Linearity

Problem 2201

Rs. 366 is shared by $A$ , $B$ , and $C$ where $A = \frac{1}{2}(B+C)$ and $B = \frac{2}{3}(A+C)$ . Find $A$ 's share.

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Problem 2202

Solve the equation: $\frac{2 x-5}{3}+\frac{1}{7}=3 x-9$ .

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Problem 2203

The volumes of bottles $A$ , $B$ , and $C$ are in the ratio $8:15:6$ . If $C = 450 \mathrm{~mL}$ , find the total volume.

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Problem 2204

Solve for $x+y$ given the equation $x+3 \sqrt{y}=1+3 \sqrt{2}$ .

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Problem 2205

Solve for $x$ in the equation $x + 3 \sqrt{4} = 1 + 3 \sqrt{2}$ and find $x + 4$ .

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Problem 2206

Solve for $y$ in the equation $\frac{y}{2}+17=29$ .

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Problem 2207

Solve for $x$ in the equation $4.5x + 3 = 16.5$ .

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Problem 2208

Solve the equation: $\frac{1}{3}(x-2)=3$ .

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Problem 2209

Solve the equation $\frac{x-4}{3}=\frac{1}{2}$ .

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Problem 2210

Resuelve la ecuación: $\frac{1}{3} + \frac{5}{4} x - \frac{5}{6} = \frac{3}{2} x$

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Problem 2211

La tercera parte de la suma de dos números consecutivos es 17. Encuentra los números. $\frac{x + (x + 1)}{3} = 17$

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Problem 2212

Simplify: $29u + 4d - 13u + 2u + 7d$ and find the result among $18u + 11d$ , $44u + 11d$ , $18u - 3d$ , $31u + 28d$ .

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Problem 2213

A purse has 100 nickels and dimes worth \$7. Find the number of each type of coin.

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Problem 2214

David's age is $2 \times 2 + 5$ . How old is David?

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Problem 2215

Bella has a 28 in. ribbon. The second piece is 2 in. longer than the first, and the third is 3 in. longer than the second. Find the lengths.

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Problem 2216

There are 5 more girls than boys at a party with 27 kids total. How many boys are there? Express girls in terms of boys.

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Problem 2217

There are 3 more baseballs than bats. Total bats and baseballs is 15. Find the number of bats, $b$ .

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Problem 2218

Zach is 4 years older than twice Maya's age. If Maya is 5, how old is Zach?

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Problem 2219

Quinn sold 3 mitts for the same price each, spent \$ 23, and had \$ 7 left. Find the price of each mitt.

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Problem 2220

Solve for $x$ in the equation $\frac{x}{5}=4$ .

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Problem 2221

Solve for $t$ in $4 t=44$ and state the property of equality used (addition, subtraction, multiplication, or division).

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Problem 2222

In a club with 23 members, there are 7 more girls than boys. How many girls are there? Let $g$ be girls; boys are $g-7$ .

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Problem 2223

Zach is 4 years older than twice Maya's age. If Maya is 5, how old is Zach? $Z = 2(5) + 4$

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Problem 2224

Find the slope of the line through points (6,3) and (4,6). Use $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

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Problem 2225

Find the equation of a line through $(3,4)$ with slope -2 using point-slope form: $y-4=[?](x-[])$ .

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Problem 2226

Convert the point-slope form $y-4=-2(x-3)$ to slope-intercept form $y=mx+b$ . What are $m$ and $b$ ?

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Problem 2227

There are 2 more horses than cows in a field with 16 animals total. How many horses are there? Use $c$ for cows.

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Problem 2228

Find the equation in point-slope form for a line through $(2,5)$ with slope 3: $y - [5] = [3](x - [2])$ .

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Problem 2229

Convert point-slope $y-5=3(x-2)$ to slope-intercept form $y=mx+b$ . Find $m$ and $b$ .

