Calculus
Limits, derivatives, optimization, and behavior of functions.
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c. \\begin{cases} y = 6x + 14 \\\\ y = -x + 21 \\end{cases}
$x=1$, $y=20$
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0.9 ÷ 10² =
\(0.009\)
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5. 0.205 × 10 =
\(2.05\)
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3.04 ÷ 10 =
\( 0.304 \)
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unit 5 practice test - graphing quadratics use the given information to…
$(-5, -12)$
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name ______________ date __________ multiplying decimals 1. 3.75 × 2 __…
1. $7.50$ 2. $26.45$ 3. $43.68$ 4. $25.50$ 5. $59.92$ 6. $34.84$ 7. $56.25$ 8. $14.85$ 9. $16.92$ 10. $24.70$ 11. $33.00$ 12. $27.36$ 13. $116.44$ 14. $16.92$ 15. $14.00$
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the functions $f(x)$, $g(x)$, and $h(x)$ are shown below. select the op…
First, calculate average rates of change on $1 \leq x \leq 3$: 1. For $f(x)$: from graph, $f(1)=-30$, $f(3)=20$. Average rate: $\frac{20 - (-30)}{3-1}=25$ 2. For $g(x)$: $g(1)=6$,…
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which consideration must a society address when deciding for whom to pr…
Who has the greatest need?
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week 7 monday evaluate and simplify. $1\\frac{1}{4} \\div \\frac{2}{8} …
Monday: $5$ Tuesday: $\$3.15$
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Question was provided via image upload.
A. The graph with a closed dot at (-8,0), open dot at (-2,6) for the first segment, and closed dots at (-2,9) and (6,5) for the second segment.
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15. in section 8, the constitution lists or enumerates the powers of co…
15. 1. Lay and collect taxes 2. Borrow money on the credit of the U.S. 3. Regulate commerce with foreign nations, among states, and with Indian tribes 4. Establish a uniform rule …
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graph each function. give the domain and range. $f(x) = \\begin{cases} …
Domain: All real numbers ($\mathbb{R}$) Range: $(-3, +\infty)$
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by the end of this lesson, you will be able to answer the following que…
### Part (a): Complete a table of values To complete a table of values for \( y = f(x) \), \( y = |f(x)| \), and \( y = f(|x|) \), we first need to identify key points on the grap…
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match each expression with its value. -9 7 -2 undefined $h(3.999)$ $h(4…
- $h(3.999)$: 7 - $h(4)$: Undefined - $h(4.0001)$: $-2$ - $h(9)$: Undefined
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question 3 (1 point) which graph is a possible sketch of the function $…
b) <The graph that is above the x-axis for $x < -3$, crosses the x-axis at $x=-3$, dips below the x-axis between $-3$ and $6$, crosses the x-axis at $x=6$, and rises above the x-a…
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which of the following graphs represents an odd function? a) b) c) d)
c) <graph symmetric about the origin>
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question 1 (1 point) if any of the factors of a polynomial function are…
c) The x-axis is tangent to the curve at these points.
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week 1 - daily math fluency friday – addition & subtraction (0–100) | s…
Row 1: 75, 44, 81, 45, 83 Row 2: 43, 80, 43, 82, 28 Row 3: 75, 27, 81, 36, 77 Row 4: 80, 37, 84, 45, 47 Row 5: 82, 32, 80, 35, 73
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week 1 – daily math fluency friday – addition & subtraction (0–100) | s…
Row 1: 35, 83, 45, 75, 81 Row 2: 43, 80, 43, 82, 28 Row 3: 27, 75, 36, 81, 77 Row 4: 37, 80, 45, 84, 47 Row 5: 32, 82, 35, 80, 73
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24. examine the two curves, shown in the graph below. are the curves in…
No
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4. a system of equations has no solution. what does this mean about the…
