Coordinates

Problem 201

Use slopes to determine if the lines are parallel, perpendicular, or neither.
27. EFundefined\overleftrightarrow{E F} and GHundefined\overleftrightarrow{G H} for E(8,2),F(3,4),G(6,1)E(8,2), F(-3,4), G(6,1), and H(4,3)H(-4,3)

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Problem 202

Use slopes to determine if the lines are parallel, perpendicular, or neither.
28. JKundefined\overleftrightarrow{J K} and LMundefined\overleftrightarrow{L M} for J(4,3),K(4,2),L(5,6)J(4,3), K(-4,-2), L(5,6), and

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Problem 203

What is the slope of the line in the graph? 43-\frac{4}{3} 34-\frac{3}{4} Mark this and return Save and Exit Next

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Problem 204

Q6 (6 points) Find the general equation of the plane containing the origin and points P(1,2,3)P(1,2,3) and Q(1,1,1)Q(1,-1,1).

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Problem 205

4cr=(0,2)(0,2)c2=164c2=±12c=±234 \left\lvert\, \begin{array}{l} c-r=(0,2)(0,-2) \\ c^{2}=16-4 \\ c^{2}= \pm \sqrt{12} \\ c= \pm 2 \sqrt{3} \end{array}\right. 3) (x1)29+(y+5)24=1\frac{(x-1)^{2}}{9}+\frac{(y+5)^{2}}{4}=1 c=(1,5)c=(1,-5) 5) x2+9y2+6x90y+225=0x^{2}+9 y^{2}+6 x-90 y+225=0

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Problem 206

The equations of three lines are given below.
Line 1: y=2x+7y=-2 x+7 Line 2: y=2x5y=-2 x-5 Line 3:6x+3y=63: 6 x+3 y=6
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2 : Parallel Perpendicular Neither Line 1 and Line 3 : Parallel Perpendicular Neither Line 2 and Line 3 : Parallel Perpendicular Neither

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Problem 207

Directions: Answer the questions re 1) 2)
How many real roots? \qquad What are they? \qquad

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Problem 208

6. What are the equation and slope of the line shown on the grid? A. y=8y=8; slope is zero B. y=8y=8; slope is undefined C. x=8x=8; slope is zero D. x=8x=8; slope is undefined

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Problem 209

8. What is the equation of the line shown on the grid? A. y=xy=x B. y=4.5y=-4.5 C. x=6x=-6 D. x=4.5x=-4.5

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Problem 210

Plot the points (0,5)(0,-5) and (2,4)(2,4) on the coordinate plane.

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Problem 211

Find an equation of the hyperbola having foci at (2,152)(2,-1-\sqrt{52}) and (2,1+52)(2,-1+\sqrt{52}) and asymptotes at y=23x73y=\frac{2}{3} x-\frac{7}{3} and y=23x+13y=-\frac{2}{3} x+\frac{1}{3}.

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Problem 212

Find an equation of the hyperbola having foci at (3,145)(3,-1-\sqrt{45}) and (3,1+45)(3,-1+\sqrt{45}) and asymptotes at y=2x7y=2 x-7 and y=2x+5y=-2 x+5.

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Problem 213

Consideremos la recta y=4x9y=4 x-9 Hallar la ecuación de la recta que es paralela a esta recta y atraviesa el punto (2,4)(-2,-4). Hallar la ecuación de la recta que es perpendicular a esta recta y atraviesa el punto (2,4)(-2,-4). Observe que la calculadora gráfica de ALEKS será útil para verificar la respuesta.
Ecuación de recta paralela:
Ecuación de recta perpendicular: \square

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Problem 214

A certain shade of orange paint is made by mixing red and yellow paint. The relationship between number of quarts of red paint in the mix, xx, and the number of quarts of yellow paint, yy, is represented by the graph below.
What does the ordered pair (9,13.5)(9,13.5) indicate?

