Math Statement

Problem 13201

Differentiate the following functions:
1. Constants and powers: (a) $\frac{d}{d x}(7)$ (b) $\frac{d}{d x}(\ln 3)$ (c) $\frac{d}{d x}(x^{3})$ (d) $\frac{d}{d x}(\frac{1}{x^{8}})$ (e) $\frac{d}{d x}(4x^{5})$
2. Find $\frac{d y}{d x}$ for: (a) $y=(x+3)(2x^{2}+4)$ (b) $y=\frac{3x^{2}-7x-4}{x^{3}}$ (c) $y=(4x-1)^{2}(x^{2}-3)$ (product rule) (d) $y=\frac{x-2}{x+4}$ (quotient rule) (e) $y=\frac{e^{3x}}{x}$ (f) $y=\log_{2} x$ (g) $y=\ln(4+9x^{2})$
3. For $y=\sqrt{3x-7}$ , find: (a) $\frac{d y}{d x}$ (b) $\frac{d^{2} y}{d x^{2}}$

See Solution

Problem 13202

Find $P(B)$ given $P(A)=0.3$ , $P(A$ OR $B)=0.63$ , and $P(A$ AND $B)=0.17$ .

See Solution

Problem 13203

Find $P(A$ OR $B)$ given $P(A)=0.7$ , $P(B)=0.2$ , and $P(A$ AND $B)=0.17$ .

See Solution

Problem 13204

Calculate the value of $8.67 \times 10^{-2}$ .

See Solution

Problem 13205

Find all real solutions of the equation $x^{2}-10x+1=0$ . Enter answers as a comma-separated list.

See Solution

Problem 13206

Find the equation of line $w$ , parallel to $y-6=-\frac{3}{5}(x+2)$ and passing through $(10,3)$ .

See Solution

Problem 13207

Find the angle measures: $3x^{\circ}=57^{\circ}$ and $(76-x)^{\circ}=$ (Type whole numbers.)

See Solution

Problem 13208

Choose expressions equivalent to $18 m-12$ : $6 m-4+6 m-4+6 m-4$ , $12 m+6-6 m-6$ , $6(3 m-2)$ , $3(6 m-4)$ , $24 n-4^{2}+8-6 m$ .

See Solution

Problem 13209

Find the partial derivatives $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ for these functions: (a) $f(x, y)=(x^{2}-1)(y+2)$ (b) $f(x, y)=e^{x+y+1}$ (c) $f(x, y)=\ln (x+y)$

See Solution

Problem 13210

List the whole numbers in the set $\{x \mid x \leq 0\}$ .

See Solution

Problem 13211

Evaluate the expression and express the result as $a + b i$ : $\frac{(7 + 2 i)(8 - i)}{2 + i}$

See Solution

Problem 13212

Solve the equation $3x + 2x - 5 = 25$ .

See Solution

Problem 13213

Given $\cos \theta=-\frac{1}{3}$ in Quadrant III, find $\sin \theta$ , $\csc \theta$ , $\sec \theta$ , $\tan \theta$ , and $\cot \theta$ .

See Solution

Problem 13214

Given $\sin \theta=-\frac{7}{9}$ in Quadrant III, find $\sin \theta$ , $\csc \theta$ , $\cos \theta$ , $\sec \theta$ , $\tan \theta$ , and $\cot \theta$ .

See Solution

Problem 13215

Find the function $g(x)$ that represents a vertical shrink of $f(x)=|x|-3$ by a factor of $\frac{1}{3}$ .

See Solution

Problem 13216

Find the limit as $x$ approaches infinity for $\sqrt{x^{2}+6}$ .

See Solution

Problem 13217

Simplify $\left(\frac{5}{8}\right)^{2}$ .

See Solution

Problem 13218

Find the function $g(x)$ that reflects $f(x)=|6x|-2$ in the $y$ -axis.

See Solution

Problem 13219

If $\sin \theta=\frac{2}{5}$ , which quadrants could the angle $\theta$ be in? Check all that apply: Quadrant 1, 2, 3, 4.

