Mathematics, 29.10.2019 15:31 giulianna41

3.
in the figure, the straight line l: 2x-y-18 = 0 cuts the x-axis and the y-axis at
a and b respectively.
l: 2x - y - 18 = 0
(a)
(i) find the slope of l.
(ii) find the coordinates of a and b.
(3 marks)
b)find the equation of the perpendicular bisector of ab in general form.

3.in the figure, the straight line l: 2x-y-18 = 0 cuts the x-axis and the y-axis ata and

Answers: 1

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Answer from: germanie123

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x - y - 18 = 0 into this form

Subtract 2x - 18 from both sides

- y = - 2x + 18 ( multiply through by - 1 )

y = 2x - 18 ← in slope- intercept form

with slope m = 2 and y- intercept B(0, - 18)

To find the x- intercept let y = 0 in the equation and solve for x

2x - 18 = 0 ( add 18 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Hence x- intercept A(9, 0)

(b)

The perpendicular bisector passes through the midpoint of AB at right angles.

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{2}$

The midpoint of AB is

[0.5(9 + 0), 0.5(0 - 18) ] = (4.5, - 9)

Thus

y = - $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute (4.5, - 9) into the partial equation

- 9 = - 2.25 + c ⇒ c = - 9 + 2.25 = - 6.75 = - $\frac{27}{4}$

y = - $\frac{1}{2}$ x - $\frac{27}{4}$ ← in slope- intercept form

Multiply through by 4

4y = - 2x - 27 ( subtract - 2x - 27 from both sides )

2x + 4y + 27 = 0 ← in general form

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240