Calculus
Limits, derivatives, optimization, and behavior of functions.
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find the sum of the infinite geometric series 125 + 25 + 5 + ⋯. select …
A. 156.25
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the function $f(x) = x^3$ is shown in red in the graph below. it is tra…
$\boldsymbol{g(x)=(x+5)^3 - 2}$ (the fourth option)
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graph the function: $f(x) = -|2x + 3| + 6$ (there are four graphs with …
The correct graph is the fourth (bottom-most) graph with vertex at $(-3, -6)$, rising to the left and falling to the right.
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which ordered pair is a solution of the equation: $y = -\\frac{5}{4}x -…
A. (-8, 8)
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• transportation. to get where you were going, school, store, work, mos…
Limiting military mobility and supply speed: armies could only move troops, weapons, and supplies slowly via walking, horses, or boats, which slowed deployment, resupply, and coor…
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select all the statements about the function in graph that are true. so…
- Some input values are negative. - Some input values are integers. - Some output values are integers. - Some output values are negative.
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1. you (safely) bungee jump from a 200-feet tall bridge in your town. y…
1. A graph starting at (0, 200), decreasing to a minimum distance above water, oscillating with decreasing amplitude until stabilizing at a constant distance. 2. Cosine wave with …
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solve: $e^{2x} - 7e^{x} = 18$ a. $x = \\ln 18$ b. $x = 9$ and $x = -2$ …
C. $x = \ln 9$
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4. solve each of the following equations. show the work that leads to y…
4. (a) $x=2.87$ (b) $n=11.241$ 5. (a) $n=12.1$ (b) $x=20.16$ 6. $m=26.52$ 7. $n=40$
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determine the range of the following graph: graph answer attempt 1 out …
# Explanation: ## Step1: Identify the lowest and highest y - values First, we look at the graph. The lowest point on the graph (the minimum y - value) is around \(y = 2\) (from th…
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find the domain of the function, $y = \\log_{4}(7 - x)$ select one: a. …
D. $(-\infty,7)$
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solve \\ln(x + 5) + 3 = 2 select one: a. \\( x = e^{-1} \\) b. \\( x = …
B. $x = e^{-1} - 5$
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find each quotient. use the space a. 688 ÷ 7 = d. 206 ÷ 4 = g. 377 ÷ 4 =
s: a. \( 688\div7 = 98\) R \( 2 \) (or \( 98\frac{2}{7}\approx98.29 \)) d. \( 206\div4 = 51.5 \) g. \( 377\div4 = 94.25 \)
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画图 $y = 2sqrt3{x^2}$，$y = x$
1. 对于$y=2\sqrt[3]{x^2}=2x^{\frac{2}{3}}$：定义域为$\mathbb{R}$，是偶函数，图像关于y轴对称；在$(-\infty,0)$上单调递减，在$(0,+\infty)$上单调递增；过点$(0,0)$、$(1,2)$、$(-1,2)$。 2. 对于$y=x$：定义域为$\mathbb{R}$，是奇函数，图像关于原点…
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the function f(x) is invertible. find $f^{-1}(-3)$. $f^{-1}(-3) = \\squ…
\( -2 \)
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the function $f(x)$ is invertible. find $f^{-1}(-7)$. $f^{-1}(-7)=\\squ…
\( \boxed{9} \)
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the function f(x) is invertible. find $f^{-1}(5)$. $f^{-1}(5) = \\squar…
\( \boldsymbol{0} \)
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the function f(x) is invertible. find $f^{-1}(-5)$.\ chart of the funct…
\( -1 \)
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sketch the graph of the rational function $f(x) = \\frac{-(x + 2)^2}{x …
To sketch the graph: 1. Draw vertical asymptote $x=-1$ (dashed line) and slant asymptote $y=-x-3$ (dashed line). 2. Plot intercepts $(-2,0)$ and $(0,-4)$. 3. For $x<-1$: The curve…
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find each quotient. use the a. 688 ÷ 7 =
If we consider the quotient with remainder: \(98\) remainder \(2\) (or \(98\frac{2}{7}\) as a mixed number, or approximately \(98.29\) as a decimal). For the boxed answer (if we t…
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the function f(x) is invertible. find $f^{-1}(-7)$. $f^{-1}(-7) = \\squ…
\( 3 \)
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the function f(x) is invertible. find $f^{-1}(2)$. $f^{-1}(2) = \\squar…
\( f^{-1}(2) = 1 \)
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select one: a. $f(x) = \\frac{-12(x+1)(x-3)}{(x+3)^2(x-4)}$. b. $f(x) =…
D. $f(x) = \frac{12(x+1)(x-3)}{(x+3)^2(x-4)}$
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use the given information about the polynomial graph to write the equat…
D. $y = \frac{1}{3}(x - 3)^2(x - 1)^2(x + 3)$
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4 longdiv 220
55
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see #56 page 207 multi-step problem solve the equation using the steps …
s: a) The discriminant \(D = -40\) (negative), so the equation has no real solutions, only two complex conjugate solutions. b) Substituted quadratic formula: \(x = \frac{4 \pm \sq…
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question 2 of 10 which graph or graphs appear to show a sinusoid? i ii …
A. I and II only
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graph the polynomial function $y = -x(x - 1)(x - 3)^2$.