See Solution

Problem 13220

Calculate: $4 \frac{1}{6} \times 8 =$

See Solution

Problem 13221

If $\cos \theta=\frac{1}{9}$ , in which quadrants could the angle $\theta$ be located? (Check all that apply)

See Solution

Problem 13222

Convert 30 m to cm: 30 m = $\square$ cm.

See Solution

Problem 13223

Find the whole number that satisfies the equation: $7 \cdot 5 \cdot 5=5 \square \cdot 7$ .

See Solution

Problem 13224

Find the function $g(x)$ that reflects $f(x)=\frac{1}{2} x-3$ in the $x$ -axis.

See Solution

Problem 13225

Factor the expression $64 - x^{2}$ completely over the integers.

See Solution

Problem 13226

Find the quotient by multiplying by the reciprocal: $\frac{1}{10} \div \frac{3}{2}$ .

See Solution

Problem 13227

Solve the quadratic equation: $x^{2}-x-6=0$

See Solution

Problem 13228

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}$ .

See Solution

Problem 13229

Solve the equation $5 x^{2} - 8 = 12 x$ .

See Solution

Problem 13230

Match the expressions using Quotient and Reciprocal Identities:
1. $-\vee \frac{1}{\csc (\theta)}$
2. $-v \frac{1}{\tan (\theta)}$
3. $-v \frac{\sin (\theta)}{\cos (\theta)}$
4. $-v \frac{1}{\sec (\theta)}$
5. $-\vee \frac{1}{\sin (\theta)}$
6. $-v \frac{1}{\cot (\theta)}$
7. $-v \frac{\cos (\theta)}{\sin (\theta)}$
8. $-v \frac{1}{\cos (\theta)}$
Options: a. $\sin (\theta)$ , b. $\cos (\theta)$ , c. $\tan (\theta)$ , d. $\csc (\theta)$ , e. $\sec (\theta)$ , f. $\cot (\theta)$ .

See Solution

Problem 13231

Solve the inequality $|x-1|-2x>1$ .

See Solution

Problem 13232

Find the limit: $\lim _{x \rightarrow \infty}\left(\sqrt{25 x^{2}+x}-5 x\right)$ . If it doesn't exist, enter DNE.

See Solution

Problem 13233

Find the other five trigonometric functions of angle $\theta$ in Quadrant IV, given $\sin(\theta)=-\frac{15}{17}$ .

See Solution

Problem 13234

Given $\cos (\alpha)=-\frac{3}{5}$ in quadrant III, find all 6 trig functions and round decimals to three places.

See Solution

Problem 13235

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[S]}{0.021+[S]}$ . What does it indicate?

See Solution

Problem 13236

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}$ . What does it signify?

See Solution

Problem 13237

Find the quotient by multiplying by the reciprocal: $\frac{9}{10} \div \frac{12}{7}$ .

See Solution

Problem 13238

Bertalanffy growth function:
1. Find $\lim_{t \rightarrow \infty} L(t)$ and interpret.
2. With $L_{0}=1 \mathrm{~cm}$ , $L_{T}=38 \mathrm{~cm}$ , graph $L(t)$ for various $k$ .

See Solution

Problem 13239

Find $\lim_{t \rightarrow \infty} B(t)$ for the biomass model $B(t)=\frac{9 \times 10^{7}}{1+3 e^{-0.72 t}}$ . What does this limit mean?

See Solution

Problem 13240

Factor the following expressions:
1. $x^{2}-9x+18$
2. $x^{2}-5x-36$
3. $x^{2}+5x-14$

See Solution

Problem 13241

Simplify the expression: $\frac{x^{2}-1}{x^{2}-6x+5}$ .

See Solution

Problem 13242

If $\sin (x)=\frac{7}{10}$ , find $\csc (x)$ as a fraction.

See Solution

Problem 13243

Simplify $x^{-7}$ to use only positive exponents.

See Solution

Problem 13244

Simplify $15 c^{-8} d^{0}$ using only positive exponents.

See Solution

Problem 13245

Find the value of the function $f(x)=4x+2$ at $x=0$ : what is $f(0)$ ?

