Math Statement

Problem 201

Which equation is equivalent to $5 x=\ln 8$ ? $e^{5 x}=e^{4} \cdot e^{2}$ $10^{5 x}=8$ $e^{5 x}=8$ $2^{3 x}=3$

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Problem 202

Find the $y$ -intercept and the slope of the line. $y=-\frac{1}{2} x+6$ $y$ -intercept: $\square$ Undefined slope:

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Problem 203

Find the $y$ -intercept and the slope of the line. $y=\frac{1}{2}$ $y$ -intercept: $\square$ Undefined slope:

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Problem 204

Which statement best describes the solution of the system of equations shown? $\begin{array}{c} 2 x-y=1 \\ 4 x-2 y=2 \end{array}$
The system has no solutions.
The system has intinitely many solutions.
The system has exactly two solutions.
The system has exactly one solution.

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Problem 205

Which expression is not equal to the expression shown? $3^{3} \times 3^{4} \div 3^{-4}$

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Problem 206

Translate $f(x)=|2 x|$ down 3 units. $f(x)=|2 x|+3$ $f(x)=|2 x-3|$ $f(x)=|2 x|-3$ $f(x)=|2 x+3|$

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Problem 207

$\sqrt{x^{2}+4 x}-x-2$

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Problem 208

(ii) The direction ratios of a line are $(-6,2,3)$ and its direction cosines

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Problem 209

4. Given $y=5 e^{3 x}+\sin x$ . Find $\frac{d y}{d x}$ a. $5 e^{3 x}+\cos x$ . b. $15 e^{\frac{d x}{d x}}-\cos x$ . c. $15 e^{3 x}+\cos x$ . d. $2.666 e^{12}-\cos x$

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Problem 210

I Let $f(x)=\frac{2 x^{3}-1 x+7}{3 x^{2}-2}$ . Find $f(3)$ a. $\frac{2}{3}$ b. $\frac{16}{39}$ c. 3 d. $\frac{1 n}{45}$

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Problem 211

Zet 475 milliliter om in liter. $\square$ liter

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Problem 212

12. The $\lim _{x \rightarrow 0} \frac{\sin (x)}{x}=1$ a. True b. false

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Problem 213

Determine the slope and $y$ -intercept. $\quad y=3 / 2 x+3$

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Problem 214

1. $\lim _{x \rightarrow c} f(x)=f(c)$ II. $f(c)$ is defined
III $\lim _{x \rightarrow c} f(x)$ must exist a. True b. false

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Problem 215

If $p-18=3$ , what is the value of $p ?$

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Problem 216

1. $47 \%$ of $70 \approx$ Shere your werk.
4. $65 \%$ of $152 \approx$ $\qquad$
7. $224 \%$ of $320 \approx$ $\qquad$
2. $39 \%$ of $120 \approx$ $\qquad$
13. $21 \%$ of $90 \approx$ $\qquad$
5. $72 \%$ of $238 \approx$ $\qquad$
6. $132 \%$ of $54 \approx$ $\qquad$
8. $\frac{3}{4} \%$ of $168 \approx$ $\qquad$
9. $0.4 \%$ of $510 \approx$ $\qquad$

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Problem 217

Given a circle with center $(8,2)$ and radius $r=8$ , write its equation in standard form. $(x-8)^{2}+(y-2)^{2}=$ $64 \sqrt{ }$ $\square$

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Problem 218

Let $(-3,-2)$ be a point on the terminal side of $\theta$ . Find the exact values of $\sin \theta, \sec \theta$ , and $\tan \theta$ . $\square$

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Problem 219

If $\frac{2 x}{3 x+5}=4$ , what is the value of $x$ ? Choose 1 mower: (A) -20 (B) -2 (C) $\frac{1}{2}$ (e) 16
Sthow calculator

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Problem 220

Find the center and the radius of the circle with the given equation. $x^{2}+y^{2}-20=0$
Center: $\square$ $(0,0)$ $\checkmark$
NOTE: Enter the radius in simplified form.
Radius: $2 \sqrt{5}$ $\square$ $\sqrt{ }$

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Problem 221

Find all solutions of the equation in the interval $[0,2 \pi)$ . $2 \cos \theta-\sqrt{2}=0$
Write your answer in radians in terms of $\pi$ . If there is more than one solution, separate them with commas. $\theta=$ $\square$

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Problem 222

Describe the long run behavior of $f(n)=3 n^{8}-4 n^{3}+n^{2}+5$ As $n \rightarrow-\infty, f(n) \rightarrow ? \vee$ As $n \rightarrow \infty, f(n) \rightarrow ? \vee$

