Calculus
Limits, derivatives, optimization, and behavior of functions.
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divide. 177 ÷ 59
3
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select all descriptions that accurately define the meaning of a functio…
- Orange: Every x-coordinate has one unique y-coordinate. - Blue: Every independent variable has one unique dependent variable.
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which of the following correctly explains why sellers in a perfectly co…
c. There are many sellers, and so the market process generates an equilibrium price that cannot be influenced by any one seller. Thus, they have no choice but to take the price ge…
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use transformations of ( f(x) = sqrt{x} ) to graph the following functi…
A. The graph of $f(x)=\sqrt{x}$ should be shifted 2 units down.
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the graph of the function g(x) and its base exponential function f(x) =…
The transformation needed is a reflection over the x-axis, so the function is $g(x) = -2^x$.
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divide: -21 ÷ -3 = submit
7
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use transformations of the graph of $f(x)=x^{2}$ to determine the graph…
B. The graph of $f(x)=x^2$ should be horizontally shifted to the right by 3 units and shrunk vertically by a factor of $\frac{1}{5}$.
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use the graph of the function f(x) to answer the question.question: wha…
$\lim_{x \to -3} f(x) = 1$
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using the graph below, determine the limit as x approaches -1, also fin…
$\lim_{x \to -1^-} f(x) = -5$
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21) determine the vertex of each quadratic function in vertex form, the…
(a): Vertex is \((5, 4)\), it is a maximum. ### Part b: \( b(x) = 2(x + 4)^2 \)
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graph the equation shown below by transforming the given graph of the p…
The graph of $y=|2x|$ is a horizontal compression of the parent absolute value function $y=|x|$ by a factor of $\frac{1}{2}$, forming a V-shape with vertex at $(0,0)$, passing thr…
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b. cot x (sec x + tan x) = csc x + 1
The identity $\cot x (\sec x + \tan x) = \csc x + 1$ is verified.
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g) \\(\\frac{10}{5} \\cdot -1 - (3^2 + 9 \\cdot 2^0) \\div 2\\)
$-11$
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homework helper stephen’s father gave him $10 to buy lunch at the conce…
\( 4.94 \) ### Problem 2: \( 71.65 - 55.12 \)
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which system of equations best represents the system shown on the graph…
\( \begin{cases}y = x+2\\y=-4x + 17\end{cases} \) (the system with equations \( y = x + 2 \) and \( y=-4x + 17 \))
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polynomial operations maze directions: start in the box labeled \start …
The path goes through the following problem - solution steps: 1. \((3x^{4}-8x)+(2x - 4x^{4})=-x^{4}-6x\) 2. \((2x - 1)(7x - 2)=14x^{2}-11x + 2\) 3. \(x^{2}-(x^{2}+9x - 3)=-9x + 3\…
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cp pre - calculus 4.3 (right triangle trig) quiz review name #1 - 6 sta…
### For #1 - 6 (Right Triangle with Opposite = 5, Hypotenuse = 7, Adjacent = $\sqrt{24}$) #### Step 1: Recall Trigonometric Ratios For an acute angle $\theta$ in a right triangle:…
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pair compare! 1; 9 ÷ 3; 3; with comparison symbols <, =, >
$\boldsymbol{=}$
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the us government gave land to the railroads to help them expand. what …
The grants allowed industries in the West to grow because they encouraged settlement and new industrial opportunities.
