微積分
極限、導數、最優化與函數性質。
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for the function $f(x) = 4x^2 - 4x + 6$, evaluate and fully simplify ea…
\( f(x + h)=4x^{2}+8xh + 4h^{2}-4x-4h + 6 \) \( \frac{f(x + h)-f(x)}{h}=8x + 4h-4 \)
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homework assignment 1.1: functions and function notation score: 10.75/1…
\( f(a) = \boldsymbol{5a + 7} \) \( f(a + h) = \boldsymbol{5a + 5h + 7} \) \( \frac{f(a + h) - f(a)}{h} = \boldsymbol{5} \)
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match each graph with its equation. $y = x^3$ $y = \\sqrt3{x}$ $y = \\f…
- \(y=\frac{1}{x^{2}}\) - Graph a - \(y=\sqrt[3]{x}\) - Graph b - \(y = |x|\) - Graph c - \(y=x^{2}\) - Graph d - \(y=x^{3}\): (would match a graph with a steeper odd - function c…
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homework assignment 1.1: functions and function notation score: 8/15 an…
- \( y = x \): f. Linear - \( y = x^2 \): h. Quadratic - \( y=\sqrt[3]{x} \): a. Cube root - \( y = \sqrt{x} \): d. Square Root - \( y = x^3 \): g. Cubic - \( y=\frac{1}{x^2} \): …
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homework assignment 1.1: functions and function notation score: 8/15 an…
- \( y = x \): f. Linear - \( y = x^2 \): h. Quadratic - \( y=\sqrt[3]{x} \): a. Cube root - \( y = \sqrt{x} \): d. Square Root - \( y = x^3 \): g. Cubic - \( y=\frac{1}{x^2} \): …
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what are the domain and range of this function? graph of a coordinate p…
B. domain: \(\{-4, - 3, 0, 1, 4, 5\}\) range: \(\{-5, - 3, - 2, 1, 2, 3\}\)
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homework assignment 1.1: functions and function notation score: 6/15 an…
\( f(-2) = 35 \) \( f(-1) = 15 \) \( f(0) = 3 \) \( f(1) = -1 \) \( f(2) = 3 \)
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what is the domain of this function? graph of a coordinate plane with p…
\(\{-4, - 1,1,2,3\}\)
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what is the range of this function? the image shows a coordinate grid w…
\(\{-5, -4, 0, 1, 5\}\) (the second option, which is \(\{-5, -4, 0, 1, 5\}\))
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which statement primarily appeals to pathos to support the position tha…
The first statement: "Like most suburbanites, I live in a house with its own yard and fences between my neighbors' properties and mine, which effectively discourages the use of sh…
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13 18 ÷ (5 + 4) · 5² - 7² color this answer yellow. 18 8² ÷ 4² - 36 ÷ 9…
Question 13: $1$ Question 18: $0$
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what is the domain of this function? the graph is a coordinate plane wi…
\(\{-5, - 2, - 1, 2, 3, 5\}\) (the third option)
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4) 3 - 8·(-2) - {3 + 8}
107
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color this answer purple. 11 $9^2 - (6^2 \\cdot 2) - 1$ color this answ…
Purple answer: $8$ Dark blue answer: $5$
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11 81 = 9² - (6² · 2) - 1 color this answer dark blue 16 7 · 6 ÷ 2 - 4²
5 --- For the first (partially visible) problem $81=9^2-(6^2 \cdot 2)-1$ (to verify equality):
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evaluate the following expression: $5 \\cdot 3 + 24 \\div 6$
19
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11 $9^2 - (6^2 + 2) - 1$ color this answer dark blue. 16 $7 \\cdot 6 \\…
First expression result: $42$ Second expression result: $5$
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color this answer green. 10 13 + 18 - (4 • 6) color this answer orange.…
Green answer: $7$ Orange answer: $2$
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what was the main goal of gatt? multiple choice ○ limit foreign competi…
increase domestic competition
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(9 + 3) + 8 + 29 12 * (4 + 1) - 100 + 2
Problem 6: $16$ Problem 7: $10$
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(9 + 3) + 6 * 2^0
98
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Question was provided via image upload.
Five points to plot: 1. Vertex: $(-5, 1)$ 2. Left point 1: $(-6, 2)$ 3. Left point 2: $(-7, 5)$ 4. Right point 1: $(-4, 2)$ 5. Right point 2: $(-3, 5)$ (Plot these points on the g…
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graph the parabola: $y = (x - 1)^2 - 5$ plot five points on the parabol…
Points to plot: 1. Vertex: $(1, -5)$ 2. Left of vertex: $(-1, -1)$, $(0, -4)$ 3. Right of vertex: $(2, -4)$, $(3, -1)$ Connect these points to graph the parabola.