B. The lines are parallel.
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18. evaluate: $75 - 3(9 + 8) - 10 \\div 5^1$
\(22\)
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2. the graph of the function $y = f(x)$ is shown below. what are the co…
The x - intercepts are the points where the graph of \(y = f(x)\) intersects the x - axis (where \(y = 0\)). From the graph, we can identify that the graph intersects the x - axis…
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given a general function f(x) and absolute value function a(x) = |x|, a…
The graph of \( f(x)=a(f(x)) \) when \( f(x)\geq0 \) for all \( x \) in the domain of \( f(x) \) (i.e., the graph of \( f(x) \) is non - negative everywhere, lying on or above the…
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7. graph: $y = 4x - 3$
To graph \( y = 4x-3 \): 1. Plot the y - intercept at \( (0, - 3) \) (since when \( x = 0 \), \( y=4(0)-3=-3 \)). 2. Use the slope \( m = 4=\frac{4}{1} \): from \( (0,-3) \), move…
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5. which factor most contributed to the united states decision to annex…
5. A. The desire of the United States to expand its territory. 6. B. Jack Coffee Hays 7. B. brought new ideas and celebrations with them
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on the set of axes below, solve the following system of equations graph…
The solution set of the system of equations (the coordinates of the intersection points) is \( (-4,0) \) and \( (-8,8) \)
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question la fonction f(x) le graphique ci - dessous représente la valeu…
4
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question given the function $g(x) = x^2 - 5x - 2$, determine the averag…
\( 5 \)
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given the function f(x) = -x² + x + 3, determine the average rate of ch…
\(-6\)
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find the inverse function in slope-intercept form (mx+b): $f(x) = \\fra…
The inverse function of \( f(x)=\frac{5}{3}x + 15 \) in slope - intercept form is \( f^{-1}(x)=\frac{3}{5}x - 9 \)
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compare the functions $f(x) = 2x^4$ and $g(x) = 4^x$ by completing part…
### Part (a) #### Step 1: Calculate \( f(x) = 2x^4 \) and \( g(x) = 4^x \) for \( x = 4 \) - For \( f(4) \): - Substitute \( x = 4 \) into \( f(x) = 2x^4 \). - \( f(4) = 2\times(4…
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use the calculator below to approximate \\(\\sqrt{84}\\) as a decimal t…
9.17
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use the calculator below to approximate \\(\\sqrt{45}\\) as a decimal t…
6.7
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a remote - control car moves toward a wall, stops, backs up, and stops.…
To solve the problem about the remote - control car's distance from the wall as a function of time, we analyze the domain and range: ### Part a: Domain The domain of a function re…
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which point of view lets readers know the thoughts, feelings, and opini…
third-person omniscient
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graph the function using transformations. $g(x) = -\frac{1}{3}|x|$ each…
*(Note: Since the visual details of the grid options are not fully clear, the correct graph is the one that is a vertical compression by a factor of $\frac{1}{3}$ and reflection o…
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describe and correct the error a student made in determining the relati…
C. The range of $f(x)=10|x|$ is not 10 times the range of $f(x)=|x|$. The range is the same for both functions, $y \geq 0$.
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the atkinson-shiffrin memory model the atkinson-shiffrin three-stage mo…
How do the arrows in the diagram connect to the text?
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3. 2x + y = 26 y = x + 5
$x=7$, $y=12$
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10. directions first, select the line a button to graph the line and ch…
1. Draw a solid line connecting the points $(0, 2)$ and $(4, 0)$ on the coordinate grid. 2. Shade the entire region that lies above this solid line.
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6. instructions first, select the line a button to graph the line and c…
1. Draw a solid line through points $(0,4)$ and $(2,0)$. 2. Shade the area that lies above this solid line.
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7. directions first, select the line a button to graph the line and cho…
1. Graph the dashed line passing through $(2, 0)$ and $(0, -6)$ (this is $y=3x-6$, dashed because the inequality is strict $<$). 2. Shade the entire region that lies below this da…
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rewrite the expression $log_{3} z + log_{3} 2 + log_{3} 4$ as a single …
\(\log_3(8z)\) (corresponding to the option: \(\boldsymbol{\log_3(8z)}\))
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you are proving the quotient rule of logarithms. the following shows yo…
C. Write the quotient of \(m\) and \(n\) as \(\frac{m}{n}=\frac{b^x}{b^y}\)
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what value is equivalent to \\(\\log_{4} 2.1\\) to the nearest thousand…
0.535
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5. directions first, select the line a button to graph the line and cho…
1. Use a solid line to graph $y = \frac{1}{2}x - 4$ (passing through $(0, -4)$ and $(8, 0)$). 2. Shade the region above this solid line.