See Solution

Problem 13246

Simplify $\frac{z^{8} \cdot z^{2}}{z^{5}}$ and express the result with positive exponents only.

See Solution

Problem 13247

Find the value of the function $f(x)=-2 x+2$ at $x=-3$ . What is $f(-3)$ ?

See Solution

Problem 13248

Find the value of $f(8)$ for the function $f(x)=|x-3|-5$ .

See Solution

Problem 13249

Evaluate $f(x)=\frac{x^{2}-3 x}{x^{2}-x-6}$ at $x=3.5,3.1,...,2.999$ and find $\lim_{x \to 3} f(x) \approx 0.600000$ .

See Solution

Problem 13250

Simplify $\left(\frac{2 x^{-2} y^{3}}{3 x y^{-4}}\right)^{4}$ using positive exponents and evaluate numerical powers.

See Solution

Problem 13251

Find the value of the function $f(x)=-3|x-4|$ at $x=3$ . What is $f(3)$ ?

See Solution

Problem 13252

Find the value of the function $f(x)=x^{2}+2x-4$ at $x=-1$ . What is $f(-1)$ ?

See Solution

Problem 13253

Evaluate $f(x)=\frac{x^{2}-8 x}{x^{2}-7 x-8}$ at $x=0,-0.5,-0.9,-0.95,-0.99,-0.999,-2,-1.5,-1.1,-1.01,-1.001$ . Find $\lim_{x \to -1} f(x)$ to six decimal places.

See Solution

Problem 13254

Calculate the products: $10 \times 1$ , $10 \times 2$ , ..., $10 \times 12$ .

See Solution

Problem 13255

Calculate the product: $\sqrt{2} \times \sqrt{13}=$

See Solution

Problem 13256

Calculate the sum of $2,156 + 1,793$ .

See Solution

Problem 13257

Find the value of $x$ that satisfies the equation: $1.2 x + 9 = 0.6 x + 1.8$ .

See Solution

Problem 13258

Calculate $x y + z$ when $x=6$ , $y=8$ , and $z=3$ .

See Solution

Problem 13259

Evaluate $2x + 3y - z$ for $x=6$ , $y=8$ , and $z=3$ . What is the result?

See Solution

Problem 13260

Calculate $y z - x$ given $x = 6$ , $y = 8$ , and $z = 3$ .

See Solution

Problem 13261

Substitute $x=6$ , $y=8$ , and $z=3$ into the expression $5x - (y + 2z)$ . What is the result?

See Solution

Problem 13262

Solve $2(x+z)-y$ for $x=6$ , $y=8$ , and $z=3$ . What is the result?

See Solution

Problem 13263

Solve the system of equations: -2x - 2y + 3z = -19, 3x - 4y - 2z = -28, 6x + 3y - 4z = 21.

See Solution

Problem 13264

Simplify: $8 + 2 \times 7$

See Solution

Problem 13265

Calculate the expression: $3 + 2 \cdot 5 - 4$ .

See Solution

Problem 13266

Calculate $9 \cdot 3 + 2 \cdot 5$ .

See Solution

Problem 13267

Calculate $5(2+4)+15 \div(9-6)$ .

See Solution

Problem 13268

Solve the equation: $-2(x-2)=-3-2 x$ .

See Solution

Problem 13269

Calculate the following sums: $-2 + (-11)$ , $9 + 4$ , and $-6 + (-1)$ .

See Solution

Problem 13270

Compute the following sums using positive and negative symbols:
1. $7 + (-2)$
2. $11 + 12$
3. $2 + (-2)$
4. $-9 + 9$
5. $3 + (-8)$
6. $-3 + (-6)$
7. $-75 + (-25)$
8. $-100 + 1$
9. $(-0.75) + (-0.25)$
10. $(-4) + 0.5$
11. $(-\frac{3}{4}) + (-\frac{1}{4})$
12. $(-2 \frac{1}{2}) + \frac{1}{4}$

See Solution

Problem 13271

Calculate the sums: $-6 + (-1)$ and $7 + (-2)$ .