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graph the parabola. \\( y=(x-2)^{2}+1 \\) plot five points on the parab…
Five points to plot: 1. Vertex: $(2, 1)$ 2. Left point 1: $(0, 5)$ 3. Left point 2: $(1, 2)$ 4. Right point 1: $(3, 2)$ 5. Right point 2: $(4, 5)$ Connect these points to graph th…
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(\frac{21}{168})
\(\frac{1}{8}\)
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calculate \\(\\frac{2,4}{2,9 - 1,4}\\)
\( 1.5 \)
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0,6·(-10)³ + 50
\(-550\)
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in the following graph, which represents the following exponential equa…
Assuming the correct option is the one that matches the described graph (passes through (0, - 1), decreasing for \( x>0 \), approaching 0 from below as \( x\to-\infty \)), if we c…
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in the following graph, which represents the following exponential equa…
Assuming the correct option is the one that matches the described graph (passes through (0, - 1), decreasing for \( x>0 \), approaching 0 from below as \( x\to-\infty \)), if we c…
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2 select the correct answer dan uses a remote control to make his drone…
C. The drone is on the ground at 0 and 4 seconds.
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select the correct answer. if ( g(x) = f(4x) ), which statement is true…
C. The graph of function \( f \) is compressed horizontally by a scale factor of \( \frac{1}{4} \) to create the graph of function \( g \)
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select the correct answer consider the graph of function g graph of a p…
B. \( g(x) = 3f(x) \)
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4. determine the interval(s) on which the function is decreasing enter …
$(0, 5)$
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the graph of f(x) and a line tangent to the curve at x = 4 are shown. i…
# Explanation: ## Step1: Find \( f(4) \) and \( f'(4) \) From the graph, the tangent line at \( x = 4 \) passes through \( (0, 5) \) and \( (7, 0) \). The slope of the tangent lin…
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concentric zone model and bid - rent curve cost apartment buildings sub…
E. The model does not show the cost - to - distance effects of multiple suburban central business districts and the pattern of residential areas that surround them.
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write an equation for the function graphed below (graph of a function w…
$y=\frac{-x^2}{(x+4)(x-3)}$ or expanded $y=\frac{-x^2}{x^2+x-12}$
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final exam (calculus 1) score: 30/31 answered: 31/31 question 13 score …
\( f^\prime(x)=-\frac{9}{2\sqrt{x}}-\frac{60}{x^{11}} \)
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value: 3 identify if the graph is even, odd, or neither. graph with x-a…
Even
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identify if the graph is even, odd, or neither.
Neither
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x | y 0 | -3 1 | -6 4 | -12 9 | -18 16 | -27 x | y 0 | 1 1 | -2 4 | -5 …
The table with the following (x,y) pairs: (-1, 0), (0, -3), (3, -6), (8, -9), (15, -12) (the bottom-left table)
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13 our congress is the voice of the people in our government. the indiv…
A. The Great Compromise ### Question 2
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13. explain how finances can be a barrier to keeping physically fit.
Finances act as a barrier to physical fitness in these key ways: 1. High costs for gym memberships, classes, equipment, and personal training exclude those with limited income fro…
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find the sum. 3.5 + (-4.5) = \\square
\(-1\)
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what is the slope of the line through $(-7, -2)$ and $(-6, 7)$? choose …
C. 9
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approximate the following number using a calculator. $6^{-1.3}$ $6^{-1.…
$6^{-1.3} \approx 0.095$
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approximate the number using a calculator. $4^{2.6}$ $4^{2.6} \\approx …
$24.981$
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approximate the number using a calculator. $4^{2.6}$ $4^{2.6} \\approx …
$24.981$
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if a ball is thrown into the air at 96 feet per second from the top of …
a. B. (The graph starting at 105 ft, peaking, then falling to near 0 at t=8) b. - Height at 2 seconds: 233 ft; Height at 4 seconds: 233 ft - Correct explanation: B. These two valu…
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graph the function with a graphing calculator using a standard viewing …
D. <The graph with a maximum at the y-axis, approaching the x-axis on both ends> The graph has a turning point (a maximum) in the standard viewing window at $(0, 3)$.
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graph the function with a graphing calculator using a standard viewing …
D. <The graph with a maximum at the y-axis, approaching the x-axis on both ends> The graph has a turning point (a maximum) in the standard viewing window at $(0, 3)$.
