Math Statement

Problem 101

1. $\begin{array}{r} 822 \\ \times \quad 9 \\ \hline \\ \hline \end{array}$

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Problem 102

$\begin{array}{r}710 \\ \times \quad 8 \\ \hline \\ \hline\end{array}$

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Problem 103

$\begin{array}{r}876 \\ \times \quad 7 \\ \hline\end{array}$

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Problem 104

$\begin{array}{r}227 \\ \times \quad 8 \\ \hline\end{array}$

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Problem 105

(1) Diffwentiale fam the first principle (i) $\sqrt{x}$ bit. m-itiply by $\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}$ $\sqrt{x+h}+\sqrt{x}$ (2) Diffenenhiahe withe naspoct to $x$ (a) $y=\left(x^{2}+4\right)\left(x^{7}+8\right)+x^{5}$ (b) $y=\sqrt{x-x^{2}}$ (c) $y=\frac{\operatorname{tn} x}{\sin x}$

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Problem 106

Part 1 of 2
Plot, compare, and order the square root, cube root, and expression. $\sqrt{\left(5^{2}-4^{2}\right)}, \sqrt[3]{-1},\left(\frac{1}{2}\right)^{2}+\sqrt{36}$

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Problem 107

$\begin{array}{l}\text { fil } a, b \\ \left(\frac{1}{6}(a+b)\right)^{-1}=\left[\begin{array}{ll}3 & 1 \\ 3 & 3\end{array}\right] \\ a b=\left[\begin{array}{cc}5 & -1 \\ -6 & 2\end{array}\right], \text { bas }\left[\begin{array}{cc}2 & 0 \\ -3 & 1\end{array}\right]\end{array}$

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Problem 108

$\frac{8^{x}+8^{x}+8^{x}}{4^{x}+4^{x}}=12$

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Problem 109

4. (Valor: 2,5) Incontre a equaçáo da hipérbole de excentricidade 2 e focos coincidentes com os focos da elipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ .
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Problem 110

4. (Valor: 2,5 ) Encontre a equaçao da hipérbole de excentricidade 2 e focos coincidentes com os focos da ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ .
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Problem 111

$x^{2}-\frac{2}{3} x-5=0$

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Problem 112

$\frac{x-4}{\sqrt{x}-2}=5 a^{0}$

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Problem 113

$x^{\frac{3}{2}}=125$

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Problem 114

$3^{-5} \cdot 3^{2}$

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Problem 115

$1 \& \quad$ For the function $f(x)=\frac{4 x-12}{x+5}$ , complete the following parts. (a) Find $f(x)$ for $x=-1$ and $d$ , if possible. (b) Find the domain of $f$ . (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\square$ A. $f(-1)=-5$ (Simplify your answer.) B. The value of $f(-1)$ is undefined.

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Problem 116

Add. $34.231+45.230$ 38.754 79.434 79.461 79.462

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Problem 117

$3 b+4=-8$

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Problem 118

$1 \& \quad$ For the function $f(x)=\frac{4 x-12}{x+5}$ , complete the following parts. (a) Find $f(x)$ for $x=-1$ and $d$ , if possible. (b) Find the domain of $f$ . (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\square$ A. $f(-1)=-4$ (Simplify your answer.) B. The value of $f(-1)$ is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $f(d)=\frac{4 d-12}{d+6}$ (Simplify your answer.) B. The value of $f(d)$ is undefined.

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Problem 119

$b^{2}-35 b+300=0$

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Problem 120

Without using a calculator, solve each problem in the set of REAL numbers. Show work. Write your Calculus 1 answer as a set of solutions (for equations) or as interval notation (for inequalities). Keep the numbers in their exact simplified form. (Example: $x=\sqrt{20}=2 \sqrt{5}$ ). If solving by factoring is easy, utilize factoring.
1. a) $x^{2}=8= \pm 2 \sqrt{2}$ b) $x^{2}<8$ $\begin{array}{l} x^{2}-8=0 \\ (x-\sqrt{8})(x+\sqrt{8}) \end{array} \left\lvert\, \begin{array}{l} 2) x+\sqrt{8}=0 ; x=-\sqrt{8} \\ =-\sqrt{4 \times 2}=-2 \sqrt{2} \\ x-\sqrt{8}=0 \Rightarrow x=\sqrt{8}=\sqrt{4 \times 2}=2 \sqrt{2} \end{array}\right.$
2. a) $x^{2}=-32$ b) $x^{2}>32$
3. a) $x^{2}=3 x+18$ b) $x^{2} \leq 3 x+18$
4. a) $-5+16 x-3 x^{2}=0$ b) $-5+16 x-3 x^{2}>0$

