Questions on Algebra: Coordinate systems, graph plotting, etc answered by real tutors!

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Question 1114745: Find the shortest distance from the origin to a point on the circle defined by x^2 + y^2 − 6x − 12y + 41 = 0
I got as far as (x-6)^2+(y-12)^2 = 5.
Click here to see answer by ikleyn(52747)

Question 1114770: Find all points on the line y = x that are 6 units from (2, 4)
Click here to see answer by josgarithmetic(39613)

Question 1114835: Get graph paper out for this one. The points A(5,4) B(1,0) and C(9,0) form a triangle. Only one of the following statements are true. The true statement is
a) the triangle is acute b) the area of the triangle is 20units2 c) the point (7,3) is inside the triangle d) the perimeter of the triangle is 16u e) angle ACB = 45 degrees

Click here to see answer by Alan3354(69443)

Question 1115299: The points with cordinate is5,5) and (-3,-1)are the ends of a diameter of a circle center A.determine the cordinates of A and determine the equation of the circle e

Click here to see answer by josgarithmetic(39613)

Question 1115362: Find the equation of the line passing through the point (2, 1) and perpendicular to the line 2y = 7 � x
Click here to see answer by stanbon(75887)

Question 1115511: what is the graph of the inequality
y_> -x-2
Click here to see answer by ikleyn(52747)

Question 1115513: I need help finding five ordered pair solutions for y=2x-3
Click here to see answer by Alan3354(69443)

Question 1115617: Estimate an equation for the line of best fit for the following scatter plot.
https://api.agilixbuzz.com/Resz/~iA4TBAAAAAwcHkPK8dzgFB.6xo9M9Vg7qJW7mY_PSzXqA/49371243,F83/Assets/Salary.JPG
Click here to see answer by MathLover1(20849)

Question 1115686: solve for x and y and graph for 6x+8y=140 and 9x+6y+132.
Click here to see answer by Alan3354(69443)

Question 1117190: How do you write an inequality in slope intercept form for (-4,0) and (4,2)
Click here to see answer by math_helper(2461)

Question 1117378: Hello there! I am studying for the GRE and since I will be taking the online version, I want to know how can I quickly solve the following problem without using a graphing calculator, since I won't have access to one on the test?

Which of the Following points are of the equation y=x+2 and the equation y=x^2 in the xy-plane? Indicate all points.
a. (-2,0)
b. (-1,1)
c. (0,2)
d. (1,1)
e. (2,4)
I would appreciate if you could show me the answer and how you got to it step by step. sorry for taking your time!
Click here to see answer by stanbon(75887)

Question 1117572: If the equation of the circle is x^2+y^2=r^2 and the equation of the tangent line is y=mx+b,Show that,
(1)r^2(1+m^2)=b^2
(Hint: The Quadratic Equation x^2+(mx+b^2)=r^2 has exactly one solution.
Click here to see answer by josgarithmetic(39613)

Question 1117843: Hi all, please help me to solve this - I have the answer, but I cannot "back engineer" how we arrived at it. Thank you!
The gradient of the line joining (4, q) to (6, 5) is twice the gradient of the line joining (0, 0) to (4, q). Find q.
Click here to see answer by stanbon(75887)

Question 1117961: The point
P(3, −3)
lies on the curve
y = 3/(2 − x).
(a) If Q is the point
(x, 3/(2 − x)),
use your calculator to find the slope
mPQ
of the secant line PQ (correct to six decimal places) for the following values of x

(i) 2.9
mPQ =

(ii) 2.99
mPQ =

(iii) 2.999
mPQ =

(iv) 2.9999
mPQ =

(v) 3.1
mPQ =

(vi) 3.01
mPQ =

(vii) 3.001
mPQ =

(viii) 3.0001
mPQ =
Click here to see answer by solver91311(24713)

Question 1118230: Write the equation of a line that is parallel to the straight line y = - 8x + 4 that goes through the point (7, -5)
Click here to see answer by Alan3354(69443)

Question 1118230: Write the equation of a line that is parallel to the straight line y = - 8x + 4 that goes through the point (7, -5)
Click here to see answer by greenestamps(13195)

Question 1118574: Find the coordinates of the midpoint of a segment having the given endpoints.
Q(1, -3), R(11, 5)

Click here to see answer by josgarithmetic(39613)

Question 1119291: The magnitude of the distance from the line 5x = By + 26 to the point (3, -5) is 49/13. Determine the value of B.
Click here to see answer by greenestamps(13195)

Question 1119291: The magnitude of the distance from the line 5x = By + 26 to the point (3, -5) is 49/13. Determine the value of B.
Click here to see answer by math_helper(2461)