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Problem 223

12 What is the value of each number? 7 $-7$ 14 $-14$ $|7|=$ $\square$ $|-14|=$ $\square$ $|14|=$ $\square$ $\square$

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Problem 224

$\frac{\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

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Problem 225

Select either < or > to make the statement true. $\begin{array}{l} -20 \ldots \quad 9 \\ -10 \quad-100 \\ -13 \_13 \end{array}$

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Problem 226

Evaluate the following I. (a) i) $\lim _{x \rightarrow 2}\left\{\frac{x^{2}-7 x+10}{x^{2}-4}\right\}$ ii) $\lim _{x \rightarrow 0}\left\{\frac{\sin 7 x}{x}\right\}$ iii) $\lim _{x \rightarrow \infty}\left\{\frac{2 x^{3}-7 x+3}{x^{2}+2}\right\}$ (b) Use the chain rule to differentiate $y=\left(3 t^{2}+2 t-9\right)^{10}$ .

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Problem 227

Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n=1$ for the first term. $\begin{array}{l} -6,-12,-18,-24, \ldots \\ a_{n}=\square \end{array}$

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Problem 228

Use the following function rule to find $f(d+7)$ . Simplify your answer. $\begin{array}{l} f(n)=n^{2}+8 \\ f(d+7)= \end{array}$ $\square$ Submit

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Problem 229

(d) Determine the following indefinite integrals i) $\int\left(2+3 x-4 x^{3}\right) d x$ ii) $\int(\cos x+3 \sin x) d x$ iii) $\int \frac{4 t-1}{2 t^{2}+t+1} d t$

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Problem 230

Solve using the standard algorithm. a. $0.64 \div 4=$ $\qquad$ b. $6.45 \div 5=$ $\qquad$ c. $16.404 \div 6=$ $\qquad$

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Problem 231

2. (a) A curve is defined by the function $y=x^{3}-3 x-5$
Find i) the gradient of the curve at the point where $x=2$ ii) the coordinates of the maximum and minimum turning point (b) Obtain from first principles the derivative of the function $y=2 x^{2}+4 x-3$ (c) Use integration by substitution to find the given integral $\int_{0}^{1}\left(3 x^{2}+2\right)^{4} d x$ (d) Use the product rule to find $\frac{d y}{d x}$ given i. $y=\left(3 x^{2}+1\right)(5 t-8)$ ii. $y=t^{2} \sin t$

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Problem 232

b. $36.012 \div 3=$ $\qquad$ 0 12 thousandths $\div 3$ ones $\div 3+$ $\qquad$ $=$ $\qquad$ ones + $\qquad$ thousandths $=$ $\qquad$ c. $3.55 \div 5=$ $\qquad$ tenths $\div 5+$ $\qquad$ hundredths $\div 5$ $=$ $\qquad$ $=$ $\qquad$ d. $3.545 \div 5=$ $\qquad$ $=$ $\qquad$ $=$ $\qquad$

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Problem 233

If the proauct of xeroes of the polynomial $a x^{2}-18 x-6 \Delta$ is 4 . Find the the value of $a$ .

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Problem 234

10 points Solve for $x:(x+3)^{2}+5=1$ $x=-5$ or -1 $x=13$ $x=-3 \pm 2 i$ $x=-3 \pm 4 i$

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Problem 235

Solve the absolute value equation. $|2 x-7|=11$

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Problem 236

3. 1 (s) Let $g(x) \sim a^{2}-5 x^{2}$ Find the dommain of $y$ at $(-\infty,(1)$ b 0 b $(\cdots n, \infty)$ \& $|\cdots, 0|$ 1) The defintern of the first derivalive of a finction $/(x)$ is a $f^{\prime}(x)=\lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$ b. $f^{\prime}(x)=\lim _{\Delta \rightarrow 0} \frac{f(x+\Delta x)+f(x)}{\Delta x}$ c. $f^{\prime}(x)=\lim _{\Delta i \rightarrow 0} \frac{(x+\Delta x)-(x)}{\Delta s}$ d. $f^{\prime}(x)=\lim _{\Delta x \rightarrow 0} \frac{(x+\Delta x) \geq(x)}{\Delta x}$
12. The $\lim _{x \rightarrow 0} \frac{\sin (x)}{x}=1$ a. True b. false
13. If $y=x^{2} y+x y^{2}=3 x$ , then $\frac{d y}{d x}$ is a. $\frac{2 x+x y^{2}}{3}$ b. $\frac{3-2 x y-y^{2}}{x^{2}+2 x y}$ c. $2 x^{2} y+y^{2}$ d. $\frac{2 x+3}{x^{2}+x}$
14. A function is said to be continuous at a point " $c$ " if:
1. $\lim _{x \rightarrow c} f(x)=f(c)$ II. $f(c)$ is defined a. True b. false

