Calculus
Limits, derivatives, optimization, and behavior of functions.
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write the equation of the line in fully simplified slope - intercept fo…
$y = -\frac{1}{2}x - 8$
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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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find the equation of a line perpendicular to $y = 2x - 6$ that passes t…
$y = -\frac{1}{2}x - 6$
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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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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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sketch the graph of the quadratic function and the axis of symmetry. st…
Vertex: $(-6, 2)$ Equation of the axis of symmetry: $x=-6$ *(For graphing: Plot the vertex $(-6,2)$. Since $a=-3<0$, the parabola opens downward. Use points like $(-5,-1)$ and $(-…
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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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solve the system of equations by graphing. first graph the equations, a…
The solutions are \((0, -6)\) and \((6, 0)\).
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which of these forms of business is a hybrid form of business? a limite…
D. Limited Liability Companies
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2 write an equation for each linear function described. a. the function…
s: a. $y=\frac{3}{2}x+\frac{9}{2}$ (or $y = 1.5x + 4.5$) b. $y=\frac{4}{5}x + 2$ (or $y=0.8x + 2$)
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the height of a ball (in feet) after t seconds is given by the quadrati…
a. 3 seconds b. 115 feet
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7 × 10 + 3 × 30
160
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\(f(x)=\sqrt{x}\), \(g(x)=9 - x\) (There are other possible answers, for example, \(f(x)=\sqrt{9 - x}\) and \(g(x)=x\) is not allowed as we need non - identity functions for \(f\)…
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which business form(s) does not benefit from pass-through taxation? a l…
C. Corporations
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55 - (5² × 3) - 5²
$5$
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in exercises 1 - 6, determine whether the equation represents an expone…
81
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which of these is not one of the basic business forms? a limited liabil…
B. Limited Partnership
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5 × (92 - 18)
# Explicación: ## Paso 1: Resolver la resta del paréntesis $92 - 18 = 74$ ## Paso 2: Multiplicar el resultado por 5 $5 \times 74 = 370$ # Respuesta: 370
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Question was provided via image upload.
Vertex: $(-4, 3)$ Equation of axis of symmetry: $x=-4$ *(For graphing: Plot the vertex $(-4,3)$, since $a=-2<0$ the parabola opens downward. Use the axis of symmetry $x=-4$ (dashe…
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expand the logarithm. assume all expressions exist and are well - defin…
$\log 17 - \log w - \log v$
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3. 12 + (4²) - 11 =
17
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expand the logarithm. assume all expressions exist and are well - defin…
$\log_{7}x + \log_{7}w + \log_{7}v$
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find $8 \\times 0.3$. $\\begin{align*}8 \\times 0.3 &= 8 \\times (3 \\t…
right
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use transformations of the graph of $f(x)=x^2$ to determine the graph o…
B. The graph of $f(x)=x^2$ should be shifted 3 units to the left.
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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 shifted 3 units to the left.
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rewrite the logarithmic expression as a single logarithm with the same …
\(\log_{y} e^{12}\)
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what is a benefit associated with free trade? increased government reve…
B. enhanced innovation and technology
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find ( 5 \times 0.9 ). find the product of the whole numbers. ( 5 \time…
First, the number in the box is 45. And the final result of \(5\times0.9\) is \(4.5\).
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use transformations of f(x)=x² to graph the following function. g(x)=x²…
C. The graph of $f(x)=x^2$ should be shifted 5 units up.
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find $5 \\times 0.9$. first, represent the decimal using place value an…
4.5
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globalization is the process of limiting exchange of goods and services…
connecting the world over time.
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globalization is the process of limiting exhange of goods and services.…
connecting the world over time.
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graphing a slope drag the purple point to graph a slope of $m = \\frac{…
To graph the slope \( m = \frac{3}{4} \), from the initial purple point, move 4 units to the right (horizontal direction, positive x - direction) and 3 units up (vertical directio…
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x = 0 to x = 2; increasing; x = 2 to x = 4; x = 3 to x = 5; x = 4 to x …
- **Increasing**: \( x = 0 \) to \( x = 2 \), \( x = 2 \) to \( x = 4 \), \( x = 0 \) to \( x = 4 \), \( x = 3 \) to \( x = 5 \) - **Decreasing**: \( x = 4 \) to \( x = 7 \), \( x…
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use transformations of $f(x)=x^2$ to graph the following function. \\( …
