a^{3} b^{7}}}{\sqrt{6 b^{5}}}

Which equations define

y

as a nonlinear function of

x

? Select all that apply.

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Multi-select Choices:

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y = 4x^2 + 5x - 8

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y = -8 + 5x

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y = x^3 + 1

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y = x - 9^2

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y = \sqrt{x} - 3

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y = x^2

2

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\int 13 e^{x} d x

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\int 3 e^{-(2 x+7)} d x

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\int\left(3 e^{x}+\frac{4}{x}\right) d x \quad(x>0)

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\int 4 x e^{x^{2}+3} d x

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\int\left(5 e^{x}+\frac{3}{x^{2}}\right) d x \quad(x \neq 0)

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\int x e^{x^{2} 19} d x

1

. Find the following:

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\int 16 x^{-3} d x \quad(x \neq 0)

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\int 2 e^{-2 x} d x

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\int 9 x^{8} d x

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\int \frac{4 x}{x^{2}+1} d x

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\int\left(x^{5}-3 x\right) d x

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\int(2 a x+b)\left(a x^{2}+b x\right)^{7} d x

\frac{a^{2}-a b+b^{2}}{a^{3}+b^{3}}

\frac{x^{3}-3 x^{2} y+3 x y^{2}-y^{3}}{x^{3}-y^{3}}

\frac{(x+y)^{2}}{x^{2}-x y+y^{2}}

\frac{x^{3}+3x^{2}y+3xy^{2}+y^{3}}{x^{3}+y^{3}}

\frac{a^{2}-a b+a b^{2}}{a^{2}-b^{2}+a b^{2}+b^{3}}

Which of the following expressions are equal to

30,600

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\sum_{n=1}^{45} 30n-10

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\sum_{n=5}^{49} 20+30(n-5)

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\sum_{n=2}^{46} -10+30(n-2)

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D. I, II, and III

4 e^{\frac{7 \pi}{4} i} i+2 e^{\frac{3 \pi}{2} i}

\frac{-z x^{4} y^{0}}{-4 x^{4} y^{0} z^{2}}

\frac{-3 h k^{-6}}{-9 h^{-7} j^{6} k^{0}}

\left(x^{3} y^{5}\right)^{3} \cdot-x^{6} y^{5}

\frac{a^{5} b^{2}}{4 b} \cdot \frac{16 a^{9} b^{4}}{a^{3} b^{7}}

What could be the value of

x

in the following equation? Select all that apply.

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x^2 = 0.25

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Multi-select Choices:

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-\sqrt{0.25}

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-0.5

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\sqrt{0.25}

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0.5

9

\left(156 u^{24} w^{4}\right)^{0}

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11

\left(-a^{3} b^{5}\right)^{7}

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\frac{21}{i} \int e^{7 i x}-e^{-7 i x} d x

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and write your answer as a trig function.

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=

\square

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+C

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f^{\prime}(x)=\frac{(2-x)^{2}}{x^{3}}

x>0

x

is always positive and

f(1)=2

, what is the equation for

f ?

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f(x)=\frac{1}{2}+\frac{4}{x}-\frac{5}{2 x^{2}}

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f(x)=\ln (x)+\frac{4}{x}-\frac{2}{x^{2}}

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f(x)=\ln (x)+\frac{1}{x^{4}}-\frac{4}{3 x^{3}}+\frac{7}{3}

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f(x)=\ln (x)-\frac{2}{x^{2}}+\frac{4}{x}+2

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Rational Algebraic expressions

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\frac{a}{b} \div \frac{c}{d}=\frac{a}{b} \cdot \frac{d}{c}=\frac{a d}{b c}

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1

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\begin{aligned} & \frac{x+y}{x-y} \div \frac{x}{y} \\ = & \frac{x+y}{x-y} \cdot \frac{y}{x} \\ = & \frac{(x+y) \cdot(y)}{(x-y) \cdot(x)} \\ = & \frac{x y+y^{2}}{x^{2}-x y} \end{aligned}

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12

48

11

Work out the value of each expression.

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5\left(x^{3}-x\right)+\frac{5 x^{2}}{3}-12 x

x=3

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\frac{3 y+16}{4}+\left(\frac{y}{2}\right)^{4}-\frac{20}{y}

y=4

\quad \frac{3 y-5}{2}+2 y^{3}-\frac{21}{y}

y=3

7

permen stroberi,

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10

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8

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10

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15

permen karamel.

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Semua permen memiliki bungkus yang sama dan identik. Anda diminta untuk mengambil sejumlah permen dengan syarat setidaknya Anda memperoleh dua rasa yang berbeda (contohnya, Anda mungkin memperoleh:

1

permen cokelat dan

1

permen stroberi; atau

1

permen cokelat dan

1

permen jeruk; dan lain-lain). Paling sedikit, berapa banyak permen yang harus Anda ambil jika pengambilan dilakukan

\(\newlineabla 4 x y^{2} z^{3} \cdot \sin 45^{\circ} \)

\frac{x^{2}+25}{x^{2}-10x+25}

(b) In the figure below,

m\angle SUT=65^\circ

and m\overparen{PR}=62^\circ. Find m\overparen{ST}.

