Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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question 5 of 40 which statements describe one of the transformations p…
B. A vertical stretch with a scale factor of 2, C. A translation of 5 units up
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25. the equation $f(x) = (x - 1)^2 - 2$ represents $f(x)$ and the graph…
1. "The line of symmetry of \( h(x) \) is \( x=-3 \)": True (select the circle in the "True" column for this row) 2. "The minimum of \( f(x) \) is less than the minimum of \( h(x)…
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23. three quadratic functions are represented below. which function has…
Function A (with \( f(x)=-(x - 1)^2+6 \)) has the highest maximum value.
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which is the graph of $f(x)=|x|$ reflected across the x - axis, transla…
The top - most graph (the first graph shown)
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which graph represents the parent function of $y = x^2 - 5$? a graph of…
D (assuming D is the graph with vertex at (0,0) opening upwards, as per the analysis of \( y = x^2 \))
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15. sketch an even degree function with these characteristics: ( a > 0 …
A possible function is \(f(x)=(x - 1)(x - 2)(x^{2}+1)=x^{4}-3x^{3}+3x^{2}-3x + 2\) (with \(a = 1>0\)) and its graph has end - behavior going to \(+\infty\) as \(x ightarrow\pm\inf…
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identify the real zeros for f(x) = 3x² + 2x + 4. a 1 and -1 b 0 and -1 …
C. no solution
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ip. writing equations in slope-intercept form - day 2 1. which equation…
C. \(y=-2x\)
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\\frac{\\cdot 10^{7}}{\\cdot 10^{7}} \\frac{10^{7}}{10^{7}}
\( 1 \)
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consider the table for f(x) and the graph for g(x). which statement is …
A. The y - intercept for \( f(x) \) is greater than the y - intercept for \( g(x) \)
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the functions f and g are defined as follows. f(x)=2x+4 g(x)=-3x² -2 fi…
\( f(-7) = -10 \) \( g(5) = -77 \)
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the functions f and g are defined as follows. f(x)=2x³ +2 g(x)=-5x-1 fi…
\( f(-2) = -14 \) \( g(5) = -26 \)
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question find the slope of the line represented by the equation below. …
$-\frac{5}{4}$
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function 1: function 2: x | 1 | 2 | 3 | 4 | 5 p(x) | 0 | 3 | 13 | 16 | …
Assuming the question is to find the slope of Function 1 (q(x)): The slope is \( \boldsymbol{-\frac{5}{3}} \) (or approximately -1.67). If comparing rates, Function 2 has a greate…
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find the slope of the line passing through the points (6, -3) and (1, -…
\(\frac{3}{5}\)
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find the slope of the line passing through the points (-7, -7) and (-3,…
\(\frac{13}{4}\)
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use the following exponential function to answer these questions. y = 9…
9000
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what is the range of the absolute value function below? (graph of an ab…
$f(x)\leq1$ (the option corresponding to "f(x) ≤ 1")
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which of the following is the value of a when the function f(x) = 3|x| …
3 (corresponding to the option with value 3, e.g., if the option is D. 3, then the answer is D. 3)
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3.58 - (-5.23)\ -7.56 + 9.258\ -7.23 - 19.56
\( 3.58 - (-5.23)=8.81 \), \( -7.56 + 9.258 = 1.698 \), \( -7.23 - 19.56=-26.79 \)
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the length of the freeway is 600 miles. if 0.5 inch represents 50 miles…
B. 6 inches
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3. caitlin graphs the function $f(x) = ax^2$, where $a$ is a positive i…
# Explanation: ## Step1: Analyze original function Original function \( f(x) = ax^2 \), \( a>0 \), so it's a parabola opening upwards (since coefficient of \( x^2 \) is positive) …
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2. if f(x) = x², which function is the result of shifting f(x) by 5 uni…
\((x - 5)^2 + 3\) (the last option)
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31 use the graph below to find the average rate of change between x=3 a…
3
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a leaf hangs from a branch 12 feet in the air. it falls to the ground a…
The Middle - Top Graph (the second graph in the top row)
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how does the structure of the highlighted paragraph show meaning? the p…
Because Guzman has experience, she is a good candidate for the job.
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what can go into your function is called the .... what you can get out …
1. What can go INTO your function is called the domain. 2. What you can get OUT of your function is called the range. 3. Question 10: The Y INTERCEPT of a function is represented …
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25. use part 1 of the fundamental theorem of calculus to find the deriv…
s: a. \( \boldsymbol{g'(x)=3x^{2}\cos(x^{6})} \) b. \( \boldsymbol{F'(x)=-\sqrt{1 + \sec x}} \) c. \( \boldsymbol{h'(x)=\frac{\sqrt{x}}{2(x^{2}+1)}} \) d. \( \boldsymbol{y' = 2x e…
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21) sketch the graph of a quadratic equation that has no real solutions.