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complete the table of values for the following function and then plot t…
| $x$ | $f(x)=4x-2$ | |-----|--------------| | $-2$ | $-10$ | | $-1$ | $-6$ | | $0$ | $-2$ | | $1$ | $2$ | | $2$ | $6$ |
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for a function that is strictly decreasing, a right hand riemann sum is…
Overestimate
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what does picture represent? left riemann sum right riemann sum middle …
Left Riemann Sum
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score: 11/12 answered: 11/12 question 12 0/1 pt let ( a(x) ) represent …
\( A(1)=\frac{3}{2} \) (or \( 1.5 \)), \( A(2)=3 \), \( A(3)=\frac{9}{2} \) (or \( 4.5 \)), \( A(4)=6 \)
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what does picture represent? left riemann sum right riemann sum middle …
Left Riemann Sum
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what does this picture represent? left riemann sum right riemann sum mi…
1. Left Riemann Sum
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what is the slope of the line with the equation $y = -\frac{3}{2}x + 4$…
B. $-\frac{3}{2}$
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(18, -19) (1, -19) what is the slope of the line that passes through th…
zero
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identify the graph of the given function: $y = \\frac{3x}{5} - 3$
C. The graph with positive shallow slope, crossing y-axis at (0, -3) and x-axis at (5, 0)
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fill in each blank so that the resulting statement is true. the graph o…
The graph of \(y = f(6x)\) is obtained by a horizontal shrink of the graph of \(y = f(x)\) by dividing each of its x-coordinates by 6.
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the graph of $y = f(6x)$ is obtained by a ______ shrink of the graph of…
First blank: horizontal Second blank: horizontal
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complete the sentence below suppose that the graph of a function f is k…
horizontal; to the right
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inés makes a wooden tongue drum with her brother. the top of the drum i…
The thickness of the thicker tongue is $\frac{7}{8}$ inch and the thickness of the thinner tongue is $\frac{5}{8}$ inch.
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5) what is $7^2 + 5^2$?
74
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5) what is $7^2 + 5^2$?
74
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which has the greatest value?\ \\(\\sqrt{22}\\) \\(2\\pi\\) 6.1 \\(\\fr…
$2\pi$
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graph the equation by plotting points. $y = -3x^3$ to graph the equatio…
Plot the points $(-2, 24)$, $(-1, 3)$, $(0, 0)$, $(1, -3)$, $(2, -24)$ on the coordinate grid, then draw a smooth curve through them to graph $y=-3x^3$.
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graph the equation by plotting points. y = |x| part: 0 / 3 part 1 of 3 …
When $x=-3$, $y=3$, ordered pair $(-3, 3)$ When $x=2$, $y=2$, ordered pair $(2, 2)$
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graph the equation by plotting points. $y = 3\\sqrt{x}$ plot four point…
The four points are: 1. Leftmost point: $(0, 0)$ 2. $(1, 3)$ 3. $(4, 6)$ 4. $(9, 9)$ To graph, plot these points on the coordinate grid and draw a smooth curve through them starti…
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use a graphing utility to graph the equation below then use the trace f…
Correct graph: C. Two points: $(-1, -4.125)$ and $(3, -3.625)$ Slope verification: The calculated slope $\frac{1}{8}$ matches the coefficient of $x$ in the equation.
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select the correct answer. which statement is true about this radical f…