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Problem 215

3. Consider the graph of f(x)f(x) as shown: a. Find f(1)f(1) and f(4)f(4) b. Find all values of xx such that f(x)=2f(x)=2 c. Find all intercepts and state them in function notation.

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Problem 216

48 The graph of a line passes through the points (3,1)(-3,1) and (5,8)(5,8).
What is the slope of the line? F 92\frac{9}{2} G 78\frac{7}{8} H 92-\frac{9}{2} J 78-\frac{7}{8}

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Problem 217

Find the coordinates of the midpoint of a segment with the endpoints (4,7)(-4,-7) and (12,6)(12,-6). (( \square , \square

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Problem 218

Question 17
Find the coordinates of the missing endpoint if BB is the midpoint of AC\overline{A C}. A(1,7),B(3,1)A(1,7), B(-3,1)
Cl \square \square

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Problem 219

Consider the following.
Use the Vertical Line Test to determine whether the curve is the graph of a function of xx. Yes, the curve is a function of xx. No, the curve is not a function of xx.
If the curve is a function, state the domain and range. (Enter your answers using interval notation. If the curve is not a function enter NONE.) domain \square range \square

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Problem 220

A system of linear equations is graphed on the xyx y-plane below.
Which system of linear equations best represents this raph?

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Problem 221

correction de Capplication 2! Srit deur nobiles Met PP d'équat ion formire respective O\{ {y=3t2x=t+1;\left\{\begin{array}{l}y=3 t-2 \\ x=t+1\end{array} ;\right. Etablir P{y=5t2+inhx=2tP\left\{\begin{array}{l}y=-5 t^{2}+i n h \\ x=2 t\end{array}\right. 1) Etablir lesequations cartésienses de chaque mobiles. 2) Quelle est la nature dela trajectoire pourchaque mobile.

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Problem 222

Find the slope of the line. Write your answer in simplest form.
The slope is \square

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Problem 223

Score: 0/1 Penalty: none
Question Watch Video Show Examples
What is an equation of the line that passes through the point (1,6)(-1,-6) and is perpendicular to the line x+4y=12x+4 y=12 ?
Answer Attempt 1 out of 4 \square Submit Answer

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Problem 224

You travel 70 miles/hour for 3 hours, then 30 miles/hour for 12\frac{1}{2} hour, then 40 miles/hour for 2 hours. (a) What is the total distance you traveled? Total distance (( in miles )=)= (b) Drag the points on the grid to graph of the velocity as a function of time for this trip. \square 당 (c) On the graph, the total distance traveled is represented by the

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Problem 225

Question 1
Graph the following system of equations and find the solution. Graph each line and plot the solution as a point on the graph. Enter the solution in the answer box as an ordered pair. 2x+3y=123xy=11\begin{array}{l} 2 x+3 y=-12 \\ -3 x-y=11 \end{array} Clear All Draw: Solution == (3,2)(-3,-2)

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Problem 226

Find v\|\mathbf{v}\|. v=3i4j\mathbf{v}=3 \mathbf{i}-4 \mathbf{j} | v=\mathbf{v} \|= \square (Type an exact answer, using radicals as needed. Simplify your answer.)

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Problem 227

5. Sketch the graph of y=2x+5y=-2 x+5 on a Cartesian plane for x=4x=-4 to x=+10x=+10. Label the xx-and yy-intercepts and the end points. 422(2)2+2 - 4×8(2)\begin{array}{l} 42-2(2)^{2}+2 \\ \text { - } 4 \times 8 \\ (2) \end{array} 1) ==

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Problem 228

Graph units are in meters.
What is the distance to the hole for the player who is farthest from the hole? Round the final answer to the nearest tenth of a meter. Do not round intermediate calculations.