The solution set for

2 x^{2}-7 x-4=0

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1

\{2,-1\}

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3

\{-2,1\}

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2

\left\{-\frac{1}{2}, 4\right\}

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4

\left\{\frac{1}{2},-4\right\}

-21a^{6}b

-3a^{2}b

, the quotient is

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1

7a^{4}

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2

-7a^{3}

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3

7a^{3}b

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4

7a^{4}b

-21 a^{6} b

b y-3 a^{2} b

, the quotient is

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1

7 a^{4}

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3

7 a^{3} b

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2

-7 a^{3}

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4

7 a^{4} b

Which of the following equations represent functions where

x

is the input and

y

is the output? Select all that apply.

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Multi-select Choices:

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y = 0

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y - 2x = 6

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2x - y = 6

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y = x^3

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y = x^2

Kepala bagian produksi PT. SHARP melaporkan bahwa rata-rata produksi televisi yang lolos quality control setiap kali produksi adalah sebesar

15\%

. Jika dari total produksi tersebut diambil secara acak sebanyak

4

televisi, berapakah peluang terdapat tepat

2

televisi yang lolos quality control ?

Kepala bagian produksi PT. SHARP melaporkan bahwa rata-rata produksi televisi yang lolos quality control setiap kali produksi adalah sebesar

15\%

. Jika dari total produksi tersebut diambil secara acak sebanyak

4

televisi, berapakah peluang tidak ada televisi yang lolos quality control ?

ntary work must be shown on this pape

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2

\frac{-3 x-15}{x^{2}+x-20}-\frac{x+2}{x-4}

Select all the expressions that are equivalent to

10^3 \times 6^3

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Multi-select Choices:

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60^3

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\frac{60^6}{60^3}

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60^9

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60^6

Select all the expressions that are equivalent to

10^2 \times 5^2

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Multi-select Choices:

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\frac{1}{50^{-2}}

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50^2

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\frac{1}{50^2}

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50^4

Select all the expressions that are equivalent to

7^3 \times 10^3

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Multi-select Choices:

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70^3

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\frac{1}{70^{-3}}

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70^9

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70^6

1

. Which expression is equivalent to

3 x^{2}-8 x-3

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(2 x+1)(x-3)

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(3 x-3)(x+1)

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(3 x+1)(x-3)

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(x+3)(3 x-1)

7

10 \mathrm{~km}

P

, on a bearing of

150^{\circ}

. It then sails

15 \mathrm{~km}

on a bearing of

020^{\circ}

. How far is the ship from P? What is its bearing from P?

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Simplify each expression. Find each answer in the decoder box to get the corresponding letter.

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1

\left(5 x^{2}-3 x+5\right)+\left(2 x^{2}-8 x-1\right)

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2

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

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3

(3 x+8)(2 x-5)

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4

(2 x+3)(2 x-3)

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5

(2 x-3)^{2}

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Your lock code is the list of code letters you got for \#

1

-5

above in order. Enter your lock code below using all capitals and no spaces. Example:

T W H B N

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\begin{tabular}{|c|c|}

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\hline Answer & Code \\

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2 x^{2}-3 x-5

\mathrm{~N}

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6 x^{2}+x-40

\mathrm{~T}

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\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

0

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

1

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\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

2

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

3

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\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

4

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

5

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\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

6

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

7

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\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

8

\left(4 x^{2}-2 x-8\right)-\left(2 x^{2}-x+3\right)

9

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(3 x+8)(2 x-5)

0

(3 x+8)(2 x-5)

1

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(3 x+8)(2 x-5)

2

(3 x+8)(2 x-5)

3

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die Minusklammer auf.

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8-(4 x+12)

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-(-4 a-5 b)

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2 x-(-10 y-4 z)

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-(4 y

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3 a-

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-5

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ie (lammer auf und fasse zusammen.

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3 x+15)

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4 x+(6-2 x)

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9 x-10 y)

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11 x-(-9 x+10 y)

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13 x

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-(-4 a-5 b)

0

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e Klammer auf und fasse zusammen.

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40 x+30)

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-(-4 a-5 b)

1

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-(-4 a-5 b)

2

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-(-4 a-5 b)

3

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-(-4 a-5 b)

4

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-(-4 a-5 b)

2

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10

9

The Giant Circle CHALLENGE!

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Findeach angle meosure!

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m \angle 1=

\qquad

m \angle 12=

\qquad

12

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m \angle 2=

\qquad

m \angle 13=

\qquad

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m \angle 3=

\qquad

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\qquad

m \angle 1=

2

\qquad

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m \angle 1=

4

\qquad

m \angle 1=

6

\qquad

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m \angle 1=

4

m \angle 1=

9

\qquad

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\qquad

\qquad

2

\qquad

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\qquad

4

\qquad

\qquad

6

\qquad

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\qquad

8

\qquad

9

m \angle 12=

0

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m \angle 12=

1

\qquad

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m \angle 12=

3

\qquad

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m \angle 12=

5

\qquad

m \angle 12=

7

\qquad

m \angle 12=

9

is the center of the circle

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\qquad

0

\qquad

1

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\qquad

2

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\qquad

3

\qquad

10

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\qquad

5

\qquad

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\qquad

7

\qquad

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\qquad

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