See Solution

Problem 13272

Calculate $11 + 12$ and $2 + (-2)$ .

See Solution

Problem 13273

What is the result of $2 + (-2)$ ?

See Solution

Problem 13274

Calculate: $-75 + (-25)$ , $(-0.75) + (-0.25)$ , and $\left(-\frac{3}{4}\right) + \left(-\frac{1}{4}\right)$ .

See Solution

Problem 13275

Calculate the following sums: $7 + (-3)$ , $-6 + 4$ , and $-5 + 1$ .

See Solution

Problem 13276

Convert the following to percentages: 4.18, 193.1, $\frac{5}{6}$ , $\frac{1}{8}$ , $\frac{5}{8}$ , $\frac{3}{5}$ .

See Solution

Problem 13277

Find the value of $b$ for the continuous piecewise function $f(x) = \{2x-5 \text{ if } x \leq 9, -3x+b \text{ if } x > 9\}$ .

See Solution

Problem 13278

Determine if the following functions are odd/even and injective/surjective/bijective:
1. $f(x)=c$
2. $f(x)=x$
3. $f(x)=x^{2}$
4. $f(x)=x^{3}$
5. $f(x)=\frac{1}{x}$
6. $f(x)=\frac{1}{x^{2}}$
7. $f(x)=\sqrt[3]{x}$
8. $f(x)=\sqrt{x}$
9. $f(x)=|x|$

See Solution

Problem 13279

Find the value of $b$ that makes the piecewise function $f(x)$ continuous at $x=9$ : $f(x)=\{2x-5 \text{ if } x \leq 9, -3x+b \text{ if } x>9\}$ .

See Solution

Problem 13280

Find the value of $m$ for the continuous function $f(x)=\left\{\begin{array}{ll}m x-8 & \text { if } \quad x<-7 \\ x^{2}+10 x-1 & \text { if } \quad x \geq-7\end{array}\right.$

See Solution

Problem 13281

Rewrite $\sec (t) \cos (t)$ using $\sin t$ and $\cos t$ , then simplify if possible.

See Solution

Problem 13282

Find $c$ for the function defined by $f(x) = x^2 - 4$ if $x \leq c$ and $f(x) = 6x - 13$ if $x > c$ to ensure continuity. $c =$

See Solution

Problem 13283

Find the value of $c$ that makes the function $f$ continuous for all $s$ where $f(s)=\{c s+5 \text{ if } s \leq 4, c(s)^{2}-5 \text{ if } s>4\}$ .

See Solution

Problem 13284

Find the value of $c$ for which the function $f$ is continuous for all $b$ in $(-\infty, \infty)$ , defined as: $f(b) = \begin{cases} c b + 6 & \text{if } b \leq 9 \\ c(b)^2 - 6 & \text{if } b > 9 \end{cases}$

See Solution

Problem 13285

Rewrite $(\csc a)(\tan a)$ using $\sin a$ and $\cos a$ , then simplify if possible.

See Solution

Problem 13286

Rewrite $\frac{\csc (t)}{\cot (t)}$ using $\sin t$ and $\cos t$ , then simplify if possible.

See Solution

Problem 13287

Calculate the value of $\frac{28.927}{34.1}$ .

See Solution

Problem 13288

Express $\sin (\theta) \cdot \cos (\theta) \cdot \cot (\theta)$ using $\sin t$ and $\cos t$ , then simplify.

See Solution

Problem 13289

Calculate $\frac{28.927}{6.72 \times 0.848}$ .

See Solution

Problem 13290

Express and simplify: $\sin (\theta) \cdot \cos ^{2}(\theta) \cdot \tan (\theta) \cdot \cot (\theta) \cdot \sec (\theta) \cdot \csc (\theta)=$

See Solution

Problem 13291

Rewrite $\sin x \cdot \cot x + \cos x$ using $\sin x$ and $\cos x$ , then simplify.

See Solution

Problem 13292

Rewrite and simplify $\cos x^{*} \cot x + \sin x$ using $\sin x$ and $\cos x$ .