B. The function is strictly decreasing.
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use a graphing utility to graph the equation below. then use the trace …
(Select the graph with a shallow positive-sloped line crossing the y-axis at $y=-4$; based on the parameters, this corresponds to the option that visually matches the line $y=\fra…
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select the correct answer from each drop - down menu. when the expressi…
When the expression representing the parent radical function is multiplied by -1, the resulting graph is a **reflection** of the parent function. When the expression representing …
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10. what is is the equation of the function shown by the green dashed l…
The equation of the green dashed line is $\boldsymbol{y = \frac{-3x}{x-6}}$ (with a removable discontinuity at $x=1$, written fully as $y = \frac{-3x(x-1)}{(x-1)(x-6)}$ for $x e…
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question # 9 multiple select why, do you suppose, an architect must hav…
B. The licensing provisions for architects typically require a minimum of a bachelor's degree in design and related coursework to assure all graduates have approximately equal tra…
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question 21 of 26 step 1 of 2 consider the equation and the following o…
For \( x = 6 \), \( y = 7 \); for \( y = 1 \), \( x = 3 \). So the completed table is: | \( x \) | \( y \) | | --- | --- | | 6 | 7 | | 3 | 1 |
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for the function $f(x) = 4x^2 + 5x$, evaluate and simplify.\ $\\frac{f(…
\( 8x + 4h + 5 \)
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homework assignment 1.1: functions and function notat score: 13.75/15 a…
\( 12x^2 + 12xh + 4h^2 + 5 \)
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homework assignment 1.1: functions and function notation score: 12.75/1…
s: \( f(x + h)=\boldsymbol{2x + 2h + 4} \) \( \frac{f(x + h)-f(x)}{h}=\boldsymbol{2} \)
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for the function $f(x) = 4x^2 - 4x + 6$, evaluate and fully simplify ea…
\( f(x + h)=4x^{2}+8xh + 4h^{2}-4x-4h + 6 \) \( \frac{f(x + h)-f(x)}{h}=8x + 4h-4 \)
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homework assignment 1.1: functions and function notation score: 10.75/1…
\( f(a) = \boldsymbol{5a + 7} \) \( f(a + h) = \boldsymbol{5a + 5h + 7} \) \( \frac{f(a + h) - f(a)}{h} = \boldsymbol{5} \)
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match each graph with its equation. $y = x^3$ $y = \\sqrt3{x}$ $y = \\f…
- \(y=\frac{1}{x^{2}}\) - Graph a - \(y=\sqrt[3]{x}\) - Graph b - \(y = |x|\) - Graph c - \(y=x^{2}\) - Graph d - \(y=x^{3}\): (would match a graph with a steeper odd - function c…
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homework assignment 1.1: functions and function notation score: 7/15 an…
### Part A: Compute \( f(-1) + f(5) \) #### Step 1: Calculate \( f(-1) \) Substitute \( x = -1 \) into \( f(x) = -2x^2 - 7x + 7 \): \[ \begin{align*} f(-1) &= -2(-1)^2 - 7(-1) + 7…
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what are the domain and range of this function? graph of a coordinate p…
B. domain: \(\{-4, - 3, 0, 1, 4, 5\}\) range: \(\{-5, - 3, - 2, 1, 2, 3\}\)
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homework assignment 1.1: functions and function notation score: 6/15 an…
\( f(-2) = 35 \) \( f(-1) = 15 \) \( f(0) = 3 \) \( f(1) = -1 \) \( f(2) = 3 \)
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what is the domain of this function? graph of a coordinate plane with p…
\(\{-4, - 1,1,2,3\}\)
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what is the range of this function? the image shows a coordinate grid w…
\(\{-5, -4, 0, 1, 5\}\) (the second option, which is \(\{-5, -4, 0, 1, 5\}\))
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which statement primarily appeals to pathos to support the position tha…
The first statement: "Like most suburbanites, I live in a house with its own yard and fences between my neighbors' properties and mine, which effectively discourages the use of sh…
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13 18 ÷ (5 + 4) · 5² - 7² color this answer yellow. 18 8² ÷ 4² - 36 ÷ 9…
Question 13: $1$ Question 18: $0$
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what is the domain of this function? the graph is a coordinate plane wi…
\(\{-5, - 2, - 1, 2, 3, 5\}\) (the third option)
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4) 3 - 8·(-2) - {3 + 8}
107
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what is an equation of the line that passes through the points (0, 7) a…
$y=-\frac{2}{5}x+7$
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color this answer purple. 11 $9^2 - (6^2 \\cdot 2) - 1$ color this answ…
Purple answer: $8$ Dark blue answer: $5$
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11 81 = 9² - (6² · 2) - 1 color this answer dark blue 16 7 · 6 ÷ 2 - 4²
5 --- For the first (partially visible) problem $81=9^2-(6^2 \cdot 2)-1$ (to verify equality):
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11 $9^2 - (6^2 + 2) - 1$ color this answer dark blue. 16 $7 \\cdot 6 \\…
First expression result: $42$ Second expression result: $5$
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color this answer green. 10 13 + 18 - (4 • 6) color this answer orange.…
Green answer: $7$ Orange answer: $2$
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what was the main goal of gatt? multiple choice ○ limit foreign competi…
increase domestic competition
-
(9 + 3) + 8 + 29 12 * (4 + 1) - 100 + 2
Problem 6: $16$ Problem 7: $10$
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(9 + 3) + 6 * 2^0
98
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Question was provided via image upload.
Five points to plot: 1. Vertex: $(-5, 1)$ 2. Left point 1: $(-6, 2)$ 3. Left point 2: $(-7, 5)$ 4. Right point 1: $(-4, 2)$ 5. Right point 2: $(-3, 5)$ (Plot these points on the g…