A. The graph of $f(x)=x^{2}$ should be shifted 5 units down.
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use transformations of $f(x)=x^{2}$ to graph the following function.\ \…
A. The graph of $f(x)=x^2$ should be shifted 5 units down.
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review questions: outlining directions: read the lesson and complete th…
## I. The Election of 1912 A. Progressive (Bull Moose); William Howard Taft; Woodrow Wilson B. New Nationalism C. New Freedom D. Woodrow Wilson ## II. Wilson’s Reforms A. Underwoo…
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next, find the product. 9 × 0.02 = 9 × 2 hundredths = hundredths
18
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here are graphs of two exponential functions, f and g. if ( f(x) = 100 …
A. $\frac{1}{3}$
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^3 \), \( g(x)=6 - x \) (Note: There are other possible answers, for example, \( f(x)=(x)^3 \) and \( g(x) = 6 - x \) is a valid pair of functions for the composition.)
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now, write the product as a decimal. 6 × 0.6 = 6 × 6 tenths = 36 tenths…
$3.6$
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^3 \), \( g(x)=6 - x \) (Note: There are other valid pairs of functions as well, but this is one common solution.)
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use the graph of ( y = f(x) ) to graph the function ( g ).( g(x) = f(2x…
The graph of $g(x)=f(2x)$ is a horizontal compression of $y=f(x)$ by a factor of $\frac{1}{2}$, with key points $(-3, 0)$, $(-1, -7)$, $(0, 0)$, $(3, 0)$, $(4, 7)$ connected seque…
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find two functions f and g such that (f ∘ g)(x) = h(x). (there are many…
\( f(x)=x^2 \), \( g(x)=4x + 6 \) (So the pair is \( (x^2, 4x + 6) \))
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analyzing tables a local maximum of the function ( f(x) ) occurs for wh…
-1
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find $f \\circ g$ and $g \\circ f$. \\( f(x) = \\dfrac{7}{x^2 - 1},\\ g…
\( \frac{x^2 + 6}{x^2 - 1} \) (or \( \frac{7}{x^2 - 1} + 1 \)) #### Domain of \( f \)
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question 7 for the following exercise, determine the interval(s) on whi…
Increasing: $(-1, \infty)$ Decreasing: $(-\infty, -1)$
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for the following exercise, determine the interval(s) on which the func…
Increasing: $(-9, \infty)$ Decreasing: $(-\infty, -9)$
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for the following exercise, use a graphing utility to estimate the loca…
Furthest left local extrema: $(0, 0)$ Furthest right local extrema: $(8, 4)$ Increasing on the interval: $(0, 8)$ Decreasing on the interval: $(-\infty, 0) \cup (8, \infty)$
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12 $\\frac{5}{6} \\cdot 9 =$
$\frac{15}{2}$ (or $7\frac{1}{2}$)
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9 2/3 · 7 =
$\frac{14}{3}$ (or $4\frac{2}{3}$)
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actions. 8 (\boldsymbol{\frac{3}{4} cdot 9 =}) ______
$\frac{27}{4}$ or $6\frac{3}{4}$
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let $f(x) = 3x + 4$ and $g(x) = x^2 - x + 3$. perform the function oper…
\( x^{2}-4x - 1 \)
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sketch a graph of: $f(x) = \\begin{cases} -2x - 7 & \\text{if } x \\leq…
To sketch the graph: 1. **First segment ($\boldsymbol{x \leq -1}$):** Plot a closed dot at $(-1, -5)$ and draw the line $y = -2x - 7$ for $x \leq -1$ (e.g., through $(-3, -1)$ and…
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determine f(x - 1) for the following function. f(x) = \\sqrt{x + 9} - 4…
$\sqrt{x+8}-4$
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select the correct text in the passage. which set of lines in this exce…
I have passed with a nod of the head / Or polite meaningless words, / Or have lingered awhile and said / Polite meaningless words,
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simplify the following expressions
\(10\) (corresponding to the option \(= 10\))
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find a formula for the linear function depicted in the following graph.