A quadratic function like \( y = x^{2}+1 \) (with \( a = 1 \), \( b = 0 \), \( c = 1 \), discriminant \( D=0 - 4\times1\times1=-4<0 \)) has a parabola opening upward with vertex a…
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which equation represents the graphed function?\ \\(\\circ\\) \\(y = -3…
\(y =-\frac{1}{3}x + 3\) (the fourth option: \(y=-\frac{1}{3}x + 3\))
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write an equation for a function that has a rate of change equal to \\(…
First equation: \(y=\boldsymbol{\frac{13}{2}}x+\boldsymbol{5}\) Second equation: \(y=\boldsymbol{-\frac{2}{7}}x+\boldsymbol{(-1)}\) (or \(y =-\frac{2}{7}x - 1\))
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c. $h(x) = \\int_{1}^{\\sqrt{x}} \\frac{z^2}{z^4 + 1} dz$
The derivative of \( h(x) \) is \( \boldsymbol{\frac{\sqrt{x}}{2(x^{2}+1)}} \) (if the question was to find the derivative; if it was another operation, adjust accordingly. Assumi…
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for the equation f(x) = 2x - 9.... f(0) = f(6) = f(-2) =
\( f(0)=-9 \), \( f(6)=3 \), \( f(-2)=-13 \)
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for the equation f(x) = \\(\\frac{1}{3}\\)x - 11.... f(0) = f(6) = f(12…
\( f(0) = -11 \) \( f(6) = -9 \) \( f(12) = -7 \)
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situation dapplication : trois fonctions polynomiales considérons les f…
To determine the rule of function \( h \), we analyze the given information about functions \( f \) and \( g \), and use the properties of quadratic functions (vertex, zeros) to f…
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04.4 -- f functions *** test *** friday 12/12/25 started: dec 15 at 9:5…
The three ways to represent a function are: tables, graphs, equations. So the correct options are: - tables - graphs - equations
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*23. (4 - 0.4) ÷ 4 answer: *24. 4 - (0.4 ÷ 4) answer: *25. mentally cal…
\(0.9\) ### Problem *24*:
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37. \\(\\sqrt3{81} \\cdot \\sqrt3{45}\\) 38. \\(\\sqrt{\\frac{845}{5}}\…
### Problem 37: # Explanation: ## Step1: Recall the property of cube roots For real numbers \(a\) and \(b\), \(\sqrt[3]{a}\cdot\sqrt[3]{b}=\sqrt[3]{a\cdot b}\). So we can multiply…
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subtract: \\(\\frac{9}{14} - \\frac{3}{7}\\) \\(\\bigcirc\\) \\(\\frac{…
\(\frac{3}{14}\) (corresponding to the first option: \(\boldsymbol{\frac{3}{14}}\))
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lesson 2.5 review - solving rational equations 3 \\(\\frac{x}{x - 2} - …
C. check if any of the x’s we just got are extraneous (assuming the option with this text is labeled C; if the option identifiers are different, adjust accordingly, e.g., if it's …
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the graphs of three functions are shown. which statements accurately co…
A. The square root and absolute value function share an \(x\) - intercept. (We assume this is correct after analyzing the graph's intersection and x - intercepts. The other statem…
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paring characteristics of functions which function has a range limited …
The graph on the Top Left
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lesson 25 review - solving rational equations ③ \\(\\frac{x}{x - 2} - \…
B. \(x - 2\) and \(x + 4\)
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multiply. give your answer in lowest terms. \\(\frac{3}{4} cdot \frac{8…
$\frac{6}{11}$ (which corresponds to the option "C. $\frac{6}{11}$" if we assume the options are labeled A, B, C, D with A being $\frac{24}{44}$, B being $\frac{1}{4}$, C being $\…
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operations with mixed numbers divide: $6\\frac{2}{3} \\div 3$ options: …
\( 2\frac{2}{9} \) (the option with \( 2\frac{2}{9} \))
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the standard diameter of a golf ball is 42.67 mm. a golf ball factory d…
The correct functions are \( \boldsymbol{f(x)=|x - 42.67|} \) (or \( \boldsymbol{f(x)=|42.67 - x|} \)) as they represent the absolute discrepancy between the measured diameter \( …
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operations with mixed numbers multiply: $4\\frac{8}{9} \\cdot 1\\frac{1…
\(6\frac{14}{27}\) (corresponding to the option with \(6\frac{14}{27}\))
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2. the path of a projectile catapulted from a cliff 20 m tall is modele…
The maximum height reached by the projectile is 100 meters.
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given the function f(x)= 3( x + 2 ) - 5 evaluate f(3) evaluate f(-2) 29…
\( f(3) = 10 \) ### For \( f(x) = 3(x + 2) - 5 \), Evaluate \( f(-2) \)
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the graph of a function f is shown below. find f(3).