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Problem 2230

Find the slope-intercept equation of the line through points $(-1,10)$ and $(3,2)$ . $y=[?] x+$

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Problem 2231

Find the slope-intercept equation of the line through points $(-1,10)$ and $(3,2)$ . $y=-2x+[?]$

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Problem 2232

Find the inputs for the point-slope formula of a line through $(-7,2)$ with slope 3: $y-[?]=3(x-[])$

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Problem 2233

Find the inputs for the point-slope formula of a line through $(-7,2)$ with slope 3: $y-2=[?](x-[])$

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Problem 2234

Find the slope-intercept equation of the line through points $(6,-12)$ and $(15,-3)$ . $y=[?] x -$

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Problem 2235

Find the inputs for the point-slope formula of a line through $(3,5)$ with slope -2: $y-[?]=-2(x-3)$

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Problem 2236

Find the point-slope formula inputs for a line through $(3,5)$ with slope -2: $y-5=-2(x-[?])$ .

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Problem 2237

Find the point-slope formula inputs for a line through $(3,5)$ with slope -2: $y-5=[?](x-[])$ .

See Solution

Problem 2238

Find the slope-intercept equation of the line through points $(-4,6)$ and $(-2,5)$ . $y=-\frac{x}{[?]}+[]$

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Problem 2239

A 30 gms mix of gold and silver is worth Rs. 1200. If weights are swapped, it's Rs. 1080. Find silver's price per gram.

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Problem 2240

A father took $\frac{1}{5}$ of a cake and had 4 times what others had. How many family members are there? (a) 16 (b) 17 (c) 18 (d) None of these

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Problem 2241

Find the ratio of shares $A$ , $B$ , and $C$ if $2A' = 3B' = 4C$ . Options: (a) $3:4:6$ (b) $4:3:6$ (c) $6:3:4$ (d) $6:4:3$ (e) None.

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Problem 2242

A 30 gm mix of gold and silver is worth Rs. 1200. If weights are swapped, it's Rs. 1080. Find silver's price per gram.

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Problem 2243

Solve for $x$ in the equation $3 x + 5 = x + 6$ .

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Problem 2244

A 30g mass of gold and silver is worth Rs. 1200. If exchanged, it's Rs. 1080. Gold is Rs. 50/g. Find silver's price/g.

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Problem 2245

Solve for $m$ in the equation: $3 + m = 6 + 3m$ .

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Problem 2246

Solve for $j$ in the equation $3 - j = 4 + j$ .

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Problem 2247

Solve the systems: 1) $2x - 5y = -17$ , $x + 3y = 8$ ; 2) $3u - 4v = -5$ , $-u + 2v = 2$ .

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Problem 2248

Solve the system of equations: $2x + y = 3$ and $3x + 2y = 2$ .

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Problem 2249

Solve the system of equations: $2x + 3y = -1$ and $4x + 7y = 5$ .

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Problem 2250

Solve the system of equations: $2x + 3y = -1$ and $4x + 7y = 5$ .

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Problem 2251

Solve the system of equations: $2x - 3y = 7$ and $4x - 5y = 13$ .

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Problem 2252

Solve the system of equations: $2x - 3y = 7$ and $4x - 5y = 13$ .

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Problem 2253

Solve the following systems of equations:
1) $2x + 3y = -1$ , $4x + 7y = 5$ 2) $2x - 3y = 7$ , $4x - 5y = 13$ 3) $4x - y = 7$ , $2x + 5y = -2$ 4) $3x + 2y = 3$ , $6x + 5y = 9$ 5) $m - n = 4$ , $3m - 10n = 5$

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Problem 2254

Solve the system of equations: $3x + 2y = 3$ and $6x + 5y = 9$ .

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Problem 2255

Solve the system of equations: $y - 4x = 5$ and $2x - 3y = 6$ .

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Problem 2256

Given $a:b=3:5$ and $5a=6c$ , find $\frac{b+3c}{a+2b}$ .

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Problem 2257

Given $(2 h-3 k):(h+2 k)=3: 5$ , show $h=3 k$ and find $h: k$ .

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Problem 2258

Given $3a = 4b = 6c$ , find the ratio $a:b:c$ and if $a-b+c=21$ , determine $b$ .

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Problem 2259

There are 356 Grade 8 students. If $34 + 4g = \frac{1}{2}b$ , find the number of boys $b$ and girls $g$ .

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Problem 2260

In a factory with 850 workers (400 male), find the male-to-female ratio and how many males were dismissed when the ratio is $4:5$ .