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Problem 121

a $\frac{1}{2} x-\frac{1}{3}=\frac{1}{3}(x-2)$

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Problem 122

Determine whether the number is a solution $4 x-4=6 x+6$ a. $x=6$ b. $x=-5$

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Problem 123

What is the solution to the system of linear
1. Whethert equations? 18 $\begin{array}{l} x+y-2 z=7 \\ 2 x-3 y=2 z \\ x-2 y-3 z=3 \end{array}$ eq I eq 2 *eq 3 \begin{tabular}{cccc} 0 & 0 & 0 & 0 \\ \hline $(2,1,-2)$ & $(2,-2,1)$ & $(1,-2,2)$ & $(1,2,-2)$ \end{tabular}

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Problem 124

Which ingution can be used to solve for $x$ ? $30 x-5=07 \quad 7 x+28=67 \quad 30 x+5=67 \quad 7 x+18=67$
Solve for $x$ . $x=$

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Problem 125

cost.
Evaluate each expression.
16. $14^{3}$

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Problem 126

(b) Show that the HCF and LCM of $x(a+4)$ and $a^{3}+64$ is $a+4$ and $x(a+4)\left(a^{2}-4 a+16\right)$ respectively.

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Problem 127

$\frac{2 x^{2}+x-6}{2 x^{2}+7 x+5} \div 2 x^{2}-2 x-8$

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Problem 128

12. The volume of a sphere, $V$ , is given by the formula $V=\frac{4}{3} \pi r^{3}$ , where $r$ is the radius of the sphere. (a) Make $r$ the subject of this formula (b) What is the radius of a sphere with volume $200 \mathrm{~cm}^{3}$ . ( 3 marks)
13. Solve the equation: $2^{x-1}+2^{x+1}=320$ . (4 marks)
14. Simplify the expression. (4 marks) $a^{3} b c\left(-2 b^{2} c\right)\left(3 c^{2}\right)+\left(-a^{2} b^{2} c^{2}\right)(2 a)\left(-3 b c^{2}\right)$
15. Make " r " the subject of $P=\frac{1}{1+\frac{1}{1+r}}$ . (4 marks)
16. Find the area of the shaded region. (4 marks)
17. Factorize: $3 m(2 m-4 n)-6(4 n-2 m)-9(6 n+3 m)$ . (4 marks)

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Problem 129

$16 \cdot 24$

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Problem 130

$(x+5)(x-4)=0$

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Problem 131

$x+5)(x-4)=0$

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Problem 132

$12 t(t-5)=0$

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Problem 133

(a) Which vector $V$ , satisfying $\|V\|_{2}=1$ , maximises $\frac{\partial f}{\partial V}(0,-1,1)$ when $f(x, y, z)=\exp (x) \arctan (y+z) .$
Given that $\int_{-\infty}^{\infty} e^{-t^{2}} d t=$

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Problem 134

2. Evaluate the following integrals (a) (5 points) $\int \mathrm{e}^{\sqrt{x}} d x$

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Problem 135

(a) Find a power series representation of $f(x)=\frac{x^{3}}{(1-x)^{2}}$ .

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Problem 136

b) Given that $\int_{-\infty}^{\infty} e^{-t^{2}} d t=\sqrt{\pi}$ , calculate the improper integral: $\int_{-\infty}^{\infty} x e^{-(x+3)^{2}} d x$

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Problem 137

$6 \frac{4}{5}+4 \frac{2}{3}$

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Problem 138

Use integration tables to evaluate the integral $\int_{0}^{\frac{\pi}{2}} 27 x \cos x d x$ .

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Problem 139

a. -18 b. -3 c. 3 d. 18
13. Hasil dari $296+12 \times 17$ adtalah.- a. 417 b. 500 c. 553 d. 5.253
14. Hasil dan $854:(8+6) \times 15$ adalah -... a. 915 b. 920 c. 935 d. 950

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Problem 140

19. Hasil dari $72 \%: \frac{4}{25} \times 1 \frac{1}{9}$ adalah ... . a. $\frac{16}{125}$ b. $\frac{32}{125}$ c. 1 d. 5
20. Hasil dari $\frac{5}{8} \times 0,48$ adalah .... a. $\frac{1}{5}$ b. $\frac{3}{10}$ c. $\frac{3}{5}$ d. $\frac{3}{7}$

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Problem 141

(7) $\int \frac{x^{2}+2 x-1}{\left(x^{3}-x^{2}\right)} d x$

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Problem 142

State ohm's law and write the formula down, showing the relation between V (voltage). and $R$ (resistance).