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Problem 229

B. The slope is undefined. 4
Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points. (6,9)(-6,-9) and (5,3)(5,3) \qquad \qquad x2y2x 2 y 2

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Problem 230

On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system. y14x+3yx+5\begin{array}{l} y \leq \frac{1}{4} x+3 \\ y \geq-x+5 \end{array} A. Region B B. Region A C. Region C D. Region D

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Problem 231

4. Check whether the points a,b\mathbf{a}, \mathbf{b} and c\mathbf{c} belong to the same straight line in R3\mathbb{R}^{3}; if so, find a parametric equation of this line, if not, find a parametric 1 equation of the plane passing through these points. (a) a=[124]\mathbf{a}=\left[\begin{array}{c}-1 \\ 2 \\ 4\end{array}\right], b=[000] and c=[51020];(b)a=[412],b=[4102] and c=[002];(c)a=[422],b=[4102] and c=[042];(d)a=[304],b=[512] and c=[113].\begin{array}{l} \mathbf{b}=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right] \text { and } \mathbf{c}=\left[\begin{array}{c} 5 \\ -10 \\ -20 \end{array}\right] ;(b) \mathbf{a}=\left[\begin{array}{c} 4 \\ -1 \\ 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{c} -4 \\ 10 \\ 2 \end{array}\right] \text { and } \mathbf{c}= \\ {\left[\begin{array}{l} 0 \\ 0 \\ 2 \end{array}\right] ;(\mathrm{c}) \mathbf{a}=\left[\begin{array}{c} 4 \\ -2 \\ 2 \end{array}\right], \mathbf{b}=\left[\begin{array}{c} -4 \\ 10 \\ 2 \end{array}\right] \text { and } \mathbf{c}=\left[\begin{array}{l} 0 \\ 4 \\ 2 \end{array}\right] ;(\mathrm{d}) \mathbf{a}=\left[\begin{array}{c} -3 \\ 0 \\ 4 \end{array}\right],} \\ \mathbf{b}=\left[\begin{array}{c} 5 \\ -1 \\ 2 \end{array}\right] \text { and } \mathbf{c}=\left[\begin{array}{l} 1 \\ 1 \\ 3 \end{array}\right] . \end{array}

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Problem 232

Look at this graph:
What is the yy-intercept? \square Submit

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Problem 233

e point QQ lies on the segment PR\overline{P R}. Find the coordinates of QQ so that PQP Q is 27\frac{2}{7} of PRP R.
Coordinates of QQ : \square , \square

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Problem 234

Look at this graph:
What is the equation of the axis of symmetry? \square Submit

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Problem 235

Find the equation of the line with the given properties. Sketch the graph of the line. The line passes through (8,3)(-8,3) and is perpendicular to the yy-axis.

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Problem 236

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Click twice to plot each segment. Click a segment to delete it.

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Problem 237

What is the slope of the line?

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Problem 238

If there is more than one answer, separate them with comn Click on "None" if applicable. (a) yy-intercept(s): \square ㅁ.... None (b) xx-intercept(s): \square

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Problem 239

Zeichnen Sie die Punkte und den Vektor PQundefined\overrightarrow{P Q} in ein Koordinatensystem. Berechnen Sie die Koordinaten des Vektors PQundefined\overrightarrow{\mathrm{PQ}} und vergleichen Sie mit der Skizze. a) P(00),Q(52)P(0 \mid 0), Q(5 \mid-2) b) P(23),Q(74)P(2 \mid 3), Q(7 \mid 4) c) P(431),Q(042)P(-4|-3|-1), Q(0|4|-2) d) P(142),Q(234)P(-1|4|-2), Q(2|-3|-4) e) P(465),Q(000)P(4|6| 5), Q(0|0| 0) f) P(731),Q(731)P(7|3| 1), Q(7|3| 1)

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Problem 240

Basisaufgaben
1. Zeichnen Sie zum Vektor drei Vektorpfeile in ein Koordinatensystem. Geben Sie jeweils die Anfangs- und Endpunkte der Pfeile an. a) (12)\binom{1}{2} b) (01)\binom{0}{-1} c) (20)\binom{2}{0} d) (13)\binom{-1}{-3} e) (100)\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right) f) (101)\left(\begin{array}{r}1 \\ 0 \\ -1\end{array}\right) g) (132)\left(\begin{array}{r}1 \\ 3 \\ -2\end{array}\right) h) (213)\left(\begin{array}{r}-2 \\ -1 \\ 3\end{array}\right)