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Problem 2261

The ratio of oranges to pears is $8:7$ . After removing 8 oranges and 2 pears, they are equal. Find the original pears.

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Problem 2262

You have \ $3200 to invest in three funds with returns of$ 10\% $,$ 7\% $, and$ 5\%$. Invest twice as much in growth as in money market. How to allocate?

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Problem 2263

If 35 men finish work in 8 days, how many days for 20 men? Use the formula: work = men × days.

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Problem 2264

Un cuadrado y un rectángulo tienen el mismo perímetro. Lado del cuadrado: $24 \mathrm{~cm}$ . Ancho del rectángulo: $12 \mathrm{~cm}$ . ¿Largo del rectángulo?

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Problem 2265

Find the value of $m$ in the equation: $3m = -15$ .

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Problem 2266

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

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Problem 2267

Solve for $x$ in the equation $g(x)=-\frac{1}{2} x+3$ where $g(x)=-1$ .

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Problem 2268

Graph the function defined by $f(x) = x + 5$ .

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Problem 2269

Solve for $y$ in the equation $0.10(50) + 0.20y = 0.18(50+y)$ to find the volume of the $20\%$ solution needed.

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Problem 2270

Solve the equation $4(3y + 2) + 2y = 50$ .

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Problem 2271

Solve for $w$ in the equation $4(5+3 w)+5=49$ .

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Problem 2272

Solve the equation: $-2(3v - 4) = 38$ .

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Problem 2273

Solve for $d$ in the equation: $28=4(3 d+3)-4 d$ .

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Problem 2274

Solve the equations: $6x - 3y = 16$ and $9x + 2y = 11$ .

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Problem 2275

Solve the equations: 6x - 3y = 16 and 9x + 2y = 11.

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Problem 2276

Find $A$ given that $AB=\frac{2}{3}CH$ and $AB+CH=30 \text{ cm}$ .

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Problem 2277

A supermarket has grape juice priced at a $4:3$ ratio. If a bottle costs \ $y, find: (a) carton price in terms of$ y$. (b) price of a bottle if Mrs. Lee pays \$102 for 2 cartons and 3 bottles.

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Problem 2278

A car travels from city $A$ to $B$ at $75 \mathrm{~km/h}$ and from $B$ to $C$ at $60 \mathrm{~km/h}$ . Total distance is $140 \mathrm{~km}$ in 130 minutes. Find time from $A$ to $B$ in minutes.

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Problem 2279

A $2.0 \mathrm{~kg}$ object on a bench is connected to a $3.0 \mathrm{~kg}$ object via a pulley. It accelerates at $4.0 \mathrm{~m/s}^2$ .
(a) Find the resultant force on the $2.0 \mathrm{~kg}$ object: $\text{force} =$
(b) Determine the upward force $F$ on the $3.0 \mathrm{~kg}$ object: $\text{force } F =$

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Problem 2280

Identify the function for the sequence: $-4, 0, 4, 8, 12, 16, \ldots$ from options A-D.

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Problem 2281

Find the slope between points (0,2) and (8,13). Which describes the temperature change per minute: $3.25^{\circ} \mathrm{C}$ , $5.25^{\circ} \mathrm{C}$ , $1.25^{\circ} \mathrm{C}$ , or $7.25^{\circ} \mathrm{C}$ ?

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Problem 2282

Sketch the function $f(x)=\frac{1}{6}(3 x+1)$ and identify the correct graph feature: A) $(0,1)$ B) $\left(\frac{1}{6}, 0\right)$ C) $\left(-\frac{1}{3}, 0\right)$ D) $\left(0,-\frac{1}{6}\right)$ .

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Problem 2283

Determine the inequality for the range of the linear function $p$ given points $(2,-3)$ and $(-4,4)$ .

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Problem 2284

What does the domain of $y=-x+175$ represent for the 175 miles from Bay Town to Oak Glen? What is the domain?

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Problem 2285

Löse das Gleichungssystem: $2x + y = 14$ und $3x - 2y = 7$ . Notiere die Lösung.

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Problem 2286

What is the fixed cost in the function $C(x)=0.75 x+3500$ for producing $x$ boxes of detergent? A) 3500 B) 0.75 C) 0.75x D) y

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Problem 2287

A store charges based on items bought. Jane paid \$15 for 4 items, George \$39 for 12. Find the cost for 22 items.