1. Plot intercepts: $(0,0)$, $(1,0)$, $(3,0)$ 2. Sketch end behavior: Both ends of the graph point downward. 3. Draw the graph crossing the x-axis at $(0,0)$ and $(1,0)$, touching…
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find the horizontal asymptotes of the rational function, $f(x) = \\frac…
C. $y = 2$
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determine the end behavior of the polynomial function: $y = 3x^2 + x - …
A. As $x \to -\infty$, $f(x) \to \infty$ and $x \to \infty$, $f(x) \to \infty$.
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a \\overline{\\smash{)}175}
25
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find $(p \\circ m)(x)$ and the domain of $(p \\circ m)(x)$ for the func…
D. $(p \circ m)(x) = \frac{1}{\sqrt{x^2-4}}$ and Domain: $(-\infty,-2)\cup(2,\infty)$
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select one: a. $f(x) = \\sqrt{x - 3} - 1$ b. $f(x) = \\sqrt{x - 3} + 1$…
C. $f(x) = \sqrt{x + 3} - 1$
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write a formula for the function g that relates when the graph of f(x) …
A. $g(x) = | - 3x|$, C. $g(x) = |3x|$
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tabular representations for the functions ( p ), ( q ), and ( r ) are g…
$q(x) = \frac{1}{2}p(x) + 3$ $r(x) = 2p(x) - 2$
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find $p(q(-2))$ for the functions $p(x) = x^2 + 1$ and $q(x) = \\sqrt{x…
D. 1
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given the function $g(x) = 5 - x^2$, evaluate $\frac{f(x + h) - f(x)}{h…
A. $-2x - h$
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describe how the graph of the function, $f(x + 43)$, is a transformatio…
C. The graph of $f(x + 43)$ is a horizontal shift of 43 units to the left of the graph of $f(x)$.
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evaluate $f(-1)$ for the function $f(c) = c^2 - 3c$. select one: a. $-4…
D. 4
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5)\\overline{480}
96
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which integer is closest to (sqrt3{-26})?
$-3$
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question 3 of 10 an advocate for limited government would most likely o…
B. The growth of bureaucracy has expanded the role of government in citizens' lives.
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which integer is closest to (sqrt3{24})?
3
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which integer is closest to $sqrt3{12}$?
2
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which integer is closest to \\(\\sqrt3{118}\\)?
5
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which integer is closest to (sqrt3{110})?