See Solution

Problem 13293

Simplify $\frac{1}{\cos x} - \cos x =$

See Solution

Problem 13294

Rewrite $\cos x^{2} \cot x + \sin x$ using $\sin x$ and $\cos x$ , then simplify.

See Solution

Problem 13295

Multiply the polynomials $(x-4)(2x-3)$ and express the result in standard form.

See Solution

Problem 13296

Express $\sin(t) \sec(t)$ using $\sin t$ and $\cos t$ , then simplify.

See Solution

Problem 13297

Find angles 1 and 2 in an isosceles triangle. Options: a. $m \angle 1=63^{\circ}, m \angle 2=45^{\circ}$ b. $m \angle 1=45^{\circ}, m \angle 2=63^{\circ}$ c. $m \angle 1=27^{\circ}, m \angle 2=45^{\circ}$ d. $m \angle 1=22.5^{\circ}, m \angle 2=13.5^{\circ}$ .

See Solution

Problem 13298

Simplify the expression $\frac{x^{2}-3 x-28}{x^{2}-16}$ .

See Solution

Problem 13299

Multiply the polynomials and write your answer in standard form: $(4)(5)(3 + 5)$

See Solution

Problem 13300

Multiply (2 cos x + 1)(3 cos x - 1)

See Solution

1 ...130 131 132 133 134 135 136 ...270

Math Statement

Problem 13201

Problem 13202

Find P(B)P(B)P(B) given P(A)=0.3P(A)=0.3P(A)=0.3, P(AP(AP(A OR B)=0.63B)=0.63B)=0.63, and P(AP(AP(A AND B)=0.17B)=0.17B)=0.17.

Problem 13203

Find P(AP(AP(A OR B)B)B) given P(A)=0.7P(A)=0.7P(A)=0.7, P(B)=0.2P(B)=0.2P(B)=0.2, and P(AP(AP(A AND B)=0.17B)=0.17B)=0.17.

Problem 13204

Calculate the value of 8.67×10−28.67 \times 10^{-2}8.67×10−2.

Problem 13205

Find all real solutions of the equation x2−10x+1=0x^{2}-10x+1=0x2−10x+1=0. Enter answers as a comma-separated list.

Problem 13206

Find the equation of line www, parallel to y−6=−35(x+2)y-6=-\frac{3}{5}(x+2)y−6=−53​(x+2) and passing through (10,3)(10,3)(10,3).

Problem 13207

Find the angle measures: 3x∘=57∘3x^{\circ}=57^{\circ}3x∘=57∘ and (76−x)∘=(76-x)^{\circ}=(76−x)∘= (Type whole numbers.)

Problem 13208

Choose expressions equivalent to 18m−1218 m-1218m−12: 6m−4+6m−4+6m−46 m-4+6 m-4+6 m-46m−4+6m−4+6m−4, 12m+6−6m−612 m+6-6 m-612m+6−6m−6, 6(3m−2)6(3 m-2)6(3m−2), 3(6m−4)3(6 m-4)3(6m−4), 24n−42+8−6m24 n-4^{2}+8-6 m24n−42+8−6m.

Problem 13209

Problem 13210

List the whole numbers in the set {x∣x≤0}\{x \mid x \leq 0\}{x∣x≤0}.

Problem 13211

Evaluate the expression and express the result as a+bia + b ia+bi: (7+2i)(8−i)2+i\frac{(7 + 2 i)(8 - i)}{2 + i}2+i(7+2i)(8−i)​

Problem 13212

Solve the equation 3x+2x−5=253x + 2x - 5 = 253x+2x−5=25.

Problem 13213

Given cos⁡θ=−13\cos \theta=-\frac{1}{3}cosθ=−31​ in Quadrant III, find sin⁡θ\sin \thetasinθ, csc⁡θ\csc \thetacscθ, sec⁡θ\sec \thetasecθ, tan⁡θ\tan \thetatanθ, and cot⁡θ\cot \thetacotθ.