\( f(3)=\boxed{-4} \)
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operations with mixed numbers subtract: $18\\frac{2}{3} - 6\\frac{1}{9}…
$12\frac{5}{9}$ (corresponding to the option with this value, e.g., if the option is labeled as, say, B. $12\frac{5}{9}$, then the answer would be B. $12\frac{5}{9}$; based on the…
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the graph of a function f is shown below. find f(0).
\( f(0) = 2 \)
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19. the polynomial $p(x) = (1 - 3x)(x^2 + 2)$ is graphed in the coordin…
As \( x ightarrow+\infty \), \( p(x) ightarrow-\infty \) and as \( x ightarrow-\infty \), \( p(x) ightarrow+\infty \)
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quatre fonctions polynomiales considérons les fonctions polynomiales du…
$f_4(x) = -\frac{1}{224}x^2 + \frac{1}{4}x + 16$
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operations with mixed numbers divide: $2\\frac{3}{4} \\div 1\\frac{1}{2…
\(1\frac{5}{6}\) (the option with \(1\frac{5}{6}\))
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operations with mixed numbers multiply: $4 \\cdot 2\\frac{2}{3}$ option…
\(10\frac{2}{3}\) (corresponding to the option with \(10\frac{2}{3}\))
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which element is often required if the primary borrower has a limited c…
a cosigner
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a quadratic function $f(x)$ is hidden from view. you must find the $y$-…
There is one y - intercept, and the y - intercept is \((0, -36)\)
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the function f(x) is graphed below. enter each x-intercept as an ordere…
The \( x \)-intercepts are \( (-4,0) \) and \( (0,0) \). If we consider one (maybe the problem has a single intercept? Wait, no, the equation gives two. Wait, maybe I made a mista…
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which of the following is a horizontal stretch of the parent function? …
The Right Graph
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3. f-if.7 identify the vertical and horizontal intercepts of this graph…
- **Vertical (y - intercept)**: \((0,6)\) - **Horizontal (x - intercepts)**: \((-3,0)\), \((1,0)\), \((2,0)\) - **End Behavior**: As \(x ightarrow+\infty\), \(y ightarrow+\infty\)…
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a quadratic function $f(x)$ is hidden from view. you must find the maxi…
3
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-300 ÷ (-1.5)
200
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a quadratic function f(x) is hidden from view. you must find the x-inte…
There are two x - intercepts, and the x - intercepts are \((2, 0)\) and \((8, 0)\)
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find the vertex of the given function. f(x) = |x - 5| + 10 the vertex i…
B. domain: \( (-\infty, \infty) \); range: \( f(x)\geq10 \)
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a quadratic function f(x) is hidden from view. you must find the y-inte…
There is one y - intercept \((0, 15)\)
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14. the function g(x) approaches positive infinity as x approaches posi…
\( g(x)=(x - 1)(x + 2)(x + 3) \) (or the expanded form \( g(x)=x^{3}+4x^{2}+x - 6 \))
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a quadratic function $f(x)$ is hidden from view. you must find the $y$-…
To find the y - intercept most efficiently, we choose the standard form \(f(x)=ax^{2}+bx + c\). The y - intercept of a quadratic function \(f(x)\) (which always exists) is \((0,c)…
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identify the intercepts of $f(x)$, which is graphed below. $f(x) = -|x …
1. \(x\) - intercept: \(\varnothing\) 2. \(y\) - intercept: \((0, - 5)\)
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a quadratic function $f(x)$ is hidden from view. you must find the $x$-…
Factored Form
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graph the absolute value function represented by the table of values. |…
The graph is a V - shaped absolute - value graph with vertex at \((-4, -5)\) and passing through the points \((-6, -7)\), \((-5, -6)\), \((-3, -6)\), \((-2, -7)\) (plotted and con…
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exponential growth vs. exponential decay drag and drop each card to att…
### Exponential Decay Cards: - 5% depreciation per year - A pesticide kills an ant population at a rate of 15% per day from the time of its application - \( f(x) = a(1 - r)^x \), …
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graph the following absolute value expression: $y = |x - 5| - 6$ show y…
The graph of \(y = |x - 5|-6\) is a V - shaped graph with vertex at \((5,-6)\), passing through points like \((0,-1)\), \((1,-2)\), \((6,-5)\), \((10,-1)\) and having a slope of \…
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elena is making an open - top box by cutting squares out of the corners…
(for maximum volume): Approximately 180 (or more accurately, by calculation, around 183, but from the graph, the peak is around 180). Wait, maybe the graph's peak is at y=180? Let…
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9. given f(x), find f⁻¹. f(x) = 2x² - 3
\( f^{-1}(x)=\pm\sqrt{\frac{x + 3}{2}}, \ x\geq - 3 \) (If we consider the inverse relation; if we restrict the domain of \( f(x) \) to \( x\geq0 \) or \( x\leq0 \), we can have a…
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questions 9-11 are worth 2 marks each, broken down as follows: - 1 mark…
(-0.5, 2)
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the function f(x) is graphed below. complete the statements regarding t…
As \( x \to -\infty \), \( f(x) \to -\infty \) (or "negative infinity"); as \( x \to \infty \), \( f(x) \to -\infty \) (or "negative infinity"). So filling in the blanks: For \( x…
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the function f(x) is graphed below. enter the y-intercept as an ordered…
\((0, 0)\)
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write an equation of the line below.
