Calculus
Limits, derivatives, optimization, and behavior of functions.
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y = -2 + \\sqrt3{x} identify the transformations. reflection and down 2…
C. Down 2 (assuming the third option is labeled as C, if the options are A:Reflection and down 2, B:Reflection and stretch by 2, C:Down 2, D:Up 2)
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f(x) = -√(x + 1) + 2 describe the transformation. options: right 1 unit…
B. Left 1 unit, Reflect over x - axis, Up 2 units
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y = -2√(x - 5) what are the transformations of this functions compared …
C. Reflected over the x - axis, vertical stretch 2, and translated right 5 (assuming the orange option is option C, if the options are labeled as A: Green, B: Purple, C: Orange, D…
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y = 2\\sqrt3{x} - 4 identify the transformations. horizontal compressio…
B. Vertical stretch by 2 and down 4
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name the parent function. cubic cube root quadratic square root
D. square root
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y = -4 + 3\\sqrt3{x + 6} describe the transformations of the graph show…
B. Shifted down 4 units, vertically compressed by a factor of 3, and shifted 6 units left.
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the function f is defined as shown. $f(x) = \\frac{1}{x - 3} - \\frac{5…
2
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f(x) = \\sqrt{x + 2} what are the transformations of this function comp…
Translated left 2 (the option in the orange box)
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f(x) = -√x describe the transformation. up 1 down 1 reflect over y-axis…
D. Reflect over x - axis
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given the function below, fill in the table of values and use the table…
| $x$ | $y=-3x$ | |-----|---------| | $-3$ | $9$ | | $-2$ | $6$ | | $-1$ | $3$ | | $0$ | $0$ | | $1$ | $-3$ | | $2$ | $-6$ | | $3$ | $-9$ | To graph this function, plot the points…
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what is the benefit of a business loaning money from the u.s. governmen…
Lower Interest Rates
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(05.01 lc) which point of view uses a narrator who is a character in th…
First person
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what is the value of $f^{-1}(-6)$ when $f(x) = \\frac{5}{2}x + 6$? ente…
\(-\frac{24}{5}\) (or -4.8)
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to the nearest hundredth, what is the largest positive value of x that …
\(1.86\)
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15. $y + 5 = \\frac{1}{4}(x - 2)$ 16. $y = -(x + 4)$ 17. $y + 1 = -\\fr…
### Problem 15: \( y + 5 = \frac{1}{4}(x - 2) \) # Explanation: ## Step 1: Identify the form The equation \( y + 5 = \frac{1}{4}(x - 2) \) is in point - slope form \( y - y_1=m(x …
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how do georgias transportation systems support they economy of the stat…
They work together to move goods and people through the state.
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what is the function rule for the linear function in this graph? slope-…
\( y = 4x + 3 \)
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what is the function rule for the linear function in this graph? slope-…
\( y = 3x + 1 \)
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what was a significant feature of cities in southwest asia during the m…
D. They were centers of trade, culture, and learning
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what is the function rule for the linear function in this table? slope-…
\( y = 5x + 2 \)
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example 3 finding displacement and total distance a particle moves in t…
The position vector of the particle is \(\mathbf{r}(t)=\langle 2t + 2, 4t + 1 angle\). At \(t = 2\), the position is \(\langle 6, 9 angle\) (if we consider the position at \(t = 2…
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the excerpt provides evidence of the : a. limited impact of new deal pr…
B. continued influence of New Deal programs in American life
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on considère lexpression e = 4x² - 9 - (x + 2)(2x - 3). 1) montrer que …
# Exercice 12 ## 1) Montrer que E est un polynôme de degré 2. # Explications étape par étape : ## Étape 1: Développer le produit $(x+2)(2x-3) = 2x^2 -3x +4x -6 = 2x^2 +x -6$ ## Ét…
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complete the steps to evaluate the following expression, given \\(\\log…
$-1.631$
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question 1-32 __________ are rules, limits, and guidelines that people …
C. Boundaries
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question 9 henrik and callie are both young adults employed at a local …
D. Callie will have the higher credit score. ### Question 10
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the graph of the parent function is shown. identify which function woul…
D. $y = \sqrt{x-5}-1$
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question 5 5 pts which category accounts for about 15% of the credit sc…
B. Length of Credit History ### Question 6
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question 3 5 pts which category accounts for about 35% of the credit sc…
C. Payment History ### Question 4
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select two functions with the same end behaviors of $f(x) = (x - 1)^{\f…
1. $f(x)=(x-1)^3+2$ 2. $f(x)=\sqrt[3]{x+5}-7$
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given the two functions, which statement is true? $f(x)=\\sqrt{x + 1}+6…