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evaluate.\\frac{7(12 - 9)+3}{4^{2}-4}
2
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(04.02 mc) the equation of line wx is 2x + y = -5. what is the equation…
The equation of the perpendicular line is \( y=\frac{1}{2}x-\frac{3}{2} \) (the option corresponding to \( y=\frac{1}{2}x-\frac{3}{2} \), which is the third option in the given ch…
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15. pedro kicks a soccer ball from the top of a hill 48 ft. above the g…
3 seconds
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9) if a population started with 20,000 members and grew continuously at…
Approximately \( \boldsymbol{6.9} \) years (or using more precise calculation, \( t = \frac{\ln 2}{0.1} \approx 6.93 \) years)
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create your own paragraph with the following prompt: 1. identify a hero…
### Rough Draft #### Topic Sentence: Harriet Tubman is a hero who has inspired me through her courage, compassion, and determination. #### Supporting Idea Sentence 1: Her courage …
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point (0,5). 30. what is the equation of a line that is perpendicular t…
$y = \frac{4}{3}x + 5$
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slope = \\frac{\\text{vertical distance}}{\\text{horizontal distance}} …
$\frac{-6}{2}$ (simplified to $-3$)
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6. $3x^{2}+10x + 8 = 0$
\(x = - 2\) or \(x=-\frac{4}{3}\)
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find the slope of the line that passes through: (10, 1) and (5, 2)
$-\frac{1}{5}$
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solution 6 ode shows his work to answer a subtraction problem. tell how…
The original subtraction problem Ode started with is $\boldsymbol{955 - 92 = 863}$, and its answer is 863. Alternatively, the equation representing the problem can be written as $…
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the graph shows g(x), which is a translation of f(x) = |x|. write the f…
$g(x) = |x + 6|$
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function a and function b are linear functions. function a \\begin{tabu…
The slope of Function A is greater than the slope of Function B.
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evaluate the following expression. \\((10 - 1)\\times 5 - 21\\div 3\\)
8
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evaluate. 68 - 13(7 - 5)^2 + 2^3
24
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3. solve 667 + 295 using two different strategies. a. b. c. explain whi…
a. Using standard addition, \(667 + 295 = 962\) b. Using compensation, \(667 + 295 = 962\) c. Preference: Compensation strategy (e.g., for simplicity in mental calculation).
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3. solve 667 + 295 using two different strategies. a. b. c. explain whi…
a. Using direct addition: \(667+295 = 962\) (shown by place - value addition) b. Using compensation: \(667 + 295=962\) (by rounding 295 to 300, adding and then adjusting) c. Prefe…
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graph the exponential function. $g(x)=4e^{x + 3}+3$ plot two points on …
Horizontal asymptote: \( y = 3 \) (dashed line). Two points: \( (-3,7) \) and \( (-2, 4e + 3)\approx(-2,13.87) \) (or other valid points from substituting \( x \)-values into \( g…
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the image shows a coordinate grid with a graph of a function. there is …
$-3$
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what is the slope of the line that goes through points a and b? solve o…
$-\frac{1}{3}$
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what is the slope of the line that goes through points a and b? subtrac…
The equivalent fraction is $\frac{-2}{8}$ (matches the second option provided)
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what is divergent thinking? being able to see different solutions. limi…
A. Being able to see different solutions
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add. $-6\frac{3}{5} + 8 = square$
\(1\frac{2}{5}\) (or \(\frac{7}{5}\))
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line m goes through points a and b. what is the slope of line m? now, u…
The expression for slope is $\frac{5-2}{8-3}$, and the slope of line $m$ is $\frac{3}{5}$.