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Problem 241

m=y1y2x1x2=161042=62=3m=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}=\frac{16-10}{4-2}=\frac{6}{2}=3

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Problem 242

5. A line passes through points (3,1)(-3,-1) and (0,5)(0,5). A second line passes through points (1,2)(1,-2) and (4,3)(-4,3). At what point do the two lines intersect?
A (1,0)(-1,0) B. (2,1)(-2,1) C. (1,3)(-1,3) D. (0,1)(0,-1)

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Problem 243

A line passes through the points (1,4)(1,4) and (5,8)(5,8). A second line passes through the points (2,10)(2,10) and (6,4)(6,4). At what point do the two lines intersect?
A (2,10)(2,10) B. (3,6)(3,6) c. (4,7)(4,7) D. (5,8)(5,8)

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Problem 244

\begin{align*} \text{Graph the following information:} \\ \text{1. Andrew started at home for the first 15 minutes.} \\ \text{2. He traveled at a constant speed and traveled a total of 4 miles for the next 10 minutes.} \\ \text{3. Andrew rested and then rode his bike home, which took 20 minutes.} \end{align*}

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Problem 245

Round intermediate calculations and final answer to four decimal places. Find the point on the parabola y=16x2y=16-x^{2} closest to the point (9,17)(9,17). Closest point is \square , \square ) with the distance of \square .

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Problem 246

Use the intercepts to graph the equation. 5x3y=155 x-3 y=15

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Problem 247

Lamar and his friends set out to sea on their annual fishing trip. They are 30 miles from shore after sailing for 3 hours. They are 40 miles from shore after sailing for 4 hours. [F3{ }_{[ } \mathrm{F}_{3} In this relationship, xx represents the time (in hours) Lamar and his friends spend sailing, and yy represents their distance from shore (in miles). rL\mathrm{r}_{\mathrm{L}}, Graph two points for this relationship and the line passing through them.

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Problem 248

Graph the following function by moving the green and blue dots (if necessary). y=13xy=\frac{1}{3} \sqrt{x}

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Problem 249

ugh the given point and has
2. (3,5);m=1(3,5) ; m=-1 (4.) (8,2);m=5(-8,-2) ; m=5
6. (0,12);m=34\left(0,-\frac{1}{2}\right) ; m=\frac{3}{4}
8. (6,8.2);m=1.5(-6,8.2) ; m=1.5

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Problem 250

Graph the following function by moving the green and blue dots (if necessary). y=14x22y=\frac{1}{4} x^{2}-2 Start Over

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Problem 251

4. a. Pintá la gráfica siguiendo las consignas. \checkmark De azul la parte creciente. \checkmark De rojo la constante. \checkmark De verde la decreciente.
Completá los puntos del gráfico. b. (4; \square d. (6(-6; \square e. (6(6; \square f. (3;(3 ; \square c. (0(0; \square g. (7(-7; \square
Colocá CR (creciente), DE (decreciente) o CO (constante) según corresponda. h. 1<x<0-1<x<0 \square j. 3<x<2-3<x<-2 \square L. 2<x<32<x<3 \square n. 5<x<65<x<6 \square i. 6<x<76<x<7 \square k. 0<x<10<x<1 \square m. 7<x<87<x<8 \square o. 6<x<5-6<x<-5 \square Escribí los intervalos donde la gráfica es p. creciente: q. decreciente: r. constante:

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Problem 252

Learn with an example or Watch a video
Graph this line: y6=2(x+4)y-6=2(x+4)
Click to select points on the graph. Submit

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Problem 253

8
Determine the slope of the line above.

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Problem 254

ixl.com
Graph this line: y1=13(x+7)y-1=-\frac{1}{3}(x+7)
Click to select points on the graph. Submit

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Problem 255

Graph this line: y5=(x+3)y-5=-(x+3)
Click to select points on the graph.