B. The y-intercept of $f(x)$ is greater than the y-intercept of $g(x)$.
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the graph of $p(x)=\\frac{1}{3}\\sqrt3{x}-1$ has - a one x-intercept an…
A. one x-intercept and one y-intercept
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multiply. $6 \\times \\frac{3}{100}$ what is the product? a. $\\frac{18…
C. $\frac{18}{100}$
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the slope m can be calculated as the ______ in y divided by the change …
change
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if $y = 3x + 5$ and $x = 2$, what is $y$? a. 6 b. 10 c. 11 d. 5
c. 11
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question 4 (5 points) for the functions ( f(x) = 3x - 8 ) and ( g(x) = …
\( 8x - 13 \) ### Part b: \( 3g(x) - f(x) \)
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a line has a slope of $-2$ and passes through the point $(3,5)$. which …
b. $y = -2x + 11$
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10. open - ended complete the subtraction problem so that you do not ne…
10. Missing digit: 5; Difference: 202 11. No, he is not correct. The correct result of $731-246$ is 485. The cousin made an error in regrouping the tens and hundreds places incorr…
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find all the roots (integral, rational, and/or complex) of the polynomi…
A. (2, -2, -4, 3) --- ### Second Question: Lowest degree polynomial with roots 5, $2-3i$
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y = 2x - 4 x | y -1 | 0 | 1 | 2 |
When \( x = -1 \), \( y = -6 \); when \( x = 0 \), \( y = -4 \); when \( x = 1 \), \( y = -2 \); when \( x = 2 \), \( y = 0 \) Filling the table: | \( x \) | \( y \) | | ---- | --…
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7. \\(\\begin{cases} x - 2y = -4 \\\\ 3x - 2y = 12 \\end{cases}\\) chec…
\(x = 8,y = 6\) or the solution is \((8,6)\) ### Problem 8: Solve the system \(\begin{cases}2x + 3y=24\\-4x-6y=-48\end{cases}\)
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
The key points are \((0,3)\), \((1,0)\), \((2,-1)\), \((3,0)\), \((5,8)\). Plot these points on a coordinate plane with x - axis as "x - value" and y - axis as "y - value" and dra…
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question 1-3 if $f\\left(x\ ight)=\\dfrac{3x + 4}{2}$, then what is the…
8 (corresponding to the option with 8)
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
The graph is a parabola opening upward with x - intercepts at \((1, 0)\) and \((3, 0)\), vertex (minimum) at \((2, -1)\), and additional points \((0, 3)\) and \((5, 8)\) plotted o…
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
The key points are: x - intercepts \((1,0)\), \((3,0)\); vertex \((2,-1)\); other points \((0,3)\), \((5,8)\). The graph is a parabola opening upward passing through these points …
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
The key points are \((1,0)\), \((3,0)\), \((2,-1)\), \((0,3)\), \((5,8)\) and the graph is a parabola opening upward passing through these points within the interval \(0\leq x\leq…
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
The key points are \((0,3)\), \((1,0)\), \((2,-1)\), \((3,0)\), \((5,8)\). The graph is a parabola opening upward passing through these points in the interval \(0\leq x\leq5\).