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Problem 143

Given $A$ is a non-singular matrix such that $A^{2}-2 A-I=0$ . $I$ and 0 are the identity matrix and null matrix respectively. Find $A^{-1}$ . $A+2 I$ I $A-2 I$ $A$

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Problem 144

* $\operatorname{Lim}_{x \rightarrow 0} \frac{-3 x}{5 \tan 3 x}$

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Problem 145

Find all the critical points of the following functions and identify them.
1. $f(x, y)=x^{2}-2 x y$
2. $\sin (x y)$
3. $y \cos (2 x)$
4. $\sin (x)+\cos (y)$
5. $x^{3} y+3 x-2 y$
6. $e^{x y}+x^{2} y^{2}$
7. $\sin x^{2} y-x y$
8. $\ln \left(x^{2}+y^{2}\right)$
9. $\ln (\sin (x y))$
10. $\frac{x}{\cos y}$

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Problem 146

18 If $x$ is a real number, what are the values that $y=\frac{x^{2}+(3+2 \sqrt{3}) x+3 \sqrt{3}}{x^{2}+3 x+2}$ can take? 1) $y \leq 3$ or $7 \leq y$ 2) $-7 \leq y \leq-3$ 3) $3 \leq y \leq 7$ 4) $y \leq-7$ or $-3 \leq y$

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Problem 147

$\sqrt{3} \sin (3 x-\pi)-\cos (3 x-\pi)=1$

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Problem 148

$(y-2)=\frac{2}{5}(x+3)$

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Problem 149

Function Operations Given the functions: $\begin{array}{l} f(x)=9 x \\ g(x)=3 x+4 \\ h(x)=-15 x^{2}-5 x+20 \end{array}$
Determine each of the following. Give your answers as simplified expressions written in descending order.

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Problem 150

(c) $\frac{6.2^{-2}}{3^{-3}}$

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Problem 151

(a) $\frac{1^{2011}}{2011^{-1}}$

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Problem 152

Evaluate the expression $\frac{\sqrt{-6}}{\sqrt{-7} \sqrt{-7}}$ and write the result in the form $a+b i$ The real number $a$ equals $\square$ The real number $b$ equals $\square$

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Problem 153

(1) $1, x_{2} \ldots, x_{n}$ be a random sample from $f(x, \theta)=\left\{\begin{array}{c}-\theta \theta^{x}, x=0_{1} \\ \frac{e^{-}}{x!}, \\ 0, w\end{array}\right.$ (Show that $f(x, \theta)$ is a member of exponential family. (2) Find a complete sufficient statistic for $\theta$ . (3) Find the MVUE for $\operatorname{Var}(x)$ (4) Find the value of $A$ , such that $E(3 A x \mid \bar{x})=15 \bar{x}$ justify your answer.

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Problem 154

6) Solve the equation. $19.2-4.4 n=6$ $n=-3$ $n=8$ $n=3$ $n=-8$

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Problem 155

For a parabola in general form, $f(x)=a x^{2}+b x+c$ , where $a \neq 0$ . If $a<0$ then the range of $f(x)$ is

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Problem 156

10) Solve the equation. $n+23-8 n=-3 n-1$ $n=6$ $n=5.5$ $n=-2.2$ $n=-4$

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Problem 157

Without sketching the graph, find the $x$ -intercepts and $y$ -intercepts of the graph of the equation. $6 x+3 y=72$
What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The x-intercept(s) is/are $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no $x$ -intercepts.

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Problem 158

Consider the Quadratic function $f(x)=x^{2}-2 x-35$ . Its vertex is ( $\square$ , $\square$ ). Its largest $x$ -intercept is $x=$ $\square$ Its $y$ -intercept is $y=$ $\square$ .

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Problem 159

4! =

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Problem 160

3) Solve the inequality. Use a calculator as needed. $9 x-4(x+7)<-42$ $x>-2.8$ $x \leq-1$ $x<-2.8$ $x<2.8$

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Problem 161

2. Simplify the expression. $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$ $\frac{11}{3} w-15$ $\frac{11}{3} w-5$ $4 w-5$ $4 w-15$

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Problem 162

$52=2 y$

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Problem 163

5) Solve the inequality and choose the graph for the solution. Use a calculator as needed. $-3.2 x-18+2.6 x>-15$ $x<-5$ $x>-7.5$ $x<-7.5$ $x>-5$

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Problem 164

5. Solve the inequality. Use a calculator as needed. $-\frac{1}{2} m+6>-4+9 \frac{1}{2}$ $m<1$ $m>\frac{9}{2}$ $m>1.1$ $m<0.2$

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Problem 165

Simplify: $\left(-5 b^{-3} p^{4}\right)^{2}$

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Problem 166

Find the quotient and remainder for the following division. a) $\frac{x^{3}-x^{2}+2 x-1}{x^{3}+1}$ c) $\frac{x^{4}-x^{3}+2 x^{2}-x+2}{x^{2}-x+1}$ b) $\frac{3 x^{4}-5 x^{2}+x-6}{x^{2}-1}$ d) $\frac{3 x^{4}+2 x^{3}-x^{2}-x-6}{x^{2}-3}$