Problem 13214

Given sin⁡θ=−79\sin \theta=-\frac{7}{9}sinθ=−97​ in Quadrant III, find sin⁡θ\sin \thetasinθ, csc⁡θ\csc \thetacscθ, cos⁡θ\cos \thetacosθ, sec⁡θ\sec \thetasecθ, tan⁡θ\tan \thetatanθ, and cot⁡θ\cot \thetacotθ.

Problem 13215

Find the function g(x)g(x)g(x) that represents a vertical shrink of f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3 by a factor of 13\frac{1}{3}31​.

Problem 13216

Find the limit as xxx approaches infinity for x2+6\sqrt{x^{2}+6}x2+6​.

Problem 13217

Simplify (58)2\left(\frac{5}{8}\right)^{2}(85​)2.

Problem 13218

Find the function g(x)g(x)g(x) that reflects f(x)=∣6x∣−2f(x)=|6x|-2f(x)=∣6x∣−2 in the yyy-axis.

Problem 13219

If sin⁡θ=25\sin \theta=\frac{2}{5}sinθ=52​, which quadrants could the angle θ\thetaθ be in? Check all that apply: Quadrant 1, 2, 3, 4.

Problem 13220

Calculate: 416×8=4 \frac{1}{6} \times 8 = 461​×8=

Problem 13221

If cos⁡θ=19\cos \theta=\frac{1}{9}cosθ=91​, in which quadrants could the angle θ\thetaθ be located? (Check all that apply)

Problem 13222

Convert 30 m to cm: 30 m = □\square□ cm.

Problem 13223

Find the whole number that satisfies the equation: 7⋅5⋅5=5□⋅77 \cdot 5 \cdot 5=5 \square \cdot 77⋅5⋅5=5□⋅7.

Problem 13224

Find the function g(x)g(x)g(x) that reflects f(x)=12x−3f(x)=\frac{1}{2} x-3f(x)=21​x−3 in the xxx-axis.

Problem 13225

Factor the expression 64−x264 - x^{2}64−x2 completely over the integers.

Problem 13226

Find the quotient by multiplying by the reciprocal: 110÷32\frac{1}{10} \div \frac{3}{2}101​÷23​.

Problem 13227

Solve the quadratic equation: x2−x−6=0x^{2}-x-6=0x2−x−6=0

Problem 13228

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: v=0.17[ S]0.021+[S]v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}v=0.021+[S]0.17[ S]​.

Problem 13229

Solve the equation 5x2−8=12x5 x^{2} - 8 = 12 x5x2−8=12x.

Problem 13230

Problem 13231

Solve the inequality ∣x−1∣−2x>1|x-1|-2x>1∣x−1∣−2x>1.

Problem 13232

Find the limit: lim⁡x→∞(25x2+x−5x)\lim _{x \rightarrow \infty}\left(\sqrt{25 x^{2}+x}-5 x\right)x→∞lim​(25x2+x​−5x). If it doesn't exist, enter DNE.

Problem 13233

Find the other five trigonometric functions of angle θ\thetaθ in Quadrant IV, given sin⁡(θ)=−1517\sin(\theta)=-\frac{15}{17}sin(θ)=−1715​.

Problem 13234

Given cos⁡(α)=−35\cos (\alpha)=-\frac{3}{5}cos(α)=−53​ in quadrant III, find all 6 trig functions and round decimals to three places.

Problem 13235

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: v=0.17[S]0.021+[S]v=\frac{0.17[S]}{0.021+[S]}v=0.021+[S]0.17[S]​. What does it indicate?

Problem 13236

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: v=0.17[ S]0.021+[S]v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}v=0.021+[S]0.17[ S]​. What does it signify?

Problem 13237

Find the quotient by multiplying by the reciprocal: 910÷127\frac{9}{10} \div \frac{12}{7}109​÷712​.

Problem 13238

Bertalanffy growth function: 1. Find lim⁡t→∞L(t)\lim_{t \rightarrow \infty} L(t)limt→∞​L(t) and interpret.2. With L0=1 cmL_{0}=1 \mathrm{~cm}L0​=1 cm, LT=38 cmL_{T}=38 \mathrm{~cm}LT​=38 cm, graph L(t)L(t)L(t) for various kkk.