\(y=-2x - 2\)
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identify the domain and then graph the function. $f(x)=\\sqrt{x} + 5$ s…
B. The domain is $x \geq 0$.
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e106b (7) (\frac{1}{2} - \frac{3}{10} = \frac{square}{10} - \frac{squar…
(7) \(\frac{1}{2}-\frac{3}{10}=\frac{5}{10}-\frac{3}{10}=\frac{2}{10}=\frac{1}{5}\) (boxes: 5, 3, 2, 1) (8) \(\frac{2}{5}\) (9) \(\frac{1}{2}\) (10) \(1\frac{1}{4}\) (11) \(2\frac…
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graph the line. $y = \\frac{3}{4}x - 2$
The graph of the line \(y=\frac{3}{4}x - 2\) is drawn by first plotting the y - intercept \((0,-2)\), then using the slope \(\frac{3}{4}\) to find additional points (e.g., \((4,1)…
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graph the systems of linear equations to find the solutions. 1.13) \\be…
The solution of the system of linear equations is \(x = 4\), \(y = 1\) (the point of intersection of the two lines is \((4,1)\)).
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7) \\( \\frac{8}{4} \\cdot 6 \\cdot 2 + 5 - 1 \\)\ 8) \\( 5 \\cdot 3 - …
s: - Problem 7 (assuming the first problem is \(\frac{8}{4}\cdot6\cdot2 + 5 - 1\)): \(28\) - Problem 9: \(6\) - Problem 10: \(5\)
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56) \\(\frac{5sqrt{4}}{2sqrt{100}}\\)
$\frac{1}{2}$
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54) \\(\\frac{5\\sqrt{15}}{4\\sqrt{3}}\\)
$\frac{5\sqrt{5}}{4}$
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conservation as a national duty, 1908 by theodore roosevelt in this spe…
The United States should work to protect its natural resources.
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divide. 57.3 ÷ 100
0.573
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divide. 3.86 ÷ 10
\( 0.386 \)
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divide. 13.8 ÷ 1000
\(0.0138\)
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solve the inequality that the graph represents.
\( x \leq 10 \) (or \( x < 10 \) if the circle is open; but based on typical problems, likely \( x \leq 10 \))
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what is the slope of the linear function described in this table? slope…
\(m = -3\) (corresponding to the option with \(m=-3\))
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27. how long does it take to travel 108 kilometres from manchester to b…
\(2.25\) hours (or \(2\) hours and \(15\) minutes)
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evaluating functions given the function $f(x) = \\frac{-5x + 7}{x + 1}$…
\( f(-2)=-17 \) \( f(-1)=DNE \) \( f(0)=7 \) \( f(1)=1 \) \( f(2)=-1 \)
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for each problem, find the: x and y intercepts, x-coordinates of the cr…
- x截距：\((0,0)\)，\((3,0)\)；y截距：\((0,0)\)。 - 临界点的x坐标：\(x = 0\)，\(x = 2\)。 - 递增区间：\((0,2)\)；递减区间：\((-\infty,0)\)，\((2,+\infty)\)。 - 拐点的x坐标：\(x = 1\)。 - 凹向上区间：\((-\infty,1)\)；凹向下区间：\(…
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ex a former has 1200 ft of fencing for enclosing a trapezoid field alon…
The largest area the farmer can enclose is \( 90000\space\text{sq ft} \)
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due december 13, 2025 at 11:59 pm why it matters that teens are reading…
C. "Of course, teens are still reading. But they're reading short texts and Instagram captions, not longform articles that explore deep themes and require critical thinking and re…
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due december 13, 2025 at 11:59 pm anti-social networks? were just as cl…
D. The author explains how Facebook caters towards a person's interests and social circles, reinforcing their established views.
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due december 13, 2025 at 11:59 pm anti - social networks? were just as …
B. "Facebook and Twitter can act as echo chambers where you interact primarily with others who have similar interests and politics." (Paragraph 6)
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due december 13, 2025 at 11:59 pm anti - social networks? were just as …
C. Due to the design of many social media platforms, people are more likely to stay within their "real life" social cliques and interest circles while online.