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graph the following function by translating ( y = |x| ). ( y = |x + 5| …
B. <Graph with vertex at (-5, 0), opening upwards in a V-shape>
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graph the following function by translating ( y = |x| ). ( y = |x + 4| …
A. (Graph with vertex at (-4, 0))
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subtract in the numerator and denominator to find the slope of line d. …
$\frac{-5}{4}$
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evaluate quadratic functions score: 2/2 penalty: 0.25 off question give…
16
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subtract. 4 - -3.1 =
\(7.1\)
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add. $-3\\frac{1}{5} + 7.8 = \\square$
\(4.6\)
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subtract. \\(\frac{1}{10} - -5\frac{1}{2} = \\) submit
$5\frac{3}{5}$ (or $\frac{28}{5}$)
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question given $f(x) = -4x^2 + 10x + 13$, find $f(7)$
$-113$
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question find the equation of a line perpendicular to $y = -3x - 5$ tha…
$\boldsymbol{y = \frac{1}{3}x}$ (corresponding to the option $y = \frac{1}{3}x$)
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20. you are playing a history quiz game where you must give the years o…
The range of valid answers is 1966 to 1972, inclusive. ---
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(\frac{3^{\frac{7}{4}}}{3^{\frac{1}{4}}})
\( 3^{\frac{3}{2}} \) (or \( 3\sqrt{3} \), or approximately \( 5.196 \))
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3 digit by 1 digit division solve each problem and show your work. use …
1. $423 \div 3 = 141$ 2. $816 \div 3 = 272$ 3. $801 \div 3 = 267$ 4. $438 \div 3 = 146$
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lets see what happens if we have point bs y - value minus point as y - …
$\boldsymbol{\frac{3}{-4}}$ (or $-\boldsymbol{\frac{3}{4}}$)
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write a word problem that results in a slope intercept equation. it can…
**Word Problem:** A bike rental shop charges a $10 initial fee plus $8 for every hour you rent a bike. Write an equation that represents the total cost $y$ of renting a bike for $…
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3 digit by 1 digit division solve each problem and show your work. use …
$413 \div 3 = 137$ remainder $2$ $816 \div 3 = 272$ $801 \div 3 = 267$ $438 \div 3 = 146$
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which function is the inverse of ( f(x) = -5x - 4 )? ( f^{-1}(x) = -\fr…
$\boldsymbol{f^{-1}(x) = -\frac{1}{5}x - \frac{4}{5}}$ (corresponding to the first option)
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5. convert each decimal to a fraction in simplest form. 0.2 = ______ 0.…
(for Q5): \( 0.2 = \boldsymbol{\frac{1}{5}} \), \( 0.28 = \boldsymbol{\frac{7}{25}} \) ### Question 6: What is the LCM of 4 and 6?
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the elevation e (in feet) of a hot air balloon and its time t (in minut…
zero
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which of these were included in the salt i (strategic arms limitation t…
a. a cap on nuclear arms, d. a limit on launch sites
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long-term memory has ________. unlimited potential infinite capacity li…
B. infinite capacity
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what is a characteristic of long - term memory? limited capacity stores…
stores procedural memories
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the graph of f(x) is shown below. if g(x) and f(x) are inverse function…
The graph that is the reflection of $f(x)$ across the line $y=x$ (i.e., swapping the $x$ and $y$ coordinates of all points on $f(x)$) represents $g(x)$. Visually, this is the mirr…
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a. graph ( g(x) = fleft( \frac{1}{3}x ight) ) b. complete the sentences…
## Part a Plot the transformed points $(-24, -2)$, $(-12, 0)$, $(6, 6)$, $(27, 5)$ and connect them to match the shape of $f(x)$, stretched horizontally. ## Part b The graph of $g…
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part b to calculate slope, you need to know the rise and the run of the…
\( \frac{7}{10} \) (or 0.7)
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the hot air balloon starts descending from an elevation of 2,400 feet. …
Every minute, the elevation decreases by 400 feet.
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directions: modified true/false in the blank, indicate whether the stat…
1. T 2. F; Woodrow Wilson entered politics as a firm progressive. 3. F; The most conspicuous limit to progressivism came in its failure to address racial injustice. 4. F; Woodrow …
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right after takeoff, a hot air balloon ascends at a constant rate of 40…
400
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12 - (3² × 4) - 30 = b
# Explicación: ## Paso1: Calcular la potencia interna $3^2 = 9$ ## Paso2: Multiplicar por 4 $9 \times 4 = 36$ ## Paso3: Restar 30 al resultado $36 - 30 = 6$ ## Paso4: Restar el va…
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what is the concept of limited liability? a the owners are solely respo…
B. The business entity itself is separated from their owners and the owners cannot be personally liable for the businesses’ debt
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which type of firm does not have the benefit of pass - through taxation…
B. Corporations
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{2 × 4 − (6 ÷ 2)} × 3
# Explicación: ## Paso 1: Resolver la división interna $6 \div 2 = 3$ ## Paso 2: Restar dentro del corchete $4 - 3 = 1$ ## Paso 3: Multiplicar dentro de la llave $2 \times 1 = 2$ …
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5 longdiv 67
The result of \( 67\div5 \) is \( 13.4 \) (or \( 13 \) with a remainder of \( 2 \)).