Problem 13239

Find lim⁡t→∞B(t)\lim_{t \rightarrow \infty} B(t)limt→∞​B(t) for the biomass model B(t)=9×1071+3e−0.72tB(t)=\frac{9 \times 10^{7}}{1+3 e^{-0.72 t}}B(t)=1+3e−0.72t9×107​. What does this limit mean?

Problem 13240

Factor the following expressions: 1. x2−9x+18x^{2}-9x+18x2−9x+18 2. x2−5x−36x^{2}-5x-36x2−5x−36 3. x2+5x−14x^{2}+5x-14x2+5x−14

Problem 13241

Simplify the expression: x2−1x2−6x+5\frac{x^{2}-1}{x^{2}-6x+5}x2−6x+5x2−1​.

Find $P(B)$ given $P(A)=0.3$ , $P(A$ OR $B)=0.63$ , and $P(A$ AND $B)=0.17$ .

Find $P(A$ OR $B)$ given $P(A)=0.7$ , $P(B)=0.2$ , and $P(A$ AND $B)=0.17$ .

Calculate the value of $8.67 \times 10^{-2}$ .

Find all real solutions of the equation $x^{2}-10x+1=0$ . Enter answers as a comma-separated list.

Find the equation of line $w$ , parallel to $y-6=-\frac{3}{5}(x+2)$ and passing through $(10,3)$ .

Find the angle measures: $3x^{\circ}=57^{\circ}$ and $(76-x)^{\circ}=$ (Type whole numbers.)

Choose expressions equivalent to $18 m-12$ : $6 m-4+6 m-4+6 m-4$ , $12 m+6-6 m-6$ , $6(3 m-2)$ , $3(6 m-4)$ , $24 n-4^{2}+8-6 m$ .

List the whole numbers in the set $\{x \mid x \leq 0\}$ .

Evaluate the expression and express the result as $a + b i$ : $\frac{(7 + 2 i)(8 - i)}{2 + i}$

Solve the equation $3x + 2x - 5 = 25$ .

Given $\cos \theta=-\frac{1}{3}$ in Quadrant III, find $\sin \theta$ , $\csc \theta$ , $\sec \theta$ , $\tan \theta$ , and $\cot \theta$ .

Given $\sin \theta=-\frac{7}{9}$ in Quadrant III, find $\sin \theta$ , $\csc \theta$ , $\cos \theta$ , $\sec \theta$ , $\tan \theta$ , and $\cot \theta$ .

Find the function $g(x)$ that represents a vertical shrink of $f(x)=|x|-3$ by a factor of $\frac{1}{3}$ .

Find the limit as $x$ approaches infinity for $\sqrt{x^{2}+6}$ .

Simplify $\left(\frac{5}{8}\right)^{2}$ .

Find the function $g(x)$ that reflects $f(x)=|6x|-2$ in the $y$ -axis.

If $\sin \theta=\frac{2}{5}$ , which quadrants could the angle $\theta$ be in? Check all that apply: Quadrant 1, 2, 3, 4.

Calculate: $4 \frac{1}{6} \times 8 =$

If $\cos \theta=\frac{1}{9}$ , in which quadrants could the angle $\theta$ be located? (Check all that apply)

Convert 30 m to cm: 30 m = $\square$ cm.

Find the whole number that satisfies the equation: $7 \cdot 5 \cdot 5=5 \square \cdot 7$ .

Find the function $g(x)$ that reflects $f(x)=\frac{1}{2} x-3$ in the $x$ -axis.

Factor the expression $64 - x^{2}$ completely over the integers.

Find the quotient by multiplying by the reciprocal: $\frac{1}{10} \div \frac{3}{2}$ .

Solve the quadratic equation: $x^{2}-x-6=0$

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}$ .

Solve the equation $5 x^{2} - 8 = 12 x$ .

Solve the inequality $|x-1|-2x>1$ .

Find the limit: $\lim _{x \rightarrow \infty}\left(\sqrt{25 x^{2}+x}-5 x\right)$ . If it doesn't exist, enter DNE.