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which expression shows \\(\\log_{4} 35\\) rewritten using the change of…
\(\frac{\log 35}{\log 4}\) (corresponding to the option: \(\boldsymbol{\frac{\log 35}{\log 4}}\))
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which of the following correctly changes \\(\\log_{25} 200\\) to an equ…
A. \(\frac{\log200}{\log25}\), B. \(\frac{\ln200}{\ln25}\) (assuming the options are labeled as: A. \(\frac{\log200}{\log25}\), B. \(\frac{\ln200}{\ln25}\), C. \(\frac{\log200}{\l…
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12) $\frac{6}{7} div \frac{7}{4}$
$\frac{24}{49}$
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find the slope of a line that goes through the points (0, 7) and (-9, 1…
$\frac{2}{3}$
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what is the y intercept? y=4x
0
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a sine function has the following key features: period = 4π amplitude =…
First point: (0, 2); Second point: (π, -1)
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graph $h(x) = 7cosleft(\\frac{1}{2}x ight) + 1$. use 3.14 for $\\pi$. u…
First point: $(0, 1)$; Second point: $(0, 8)$
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graph $g(t) = 4sin(3t) + 2$. use 3.14 for $pi$. use the sine tool to gr…
First point: (0, 2); Second point: (0.523, 6)
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graph $h(x) = 7\\sin x$. use 3.14 for $\\pi$. use the sine tool to grap…
First point: (0, 0); Second point: (1.57, 7)
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calculator which function is shown on the graph? \\( f(x) = -\frac{1}{2…
\( f(x)=\frac{1}{2}\cos x \)
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find the x-intercept and the y-intercept of the line below. click on on…
(a) \(x\) - intercept: \(1\) (b) \(y\) - intercept: \(-2\)
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question find the inverse function in slope-intercept form (mx+b): $f(x…
\( f^{-1}(x) = -\frac{1}{3}x - 1 \)
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given the function $h(x) = -x^2 - 4x + 7$, determine the average rate o…
The average rate of change of the function \( h(x) \) over the interval \(-7\leq x\leq0\) is \( 3 \).
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3 drag each value and description to the correct location on the table.…
| Method of Approximation | Solutions | Level of Accuracy | |-------------------------|-----------|-------------------| | Table of Values (nearest $\frac{1}{4}$ of a unit) | 1.5 |…
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use a graphing tool to solve the equation below for x. $-3^{(-x)} - 6 =…
A. \(x\approx2.50\)
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use a graphing tool to solve the equation below for x. $-3^{(-x)} - 6 =…
A. \(x\approx2.50\)
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select the correct answer. how many real solutions exist for this syste…
C. two
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what is the range of the absolute value function shown in the graph? op…
C. \(-6\leq y<\infty\)
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all exponential functions can be written in many forms. write the funct…
\(f(t)=78000\times1.0305^{5t}\) (where \(a = 78000\) and \(b\approx1.0305\))
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match each equation of the piecewise function represented in the graph …
To solve this, we analyze each segment of the piecewise function by examining the domain (x - values) and the corresponding graph: ### 1. Segment from \( x = 0 \) (closed dot) to …
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all exponential functions can be written in many forms. write the funct…
\( f(t) = 490.0000(2)^{\frac{t}{2.4754}} \) (or with more precise rounding during calculation, but following the steps above gives this result)
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3 select all the correct answers. exponential function f is represented…
The correct statements are: - The functions have the same y - intercept. - Both functions are increasing on all intervals of \(x\). - Both functions approach \(-\infty\) as \(x\) …
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2 select the correct answer. exponential function f is represented by t…
A. Both functions are decreasing on \([0, 3]\), and function \( f \) is decreasing at a faster rate.
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what are the features of the function $f(x) = 3^x - 4$ graphed below? g…
The function \( f(x) \) is an **exponential** function with a **horizontal** asymptote of \( y = - 4 \). The range of the function is \( (-4,\infty) \), and it is **increasing** o…
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what are the features of the function $f(x) = \\log_{2}(x + 2)$ graphed…
The function \( f(x) \) is a \(\boldsymbol{\text{logarithmic}}\) function with a \(\boldsymbol{\text{vertical}}\) asymptote of \(\boldsymbol{x=-2}\). The range of the function is …
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a quantity with an initial value of 790 decays continuously at a rate o…
194.81
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a quantity with an initial value of 110 grows continuously at a rate of…
\( 113.35 \)
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select the correct answer. consider the function $f(x) = 2^x$ and the f…
A. The graph of \( g(x) \) is the graph of \( f(x) \) shifted 4 units to the left.
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select the correct answer. in which direction must the graph of $f(x) =…
D. right
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2 enter the correct answer in the box. the function ( f(x) = 7^x + 1 ) …
\( 3 \)
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select the correct answer. which function is decreasing and approaches …
B. f(x) = -3(6)^x + 2
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select the correct answer. what are the solutions of this quadratic equ…
D. $x = -4 \pm \sqrt{13}$
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select all the correct answers. which of the following statements are t…
The extreme value is at the point (3, -7), The solutions are \(x = 3 \pm \sqrt{7}\), The graph of the quadratic equation has a minimum value.