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Problem 167

Determine the domain of the function. $f(x)=-\frac{5 x}{2 x^{2}+x-15}$

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Problem 168

In 14-25, find each quotient.
14. $\frac{2}{3} \div \frac{1}{3}$
15. $\frac{1}{2} \div \frac{1}{16}$
16. $\frac{1}{4} \div \frac{1}{12}$
17. $\frac{6}{7} \div \frac{3}{7}$
18. $\frac{5}{14} \div \frac{4}{7}$
19. $\frac{5}{8} \div \frac{1}{2}$
20. $\frac{7}{12} \div \frac{3}{4}$
21. $\frac{2}{7} \div \frac{1}{2}$
24. $\frac{3}{10} \div \frac{3}{5}$
25. $\frac{2}{5} \div \frac{1}{8}$
22. $\frac{4}{9} \div \frac{2}{3}$
23. $\frac{7}{12} \div \frac{1}{8}$

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Problem 169

Simplify the radical expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$

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Problem 170

The following expression equals -2 : $-2^{4} \div 4-4(x \div 6)+10$
Solve for the variable $x$ .

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Problem 171

$-48.3 \div(-7)=$

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Problem 172

$1 \frac{8}{9} \div \frac{1}{3}=$

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Problem 173

Express the product and the quotients of the following with the appropriate number of sig figs: 1) $\left(3.56 \times 10^{5}\right)\left(4.21 \times 10^{6}\right)=$ 2) $\left(2 \times 10^{7}\right)\left(8 \times 10^{-9}\right)=$ 3) $\left(4.11 \times 10^{-5}\right)\left(7.51 \times 10^{-4}\right)=$ 4) $8.45 \times 10^{7} / 6.74 \times 10^{3}=$ 5) $9.7 \times 10^{8} / 8.6 \times 10^{-2}=$ 6) $4.7 \times 10^{-2} / 5.7 \times 10^{-6}=$

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Problem 174

Solve using Gauss-Jordan elimination. $\begin{array}{rrr} x_{1}-x_{2}+3 x_{3}- & x_{4}=0.1 \\ -3 x_{1}+5 x_{2}-6 x_{3} & =2.9 \\ 2 x_{1}+5 & 5 x_{3}- & x_{4}=0.2 \\ 4 x_{1}-3 x_{2}+8 x_{3}+ & x_{4}=-3 \end{array}$
Select the correct choice below and fill in the answer box(es) within your choic

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Problem 175

$\begin{array}{l} f(x)=3 x+3 \\ g(x)=x^{2}+3 x+2 \\ r(x)=\frac{2 x+1}{x-1} \\ q(x)=\sqrt{x+1} \end{array}$ $1 \cdot(g \circ f)(x)=3 x+2$

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Problem 176

Solve using Gauss-Jordan elimination. $\begin{array}{rr} x_{1}-x_{2}+x_{3}+2 x_{4}= & -1.6 \\ -3 x_{1}+5 x_{2}+4 x_{3}-14 x_{4}= & 13.7 \\ 4 x_{1}-2 x_{2}+9 x_{3}+5 x_{4}= & -2.1 \\ 3 x_{1}-2 x_{2}+x_{3}+10 x_{4}= & -8.4 \end{array}$
Select the correct choice below and fill in the answer box(es) within your choice.

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Problem 177

MATHEMATICS 1 SMO15 QUIZ 3 1) Given $z_{1}=3-3 i$ and $z_{2}=3+2 i$ . (a) Write $\bar{z}_{1}$ in polar form. (b) Express $\frac{\bar{z}_{1} z_{2}}{13}+\overline{\left(\frac{i^{3}}{-z_{2}}\right)}$ in the form $a+b i$ , ( 6 m ] [6m] 2) Given that $z$ denotes the complex number $2\left(\cos \frac{1}{3} \pi+i \sin \frac{1}{3} \pi\right)$ . Find its standard forn $a+b i$ , where $a$ and $b$ are real values. Hence, find $z-\frac{2}{\bar{z}^{2}}$ . 3) Obtain the solution set for $-x+2 \leq \frac{5 x-4}{x}$ . $(5 m)$ 4) Given the function $g(x)=-3 x^{2}+12 x+1$ for $x \leq 1$ (a) Find the domain and range of $g(x)$ . $(3 n$ (b) Show that $g(x)$ is a one-to-one function. Hence, find $g^{-1}(x)$ . $(5 n$ (c) On the same axes, sketch the graph of $g(x)$ and $g^{-1}(x)$ . $(3 m$

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Problem 178

Simplify the follow a way that only exp
1. $b^{-4}=\frac{1}{b^{4}}$
2. $\frac{c^{2}}{d^{-8}}=c^{2} d^{8}$
3. $5 a^{0} b=$

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Problem 179

(a) Show that $3 \tan 2 \theta+\tan \left(\theta+45^{\circ}\right) \equiv \frac{\tan ^{2} \theta+8 \tan \theta+1}{1-\tan ^{2} \theta}$ .