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Problem 237

$(5 \sqrt[2]{11}+7 \sqrt[2]{3}) \cdot(5 \sqrt[2]{11}-7 \sqrt[2]{3})$

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Problem 238

17. When the second derivative of a curve is positive then the type of stationary point is a. Maximum b. Minimum c. Neutral d. Inflexion

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Problem 239

Evaluate: $\begin{array}{c} x=4, y=5 \\ 3 y-x \end{array}$

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Problem 240

Evaluate: $\begin{array}{c} a=1, b=6, c=3 \\ c^{2} \cdot a-b \end{array}$

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Problem 241

Evaluate: $\sqrt{9}$

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Problem 242

Question 10 of 10
What is the simplest form of the fraction below? $\frac{15}{30}$ A. $\frac{3}{7}$ B. $\frac{2}{3}$ C. $\frac{1}{2}$ D. $\frac{3}{8}$

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Problem 243

Let $x$ be $2x - 3$ . Evaluate $\text{1. } f(x) = x + 5$

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Problem 244

$11 x^{2}-34 x+28=$

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Problem 245

3. Si el punto $\left(\frac{\pi}{3} ; \frac{2 n-1}{2 n+1}\right)$ pertenece a la gráfica de la función $y=\cos x$ , demuestra que $n=3 / 2$

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Problem 246

Answer this in your notehook. I Find the slope of a line given two points
1. $(1,12)(3,14)$
2. $(7,2)(5,8)$
3. $(-3,4) \quad(2,-5)$
4. $(5,3) \quad(-2,3)$ $5 .(7,-9) \quad(7,-2)$

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Problem 247

Ch. 6 Polynomials Session 2024/2025 EXAMPLE 10 Given that $(x+1)$ and $(x-2)$ are factors of $P(x)=2 x^{4}+a x^{3}+b x^{2}-2 x$ . (a) Find the values of $a$ and $b$ . (b) Factorise $P(x)$ completely. Hence, state the factors, roots and zeroes of $P(x)$ .

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Problem 248

Find the inverse of each matrix. 17) $\left[\begin{array}{ccc}-2 & 5 & -2 \\ -2 & 2 & 0 \\ -3 & -2 & 2\end{array}\right]$

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Problem 249

ssion³x-15 2x2-50 -15 2x2 + 16x + 30 * 6x +9

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Problem 250

If $\frac{\sqrt{x}}{16}=\frac{15}{8}$ then the value of $x$ is:

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Problem 251

$\begin{array}{l}-18=10+4(5-3 g) \\ -18=10+20-12 g \\ -18=30-12 g \\ -48=-12 g \\ 12=g\end{array}$

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Problem 252

$\sin 2 x-\sin x=0$

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Problem 253

$\left(2^{-1}+3^{-1}+4^{-1}\right) \times \frac{3}{4}$

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Problem 254

Tutorial Sheet 5 - Exponential and Log Functions August, 2024
1. Given the function $f(x)=\left(\frac{1}{4}\right)^{x}$ , evaluate each of the following. (a) $f(-3)$ (b) $f\left(-\frac{1}{2}\right)$ (c) $f(0)$ (d) $f\left(\frac{1}{3}\right)$

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Problem 255

Lab Homework Question 1, 4.4.C2
Fill in the blank so that the resulting statement is true. If $5^{4 x-1}=5^{11}$ , then $\_=11$
If $5^{4 x-1}=5^{11}$ , then $\square=11$

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Problem 256

Evaluate. Write your answers as fractions. $\begin{array}{c} -\left(\frac{3}{5}\right)^{3}= \\ \frac{5^{2}}{-2}= \end{array}$

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Problem 257

Simplify. $\frac{a^{2} b^{6}}{a^{3} b^{4}}$

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Problem 258

( Lab Homework Question 13, 4.4-20 Points: of of 1
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. $\log _{3} x=4$ A. $\{1.262\}$ B. (64) C. (12) D. (81)

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Problem 259

$\begin{array}{l}\sin \theta(1+\tan \theta)+\cos \theta \quad(1+\cot \theta) \\ \qquad=(\sec \theta+\operatorname{cosec} \theta)\end{array}$

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Problem 260

$\frac{1+\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta$

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Problem 261

$(1+\sqrt{3})(1-\sqrt{3})$
1. simplify $\frac{1}{1+\sqrt{3}} \text { to } 3 \text { s.f. given that } \sqrt{3} \times 1.732$

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Problem 262

Which ordered pair is a solution to the system of inequalities? $\left\{\begin{array}{c} y>-2 \\ x+y<4 \end{array}\right.$ $(-3,5)$ $(0,4)$ $(1,4)$ $(-2,-3)$