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Problem 2288

Super Suds' cost function is $C(x)=0.75 x+3500$ . What is the fixed cost and the cost per box? A) 3500, B) 0.75

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Problem 2289

Find $x$ such that $f(x)=x$ for $f(x)=\frac{3}{4} x+12$ .

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Problem 2290

Solve the system of equations: $6x - 4y = -8$ and $y = -6x + 2$ .

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Problem 2291

Berechnen Sie die Vektor-Koordinaten aus den folgenden Linearkombinationen: a) $\left(\begin{array}{l}2 \\ 1 \\ 3\end{array}\right)+\left(\begin{array}{r}1 \\ 4 \\ -5\end{array}\right)+2 \cdot\left(\begin{array}{l}1 \\ 1 \\ 4\end{array}\right)$ b) $3 \cdot\left(\begin{array}{r}2 \\ 10 \\ 0\end{array}\right)+2 \cdot\left(\begin{array}{r}0 \\ 3 \\ -1\end{array}\right)-5 \cdot\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right)$ c) $\frac{1}{2} \cdot\left(\begin{array}{l}3 \\ 1 \\ 2\end{array}\right)+\frac{1}{3} \cdot\left(\begin{array}{r}1 \\ 2 \\ -2\end{array}\right)-\frac{1}{4} \cdot\left(\begin{array}{l}2 \\ 2 \\ 4\end{array}\right)$

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Problem 2292

Solve the linear inequality: $3 + 2x \leq 7$

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Problem 2293

Find the minimum tortillas Chloe needs to sell to break even if cost is R5 and selling price is R15.

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Problem 2294

Solve the system of equations: $2x + 3y = 16$ and $-7x - y = 20$ .

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Problem 2295

Solve for $d$ in the equation $d - 4 = 12$ .

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Problem 2296

A grocery store sells bananas and oranges. Oranges cost twice as much as bananas. They sold 65 oranges and 88 bananas for a total of \$ 109.
a. Write an equation for the price of a banana, $b$ , and an orange, $g$ .
b. Write an equation for the total sales in dollars: $65g + 88b = 109$ .
c. Find the price of one banana.

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Problem 2297

Find the miles Amiyah must drive for equal costs at Al's Autos ( $100 + 0.89m$ ) and Roadster ( $130 + 0.65m$ ).

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Problem 2298

Solve the inequality: $-7x > 56$ . Find the value of $x$ .

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Problem 2299

Find the equation for the road length $L$ after $D$ days if it starts at 47 miles and grows by 1 mile daily. Calculate $L$ after 12 days.

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Problem 2300

Solve for $y$ in the equation: $5 y + 15 = 65$ .

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Linearity

Problem 2201

Rs. 366 is shared by AAA, BBB, and CCC where A=12(B+C)A = \frac{1}{2}(B+C)A=21​(B+C) and B=23(A+C)B = \frac{2}{3}(A+C)B=32​(A+C). Find AAA's share.

Problem 2202

Solve the equation: 2x−53+17=3x−9\frac{2 x-5}{3}+\frac{1}{7}=3 x-932x−5​+71​=3x−9.

Problem 2203

The volumes of bottles AAA, BBB, and CCC are in the ratio 8:15:68:15:68:15:6. If C=450 mLC = 450 \mathrm{~mL}C=450 mL, find the total volume.

Problem 2204

Solve for x+yx+yx+y given the equation x+3y=1+32x+3 \sqrt{y}=1+3 \sqrt{2}x+3y​=1+32​.

Problem 2205

Solve for xxx in the equation x+34=1+32x + 3 \sqrt{4} = 1 + 3 \sqrt{2}x+34​=1+32​ and find x+4x + 4x+4.

Problem 2206

Solve for yyy in the equation y2+17=29\frac{y}{2}+17=292y​+17=29.

Problem 2207

Solve for xxx in the equation 4.5x+3=16.54.5x + 3 = 16.54.5x+3=16.5.

Problem 2208

Solve the equation: 13(x−2)=3\frac{1}{3}(x-2)=331​(x−2)=3.