$y=\frac{2}{5}x - 2$
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use the graph of $f(x) = \\sqrt{x}$ to write an equation for the functi…
(a) \( \boldsymbol{y = \sqrt{x + 1} - 5} \) (b) \( \boldsymbol{y = \sqrt{x + 5} - 5} \) (Note: There might be a mistake in the grid interpretation, but based on the transformation…
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what is $(f - g)(x)$? $f(x) = -3x^2 + 7x$ $g(x) = -x + 2$ write your an…
\(-3x^{2}+8x - 2\)
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use transformations to sketch a graph of f\\(f(x) = (x - 1)^3\\)\\(\\do…
To graph \( f(x)=(x - 1)^3 \), shift the graph of \( y = x^3 \) 1 unit to the right. Key points of \( f(x) \) are \((-1,-8)\), \((0,-1)\), \((1,0)\), \((2,1)\), \((3,8)\) (among o…
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question use a graphing calculator to solve the following inequality. $…
$x < -9$ or $x > 1$ (in interval notation: $(-\infty, -9) \cup (1, \infty)$)
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solve for h. 17 - 9 = h h = submit
8
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complete the table and then graph the function. $f(x) = 6x + 28$ | $x$ …
Completed table: | $x$ | $f(x)$ | |-----|--------| | $-6$ | $-8$ | | $-4$ | $4$ | | $-3$ | $10$ | Points to plot on the graph: $(-6, -8)$, $(-4, 4)$, $(-3, 10)$ (connect these poi…
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put these values in order from least to greatest. 3π 32.3 √66 39/4
\(\sqrt{66}\), \(3\pi\), \(\frac{39}{4}\), \(32.3\)
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12 3(12 - 5) + 8(4) 4) 6 - (9 - 2) + 3(6)
$3(12 - 5) + 8(4) = 53$ $6 - (9 - 2) + 3(6) = 17$
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find \\(\frac{3}{4} \\times 8\\). find the product. \\(\\frac{3}{4} \\t…
6
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use the graph to find the intervals on which the function is increasing…
Increasing: $(-3, \infty)$ Decreasing: $(-\infty, -3)$
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write the equation of the line in fully simplified slope - intercept fo…
$y=x-7$
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graph the line with the equation ( y = -\frac{3}{4}x + 5 ).
To graph \(y =-\frac{3}{4}x + 5\): 1. Plot the y - intercept \((0,5)\). 2. Use the slope \(-\frac{3}{4}\) to find additional points (e.g., from \((0,5)\), move down 3, right 4 to …
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ewrite fractions enter the result. $x = \\frac{115}{10}$ $x = \\square$
$11.5$
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write the equation of the line in fully simplified slope - intercept fo…
$y=x+6$
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write your answers as fractions. 7 (\frac{2}{9} cdot 5 = ) 8 (\frac{3}{…
7. $\frac{10}{9}$ 10. $\frac{35}{4}$
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raph the following features: - slope = -2 - y-intercept = 3
The graph is a straight line with equation $y = - 2x+3$, passing through $(0,3)$ and other points determined by the slope (e.g., $(1,1)$) as described in the steps. To visualize, …
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8. indirect measurement kenneth is sitting at the end of a pier and usi…
96.5 feet
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write the equation of the line in fully simplified slope - intercept fo…
$y=\frac{3}{4}x+6$
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7. $6\\frac{1}{4} - 3\\frac{9}{10}$
$2\frac{7}{20}$ (or $\frac{47}{20}$)
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1/10 27÷\\frac{3}{1} 1 \\frac{27}{1}÷\\frac{3}{1} 2 \\frac{1}{27}×\\fra…
The correct option is the first one: $\boldsymbol{\frac{27}{1}\div\frac{3}{1}}$ (or the first boxed option with the expression $\frac{27}{1}\div\frac{3}{1}$)
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graph the following features: - y-intercept = 2 - slope = $-\frac{6}{5}$
The equation of the line is $y =-\frac{6}{5}x + 2$, and the line is graphed by plotting the point $(0,2)$ and using the slope $-\frac{6}{5}$ to find another point (e.g., $(5,-4)$ …
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add. show how you know.1. 135 + 59 = 2. 28 + 146 =
1. $135 + 59 = 194$ Number line: $135 ightarrow 185 ightarrow 194$ 2. $28 + 146 = 174$ Number line: $146 ightarrow 166 ightarrow 174$
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graph the line with the equation ( y = \frac{1}{5}x - 1 ).
The line is graphed by plotting the y - intercept \( (0, - 1) \), using the slope \( \frac{1}{5} \) to find another point \( (5,0) \) (and others), and drawing a straight line thr…
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6 66·75 = ——
4950
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write the equation of the line in fully simplified slope - intercept fo…
\(y=\frac{2}{3}x - 3\)