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resuelve si x = 9. 4x + 27 =
63
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use the graph to determine a. open intervals on which the function is i…
a. A. The function is increasing on the interval(s) $(-\infty, 2)$ b. The function is decreasing on the interval(s) $(2, \infty)$ c. B. There is no interval on which the function …
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determine the domain on which the following function is increasing.
$(-\infty, -2)$
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mine the domain on which the following function is increasing.
$[0, 6]$
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graph a function where interval (1) is an increasing interval, interval…
The correct graph is the one that satisfies: (1) increasing (rises with \( x \)), (2) decreasing (falls with \( x \)), (3) constant (horizontal), (4) decreasing (falls with \( x \…
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find and simplify the difference quotient \\(\\frac{f(x + h) - f(x)}{h}…
$-4x - 2h - 1$
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analyzing the graph of a quadratic function the function ( f(x) = -0.3(…
- The axis of symmetry is $x = 5$ - The domain is $\{x \mid x \text{ is a real number}\}$ - The function is increasing over $(-\infty, 5)$
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find the difference quotient of f, that is, find \\(\\frac{f(x + h) - f…
$4x+2h-1$
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doug tried to evaluate an expression. here is his work: $65 - 20 \\div …
No, Doug made a mistake going from Step 3 to Step 4. Doug should have divided 20 by 2 before multiplying. The order of operations says to multiply and divide from left to right.
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kiara tried to evaluate an expression. here is her work: $5^3 - 3 + 24 …
Yes, Kiara's work is correct.
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monica tried to evaluate an expression. here is her work: $(7 + 9) - (2…
Yes, Monica's work is correct.
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find the difference quotient of f, that is, find \\(\\frac{f(x + h) - f…
$-8$
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nina tried to evaluate an expression. here is her work: $(5\\cdot 4 - 1…
No, Nina made a mistake going from Step 4 to Step 5. Nina should have divided 16 by 2 before adding. The order of operations says to divide before you add.
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find and simplify the difference quotient \\(\frac{f(x + h) - f(x)}{h}\…
$-7$
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joey tried to evaluate an expression. here is his work: $97 - 3 + 5^3 \…
No, Joey made a mistake going from Step 4 to Step 5. Joey should have subtracted 3 from 97 before adding. The order of operations says to add and subtract from left to right.
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evaluate the piecewise function at the given values of the independent …
a. $g(0)=3$ b. $g(-6)=3$ c. $g(-3)=0$
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$h(-6)=4$ Additionally, completing the table: | $x$ | $y$ | |-----|-----| | $-6$ | $4$ | | $-4$ | $-2$ | | $-2$ | $-4$ | | $0$ | $-2$ | | $2$ | $1$ | The axis of symmetry is $x=-2…
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$-2$
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$-2$
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$h=-2$
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$a = 0.5$
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graph ( h(x) = 0.5(x + 2)^2 - 4 ) by following these steps: step 1: ide…
- $a=0.5$, $h=-2$, $k=-4$ - Sample $(x,y)$ points: $(-6, 4)$, $(-4, -2)$, $(-2, -4)$, $(0, -2)$, $(2, 4)$ - The graph is a upward-opening parabola with vertex at $(-2, -4)$ passin…
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use square roots to answer each exercise (just type the final answer/nu…
$5$ $36$ $102$
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the graph of a function ( f(x) ) passes through the following points: (…
$\boldsymbol{f(x)=2x^2-2}$
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in the derivation of the quadratic formula by completing the square, th…
B. $x + \frac{b}{2a} = \frac{\pm\sqrt{b^2 - 4ac}}{2a}$
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1) graph the following inequality $y \\leq \\frac{2}{3}x - 4$ $m = \\un…
- $m = \frac{2}{3}$ - $b = -4$ - Línea a marcar: Solid Line - Región a sombrear: Lower Region - (La gráfica consiste en una línea sólida que pasa por $(0, -4)$ y $(3, -2)$, con la…