Problem 2209

Solve the equation x−43=12\frac{x-4}{3}=\frac{1}{2}3x−4​=21​.

Problem 2210

Resuelve la ecuación: 13+54x−56=32x \frac{1}{3} + \frac{5}{4} x - \frac{5}{6} = \frac{3}{2} x 31​+45​x−65​=23​x

Problem 2211

La tercera parte de la suma de dos números consecutivos es 17. Encuentra los números. x+(x+1)3=17\frac{x + (x + 1)}{3} = 173x+(x+1)​=17

Problem 2212

Simplify: 29u+4d−13u+2u+7d29u + 4d - 13u + 2u + 7d29u+4d−13u+2u+7d and find the result among 18u+11d18u + 11d18u+11d, 44u+11d44u + 11d44u+11d, 18u−3d18u - 3d18u−3d, 31u+28d31u + 28d31u+28d.

Problem 2213

A purse has 100 nickels and dimes worth \$7. Find the number of each type of coin.

Problem 2214

David's age is 2×2+52 \times 2 + 52×2+5. How old is David?

Problem 2215

Bella has a 28 in. ribbon. The second piece is 2 in. longer than the first, and the third is 3 in. longer than the second. Find the lengths.

Problem 2216

There are 5 more girls than boys at a party with 27 kids total. How many boys are there? Express girls in terms of boys.

Problem 2217

There are 3 more baseballs than bats. Total bats and baseballs is 15. Find the number of bats, bbb.

Problem 2218

Zach is 4 years older than twice Maya's age. If Maya is 5, how old is Zach?

Problem 2219

Quinn sold 3 mitts for the same price each, spent \$ 23, and had \$ 7 left. Find the price of each mitt.

Problem 2220

Solve for xxx in the equation x5=4\frac{x}{5}=45x​=4.

Problem 2221

Solve for ttt in 4t=444 t=444t=44 and state the property of equality used (addition, subtraction, multiplication, or division).

Problem 2222

In a club with 23 members, there are 7 more girls than boys. How many girls are there? Let ggg be girls; boys are g−7g-7g−7.

Problem 2223

Zach is 4 years older than twice Maya's age. If Maya is 5, how old is Zach? Z=2(5)+4Z = 2(5) + 4Z=2(5)+4

Problem 2224

Find the slope of the line through points (6,3) and (4,6). Use m=y2−y1x2−x1m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}m=x2​−x1​y2​−y1​​.

Problem 2225

Find the equation of a line through (3,4)(3,4)(3,4) with slope -2 using point-slope form: y−4=[?](x−[])y-4=[?](x-[])y−4=[?](x−[]).

Problem 2226

Convert the point-slope form y−4=−2(x−3)y-4=-2(x-3)y−4=−2(x−3) to slope-intercept form y=mx+by=mx+by=mx+b. What are mmm and bbb?

Problem 2227

There are 2 more horses than cows in a field with 16 animals total. How many horses are there? Use ccc for cows.

Problem 2228

Find the equation in point-slope form for a line through (2,5)(2,5)(2,5) with slope 3: y−[5]=[3](x−[2])y - [5] = [3](x - [2])y−[5]=[3](x−[2]).

Problem 2229

Convert point-slope y−5=3(x−2)y-5=3(x-2)y−5=3(x−2) to slope-intercept form y=mx+by=mx+by=mx+b. Find mmm and bbb.

Problem 2230

Find the slope-intercept equation of the line through points (−1,10)(-1,10)(−1,10) and (3,2)(3,2)(3,2). y=[?]x+y=[?] x+y=[?]x+

Problem 2231

Find the slope-intercept equation of the line through points (−1,10)(-1,10)(−1,10) and (3,2)(3,2)(3,2). y=−2x+[?]y=-2x+[?]y=−2x+[?]