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Problem 256

Graph this line: y2=15(x+2)y-2=-\frac{1}{5}(x+2)
Click to select points on the graph. Submit Practice in the app

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Problem 257

The coordinates of the endpoints of CD\overline{C D} are C(7,9)C(-7,9) and D(8,6)D(8,-6). Point EE is on CD\overline{C D} and divides it such that CE:DEC E: D E is 2:32: 3.
What are the coordinates of EE ? Write your answers as integers or decimals. \square , \square Submit

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Problem 258

Buscar 5:52 p.m. Dom nov 17 ixl.com
Graph this line: y+2=3(x6)y+2=3(x-6)
Click to select points on the graph. Submit Work it out Practice in the app

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Problem 259

The coordinates of the endpoints of ST\overline{S T} are S(10,2)S(10,2) and T(17,16)T(17,16). Point UU is on ST\overline{S T} and divides it such that SU:TUS U: T U is 2:52: 5.
What are the coordinates of UU ? Write your answers as integers or decimals. \square \square Submit

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Problem 260

Illustrative Mathernat
8. To grow properly, each tomato plant needs 1.5 square feet of soil and each broccoli plant needs 2.25 square feet of soil. The graph shows the different combinations of broccoli and tomato plants in an 18 square foot plot of soil.

Match each point to the statement that describes it. A. Point A
1. The soil is fully used when 6 tomato B. Point B plants and 4 broccoli plants are planted. C. Point C D. Point D
2. Only broccoli was planted, but the plot is fully used and all plants can grow properly.
3. After 3 tomato plants and 2 broccoli plants were planted, there is still extra space in the plot.
4. With 4 tomato plants and 6 broccoli plants planted, the plot is overcrowded.

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Problem 261

9. The points (2.1,4.2)(2.1,-4.2) and (2.5.5)(2.5 .-5) form a proportional relationship. What is the slope of the line that passes through these two points?

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Problem 262

1. The graph shows the distance that an athlete runs. Find the slope of the line. (Example 1)
Running Distance

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Problem 263

What is the perimeter, in units, of polygon EFGHJK?

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Problem 264

Identify the vertex of the parabola: \square Remember that the vertex is a point! Identify the yy-intercept of the parabola: \square Remember that the yy-intercept is a point! Identify the xx-intercepts: \square and \square Remember tllat the xx-intercepts represent points on the graph! Given the xx-intercepts above, write an equation for the parabola in factored for y=y= \square Hint: Think about the zero-product property. Write an equation for the axis of symmetry: \square

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Problem 265

Solve the following system of equations graphically on the set of axes below. y=32x6y=x1\begin{array}{c} y=-\frac{3}{2} x-6 \\ y=x-1 \end{array}
Plot two lines by clicking the graph. Click a line to delete it.

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Problem 266

12. Identify the graph of the system of linear inequalities. y<1x>4\begin{array}{l} y<-1 \\ x>4 \end{array}
No solution
Identify a solution. (4,6)(4,-6) (6,4)(6,4) (4,6)(4,6) No solution (6,4)(6,-4) (4,4)(-4,-4)

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Problem 267

Exercises Describe a pair of number cube rolls that would result in a point plotted at the given location.
1. (3,4)(-3,4)
2. (4,3)(4,-3)
3. in Quadrant III
4. the origin

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Problem 268

Find the xx-intercept and the yy-intercept of the graph of the equation. 3x+4y=243 x+4 y=24
The xx-intercept is \square . (Type an integer.)

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Problem 269

4. The points (3,8)(-3,8) and (9,8)(9,8) lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

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Problem 270

Review Question 23, *5.6.12
Find the equation of a line that is parallel to the line x=17x=-17 and contains the point (2,9)(-2,9).
The equation of the parallel line is \square (Type an equation.)