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select the correct answer. this table represents a quadratic function. …
C. The value of a is positive, so the vertex is a minimum.
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5 select the correct answer. if function ( g(x) = x^2 + 2 ) is a transf…
C. \((0,2)\)
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4.2 3. complete each table of values. a) $y = x + 1$\ \ | $x$ | $y$ |\ …
### Question 3 (already completed correctly): a) For $y=x+1$: $x=1, y=2$; $x=2, y=3$; $x=3, y=4$; $x=4, y=5$ b) For $y=x-1$: $x=2, y=1$; $x=4, y=3$; $x=6, y=5$; $x=8, y=7$ ### Que…
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find the domain of the function below. $f(x) = \\sqrt{\\frac{x^2 + 13x …
The domain of the function is \([-7,-6]\cup(-4,1)\cup(2,\infty)\)
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which is the minimum or maximum value of the given function? graph of a…
B. The function has a minimum value of -4.
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question 10 of 10 use the quadratic formula to find the solution to the…
B. \(x=\frac{3}{2}\), C. \(x = \frac{3-\sqrt{\frac{9}{4}}}{2}\), E. \(x=\frac{3+\sqrt{\frac{9}{4}}}{2}\) (Note: When \(\Delta = 0\), the two roots (from the \(\pm\) in quadratic f…
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consider the equation below. $log_{4}(x + 3)=log_{2}(2 + x)$ which syst…
A. $y_{1}=\frac{\log(x + 3)}{\log4},y_{2}=\frac{\log(2 + x)}{\log2}$
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which system of equations could be graphed to solve the equation below?…
$y_1=\frac{\log x}{\log 0.5},y_2=\frac{\log 2}{\log 3}+x$ (the last option among the given choices)
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which system of equations could be graphed to solve the equation below?…
B. \(y_1=\log(2x + 1),y_2 = 3x-2\)
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what is the approximate value of x in the equation below?\\(\\log_{5}15…
-1.317 (corresponding to the option: -1.317)
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kim solved the equation below by graphing a system of equations.\\(\\lo…
1.4 (the option corresponding to 1.4, e.g., if the options are A. 0.6, B. 0.9, C. 1.4, D. 1.6, then the answer is C. 1.4)
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the function $f(x)$ is invertible. find $f^{-1}(-2)$. graph of $f(x)$ i…
\( \boxed{0} \)
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complete the text with the best transition. technology is supposed to m…
Moreover, it's true
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find the equation of the exponential function. | x | f(x) | |----|----|…
$f(x)=4\cdot2^x$
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3. \\begin{cases} y = x - 1 \\\\ x + 4y = 16 \\end{cases}
The solution of the system of equations is \( x = 4,y = 3 \) (or the ordered pair \((4,3)\)).
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add. (1) $3\\frac{5}{7} + 2\\frac{5}{14} =$ (2) $\\frac{5}{6} + 2\\frac…
$6\frac{3}{14}$ $2\frac{13}{15}$ $5\frac{43}{48}$ $9\frac{1}{4}$ $\frac{11}{42}$ $9\frac{27}{50}$
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dividing 2 digits \\begin{array}{c|c|c|c|c} \\times & 1 & 2 & 3 & 4 & 5…
1. a. Quotient 5, remainder 1 b. Quotient 8, remainder 2 c. Quotient 7, remainder 3 d. Quotient 9, remainder 1 e. Quotient 5, remainder 5 2. a. Quotient 8, remainder 2 b. Quotient…
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a table representing a continuous unrestricted exponential function is …
B. It is decreasing and positive
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a graph of an exponential function w(x) is shown. use the graph to find…
The y - intercept of \(w(x)\) is \(2\) and the horizontal asymptote is \(y = 0\).
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evaluate the function. (see example 1) ( g(x)=\begin{cases}-x + 4, & \t…
\( -1 \)