Problem 2232

Find the inputs for the point-slope formula of a line through (−7,2)(-7,2)(−7,2) with slope 3: y−[?]=3(x−[])y-[?]=3(x-[])y−[?]=3(x−[])

Problem 2233

Find the inputs for the point-slope formula of a line through (−7,2)(-7,2)(−7,2) with slope 3: y−2=[?](x−[])y-2=[?](x-[])y−2=[?](x−[])

Problem 2234

Find the slope-intercept equation of the line through points (6,−12)(6,-12)(6,−12) and (15,−3)(15,-3)(15,−3). y=[?]x−y=[?] x -y=[?]x−

Problem 2235

Find the inputs for the point-slope formula of a line through (3,5)(3,5)(3,5) with slope -2: y−[?]=−2(x−3)y-[?]=-2(x-3)y−[?]=−2(x−3)

Problem 2236

Find the point-slope formula inputs for a line through (3,5)(3,5)(3,5) with slope -2: y−5=−2(x−[?])y-5=-2(x-[?])y−5=−2(x−[?]).

Problem 2237

Find the point-slope formula inputs for a line through (3,5)(3,5)(3,5) with slope -2: y−5=[?](x−[])y-5=[?](x-[])y−5=[?](x−[]).

Problem 2238

Find the slope-intercept equation of the line through points (−4,6)(-4,6)(−4,6) and (−2,5)(-2,5)(−2,5). y=−x[?]+[]y=-\frac{x}{[?]}+[]y=−[?]x​+[]

Problem 2239

A 30 gms mix of gold and silver is worth Rs. 1200. If weights are swapped, it's Rs. 1080. Find silver's price per gram.

Problem 2240

Rs. 366 is shared by $A$ , $B$ , and $C$ where $A = \frac{1}{2}(B+C)$ and $B = \frac{2}{3}(A+C)$ . Find $A$ 's share.

Solve the equation: $\frac{2 x-5}{3}+\frac{1}{7}=3 x-9$ .

The volumes of bottles $A$ , $B$ , and $C$ are in the ratio $8:15:6$ . If $C = 450 \mathrm{~mL}$ , find the total volume.

Solve for $x+y$ given the equation $x+3 \sqrt{y}=1+3 \sqrt{2}$ .

Solve for $x$ in the equation $x + 3 \sqrt{4} = 1 + 3 \sqrt{2}$ and find $x + 4$ .

Solve for $y$ in the equation $\frac{y}{2}+17=29$ .

Solve for $x$ in the equation $4.5x + 3 = 16.5$ .

Solve the equation: $\frac{1}{3}(x-2)=3$ .

Solve the equation $\frac{x-4}{3}=\frac{1}{2}$ .

Resuelve la ecuación: $\frac{1}{3} + \frac{5}{4} x - \frac{5}{6} = \frac{3}{2} x$

La tercera parte de la suma de dos números consecutivos es 17. Encuentra los números. $\frac{x + (x + 1)}{3} = 17$

Simplify: $29u + 4d - 13u + 2u + 7d$ and find the result among $18u + 11d$ , $44u + 11d$ , $18u - 3d$ , $31u + 28d$ .

David's age is $2 \times 2 + 5$ . How old is David?

There are 3 more baseballs than bats. Total bats and baseballs is 15. Find the number of bats, $b$ .

Solve for $x$ in the equation $\frac{x}{5}=4$ .

Solve for $t$ in $4 t=44$ and state the property of equality used (addition, subtraction, multiplication, or division).

In a club with 23 members, there are 7 more girls than boys. How many girls are there? Let $g$ be girls; boys are $g-7$ .

Zach is 4 years older than twice Maya's age. If Maya is 5, how old is Zach? $Z = 2(5) + 4$

Find the slope of the line through points (6,3) and (4,6). Use $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

Find the equation of a line through $(3,4)$ with slope -2 using point-slope form: $y-4=[?](x-[])$ .

Convert the point-slope form $y-4=-2(x-3)$ to slope-intercept form $y=mx+b$ . What are $m$ and $b$ ?

There are 2 more horses than cows in a field with 16 animals total. How many horses are there? Use $c$ for cows.

Find the equation in point-slope form for a line through $(2,5)$ with slope 3: $y - [5] = [3](x - [2])$ .

Convert point-slope $y-5=3(x-2)$ to slope-intercept form $y=mx+b$ . Find $m$ and $b$ .