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Problem 263

$\begin{array}{r}-29+55=84 \\ -37+(-48)=7\end{array}$

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Problem 264

$\begin{array}{l}29+(-41)=\square \\ -42+(-33)=\square\end{array}$

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Problem 265

$\left(2-\frac{1}{6}\right)-\left\{\left(\frac{1}{2}+\frac{1}{3}\right)+\left[\frac{19}{7}-\frac{7}{4}-\left(\frac{11}{4}-\frac{8}{3}+\frac{2}{7}\right)\right]\right\}-\left[\left(\frac{9}{7}-\frac{4}{21}-\frac{1}{2}\right)-\left(\frac{1}{2}-\frac{1}{7}\right)\right]$

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Problem 266

$-4+8-5$

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Problem 267

Exponential Growth $A=\mathrm{Pe}^{\text {rt }}$ Population of city Santa Clava in 2003 was 98,000 Population now of Santa Clara in 2022 was 131,886 Based on these numbers and exponelitial growth, estimate the population of Santa Clara in 2050

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Problem 268

$\begin{array}{l}f(x)=\frac{x \cdot \sin x}{\sqrt{x^{2}+1}-1} \\ g(x)=\frac{x-\cos x}{x^{2}} \\ \left.\lim _{x \rightarrow+\infty} \operatorname{fl}_{x \rightarrow+\infty}(x)\right)\end{array}$

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Problem 269

$(\sqrt{16}-\sqrt{4}) \cdot 2^{4}+4^{33}: 4^{31}=$

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Problem 270

f. $12 \div \frac{7}{8}$

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Problem 271

$-4.05+3.18$

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Problem 272

2) $\sqrt[5]{32}+(14-2)^{2}: \sqrt{144}=$

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Problem 273

$30:(4-14)+(-8: 2-3) \cdot 2=$

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Problem 274

$30:(4-14)+(-8: 2-3) \cdot 2=$

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Problem 275

$30:(4-14)+(-8: 2-3) \cdot 2=$

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Problem 276

2) $92 \times 75=$

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Problem 277

c lattice multiplication to solve each problem 2) $92 \times 75$

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Problem 278

The volume of a cylinder with a base of radius $r$ is the area of the base times the length of its height ( $h$ ). Which of the following is the formula for the volume of a cylinder? A. $V=\pi r h$ B. $V=\pi r^{2} h$ C. $V=\frac{1}{2} \pi r h$ D. $V=2 \pi r h$

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Problem 279

Compute. $49.83-4.61+6$

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Problem 280

An expression is shown. $\frac{(2.7)^{-2} \cdot(2.7)^{3}}{(2.7)^{1} \cdot(2.7)^{-4}}$
Apply the Laws of what Exponents to determine the value of the expression.
The value of the expression is

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Problem 281

(7) Halla el término que falta para que fracciones sean equivalentes. $\begin{array}{ll} \frac{2}{3}=\frac{8}{19} & \cdot \frac{5}{7}=\frac{\square}{35} \\ \cdot \frac{2}{9}=\frac{10}{45} & \cdot \frac{4}{\square}=\frac{28}{49} \end{array}$

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Problem 282

5. $\left(2 x^{2} y\right)^{5}$

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Problem 283

$y=\frac{2 x}{2 x+7}$ Oive the domains of the Jollowing function

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Problem 284

1) $-9(-5-7)-3 v-9 v$

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Problem 285

Perform the indicated multiplication. $\begin{array}{c} 6(-9) \\ 6(-9)= \end{array}$

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Problem 286

Find the centre whose equation is : $2 x^{2}+2 y^{2}-3 x+2 y+1=0$

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Problem 287

Tatenda has a circle with an equation $x^{2}+y^{2}-8 x+4 y+4=0$ . Find the coordinates of the centre of this circle.

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Problem 288

Show that the line passing through the points $A(6,4)$ and $B(7,11)$ is parallel to the line passing through $P(0,0)$ and $Q(2,14)$ .

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Problem 289

Find the values of $x$ that satisfy the inequalities. (Enter your answer using interval notation.) $x+1>6 \text { or } x+4<-1$

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Problem 290

$(4-7)^{2}+\sqrt{2 \cdot 8+9}-(32: 8-6)^{3}+(-2-8)=$

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Problem 291

Solve the Absolute Value Equation T2ES1
Solve each equation. 1) $|x-3|=5$ 2) $|x+7|=2$ 3) $\left|\frac{2}{3}-x\right|=1$
Solution $=$ Solution $=$ Solution $=$

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Problem 292

9. $\left(\frac{1}{2} a^{3} b^{4} c^{5}\right)^{3}$

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Problem 293

Simplify the expression. $\frac{(4 x-1)(5)-(5 x+1)(4)}{(4 x-1)^{2}}$

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Problem 294

5) $|-x+9|=3$
Solution $=$

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Problem 295

6. $\frac{x^{20} y^{9} z^{2}}{x^{5} y^{9} z}$

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Problem 296

Solve for $y$ . $4+3 y=10$
Simplify your answer as much as possible. $y=$ $\square$

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Problem 297

Find the real roots of the equation by factorin $x^{2}+x-56=0$

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Problem 298

Solve for $y$ . $2(3 y+7)=68$
Simplify your answer as much as possible. $y=$

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Problem 299

$\frac{1}{6}-\frac{3}{5}=$ $\square$ (Type an integer or a simplifed fraction.)