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Problem 180

Factor $4 x^{2}+32 x+60$

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Problem 181

D. 119
32. Because of their devotion to absolute truth, several mathematicians are also well known A. novelists $\qquad$ B. explorers C. illustrators D. philosophers
33. Find the domain of the function of $y=3 x-5$ A. all real numbers B. 85 C. $\times 3$ D. $\times 3$

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Problem 182

20. Simplify: $3(x-4 y)-(4 x-3 x)-(2 x+y)+2(x-y)$

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Problem 183

III. Do all expressions in parenthesis IV. Do all multiplication and division (from left to right) A. IV, III, II, I C. I, II, III, IV B. III, I, IV, II D. II, III, IV, I
43. Perform the indicated operation and reduce the result to simplest form., $\frac{a^{4}-b^{4}}{a-b} \cdot \frac{b^{2}}{a^{2}-b^{2}} \cdot \frac{a-b}{a^{2}+b^{2}}$ A. $a-b$ B. $a+b$ C. b D. a

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Problem 184

Solve the system of linear equations by substitution. $\begin{array}{l} y=x-7 \\ 2 x+3 y=14 \end{array}$
If there are an infinite number of solutions, enter IS in each answer field. If there are no solutions, enter NS in each answer $x=$ $\square$ $y=$ $\square$

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Problem 185

3) Given $A=\left[\begin{array}{cc}3 & -5 \\ -1 & 7\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 4 \\ 8 & 3\end{array}\right]$ find the following a) $A+B$ b) $A B$ c) $B^{\top} A^{\top}$ d) $(A B)^{\top}$ e) $2(A-B)$

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Problem 186

X incorrect.
Solve the system of linear equations. $\begin{array}{l} 2 y+z-x=62 \\ 2 x+3 z-2 y=0 \\ -2 z+y-4 x=44 \end{array}$
If there are an infinite number of solutions, enter IS in each answer field. If there are no solutions, enter NS in each answer huchit. $\begin{array}{l} x=-105.272 \\ y=4 \\ z=42545 \\ z=4.818 \end{array}$

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Problem 187

60. Evaluate $\lim x \rightarrow 1$ $\lim _{x \rightarrow 1} \frac{x^{5}-32}{x-2}$ A. 50 B. 64 C. 48 D. 31

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Problem 188

Given the following sets, find the set $(A \cup B) \cap(A \cup C)$ . $\begin{array}{l} U=\{1,2,3, \ldots, 10\} \\ A=\{1,2,3,10\} \\ B=\{1,5,10\} \\ C=\{2,4,5,6,7\} \end{array}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $(A \cup B) \cap(A \cup C)=$ $\square$ \} (Use a comma to separate answers as needed. Use ascending order.) B. $(A \cup B) \cap(A \cup C)$ is the empty set.

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Problem 189

$\left(\cos 2 y-3 x^{2} y^{2}\right) d x+\left(\cos 2 y-2 x \sin 2 y-2 x^{3} y\right) d y=0$

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Problem 190

Find the inverse Laplace transform of $\frac{2s}{s^{2}+6s+1}$ .

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Problem 191

3 Find the value of $x$ in (1) $\sqrt[3]{x}=5$

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Problem 192

P مجموعة حل المعادلة : س - 1 = . ب ح هي {1}\ 0 {-1} ..... ۲ مجموعة حل المعادلة : س - اس + ٩ = . في ح هي P {r}0 {1} ۲ مجموعة حل المعادلة : س؟ - س { }0 = {-} في ح هي {..} مجموعة حل المعادلة : س٢ + ۲ س ت في ح هي {r-. } P ٦ {-}O ٢ {r. .} مجموعة حل المعادلة : س + 9 - . بي هي. - ،} {1} - {-1}0 {-}0 الجزر المشترك للمعادلتين : س ا س ٢- اس ٢ - ٥س +٢ = . هر .... ۲ س = ٢ س 1=14 س = -- += c S

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Problem 193

b. $5.36 \div 4=$

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Problem 194

$(i+5)^{2} \times 2^{3}+\sqrt{8}=$

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Problem 195

Use the associative property to simplity the expression. $50+20+37$ A. $(50+20)+37=70+37$ $=107$ B. $10(5+2)+37=10(7)+37$ $=70+37$ $=107$ C. $50+20+37=50+57$ $=107$ D. $50+37+20=87+20$ $=107$

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Problem 196

(2.) প্রমাণ করি যে, $(3,-2),(-5,4)$ এবং $(-1,1)$ বিन্দু তিनটি সমরেখ।

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Problem 197

Approximate each number using a calculator. $5^{\sqrt{2}}$ $5^{\sqrt{2}} \approx 11.090$ (Round to three decimal places.)