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Problem 271

tps://scvcsk12.schoology.com/external_tool/3085607572/launch
Answer Attempt 2 out of 2
Slope of the Line: \square Submit Answer

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Problem 272

Watch Video
What is an equation of the line that passes through the points (4,8)(4,8) and (2,7)(-2,-7) ?
Answer Attemptiout of 2 \square Stlunit Answer

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Problem 273

Watch Video Show Examp
Vhat is an equation of the line that passes through the points (7,3)(7,-3) and (8,3)(-8,-3) ? Answer Attempt 1 out of 2

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Problem 274

The line in R3\mathbb{R}^{3} that is parallel to the yy-axis and passes through the point (1,2,3)(1,2,3) has equation [xyz]=+t\left[\begin{array}{l} x \\ y \\ z \end{array}\right]=\square+t \square
Select a blank to input an answer

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Problem 275

Leaming Task 4: Determine the standard form of the equation of an ellipae and identify its parts. After identifying. plot the caurdinatea of its parts and graph the equations in one rectangular coordinate syatem then determine what real-life picture is in the graph. \begin{tabular}{|c|c|c|} \hline General Form & 9x2+81y2729=09 x^{2}+81 y^{2}-729=0 & 121x2+16y21936=0121 x^{2}+16 y^{2}-1936=0 \\ \hline Standard Farm & & \\ \hlineaa & & \\ \hlinebb & & \\ \hlinecc & & \\ \hline \end{tabular}

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Problem 276

MULTIPLE CHOICE QUESTION
Is the slope of this line positive or negative? Positive Negative
Rewatch Submit

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Problem 277

What is the yy-intercept?

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Problem 278

(1,6),(8,2);a(1,6),(8,2) ; a a. m=m= \qquad b. \qquad c. \qquad

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Problem 279

Graph the line whose yy-intercept is 6 and whose xx-intercept is 2 .

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Problem 280

Graph the line with yy-intercept 4 and slope 2.

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Problem 281

Jane wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in m2\mathrm{m}^{2} ) versus the length (in m ).
Find the domain and the range of the function shown.
Write your answers as inequalities, using xx or yy as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: \square < \square >>\square \square口 (b) range: \square Empty All set reals Check Save For Later Submit Assianment

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Problem 282

5 Geben Sie eine Gleichung für eine Gerade h an, die die Gerade g schneidet, eine Gerade i, die zur Geraden g parallel ist, und eine Gerade j, die zur Geraden g windschief ist. a) g:x=(100)+t(731)g: \vec{x}=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)+t \cdot\left(\begin{array}{l}7 \\ 3 \\ 1\end{array}\right)

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Problem 283

Key Concept Two points lie on a horizontal line in the coordinate plane when their yy-coordinates are the same. For instance, we know that (2,4)(2,4) and (5,4)(5,4) lie on a horizontal line because they both have a yy-coordinate of 4 .
If the Ys are the same, look at the Xs . slide sv
What is the distance? Students, enter a number! Pear Oeck Interactive Slide Do not remove this bar

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Problem 284

Determine another point on a line given two points: (2,9)(-2, 9) and (2,1)(2, -1).

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Problem 285

Basisaufgaben
7. Zeichnen Sie einen Vektorpfeil des Vektors v\vec{v} in ein Koordinatensystem (LE: 1 cm ) und messen Sie die Länge des Pfeils. Kontrollieren Sie, indem Sie den Betrag des Vektors berechnen. a) v=(04)\vec{v}=\binom{0}{4} b) v=(20)\vec{v}=\binom{-2}{0} c) v=(34)\vec{v}=\binom{3}{4} d) v=(34)\vec{v}=\binom{3}{-4} e) v=(25)\vec{v}=\binom{2}{-5}

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Problem 286

Activity: 1) Pick any 2 points on the line (it's easier if you pick points on an intersection of grid lines) in grid Count the vertical distance 2) Cuares between the points: 3) Count the horizontal \longleftrightarrow distance in grid squares between the points. 4) Slope = vertical distance  horizontal distance ==\frac{\text { vertical distance }}{\text { horizontal distance }}= \qquad 5)
Look at your neighbour's notes. Did they choose the same points? How do your slopes compare?