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Problem 300

Solve for $x$ $\frac{3 x+14}{4}=2$
Simplify your answer as much as possible. $x=$ $\square$

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1 2 3 4 5 6 ...268

Math Statement

Problem 201

Which equation is equivalent to 5x=ln⁡85 x=\ln 85x=ln8 ? e5x=e4⋅e2e^{5 x}=e^{4} \cdot e^{2}e5x=e4⋅e2 105x=810^{5 x}=8105x=8 e5x=8e^{5 x}=8e5x=8 23x=32^{3 x}=323x=3

Problem 202

Find the yyy-intercept and the slope of the line. y=−12x+6y=-\frac{1}{2} x+6y=−21​x+6 yyy-intercept: □\square□ Undefined slope:

Problem 203

Find the yyy-intercept and the slope of the line. y=12y=\frac{1}{2}y=21​ yyy-intercept: □\square□ Undefined slope:

Problem 204

Problem 205

Which expression is not equal to the expression shown? 33×34÷3−43^{3} \times 3^{4} \div 3^{-4}33×34÷3−4

Problem 206

Translate f(x)=∣2x∣f(x)=|2 x|f(x)=∣2x∣ down 3 units. f(x)=∣2x∣+3f(x)=|2 x|+3f(x)=∣2x∣+3 f(x)=∣2x−3∣f(x)=|2 x-3|f(x)=∣2x−3∣ f(x)=∣2x∣−3f(x)=|2 x|-3f(x)=∣2x∣−3 f(x)=∣2x+3∣f(x)=|2 x+3|f(x)=∣2x+3∣

Problem 207

x2+4x−x−2\sqrt{x^{2}+4 x}-x-2x2+4x​−x−2

Problem 208

(ii) The direction ratios of a line are (−6,2,3)(-6,2,3)(−6,2,3) and its direction cosines

Problem 209

4. Given y=5e3x+sin⁡xy=5 e^{3 x}+\sin xy=5e3x+sinx. Find dydx\frac{d y}{d x}dxdy​ a. 5e3x+cos⁡x5 e^{3 x}+\cos x5e3x+cosx. b. 15edxdx−cos⁡x15 e^{\frac{d x}{d x}}-\cos x15edxdx​−cosx. c. 15e3x+cos⁡x15 e^{3 x}+\cos x15e3x+cosx. d. 2.666e12−cos⁡x2.666 e^{12}-\cos x2.666e12−cosx

Problem 210

I Let f(x)=2x3−1x+73x2−2f(x)=\frac{2 x^{3}-1 x+7}{3 x^{2}-2}f(x)=3x2−22x3−1x+7​. Find f(3)f(3)f(3) a. 23\frac{2}{3}32​ b. 1639\frac{16}{39}3916​ c. 3 d. 1n45\frac{1 n}{45}451n​

Problem 211

Zet 475 milliliter om in liter. □\square□ liter

Problem 212

12. The lim⁡x→0sin⁡(x)x=1\lim _{x \rightarrow 0} \frac{\sin (x)}{x}=1limx→0​xsin(x)​=1 a. True b. false

Problem 213

Determine the slope and yyy-intercept. y=3/2x+3\quad y=3 / 2 x+3y=3/2x+3

Problem 214

1. lim⁡x→cf(x)=f(c)\lim _{x \rightarrow c} f(x)=f(c)limx→c​f(x)=f(c) II. f(c)f(c)f(c) is definedIII lim⁡x→cf(x)\lim _{x \rightarrow c} f(x)limx→c​f(x) must exist a. True b. false

Problem 215

If p−18=3p-18=3p−18=3, what is the value of p?p ?p?

