All categories

3 years ago

Which of the following is the equation of a line perpendicular to the line y =

Mathematics

1 answer:

makvit [3.9K]3 years ago

5 0

Answer:

y = $\frac{1}{10}$ x + $\frac{13}{2}$

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 )

y = - 10x + 1 ← is in slope- intercept form

with slope m = - 10

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-10}$ = $\frac{1}{10}$ , thus

y = $\frac{1}{10}$ x + c ← is the partial equation

To find c substitute (5, 7) into the partial equation

7 = $\frac{1}{2}$ + c ⇒ c = 7 - $\frac{1}{2}$ = $\frac{13}{2}$

y = $\frac{1}{10}$ x + $\frac{13}{2}$ ← equation of line

You might be interested in

1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

$m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}$

7 0

3 years ago

Find the value of x. RZ = 30 SW = 5x - 20

Murrr4er [49]

|RZ|=0.5|SW| therefore 2|RZ|=|SW|.

5x - 20 = 2 · 30

5x - 20 = 60 |add 20 to both sides

5x = 80 |divide both sides by 5

x = 16

5 0

3 years ago

What is f(6)? Enter your answer rounded to the nearest tenth in the box.

iren2701 [21]

I think like that but I’m not sure

3 0

3 years ago

2) A pool is being filled with a hose. The equation y=12x represents the relationship between

faltersainse [42]

Answer:

Step-by-step explanation:

y = 12x.

A) x=8, so that y = 12(8) = 96. It's on the line

B) x = 10, so that y = 12(10) = 120. It's on the line

C) x = 15, so that y = 15(12) = 180. It's on the line

D) x = 18, so that y = 18(12) = 216, not equal to 206. So, the point is not on the line.

8 0

2 years ago

What is the solution to the equation below?

hram777 [196]

Answer:

$\large\boxed{A)\ x=-4}$

Step-by-step explanation:

$\dfrac{x}{4}=\dfrac{x+1}{3}\qquad\text{cross multiply}\\\\3x=4(x+1)\qquad\text{use the distributive property}\\\\3x=4x+4\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\-x=4\qquad\text{change the signs}\\\\x=-4$

4 0

3 years ago