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Problem 287

What are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (2,0),(1,0),(3,0)(-2,0),(1,0),(3,0) (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no x-intercept.
What are the yy-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \square (Type an ordered pair. Use a comma to separate answers as needed.) B. There is no yy-intercept.

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Problem 288

58:0258: 02
The coordinates of midpoint MM and endpoint EE of a segment are M(35,3)M(35,-3) and E(15,26)E(15,26). Students were asked to find two equations that could be used to find the coordinates of the other endpoint, F(x2,y2)F\left(x_{2}, y_{2}\right). Josiah set up the equations as follows: 15+x22=3,26+v22=35\frac{15+x_{2}}{2}=-3, \frac{26+v_{2}}{2}=35
Which statement best describes Josiah's work? The -3 and 35 should be switched. The 15 and 26 should be switched. The equations should be 35+x22=15,3+y22=26\frac{35+x_{2}}{2}=15, \frac{-3+y_{2}}{2}=26 The equations are correct.

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Problem 289

{xy>3x6\left\{ \begin{array}{l} x - y > 3 \\ x \geq 6 \end{array} \right. Graph system of inequalities to show all possible solutions.

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Problem 290

6. Sketch the graph of the piecewise defined function. [7 points] f(x)={x4 if x3x1 if 3<x33 if x>3f(x)=\left\{\begin{array}{c} -x-4 \text { if } x \leq-3 \\ x-1 \text { if }-3<x \leq 3 \\ 3 \text { if } x>3 \end{array}\right.

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Problem 291

A line segment has the endpoints P(12,0)P(12,0) and Q(12,8)Q(-12,-8). Find the coordinates of its midpoint MM.
Write the coordinates as decimals or integers. M=(M=( \square \square

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Problem 292

e entire graph of the function hh is shown in the figure belo Write the domain and range of hh using interval notation. (a) domain == \square (b) range == \square

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Problem 293

Brian sets up the distance formula to find the length, dd, of the line segment. His work is shown. What error, if any, did Brian make? d=(x2(31))2+(y1(01)2d=\sqrt{\left(x_{2}-\left(-3_{1}\right)\right)^{2}+\left(y_{1}-\left(0_{1}\right)^{2}\right.} A. He subtracted the coordinates instead of adding them to get the distance terms. B. He incorrectly found dd, instead of d2d^{2}. C. The point he chose to draw the legs of the triangle does not form a right angle. D. He incorrectly squared each distance term

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Problem 294

3. The pair of points (6,y)(6, y) and (10,1)(10,-1) lie on a line with slope 14\frac{1}{4}. What is the value of yy ?

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Problem 295

3. Given two complex numbers z1=a+biz_{1}=a+b i and z2=c+diz_{2}=c+d i, construct a picture in the coordinate plane that justifies the fact that z1+z2=(a+bi)+(c+di)=(a+c)+(bi+di)=(a+c)+(b+d)i\begin{aligned} z_{1}+z_{2} & =(a+b i)+(c+d i) \\ & =(a+c)+(b i+d i) \\ & =(a+c)+(b+d) i \end{aligned}

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Problem 296

1) Find the slope of the line through each pair of points.  Slope =y2y1x2x1\text { Slope }=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} a. (8,7)(8,-7) and (5,3)(5,-3). b. (5,9)(-5,9) and (5(5, c. (8,4)(-8,-4) and 11). (4,9)(-4,-9).

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Problem 297

(4) Find the slope of each line described below. (a) The line through (3,7)(3,7) and (1,4)(-1,4). (b) The line passing through the two points, (3,2)(-3,2) and (6,2)(6,2). (c) A vertical line. (d) A horizontal line.