Problem 216

Problem 217

Given a circle with center (8,2)(8,2)(8,2) and radius r=8r=8r=8, write its equation in standard form. (x−8)2+(y−2)2=(x-8)^{2}+(y-2)^{2}=(x−8)2+(y−2)2= 6464 \sqrt{ }64​ □\square□

Problem 218

Let (−3,−2)(-3,-2)(−3,−2) be a point on the terminal side of θ\thetaθ. Find the exact values of sin⁡θ,sec⁡θ\sin \theta, \sec \thetasinθ,secθ, and tan⁡θ\tan \thetatanθ. □\square□

Problem 219

If 2x3x+5=4\frac{2 x}{3 x+5}=43x+52x​=4, what is the value of xxx ? Choose 1 mower: (A) -20 (B) -2 (C) 12\frac{1}{2}21​ (e) 16Sthow calculator

Problem 220

Find the center and the radius of the circle with the given equation. x2+y2−20=0x^{2}+y^{2}-20=0x2+y2−20=0Center: □\square□ (0,0)(0,0)(0,0) ✓\checkmark✓NOTE: Enter the radius in simplified form.Radius: 252 \sqrt{5}25​ □\square□ \sqrt{ }​

Problem 221

Find all solutions of the equation in the interval [0,2π)[0,2 \pi)[0,2π). 2cos⁡θ−2=02 \cos \theta-\sqrt{2}=02cosθ−2​=0Write your answer in radians in terms of π\piπ. If there is more than one solution, separate them with commas. θ=\theta=θ= □\square□

Problem 222

Describe the long run behavior of f(n)=3n8−4n3+n2+5f(n)=3 n^{8}-4 n^{3}+n^{2}+5f(n)=3n8−4n3+n2+5 As n→−∞,f(n)→?∨n \rightarrow-\infty, f(n) \rightarrow ? \veen→−∞,f(n)→?∨ As n→∞,f(n)→?∨n \rightarrow \infty, f(n) \rightarrow ? \veen→∞,f(n)→?∨

Problem 223

12 What is the value of each number? 7 −7-7−7 14 −14-14−14 ∣7∣=|7|=∣7∣= □\square□ ∣−14∣=|-14|=∣−14∣= □\square□ ∣14∣=|14|=∣14∣= □\square□ □\square□

Problem 224

35+3\frac{\sqrt{3}}{\sqrt{5}+\sqrt{3}}5​+3​3​​

Problem 225

Select either < or > to make the statement true. −20…9−10−100−13_13\begin{array}{l} -20 \ldots \quad 9 \\ -10 \quad-100 \\ -13 \_13 \end{array}−20…9−10−100−13_13​

Problem 226

Problem 227

Write an expression to describe the sequence below. Use nnn to represent the position of a term in the sequence, where n=1n=1n=1 for the first term. −6,−12,−18,−24,…an=□\begin{array}{l} -6,-12,-18,-24, \ldots \\ a_{n}=\square \end{array}−6,−12,−18,−24,…an​=□​

Problem 228

Use the following function rule to find f(d+7)f(d+7)f(d+7). Simplify your answer. f(n)=n2+8f(d+7)=\begin{array}{l} f(n)=n^{2}+8 \\ f(d+7)= \end{array}f(n)=n2+8f(d+7)=​ □\square□ Submit

Problem 229

(d) Determine the following indefinite integrals i) ∫(2+3x−4x3)dx\int\left(2+3 x-4 x^{3}\right) d x∫(2+3x−4x3)dx ii) ∫(cos⁡x+3sin⁡x)dx\int(\cos x+3 \sin x) d x∫(cosx+3sinx)dx iii) ∫4t−12t2+t+1dt\int \frac{4 t-1}{2 t^{2}+t+1} d t∫2t2+t+14t−1​dt

Problem 230

Solve using the standard algorithm. a. 0.64÷4=0.64 \div 4=0.64÷4= \qquad b. 6.45÷5=6.45 \div 5=6.45÷5= \qquad c. 16.404÷6=16.404 \div 6=16.404÷6= \qquad

Problem 231

Problem 232

Problem 233

If the proauct of xeroes of the polynomial ax2−18x−6Δa x^{2}-18 x-6 \Deltaax2−18x−6Δ is 4 . Find the the value of aaa.

Problem 234

10 points Solve for x:(x+3)2+5=1x:(x+3)^{2}+5=1x:(x+3)2+5=1 x=−5x=-5x=−5 or -1 x=13x=13x=13 x=−3±2ix=-3 \pm 2 ix=−3±2i x=−3±4ix=-3 \pm 4 ix=−3±4i

Problem 235

Solve the absolute value equation. ∣2x−7∣=11|2 x-7|=11∣2x−7∣=11

Problem 236

Problem 237

(5112+732)⋅(5112−732)(5 \sqrt[2]{11}+7 \sqrt[2]{3}) \cdot(5 \sqrt[2]{11}-7 \sqrt[2]{3})(5211​+723​)⋅(5211​−723​)

Problem 238

17. When the second derivative of a curve is positive then the type of stationary point is a. Maximum b. Minimum c. Neutral d. Inflexion