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consider the quadratic function $y = x^2 - 4x + 3$ for $0 \\leq x \\leq…
- x - intercepts: \((1,0)\), \((3,0)\) - Minimum point (vertex): \((2,-1)\) - Other points: \((0,3)\), \((5,8)\) (and the parabola is drawn through these points with x - axis labe…
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graph the solution to the following system of inequalities. y < -3x + 4…
The solution is the region that is below the dashed line \( y=-3x + 4\) and above the solid line \( y = 3x - 2\), with the intersection point of the two lines at \((1,1)\). When g…
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graph the solution to the following system of inequalities. y < -3x + 4…
The solution is the region that is above the solid line \( y = 3x - 2\), below the dashed line \( y=-3x + 4\), and includes the intersection point \((1,1)\) (and the line \( y = 3…
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question: consider the function $y = 2\\sin(x)$ for $0^\\circ \\leq x \…
The key points of the function \( y = 2\sin(x) \) for \( 0^\circ\leq x\leq360^\circ \) are \( (0^\circ, 0) \), \( (90^\circ, 2) \), \( (180^\circ, 0) \), \( (270^\circ, - 2) \), \…
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graph the solution to the following system of inequalities. y < -3x + 4…
The solution is the region that is below the dashed line \( y=-3x + 4 \) and above the solid line \( y = 3x-2 \), with the intersection point at \((1,1)\). (To graph it, follow th…
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use technology to find points and then graph the function $y = 2^{x - 3…
Equation of asymptote: $y=1$ Points to plot: $(1, 1.25)$, $(2, 1.5)$, $(3, 2)$, $(4, 3)$ (or $(5, 5)$ as an additional point)
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is the c - value of this quadratic positive or negative? unknown at thi…
positive
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sketch the graph of the quadratic function $f(x) = x^2 - 4x + 3$, label…
- Vertex: \( (2, -1) \) - Axis of symmetry: \( x = 2 \) - X-intercepts: \( (1, 0) \), \( (3, 0) \) - Y-intercept: \( (0, 3) \) - The graph is a parabola opening upward with the ab…
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question: consider the function $y = 2\\sin(x)$ for $0^\\circ \\leq x \…
The key points for the graph of \( y = 2\sin(x) \) in the interval \( 0^\circ\leq x\leq360^\circ \) are \( (0^\circ, 0) \), \( (90^\circ, 2) \), \( (180^\circ, 0) \), \( (270^\cir…
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4. for the graph of g(x) pictured on the right, over which of the follo…
3. \( - 2<x < 6\)
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1. evaluate the expression ( x^2 + 2x - 10 ) for ( x = -3 ) 2. evaluate…
2) \( -8 < x < -2 \)
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4. write an equation for an exponential growth model with an initial va…
A possible exponential growth model equation is \( y = 5(1 + r)^t \) (or \( y = 5b^t, b>1 \), or \( y = 5e^{kt}, k>0 \)). A specific example (taking \( r = 0.1\) for illustration,…
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2. find the average rate of change from x = -1 to x = 1.
\( -1.5 \) (or \( -\frac{3}{2} \))
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q2 week 8 1. identify each. function family: domain: range: asymptote:
- Function Family: Exponential (Decay) Function Family - Domain: \(x>-2\) (or \((-2,\infty)\)) - Range: \(y > 2\) (or \((2,\infty)\)) - Asymptote: \(y = 2\)
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write the limit as a definite integral on the interval a, b, where ( c_…
$\int_{-7}^{3} (7x + 13) dx$
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use sigma notation to write the sum. \\(\\frac{1}{6(1)} + \\frac{1}{6(2…
$$\sum_{i=1}^{20} \frac{1}{6i}$$
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the function h is defined as follows. ( h(x) = 4x^2 + 7 ) if the graph …
\( f(x)=4x^{2}-2 \)
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find the sum by adding each term together. use the summation capabiliti…
0.2166
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the function h is defined as follows. ( h(x) = -4x^2 - 1 ) if the graph…
\( f(x)=-4x^{2}+2 \)
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the function f is defined as follows. $f(x) = -3x^2 + 3$ if the graph o…
\( g(x)=-3x^{2}+6 \)
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finding slope #1 (graphing method) graph the points and find slope usin…
\(\frac{1}{4}\) ### Problem 2:
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add: -4 + -23 + 98 + 65 = \\boxed{}
136
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add: 13 + -9 + -40 = submit
$-36$
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add: -31 + 12 + 50 + -29 =
2
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add: -2 + 5 + -82 + 39 + -67 = \\boxed{}
$-107$
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add: -16 + -12 + -10 = \\square
-38
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y = -4x y = 3x + 28
The solution is \( x = -4 \), \( y = 16 \)
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y = -x\ y = -5x + 40
The solution is \( x = 10 \), \( y = -10 \)
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y = -5x - 40 y = 5x
The solution to the system is \( x = -4 \), \( y = -20 \) (or the ordered pair \((-4, -20)\))
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a line has a slope of -2 and passes through the point (-3, 6). write it…
$y=-2x + 2$
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1. if $g(x) = -2x^2 + 16$, then $g(-3)$ equals (1) $-20$ \t\t\t(3) $34$…
(2) \(-2\) ### Question 2
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write \\(\frac{7}{100}\\) as a decimal.