Find the slope-intercept equation of the line through points $(-1,10)$ and $(3,2)$ . $y=[?] x+$

Find the slope-intercept equation of the line through points $(-1,10)$ and $(3,2)$ . $y=-2x+[?]$

Find the inputs for the point-slope formula of a line through $(-7,2)$ with slope 3: $y-[?]=3(x-[])$

Find the inputs for the point-slope formula of a line through $(-7,2)$ with slope 3: $y-2=[?](x-[])$

Find the slope-intercept equation of the line through points $(6,-12)$ and $(15,-3)$ . $y=[?] x -$

Find the inputs for the point-slope formula of a line through $(3,5)$ with slope -2: $y-[?]=-2(x-3)$

Find the point-slope formula inputs for a line through $(3,5)$ with slope -2: $y-5=-2(x-[?])$ .

Find the point-slope formula inputs for a line through $(3,5)$ with slope -2: $y-5=[?](x-[])$ .

Find the slope-intercept equation of the line through points $(-4,6)$ and $(-2,5)$ . $y=-\frac{x}{[?]}+[]$

A father took $\frac{1}{5}$ of a cake and had 4 times what others had. How many family members are there? (a) 16 (b) 17 (c) 18 (d) None of these

Find the ratio of shares $A$ , $B$ , and $C$ if $2A' = 3B' = 4C$ . Options: (a) $3:4:6$ (b) $4:3:6$ (c) $6:3:4$ (d) $6:4:3$ (e) None.

Solve for $x$ in the equation $3 x + 5 = x + 6$ .

Solve for $m$ in the equation: $3 + m = 6 + 3m$ .

Solve for $j$ in the equation $3 - j = 4 + j$ .

Solve the systems: 1) $2x - 5y = -17$ , $x + 3y = 8$ ; 2) $3u - 4v = -5$ , $-u + 2v = 2$ .

Solve the system of equations: $2x + y = 3$ and $3x + 2y = 2$ .

Solve the system of equations: $2x + 3y = -1$ and $4x + 7y = 5$ .

Solve the system of equations: $2x + 3y = -1$ and $4x + 7y = 5$ .

Solve the system of equations: $2x - 3y = 7$ and $4x - 5y = 13$ .

Solve the system of equations: $2x - 3y = 7$ and $4x - 5y = 13$ .

Solve the system of equations: $3x + 2y = 3$ and $6x + 5y = 9$ .

Solve the system of equations: $y - 4x = 5$ and $2x - 3y = 6$ .

Given $a:b=3:5$ and $5a=6c$ , find $\frac{b+3c}{a+2b}$ .

Given $(2 h-3 k):(h+2 k)=3: 5$ , show $h=3 k$ and find $h: k$ .

Given $3a = 4b = 6c$ , find the ratio $a:b:c$ and if $a-b+c=21$ , determine $b$ .

There are 356 Grade 8 students. If $34 + 4g = \frac{1}{2}b$ , find the number of boys $b$ and girls $g$ .

In a factory with 850 workers (400 male), find the male-to-female ratio and how many males were dismissed when the ratio is $4:5$ .

The ratio of oranges to pears is $8:7$ . After removing 8 oranges and 2 pears, they are equal. Find the original pears.

You have \ $3200 to invest in three funds with returns of$ 10\% $,$ 7\% $, and$ 5\%$. Invest twice as much in growth as in money market. How to allocate?

Un cuadrado y un rectángulo tienen el mismo perímetro. Lado del cuadrado: $24 \mathrm{~cm}$ . Ancho del rectángulo: $12 \mathrm{~cm}$ . ¿Largo del rectángulo?

Find the value of $m$ in the equation: $3m = -15$ .

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

Solve for $x$ in the equation $g(x)=-\frac{1}{2} x+3$ where $g(x)=-1$ .

Graph the function defined by $f(x) = x + 5$ .

Solve for $y$ in the equation $0.10(50) + 0.20y = 0.18(50+y)$ to find the volume of the $20\%$ solution needed.

Solve the equation $4(3y + 2) + 2y = 50$ .

Solve for $w$ in the equation $4(5+3 w)+5=49$ .

Solve the equation: $-2(3v - 4) = 38$ .

Solve for $d$ in the equation: $28=4(3 d+3)-4 d$ .

Solve the equations: $6x - 3y = 16$ and $9x + 2y = 11$ .