Problem 239

Evaluate: x=4,y=53y−x\begin{array}{c} x=4, y=5 \\ 3 y-x \end{array}x=4,y=53y−x​

Problem 240

Evaluate: a=1,b=6,c=3c2⋅a−b\begin{array}{c} a=1, b=6, c=3 \\ c^{2} \cdot a-b \end{array}a=1,b=6,c=3c2⋅a−b​

Problem 241

Evaluate: 9\sqrt{9}9​

Problem 242

Question 10 of 10What is the simplest form of the fraction below? 1530\frac{15}{30}3015​ A. 37\frac{3}{7}73​ B. 23\frac{2}{3}32​ C. 12\frac{1}{2}21​ D. 38\frac{3}{8}83​

Problem 243

Which equation is equivalent to $5 x=\ln 8$ ? $e^{5 x}=e^{4} \cdot e^{2}$ $10^{5 x}=8$ $e^{5 x}=8$ $2^{3 x}=3$

Find the $y$ -intercept and the slope of the line. $y=-\frac{1}{2} x+6$ $y$ -intercept: $\square$ Undefined slope:

Find the $y$ -intercept and the slope of the line. $y=\frac{1}{2}$ $y$ -intercept: $\square$ Undefined slope:

Which expression is not equal to the expression shown? $3^{3} \times 3^{4} \div 3^{-4}$

Translate $f(x)=|2 x|$ down 3 units. $f(x)=|2 x|+3$ $f(x)=|2 x-3|$ $f(x)=|2 x|-3$ $f(x)=|2 x+3|$

$\sqrt{x^{2}+4 x}-x-2$

(ii) The direction ratios of a line are $(-6,2,3)$ and its direction cosines

4. Given $y=5 e^{3 x}+\sin x$ . Find $\frac{d y}{d x}$ a. $5 e^{3 x}+\cos x$ . b. $15 e^{\frac{d x}{d x}}-\cos x$ . c. $15 e^{3 x}+\cos x$ . d. $2.666 e^{12}-\cos x$

I Let $f(x)=\frac{2 x^{3}-1 x+7}{3 x^{2}-2}$ . Find $f(3)$ a. $\frac{2}{3}$ b. $\frac{16}{39}$ c. 3 d. $\frac{1 n}{45}$

Zet 475 milliliter om in liter. $\square$ liter

12. The $\lim _{x \rightarrow 0} \frac{\sin (x)}{x}=1$ a. True b. false

Determine the slope and $y$ -intercept. $\quad y=3 / 2 x+3$

1. $\lim _{x \rightarrow c} f(x)=f(c)$ II. $f(c)$ is defined
III $\lim _{x \rightarrow c} f(x)$ must exist a. True b. false

If $p-18=3$ , what is the value of $p ?$

Given a circle with center $(8,2)$ and radius $r=8$ , write its equation in standard form. $(x-8)^{2}+(y-2)^{2}=$ $64 \sqrt{ }$ $\square$

Let $(-3,-2)$ be a point on the terminal side of $\theta$ . Find the exact values of $\sin \theta, \sec \theta$ , and $\tan \theta$ . $\square$

If $\frac{2 x}{3 x+5}=4$ , what is the value of $x$ ? Choose 1 mower: (A) -20 (B) -2 (C) $\frac{1}{2}$ (e) 16
Sthow calculator

Find the center and the radius of the circle with the given equation. $x^{2}+y^{2}-20=0$
Center: $\square$ $(0,0)$ $\checkmark$
NOTE: Enter the radius in simplified form.
Radius: $2 \sqrt{5}$ $\square$ $\sqrt{ }$

Find all solutions of the equation in the interval $[0,2 \pi)$ . $2 \cos \theta-\sqrt{2}=0$
Write your answer in radians in terms of $\pi$ . If there is more than one solution, separate them with commas. $\theta=$ $\square$

Describe the long run behavior of $f(n)=3 n^{8}-4 n^{3}+n^{2}+5$ As $n \rightarrow-\infty, f(n) \rightarrow ? \vee$ As $n \rightarrow \infty, f(n) \rightarrow ? \vee$

12 What is the value of each number? 7 $-7$ 14 $-14$ $|7|=$ $\square$ $|-14|=$ $\square$ $|14|=$ $\square$ $\square$

$\frac{\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

Select either < or > to make the statement true. $\begin{array}{l} -20 \ldots \quad 9 \\ -10 \quad-100 \\ -13 \_13 \end{array}$

Write an expression to describe the sequence below. Use $n$ to represent the position of a term in the sequence, where $n=1$ for the first term. $\begin{array}{l} -6,-12,-18,-24, \ldots \\ a_{n}=\square \end{array}$

Use the following function rule to find $f(d+7)$ . Simplify your answer. $\begin{array}{l} f(n)=n^{2}+8 \\ f(d+7)= \end{array}$ $\square$ Submit

(d) Determine the following indefinite integrals i) $\int\left(2+3 x-4 x^{3}\right) d x$ ii) $\int(\cos x+3 \sin x) d x$ iii) $\int \frac{4 t-1}{2 t^{2}+t+1} d t$

Solve using the standard algorithm. a. $0.64 \div 4=$ $\qquad$ b. $6.45 \div 5=$ $\qquad$ c. $16.404 \div 6=$ $\qquad$

If the proauct of xeroes of the polynomial $a x^{2}-18 x-6 \Delta$ is 4 . Find the the value of $a$ .