5
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3. draw an area model. then, solve using the standard algorithm. 321 × …
### Problem 3: \( 321 \times 215 \) #### Area Model: We can break down \( 321 \) into \( 300 + 20 + 1 \) and \( 215 \) into \( 200 + 10 + 5 \). Then we create a table to find the …
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15. convert 3.75 radians into degrees to the nearest two decimal places…
\( 214.86^\circ \)
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10. if \\(\\tan\\theta = \\frac{3}{4}\\) and \\(\\theta\\) is an acute …
\(\frac{4}{5}\) ### Question 11:
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y = x - 7\ y = -\\frac{1}{3}x - 3\ plot two lines by clicking the graph…
- Line 1 ($y=x-7$) passes through $(0, -7)$ and $(7, 0)$. - Line 2 ($y=-\frac{1}{3}x-3$) passes through $(0, -3)$ and $(-9, 0)$. (Plot these points and connect them to form the tw…
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y = -\\frac{1}{2}x - 6\ y = \\frac{3}{2}x + 2
The solution to the system is $x=-4$, $y=-4$, or the point $(-4, -4)$
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after a golfer hits a golf ball, the ball leaves the ground with an ini…
6.25 seconds (corresponding to the option: 6.25 seconds)
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now try this one: a skydiver jumps from a plane that is 5000 feet above…
3400 feet (corresponding to the option "3400 feet")
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find the slope of the line that passes through (10, 10) and (1, 2). sim…
$\frac{8}{9}$
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find the slope of the line that passes through (6, 15) and (9, 7). simp…
$\frac{-8}{3}$
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find the slope of the line that passes through (2, 14) and (8, 7). simp…
$\frac{-7}{6}$
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find the slope of the line that passes through (2, 6) and (5, 10). simp…
$\frac{4}{3}$
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find the slope of the line that passes through (2, 14) and (9, 10). sim…
$\frac{-4}{7}$
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find the slope of the line that passes through (8, 10) and (2, 3). simp…
$\frac{7}{6}$
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evaluate 16 + 12 ÷ 3 • 5. solve on paper. then check your answer on zea…
36
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evaluate 43 - 30 ÷ 6. 43 - 30 ÷ 6 = \\square
38
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evaluate 7 + (12-3)². 7 + (12-3)² =
88
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divide. 19.68 ÷ 0.12
164
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watch above video then graph this function.\\(y = (x + 3)^2 - 1\\)
The graph of \( y=(x + 3)^2-1 \) is a parabola with vertex at \((-3,-1)\), axis of symmetry \( x=-3 \), opening upward, and passing through points such as \((-2,0)\), \((-4,0)\), …
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4) find the value of each expression. put them in order from greatest t…
Greatest to Least: $\boldsymbol{4^2}$, $\boldsymbol{|-1-5|}$, $\boldsymbol{\sqrt{3}}$, $\boldsymbol{-\frac{2}{3}}$, $\boldsymbol{-2.6}$
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2. $y = -\frac{1}{2}x + 3$ $y = 5$ solution: $(-4, 5)$ check: desmos
$(-4, 5)$
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question 7 of 10 5 radians is the same as ____ °. round to the nearest …
\( 286.48 \)
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4 a standard ticket for the neesing metro system costs $10 and is valid…
The 8th has the highest number of every ticket type sold among all 14 days; since each ticket has a positive cost, this guarantees the highest total income for that day.
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cc.2.2.hs.d.7 determine whether $f(x) = 4x^2 - 16x + 6$ has a maximum o…
A. minimum; (2, - 10)
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cc.2.2.hs.d.4 the quadratic equation graphed below has graph of a quadr…
Two real solutions (the option: Two real solutions)
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type the missing digits: 9 4 8 - □ 5 □ ------- 2 □ 0 submit
The subtrahend is \(658\) and the difference is \(290\). So the missing digits are: subtrahend's hundreds digit \(6\), units digit \(8\), and difference's tens digit \(9\). So the…
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6. what is the value of the expression below? $6 + 5(9 \\div 3)^2$ a. 3…
b. 51
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type the missing digits: 5 6 □ - 4 3 9 ------- □ □ 9 submit
The missing digits are 8 (in the minuend's units place), 1 (in the result's hundreds place), and 2 (in the result's tens place). So the filled numbers are: Minuend units: 8, Resul…
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read the claim below. the u.s. government should increase funding for s…