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Problem 198

NOTE: The concept, procedure or solution in solving for the definite integral of one function is just the same on how we solve for the indefinite integral. We just substitute the limits 3 .
Activity 3: Skill-building Activities (with answer key)
Evaluate the following integrals:
1. $\int_{2}^{2} x^{3} d x$
2. $\int_{2}^{4} 25 d x$
3. $\int_{2}^{4}(x-9) d x$
4. $\int_{2}^{4}\left(10+4 x-3 x^{3}\right) d x$
5. $\int_{-1}^{1}(1-|x|) d x$
6. $\int_{2}^{7} \frac{x+6}{\sqrt{x}} d x$

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Problem 199

Evaluate the expression without using a calculator. $\log _{3} 3^{8}$ $\square$

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Problem 200

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. \begin{tabular}{|c|c|} \hline \begin{tabular}{l} System A \\ \begin{tabular}{r} $-x+2 y=8$ \\ $x-2 y=8$ \end{tabular} \end{tabular} & \begin{tabular}{l} The system has no solution. \\ The system has a unique solution: \\ $(x, y)=(\square, \square)$ \\ The system has infinitely many solutions. \\ They must satisfy the following equation: \\ $y=$ \end{tabular} \\ \hline \begin{tabular}{l} System B \\ \begin{aligned}x-3 y & =9 \\ -x+3 y & =-9\end{aligned} \end{tabular} & \begin{tabular}{l} The system has no solution. \\ The system has a unique solution: \\ $(x, y)=$ \\ The system has infinitely many solutions. \\ They must satisfy the following equation: \\ $y=$ \end{tabular} \\ \hline \end{tabular}

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1 2 3 4 5 ...269

Math Statement

Problem 101

1. 822×9\begin{array}{r} 822 \\ \times \quad 9 \\ \hline \\ \hline \end{array}822×9​​

Problem 102

710×8\begin{array}{r}710 \\ \times \quad 8 \\ \hline \\ \hline\end{array}710×8​​

Problem 103

876×7\begin{array}{r}876 \\ \times \quad 7 \\ \hline\end{array}876×7​​

Problem 104

227×8\begin{array}{r}227 \\ \times \quad 8 \\ \hline\end{array}227×8​​

Problem 105

Problem 106

Part 1 of 2Plot, compare, and order the square root, cube root, and expression. (52−42),−13,(12)2+36\sqrt{\left(5^{2}-4^{2}\right)}, \sqrt[3]{-1},\left(\frac{1}{2}\right)^{2}+\sqrt{36}(52−42)​,3−1​,(21​)2+36​

Problem 107

Problem 108

8x+8x+8x4x+4x=12\frac{8^{x}+8^{x}+8^{x}}{4^{x}+4^{x}}=124x+4x8x+8x+8x​=12

Problem 109

4. (Valor: 2,5) Incontre a equaçáo da hipérbole de excentricidade 2 e focos coincidentes com os focos da elipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}=125x2​+9y2​=1.Faça upload de 1 arquivo aceito: PDF ou image. O tamanho maximo e de 10 MB . I. Adtcionar arquivoVoltar Enviar

Problem 110

4. (Valor: 2,5 ) Encontre a equaçao da hipérbole de excentricidade 2 e focos coincidentes com os focos da ellipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}=125x2​+9y2​=1.Faca upload de 1 arquivo aceito: PDF ou image. o tamanho maximo e de 10 MB Adiclonar arquivo

Problem 111

x2−23x−5=0x^{2}-\frac{2}{3} x-5=0x2−32​x−5=0

Problem 112

x−4x−2=5a0\frac{x-4}{\sqrt{x}-2}=5 a^{0}x​−2x−4​=5a0

Problem 113

x32=125x^{\frac{3}{2}}=125x23​=125

Problem 114

3−5⋅323^{-5} \cdot 3^{2}3−5⋅32

Problem 115

Problem 116

Add. 34.231+45.23034.231+45.23034.231+45.230 38.754 79.434 79.461 79.462

Problem 117

3b+4=−83 b+4=-83b+4=−8

Problem 118

Problem 119

b2−35b+300=0b^{2}-35 b+300=0b2−35b+300=0

Problem 120

Problem 121

a 12x−13=13(x−2)\frac{1}{2} x-\frac{1}{3}=\frac{1}{3}(x-2)21​x−31​=31​(x−2)

Problem 122

Determine whether the number is a solution 4x−4=6x+64 x-4=6 x+64x−4=6x+6 a. x=6x=6x=6 b. x=−5x=-5x=−5

Problem 123

Problem 124

Which ingution can be used to solve for xxx ? 30x−5=077x+28=6730x+5=677x+18=6730 x-5=07 \quad 7 x+28=67 \quad 30 x+5=67 \quad 7 x+18=6730x−5=077x+28=6730x+5=677x+18=67Solve for xxx. x=x=x=

Problem 125

cost.Evaluate each expression.16. 14314^{3}143

Problem 126

(b) Show that the HCF and LCM of x(a+4)x(a+4)x(a+4) and a3+64a^{3}+64a3+64 is a+4a+4a+4 and x(a+4)(a2−4a+16)x(a+4)\left(a^{2}-4 a+16\right)x(a+4)(a2−4a+16) respectively.