0.07
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divide. 45.7÷100
0.457
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divide. 4.56 ÷ 10
0.456
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divide. 39.9 ÷ 1000
0.0399
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a ball is launched from a sling shot. its height, h(x), can be represen…
$h(x) = -10x^2 + 120x$
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find the slope of the line passing through the points (-3, 3) and (5, 9…
$\frac{3}{4}$
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4. $y = -3x + 1$ $y = x - 7$ (2,-1)
The solution is $(2, -5)$
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¿cuál es el valor de? $\\log_{6} \\frac{1}{36}$? options: 2, -6, -2, 6
# Explicación: ## Paso 1: Escribir el logaritmo como ecuación Sea $x = \log_{6} \frac{1}{36}$. Por definición de logaritmo, esto se convierte en: $$6^x = \frac{1}{36}$$ ## Paso 2:…
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¿cuál es el valor de? $\\log_{7} 343$?\ \ $\\frac{1}{3}$\ \ $3$\ \ $-\\…
3
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1.92)1.152
0.6
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8. jennifer had $3\\frac{3}{4}$ lbs of tomatoes. she used $\\frac{1}{3}…
\( 1\frac{1}{4} \) (or \( \frac{5}{4} \)) pounds
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m(x) = 3(2)^x + 4, g(x) = 2(3)^x + 4, h(x) = 3(3)^x + 2, k(x) = 4(3)^x …
Top-left graph: $\boldsymbol{m(x)=3(2)^x + 4}$ Top-right graph: $\boldsymbol{g(x)=2(3)^x + 4}$ Bottom-left graph: $\boldsymbol{h(x)=3(3)^x + 2}$ Bottom-right graph: $\boldsymbol{k…
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6. simplify if necessary. $4\\frac{1}{2} \\times 1\\frac{3}{5}$ type a …
\(7\frac{1}{5}\) (or \(\frac{36}{5}\) or \(7.2\))
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5. simplify if necessary. 1\\frac{3}{4} \\times 2\\frac{1}{5} type a re…
\(3\frac{17}{20}\)
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4. simplify if necessary. $1\\frac{1}{3} \\times 2\\frac{3}{4}$ type a …
\(3\frac{2}{3}\) (or \(\frac{11}{3}\))
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what is the amplitude of this function $f(x)$? $f(x) = 3cos(2x) + 5$ en…
3
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complete the table for the function $y = 5^x$. | $x$ | $y$ | | --- | --…
### Completed Table: | $x$ | $y$ | |-----|-----| | -1 | $\frac{1}{5}$ or $0.2$ | | 0 | $1$ | | 1 | $5$ | | 2 | $25$ | ### Graph Points: Plot the points $(0, 1)$ and $(1, 5)$ on th…
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1. simplify if necessary. \\frac{2}{3} \\times 1\\frac{3}{4} type a res…
\(\frac{7}{6}\) (or \(1\frac{1}{6}\))
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what is the minimum value for the function shown in the graph? enter yo…
-5.5
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a line that includes the point (6, 7) has a slope of 2. what is its equ…
\(y - 7 = 2(x - 6)\)
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does the text contain a vague pronoun reference? at lunchtime, ron can …
no
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problem: will the ball clear the crossbar of the goal post, which is 10…
When $x=40$, the ball's height is 0 feet. The ball will NOT clear the 10-foot crossbar.