B. NASA helps advance scientific knowledge and provides many jobs for engineers and researchers.
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type the missing digits: □ 0 □ - 6 3 2 ------- 1 □ 6
Top number (hundreds digit): 8, top number (units digit): 8, difference (tens digit): 7 (So the blanks: first blank (top left) is 8, second blank (top right) is 8, third blank (bo…
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type the missing digits: 7 5 4 - 3 7 9 □□□ submit
3, 7, 5 (the three digits from top to bottom in the boxes)
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eli has 12 eggs. he uses his grandpas recipe to bake 4 loaves of challa…
8
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c) f(x) = 3x² - 3x - 6
The x - intercepts of the function \(f(x)=3x^{2}-3x - 6\) are \(x=-1\) and \(x = 2\). If we were asked for the roots (or x - intercepts) of the function, the solutions are \(x=-1\…
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the table represents a linear function. | x | y | | -2 | -2 | | -1 | 1 …
3
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alejandra correctly wrote the equation $y - 3 = \\frac{1}{5}(x - 10)$ t…
\(y - 3=2(x - 10)\) (the fourth option)
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pauley graphs the change in temperature of a glass of hot tea over time…
It is nonlinear because linear functions increase or decrease at the same rate.
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what is the amplitude of the sinusoidal function? enter your answer in …
3
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what is the maximum of the sinusoidal function? enter your answer in th…
2
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find the quotient. write fractions in simplest form. $-\frac{5}{6} div …
$-\frac{25}{9}$
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6. a proportional relationship is modeled by the equation $y = \\frac{1…
| Input $x$ | Output $y$ | |-----------|------------| | 0 | 0 | | 1 | $\frac{1}{2}$ | | 2 | 1 | | 3 | $\frac{3}{2}$ | | 4 | 2 | Unit Rate (Constant of Proportionality): $\frac{1}{…
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sinusoidal graphs what is the period of the sinusoidal function? enter …
4
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true or false: the equation $y = -3$ is a function. enter 1 for true or…
1
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the graph shows the relationship between the volume of a rectangular pr…
3
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linear functions the graph of a relation is shown. graph of a line with…
A. 3, C. $\frac{7}{4}$ (Here we assume the options are labeled as A: 3, B: - 2, C: $\frac{7}{4}$, D: 0, E: $-\frac{8}{5}$)
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graph the function $f(x) = \\frac{1}{4}x^2 + 5$. plot the vertex. then …
The vertex of the parabola \( f(x)=\frac{1}{4}x^2 + 5 \) is \( (0,5) \), and another point on the parabola is \( (4,9) \) (or \( (-4,9) \)). To graph the function, plot the vertex…
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the table represents a linear function. | x | y | | ---- | ---- | | -4 …
5
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complete the square to identify the two values that solve the following…
\(17,-1\)
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a pirate has 60 gold coins. the gold coins can be put into groups of 10.
6
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adding & subtracting decimals maze name adriana spencer date 1/7/2026 c…
The correct path is: START ($4.2 + 16.07$) → $19.6 - 8.04$ → $16.8 + 77$ → $13 - 4.08$ → $42.18 - 2.49$ → $37.6 + 5.08$ → $45.83 + 7.4$ → $9.3 - 8.27$ → $46.1 + 5.07$ → $90.02 - 8…
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which graph is the result of reflecting $f(x) = \\frac{1}{4}(8)^x$ acro…
# Explanation: ## Step1: Reflect across y - axis To reflect a function \( y = f(x) \) across the \( y \) - axis, we replace \( x \) with \( -x \). So for \( f(x)=\frac{1}{4}(8)^{x…
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which graph matches the equation $y + 3 = 2(x + 3)$? four graphs with l…
The second graph (with points \((0,3)\) and \((-3,-3)\) marked on it)
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step 1: choose a point on the line, such as (2, 5). step 2: choose anot…
Step 3 is incorrect because it shows an incorrect ratio for the slope.
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which equation represents a line that passes through (5, 1) and has a s…
\(y - 1=\frac{1}{2}(x - 5)\) (the third option)
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which equation represents a line that passes through \\(\\left(4, \\fra…
\(y-\frac{1}{3}=\frac{3}{4}(x - 4)\) (the second option)
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which graph matches the equation $y + 6 = \\frac{3}{4}(x + 4)$? first g…
The third graph (the one with points \((-4,-6)\), \((0,-3)\), \((4,0)\))