Problem 127

2x2+x−62x2+7x+5÷2x2−2x−8\frac{2 x^{2}+x-6}{2 x^{2}+7 x+5} \div 2 x^{2}-2 x-82x2+7x+52x2+x−6​÷2x2−2x−8

Problem 128

Problem 129

16⋅2416 \cdot 2416⋅24

Problem 130

(x+5)(x−4)=0(x+5)(x-4)=0(x+5)(x−4)=0

Problem 131

x+5)(x−4)=0x+5)(x-4)=0x+5)(x−4)=0

Problem 132

12t(t−5)=012 t(t-5)=012t(t−5)=0

Problem 133

Problem 134

2. Evaluate the following integrals (a) (5 points) ∫exdx\int \mathrm{e}^{\sqrt{x}} d x∫ex​dx

Problem 135

(a) Find a power series representation of f(x)=x3(1−x)2f(x)=\frac{x^{3}}{(1-x)^{2}}f(x)=(1−x)2x3​.

Problem 136

b) Given that ∫−∞∞e−t2dt=π\int_{-\infty}^{\infty} e^{-t^{2}} d t=\sqrt{\pi}∫−∞∞​e−t2dt=π​, calculate the improper integral: ∫−∞∞xe−(x+3)2dx\int_{-\infty}^{\infty} x e^{-(x+3)^{2}} d x∫−∞∞​xe−(x+3)2dx

Problem 137

645+4236 \frac{4}{5}+4 \frac{2}{3}654​+432​

Problem 138

Use integration tables to evaluate the integral ∫0π227xcos⁡xdx\int_{0}^{\frac{\pi}{2}} 27 x \cos x d x∫02π​​27xcosxdx.

Problem 139

a. -18 b. -3 c. 3 d. 1813. Hasil dari 296+12×17296+12 \times 17296+12×17 adtalah.- a. 417 b. 500 c. 553 d. 5.25314. Hasil dan 854:(8+6)×15854:(8+6) \times 15854:(8+6)×15 adalah -... a. 915 b. 920 c. 935 d. 950

Problem 140

Problem 141

(7) ∫x2+2x−1(x3−x2)dx\int \frac{x^{2}+2 x-1}{\left(x^{3}-x^{2}\right)} d x∫(x3−x2)x2+2x−1​dx

Problem 142

State ohm's law and write the formula down, showing the relation between V (voltage). and RRR (resistance).

Problem 143

Given AAA is a non-singular matrix such that A2−2A−I=0A^{2}-2 A-I=0A2−2A−I=0. III and 0 are the identity matrix and null matrix respectively. Find A−1A^{-1}A−1. A+2IA+2 IA+2I I A−2IA-2 IA−2I AAA

Problem 144

* Lim⁡x→0−3x5tan⁡3x\operatorname{Lim}_{x \rightarrow 0} \frac{-3 x}{5 \tan 3 x}Limx→0​5tan3x−3x​

1. $\begin{array}{r} 822 \\ \times \quad 9 \\ \hline \\ \hline \end{array}$

$\begin{array}{r}710 \\ \times \quad 8 \\ \hline \\ \hline\end{array}$

$\begin{array}{r}876 \\ \times \quad 7 \\ \hline\end{array}$

$\begin{array}{r}227 \\ \times \quad 8 \\ \hline\end{array}$

Part 1 of 2
Plot, compare, and order the square root, cube root, and expression. $\sqrt{\left(5^{2}-4^{2}\right)}, \sqrt[3]{-1},\left(\frac{1}{2}\right)^{2}+\sqrt{36}$

$\frac{8^{x}+8^{x}+8^{x}}{4^{x}+4^{x}}=12$

4. (Valor: 2,5) Incontre a equaçáo da hipérbole de excentricidade 2 e focos coincidentes com os focos da elipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ .
Faça upload de 1 arquivo aceito: PDF ou image. O tamanho maximo e de 10 MB . I. Adtcionar arquivo
Voltar Enviar

4. (Valor: 2,5 ) Encontre a equaçao da hipérbole de excentricidade 2 e focos coincidentes com os focos da ellipse $\frac{x^{2}}{25}+\frac{y^{2}}{9}=1$ .
Faca upload de 1 arquivo aceito: PDF ou image. o tamanho maximo e de 10 MB Adiclonar arquivo

$x^{2}-\frac{2}{3} x-5=0$

$\frac{x-4}{\sqrt{x}-2}=5 a^{0}$

$x^{\frac{3}{2}}=125$

$3^{-5} \cdot 3^{2}$

Add. $34.231+45.230$ 38.754 79.434 79.461 79.462

$3 b+4=-8$

$b^{2}-35 b+300=0$

a $\frac{1}{2} x-\frac{1}{3}=\frac{1}{3}(x-2)$

Determine whether the number is a solution $4 x-4=6 x+6$ a. $x=6$ b. $x=-5$

Which ingution can be used to solve for $x$ ? $30 x-5=07 \quad 7 x+28=67 \quad 30 x+5=67 \quad 7 x+18=67$
Solve for $x$ . $x=$

cost.
Evaluate each expression.
16. $14^{3}$

(b) Show that the HCF and LCM of $x(a+4)$ and $a^{3}+64$ is $a+4$ and $x(a+4)\left(a^{2}-4 a+16\right)$ respectively.