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Problem 298

Name Date: Graphing on the Coordinate Plane HH 13 12 HO 4 8 7 АУ Graph and connect each consecutive point until you reach the word STOP. Then start a new line, continuing to connect each point until you reach STOP again (8,-1) (-4,14) (-8.5, 9) (8.5,-0.5) (-4, 12) (-8.5, 11) (10,-2) (-3, 6) (12,-7) (-2.5, 5) (10,-4) (9,-2.5) (-1.5, 3.5) (-1, 4.5) (-1,5.5) (-0.5, 5.5) (-0.5, 4.5) (0.5, 4.5) (0.5, 5.5) (1, 5.5) (1,4.5) (1.5, 3.5) (2.5, 5) (3,6) (8, -1.5) (6,0) (4, -0.5) (2.5, -0.5) (3,-1) (3.5, -2) (3.5, -4) (3, -5.5) (2,-7) (0.5, -8.5) (-0.5, -8.5) (-8,9) (-7,7) (-5, 3.5) (-3,2) (-1.5, 1.5) (-1.5, 2) (-3,4) (-4, 5.5) (-3.5, 6) (-4,7) (-4.5, 10) (-4.5, 13) (-4,14) Stop 1 -4 -8 -7 -6 -5 +3 23 L 10 13 5 6 7 8 9 10 11 12 13 14 (4,12) (4,14) (4.5, 13) (4.5, 10) (4,7) (3.5, 6) (4, 5.5) (3,4) (1.5, 2) (1.5, 1.5) (3,2) (-3, -5.5) (-2, -7) (3,-1) (-3.5, -4) (5,-2) (-3.5, -2) (5.5, -3) (-3, -1) (-2.5, -0.5) (6.5, -7) (7,-9) (6.5, -13.5) (-4, -0.5) (-6, 0) (-8, -1.5) (-9, -2.5) (6,-8) (5,-4) (4.5, -3) (-10, -4) (3.5, -2.5) (5, 3.5) (-12,-7) Stop (7,7) (-10, -2) (8, 9) (-3, -1) (8.5, (-8.5,-0.5) 11) (-5, -2 (-8,-1) (8.5, 9) (-5.5, (8,7) (-6, 0.5) (-6.5, (-6, 1) (7,5) (-7, (5.5, 3) (-4, 0.5) (-6.5, (3, 1) (-2, 0) (-6 (1.5, 0.5) (-1.5, 0.5) (-5 (2,0) (-3,1) (-4 (4,0.5) (-5.5, 3) (6,1) (-7,5) (-3 (6,0.5) (-8,7) OR. Davenport 2018

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Problem 299

The endpoints of AB\overline{A B} are A(3,4)A(-3,-4) and B(2,1)B(2,1). Point CC lies on AB\overline{A B} and is 15\frac{1}{5} of the way from AA to BB. What are the coordinates of point CC ? Explain how you found your answer.
Select the correct answer below and fill in the answer box to complete your answer. (Type an ordered pair.) A. First, find 15\frac{1}{5} of the horizontal and vertical distances from AA to BB. Then, move this amount from AA to CC. The coordinates of point CC are \square B. Use the Distance Formula to find 15\frac{1}{5} the length of AB\overline{\mathrm{AB}}. The coordinates of point C are \square c. First, find 15\frac{1}{5} of the horizontal and vertical distances from AA to BB. Then, move this amount from B to C. The coordinates of point C are \square \square 7. D. CC is the midpoint of AB\overline{A B}, so use the Midpoint Formula. The coordinates of point CC are \square .

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Problem 300

The equations of three lines are given below. Line 1: 3y=4x+73 y=-4 x+7 Line 2:8x+6y=82: 8 x+6 y=-8 Line 3:y=43x63: y=-\frac{4}{3} x-6
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither
Line 2 and Line 3: Parallel Perpendicular Neither

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