10 points Solve for $x:(x+3)^{2}+5=1$ $x=-5$ or -1 $x=13$ $x=-3 \pm 2 i$ $x=-3 \pm 4 i$

Solve the absolute value equation. $|2 x-7|=11$

$(5 \sqrt[2]{11}+7 \sqrt[2]{3}) \cdot(5 \sqrt[2]{11}-7 \sqrt[2]{3})$

Evaluate: $\begin{array}{c} x=4, y=5 \\ 3 y-x \end{array}$

Evaluate: $\begin{array}{c} a=1, b=6, c=3 \\ c^{2} \cdot a-b \end{array}$

Evaluate: $\sqrt{9}$

Question 10 of 10
What is the simplest form of the fraction below? $\frac{15}{30}$ A. $\frac{3}{7}$ B. $\frac{2}{3}$ C. $\frac{1}{2}$ D. $\frac{3}{8}$

Let $x$ be $2x - 3$ . Evaluate $\text{1. } f(x) = x + 5$

$11 x^{2}-34 x+28=$

3. Si el punto $\left(\frac{\pi}{3} ; \frac{2 n-1}{2 n+1}\right)$ pertenece a la gráfica de la función $y=\cos x$ , demuestra que $n=3 / 2$

Find the inverse of each matrix. 17) $\left[\begin{array}{ccc}-2 & 5 & -2 \\ -2 & 2 & 0 \\ -3 & -2 & 2\end{array}\right]$

If $\frac{\sqrt{x}}{16}=\frac{15}{8}$ then the value of $x$ is:

$\begin{array}{l}-18=10+4(5-3 g) \\ -18=10+20-12 g \\ -18=30-12 g \\ -48=-12 g \\ 12=g\end{array}$

$\sin 2 x-\sin x=0$

$\left(2^{-1}+3^{-1}+4^{-1}\right) \times \frac{3}{4}$

Lab Homework Question 1, 4.4.C2
Fill in the blank so that the resulting statement is true. If $5^{4 x-1}=5^{11}$ , then $\_=11$
If $5^{4 x-1}=5^{11}$ , then $\square=11$

Evaluate. Write your answers as fractions. $\begin{array}{c} -\left(\frac{3}{5}\right)^{3}= \\ \frac{5^{2}}{-2}= \end{array}$

Simplify. $\frac{a^{2} b^{6}}{a^{3} b^{4}}$

( Lab Homework Question 13, 4.4-20 Points: of of 1
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. $\log _{3} x=4$ A. $\{1.262\}$ B. (64) C. (12) D. (81)

$\begin{array}{l}\sin \theta(1+\tan \theta)+\cos \theta \quad(1+\cot \theta) \\ \qquad=(\sec \theta+\operatorname{cosec} \theta)\end{array}$

$\frac{1+\cot ^{2} \theta}{1+\operatorname{cosec} \theta}=\operatorname{cosec} \theta$

$(1+\sqrt{3})(1-\sqrt{3})$
1. simplify $\frac{1}{1+\sqrt{3}} \text { to } 3 \text { s.f. given that } \sqrt{3} \times 1.732$

Which ordered pair is a solution to the system of inequalities? $\left\{\begin{array}{c} y>-2 \\ x+y<4 \end{array}\right.$ $(-3,5)$ $(0,4)$ $(1,4)$ $(-2,-3)$

$\begin{array}{r}-29+55=84 \\ -37+(-48)=7\end{array}$

$\begin{array}{l}29+(-41)=\square \\ -42+(-33)=\square\end{array}$

$-4+8-5$

Exponential Growth $A=\mathrm{Pe}^{\text {rt }}$ Population of city Santa Clava in 2003 was 98,000 Population now of Santa Clara in 2022 was 131,886 Based on these numbers and exponelitial growth, estimate the population of Santa Clara in 2050

$(\sqrt{16}-\sqrt{4}) \cdot 2^{4}+4^{33}: 4^{31}=$

f. $12 \div \frac{7}{8}$

$-4.05+3.18$

2) $\sqrt[5]{32}+(14-2)^{2}: \sqrt{144}=$

$30:(4-14)+(-8: 2-3) \cdot 2=$

$30:(4-14)+(-8: 2-3) \cdot 2=$