Is there anything special about the relationship between the lines Ax + By = C1 and Bx - Ay = C2 (A ≠ 0, B ≠ 0)? Give rea-sons for your answer.

Q: What is the equation of a line parallel to 킹 =Dz+ 2 that passes through (1, 2)?

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Q: For what value of k is the line 2x + ky = 3 perpendicular to the line 4x + y = 1? For what value of…

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Q: (1) What is the relationship between the lines L1 and L2? where ) L1:x = 1-t, y = 4 +t, z = 2+3t…

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Q: Find r so that the line through (2,6) and (-4,r) a).parallel to 2x-3y=4 b). Pendicular to x+2y=1

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Q: Is there anything special about the relationship between the lines Ax + By = C1 and Bx - Ay = C2 (A…

A: Ax+By=C1 and Bx-Ay=C2 are the equation of two lines. We need to find the relationship between the…

Q: Find the image of the line x = 1 under (a) flz) = z²

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Q: When is the line ax+ by = c parallel to the y-axis? To the x-axis?

A: ax+by+c=0        When a=0, then the line equation becomes               bx+c=0…

Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

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Q: 8 What is the slope of the line perpendicular to tne line represented by the equation 2x+4y = 12?…

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Q: (1) What is the relationship between lines 11 and 12? where L:x = 2, y = 1+2t, z = 1+t L2:x = 4 -t,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate ∫C x ds, where C is the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: find value(s) of k so that the lines described by 3x = 2y+11 and kx = 40 - 6y are perpendicular

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Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: TRUE or FALSE: y = mx + 1 represents the family of lines passing through (0,1). %3D

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Q: Determine if the following lines are parallel (never intersect), perpendicular (int intersecting…

A: Given: - The equation of the lines, y=-x+11,2y=-2x+22 To determine: - The given lines are parallel,…

Q: For what values of a and b is the line-3x + y-b tangent to the curve y = az3 when x-5? a=

A: The value of slope of tangent to the curve at the point is the value of its derivative at that…

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: The line y 을 16 has x-intercept 3. -8)-and is perpendieular to Ahe line Passes through (4,pand…

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Q: Y = , cx. y) = (9,5) X-8 会? Jengent line -? at (9,5)

A: Explanation of the answer is as follows

Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: 1. (x² +y² +z?) ds , where Cis straight line from (1,2,3) to (4,1,4).

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Q: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

Q: What is the equation of the line tangent to the curve 9x^2 + 25y^2 – 225 = 0 at (0, 3)?  a. x + 3 =…

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Q: Show that the equation of the line in R² can be written as х det 1 X1 У1 X2 У2.

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Q: What is the relationship between the lines L1 and L2? where L1:x = 1-t, y = 1+ 2t, z = 2-t L2:x =…

A: The given lines are:L1: x=1-t ; y=1+2t ; z=2-tL2: x=1+t ; y=1-t ; z=2-3t

Q: * Let LIEX-54+10=D0 L2=4X+y-1-O be two lines. 1 Show that the lines L and Lz are not parallel.

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Q: Consider the following diagram of a transverse line to a pair of parallel lines, l1 and l2. (2x…

A: Given : l1 and l2 are parallel lines.

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: How is the line y = 1 converted by mapping w = e? ?

A: In this question, we convert the line y=1 by mapping w=e^z.

Q: 4) Evaluate , -dz, where y is the line from 1 → 1+ i

A: In complex integration, we have to convert our given question into complex terms. But in our…

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: (1) What is the relationship between the lines L1 and L2? where L:x = 1-t, y = 4 + t, z = 2+3t L2:x…

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Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: Show that the two lines X= 2+ St J= 4 - 36 Z: 5+t X= 1+4t and y= 5-4t Z: -1+ SE skew Rind the…

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Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: For what values of a and b is the line 2x + y = b tangent to the curve y = ax² when x = 4?

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Q: The slope of line I is x, and the slope of line m is x +2. If llm, what is x?

A: Perpendicular lines have slopes that are the opposite of the reciprocal of each other. in given…

Q: suppose the equation for the best fitting line is Y3(1/4)-3x then from this equation we can conclude…

A: Linear regression uses the values from an existing data set consisting of measurements of the values…

Q: The lines joining the origin to the point of intersection of the line lx+my=1 and y²=4ax are at…

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Q: I thought at least meant greater than or equal to. Therefore the correct answer should have been A…

A: Here, the term used is at least $10,000.

Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

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Q: What is the relationship between the lines L1 and L2? where L:x =1+4t, y = 3-t, z = 1+t L2:x = -3t ,…

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Q: 13. Evaluate (2x + y + 3z) ds, where C is the straight line from (0, 1, 1) to (1,0, 1).

A: we have to evaluate

Q: how to find equation of a tagent line y=x^4 +2e^x  at (0,2)

A: In the question we have to find the tangent at point (0,2)

Q: suppose I tell you that the line ax+5y=7 is parallel to the line 4x-2y=11. What is a?

A: Given equation of the line 4x -2y = 11   .......(1)and another line 9x+5y = 7 .....(2)we find the…

Q: If ax +2hxy+by 0 represents two straight lines such that the slope of one %3D line is twice the…

A: We have to prove that

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.