Find the other five trigonometric functions of angle $\theta$ in Quadrant IV, given $\sin(\theta)=-\frac{15}{17}$ .

Given $\cos (\alpha)=-\frac{3}{5}$ in quadrant III, find all 6 trig functions and round decimals to three places.

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[S]}{0.021+[S]}$ . What does it indicate?

Find the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}$ . What does it signify?

Find the quotient by multiplying by the reciprocal: $\frac{9}{10} \div \frac{12}{7}$ .

Bertalanffy growth function:
1. Find $\lim_{t \rightarrow \infty} L(t)$ and interpret.
2. With $L_{0}=1 \mathrm{~cm}$ , $L_{T}=38 \mathrm{~cm}$ , graph $L(t)$ for various $k$ .

Find $\lim_{t \rightarrow \infty} B(t)$ for the biomass model $B(t)=\frac{9 \times 10^{7}}{1+3 e^{-0.72 t}}$ . What does this limit mean?

Factor the following expressions:
1. $x^{2}-9x+18$
2. $x^{2}-5x-36$
3. $x^{2}+5x-14$

Simplify the expression: $\frac{x^{2}-1}{x^{2}-6x+5}$ .

If $\sin (x)=\frac{7}{10}$ , find $\csc (x)$ as a fraction.

Simplify $x^{-7}$ to use only positive exponents.

Simplify $15 c^{-8} d^{0}$ using only positive exponents.

Find the value of the function $f(x)=4x+2$ at $x=0$ : what is $f(0)$ ?

Simplify $\frac{z^{8} \cdot z^{2}}{z^{5}}$ and express the result with positive exponents only.

Find the value of the function $f(x)=-2 x+2$ at $x=-3$ . What is $f(-3)$ ?

Find the value of $f(8)$ for the function $f(x)=|x-3|-5$ .

Evaluate $f(x)=\frac{x^{2}-3 x}{x^{2}-x-6}$ at $x=3.5,3.1,...,2.999$ and find $\lim_{x \to 3} f(x) \approx 0.600000$ .

Simplify $\left(\frac{2 x^{-2} y^{3}}{3 x y^{-4}}\right)^{4}$ using positive exponents and evaluate numerical powers.

Find the value of the function $f(x)=-3|x-4|$ at $x=3$ . What is $f(3)$ ?

Find the value of the function $f(x)=x^{2}+2x-4$ at $x=-1$ . What is $f(-1)$ ?

Calculate the products: $10 \times 1$ , $10 \times 2$ , ..., $10 \times 12$ .

Calculate the product: $\sqrt{2} \times \sqrt{13}=$

Calculate the sum of $2,156 + 1,793$ .

Find the value of $x$ that satisfies the equation: $1.2 x + 9 = 0.6 x + 1.8$ .

Calculate $x y + z$ when $x=6$ , $y=8$ , and $z=3$ .

Evaluate $2x + 3y - z$ for $x=6$ , $y=8$ , and $z=3$ . What is the result?

Calculate $y z - x$ given $x = 6$ , $y = 8$ , and $z = 3$ .

Substitute $x=6$ , $y=8$ , and $z=3$ into the expression $5x - (y + 2z)$ . What is the result?

Solve $2(x+z)-y$ for $x=6$ , $y=8$ , and $z=3$ . What is the result?

Simplify: $8 + 2 \times 7$

Calculate the expression: $3 + 2 \cdot 5 - 4$ .

Calculate $9 \cdot 3 + 2 \cdot 5$ .

Calculate $5(2+4)+15 \div(9-6)$ .

Solve the equation: $-2(x-2)=-3-2 x$ .

Calculate the following sums: $-2 + (-11)$ , $9 + 4$ , and $-6 + (-1)$ .

Calculate the sums: $-6 + (-1)$ and $7 + (-2)$ .

Calculate $11 + 12$ and $2 + (-2)$ .

What is the result of $2 + (-2)$ ?

Calculate: $-75 + (-25)$ , $(-0.75) + (-0.25)$ , and $\left(-\frac{3}{4}\right) + \left(-\frac{1}{4}\right)$ .