Mathematics, 09.01.2020 07:31 gabby4623

1.
a. write an equation of the line that passes through the origin that intersects the line 2x + 5y = 7 to form a
right angle.
b. determine whether the lines given by the equations 2x + 3y = 6 and y = 3 / 2 x + 4 are perpendicular. support
your answer.
c. two lines having the same yy-intercept are perpendicular. if the equation of one of these lines is y = − 4 / 5 x + 6,
what is the equation of the second line?

Answers: 1

Show answers

Answers

Answer from: UltimateGoal

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form y = mx + c

5y = 7 - 2x

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the y = mx + c , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

m_1m_2=-1 .

here both slopes m_1 and m_2 are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

(y-y_1)=m(x-x_1)

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether m_1m_2=-1 ?

the slopes can be easily found through rearranging both equations to y=mx+c

Line:1

2x + 3y =6

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

m_1m_2=-1

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

-1=-1

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is c=6 the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

m_1m_2=-1

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

(y-y_1)=m(x-x_1)

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

Answer from: Quest

your answer is d 2,500

step-by-step explanation:

The circle graph represents a family’s monthly budget if the total monthly budget is 5,000 how much

Answer from: Quest

what

Another question on Mathematics

Mathematics, 21.06.2019 15:00

The water has been on the stove y=9.5x+62.1 after how many minutes will the tempature be 138.1 f

Answers: 1

Answer

Mathematics, 21.06.2019 15:30

Which of the following are parts of a sphere

Answers: 1

Answer

Mathematics, 21.06.2019 17:30

The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of the productwhen it is sold at a unit price of x dollars.-0.5x^2 + 22x - 224what is represented by the zero(s) of the expression? a.the profit when the unit price is equal to 0b.the unit price(s) when the profit is equal to 0c.the profit when the unit price is greatestd.the unit price(s) when profit is greatest

Answers: 3

Answer

Mathematics, 22.06.2019 01:00

The stairs leading from the ground to the entrance of a plane forms a right triangle with the ground. if the distance of the stairs measures 22 feet and the ground distance measures 11 feet, how high is the entrance to the plane from the ground? which diagram represents this scenario? / 22ft © 22ft 11 ft 11 ft 22 it

Answers: 3

Answer

You know the right answer?

1.
a. write an equation of the line that passes through the origin that intersects the line 2x...

Questions

Engineering, 13.09.2019 22:10

The revolving joint (type v) of an industrial robot has a range of 192 rotation. the mechanical errors in the joint and the input/output links can be...

Engineering, 13.09.2019 22:10

Afirm is considering either leasing or buying a microcomputer system. if purchased, the initial cost will be $250,000; annual operating and maintenan...

Engineering, 13.09.2019 22:10

What deposit is required today to accumulate the following amounts at the given time? a. $15,000 in 10 years at 6% compounded annually b. $1,200,000...

Engineering, 13.09.2019 22:10