Question 1119457: Sketch the graph of the below function:
y=-x^2+5x-6
Click here to see answer by Alan3354(69443)

Question 1119457: Sketch the graph of the below function:
y=-x^2+5x-6
Click here to see answer by josgarithmetic(39613)

Question 1119458: Sketch the graph of the below piecewise function:
f(x) = {5 , x>2}
2x-1 , x<+2

Click here to see answer by Alan3354(69443)

Question 1119454: Hello,
I know the answer to the following is 45 but I am not sure of the process.
Can someone please help. Thanks
Given:
Line AD and line BC meet at the point P (6,6)
BC is y = mx+3
The area of ABP is 27
Point O is (0,0)
Find the area of polygon BODP

Click here to see answer by solver91311(24713)

Question 1119483: Let A= (-6,7), B= (-4,11), and C= (-2,10) be three points in the xy-coordinate plane.
(a) Verify that the three points form a right triangle, and identify the point at the vertex where the right angle is.
(b) Determine the midpoint of the hypotenuse of the right triangle.
(c) Find the equation of the line through the midpoint of the hypotenuse and the vertex opposite the hypotenuse (where the right angle is).
Click here to see answer by josgarithmetic(39613)

Question 1119595: In the xy-plane, line L passes through the origin and is
perpendicular to the line 2x - y = b, where b is a
constant. If the two lines intersect at the point (2a, a + 1),
what is the value of b?
Click here to see answer by josgarithmetic(39613)

Question 1119539: + + +

Click here to see answer by solver91311(24713)

Question 1119539: + + +

Click here to see answer by ikleyn(52747)

Question 1120104: Hardware f�Hardware f�
Click here to see answer by ikleyn(52747)

Question 1120104: Hardware f�Hardware f�
Click here to see answer by Shin123(626)

Question 1120234: How often in a 12- hour period of time does the sum of the digits on a digital clock equal 9?
Click here to see answer by Alan3354(69443)

Question 1120234: How often in a 12- hour period of time does the sum of the digits on a digital clock equal 9?
Click here to see answer by greenestamps(13195)

Question 1120392: The coordinate of a particle in meters is given by x(t) = 16t − 3.0t
3, where the time t is in
seconds. The particle is momentarily at rest at t =
Click here to see answer by Alan3354(69443)

Question 1121135: draw a line through the points (-3,-1) with the inclination of 60 degrees.
Click here to see answer by Alan3354(69443)

Question 1121324: A waste paper baskets consist of an open circular cylinder. If the volume of the basket is to be 200cm^3 Fnd the radius when the materials being used is a minimum
Click here to see answer by josgarithmetic(39613)

Question 1121325: A stone is projected vertically upward and after time (t) seconds it's distance from the starting point x is given by x = 48t - 6t^2
1) Calculate the initial velocity of the stone particle.
2) Calculate the time taken to reach it's highest point.
3) What is it's velocity after 3 seconds.
Click here to see answer by ikleyn(52747)

Question 1121326: Find the equation of the tangent at the point (2,3) to the parabola 3y = x^2 + 5. Also obtain the equation of the line through the point (2,3) perpendicular to this tangent. If the x axis meet this line an the tangent at A and B respectively. Find the length of AB
Click here to see answer by josgarithmetic(39613)

Question 1121463: Plot (3, π/4) in polar coordinate
Click here to see answer by ikleyn(52747)

Question 1121468: Find the equations of the tangents to the curve y = x^3 - x^2 - 2 at the point where x = 2. Find the coordinates of the point where the tangent intersect the curve.
Click here to see answer by josgarithmetic(39613)

Question 1121467: The tangent to the curve y = x^2 - 5x + 3 at a certain point is parallel to the line y = x. Find its equations and where it intersect the x-axis
Click here to see answer by josgarithmetic(39613)

Question 1121466: Find the coordinates of the points on the curve y = x^3 - 2x^2 - x + 5 where the tangents are parallel to the line y = 2x + 3. Find the equations of these tangents
Click here to see answer by josgarithmetic(39613)

Question 1121508: Express (-5, 0) in polar coordinates with r is greater than or equal to 0 and 0 < theta < 2π
Click here to see answer by ikleyn(52747)

Question 1121507: Express (-5, 0) in polar coordinates with r is greater than or equal to 0 and -π < theta < π
Click here to see answer by ikleyn(52747)

Question 1121469: Find the equations of the tangent to the curve y = x(x - 2)(x - 4) at the origin. Show that this tangent is parallel to the tangent at the point where x = 4 ( and not at the point x = -4
Click here to see answer by greenestamps(13195)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680