$\frac{2 x^{2}+x-6}{2 x^{2}+7 x+5} \div 2 x^{2}-2 x-8$

$16 \cdot 24$

$(x+5)(x-4)=0$

$x+5)(x-4)=0$

$12 t(t-5)=0$

2. Evaluate the following integrals (a) (5 points) $\int \mathrm{e}^{\sqrt{x}} d x$

(a) Find a power series representation of $f(x)=\frac{x^{3}}{(1-x)^{2}}$ .

b) Given that $\int_{-\infty}^{\infty} e^{-t^{2}} d t=\sqrt{\pi}$ , calculate the improper integral: $\int_{-\infty}^{\infty} x e^{-(x+3)^{2}} d x$

$6 \frac{4}{5}+4 \frac{2}{3}$

Use integration tables to evaluate the integral $\int_{0}^{\frac{\pi}{2}} 27 x \cos x d x$ .

a. -18 b. -3 c. 3 d. 18
13. Hasil dari $296+12 \times 17$ adtalah.- a. 417 b. 500 c. 553 d. 5.253
14. Hasil dan $854:(8+6) \times 15$ adalah -... a. 915 b. 920 c. 935 d. 950

(7) $\int \frac{x^{2}+2 x-1}{\left(x^{3}-x^{2}\right)} d x$

State ohm's law and write the formula down, showing the relation between V (voltage). and $R$ (resistance).

Given $A$ is a non-singular matrix such that $A^{2}-2 A-I=0$ . $I$ and 0 are the identity matrix and null matrix respectively. Find $A^{-1}$ . $A+2 I$ I $A-2 I$ $A$

* $\operatorname{Lim}_{x \rightarrow 0} \frac{-3 x}{5 \tan 3 x}$

$\sqrt{3} \sin (3 x-\pi)-\cos (3 x-\pi)=1$

$(y-2)=\frac{2}{5}(x+3)$

Function Operations Given the functions: $\begin{array}{l} f(x)=9 x \\ g(x)=3 x+4 \\ h(x)=-15 x^{2}-5 x+20 \end{array}$
Determine each of the following. Give your answers as simplified expressions written in descending order.

(c) $\frac{6.2^{-2}}{3^{-3}}$

(a) $\frac{1^{2011}}{2011^{-1}}$

Evaluate the expression $\frac{\sqrt{-6}}{\sqrt{-7} \sqrt{-7}}$ and write the result in the form $a+b i$ The real number $a$ equals $\square$ The real number $b$ equals $\square$

6) Solve the equation. $19.2-4.4 n=6$ $n=-3$ $n=8$ $n=3$ $n=-8$

For a parabola in general form, $f(x)=a x^{2}+b x+c$ , where $a \neq 0$ . If $a<0$ then the range of $f(x)$ is

10) Solve the equation. $n+23-8 n=-3 n-1$ $n=6$ $n=5.5$ $n=-2.2$ $n=-4$

Consider the Quadratic function $f(x)=x^{2}-2 x-35$ . Its vertex is ( $\square$ , $\square$ ). Its largest $x$ -intercept is $x=$ $\square$ Its $y$ -intercept is $y=$ $\square$ .

3) Solve the inequality. Use a calculator as needed. $9 x-4(x+7)<-42$ $x>-2.8$ $x \leq-1$ $x<-2.8$ $x<2.8$

2. Simplify the expression. $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$ $\frac{11}{3} w-15$ $\frac{11}{3} w-5$ $4 w-5$ $4 w-15$

$52=2 y$

5) Solve the inequality and choose the graph for the solution. Use a calculator as needed. $-3.2 x-18+2.6 x>-15$ $x<-5$ $x>-7.5$ $x<-7.5$ $x>-5$

5. Solve the inequality. Use a calculator as needed. $-\frac{1}{2} m+6>-4+9 \frac{1}{2}$ $m<1$ $m>\frac{9}{2}$ $m>1.1$ $m<0.2$

Simplify: $\left(-5 b^{-3} p^{4}\right)^{2}$

Determine the domain of the function. $f(x)=-\frac{5 x}{2 x^{2}+x-15}$

Simplify the radical expression $\sqrt{\frac{2 x^{2}}{9 y^{4}}}$

The following expression equals -2 : $-2^{4} \div 4-4(x \div 6)+10$
Solve for the variable $x$ .

$-48.3 \div(-7)=$

$1 \frac{8}{9} \div \frac{1}{3}=$