Math what is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ? enter your answer in the box. line a is represented by the equation y=−2x+3 . how do these equations compare to line a? drag and drop the equations into the boxes to complete the table. parallel to line a perpendicular to line a neither parallel nor perpendicular to line a what is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10? enter your answer in the box what is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5? enter your answer in the box. in this diagram, which equation could you prove to be true in order to conclude that the lines are parallel? −ab=−cd −ab⋅−cd=−1 −ab⋅−dc=−1 −ab=−dc

Part A. What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7?

Rewrite the equation  −2y=3x+7 in the form Here the slope of the given line is   If is the slope of perpendicular line, then

Answer 1:

Part B. The slope of the line y=−2x+3 is -2. Since then lines from part A are not parallel to line a.

Since both lines are not perpendicular to line a.

Answer 2: Neither parallel nor perpendicular to line a

Part C. The line parallel to the line 2x+5y=10 has the equation 2x+5y=b. This line passes through the point (5,-4), then

2·5+5·(-4)=b,

10-20=b,

b=-10.

Answer 3: 2x+5y=-10.

Part D. The slope of the line is Then the slope of perpendicular line is -4 and the equation of the perpendicular line is y=-4x+b. This line passes through the point (2,7), then

7=-4·2+b,

b=7+8,

b=15.

Answer 4: y=-4x+15.

Part E. Consider vectors These vectors are collinear, then

Answer 5:

(a) 2/3

(b) neither parallel nor perpendicular ; parallel; perpendicular

(c) y = (-2/5)*x - 2

(d) y = -4*x + 15

(e) -a*c = -d*b

Step-by-step explanation:

(a)

What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?

First you need to rearrange the equation so that y term is isolated, in this case you should pass the -2 (which multiplies in one side) dividing to the other side.

y = (3*x + 7)/(-2)  

y = (-3/2)*x + 7

The slope of any line is the term next to x, in this case -3/2

Two lines are perpendicular if the multiplication of each line slopes is equal to -1. For example, given lines y = m1*x+b1 and y = m2*x+b2 where m1 is the slope of the first line and m2 of the second one, they are perpendicular if m1*m2 = -1

In this case we should solve:

(-3/2)*m2 = -1

m2 = 2/3

(b)

Line a is represented by the equation y=−2x+3 . How do these equations compare to line a? Drag and drop the equations into the boxes to complete the table. Parallel to line a Perpendicular to line a Neither parallel nor perpendicular to line a y=2x−1, y=−2x+5, y=1/2x+7

Two lines are parallel if they have the same slope.  

a's slope is -2  

Any line perpendicular to a must have an slope of 1/2,  so that -2*1/2 = -1

in y=2x−1 slope is 2 -> they are neither parallel nor perpendicular

in y=−2x+5 slope is -2 -> they are parallel  

in y=1/2x+7 slope is 1/2 -> they are perpendicular

(c)

What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

Rearranging the equation:

5*y = -2*x + 10  

y = (-2*x + 10)/5

y = (-2/5)*x + 2

Our equation has the form y = m*x + b where m = -2/5. In order to find b we replace the known point (5, -4) in the equation:

y = (-2/5)*x + b  

-4 = (-2/5)*5 + b  

-4 = -2 + b

-2 = b

Finally, y = (-2/5)*x - 2

(d)

What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5?

Calling m1 = 1/4 the slope of the known equation, we have to find a slope m2 which fulfill m1*m2 = -1. Replacing:

1/4*m2 = -1

m2 = -4

In the same way as before, we replace the point (2, 7) in the general equation form:

y = -4*x + b

7 = -4*2 + b

7 = -8 +b

15 = b

Finally, y = -4*x + 15

(e)

In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

The slope of a line can be  computed by m = (y1 - y2)/(x1 -x2) where (x1, y1) and (x2, y2) are points in the line

For the above line  

(x1, y1) = (b, 0)

(x2, y2) = (0, a)

Replacing

m1 = (0 - a)/(b -0) = -a/b

For the below line  

(x1, y1) = (-c, 0)

(x2, y2) = (0, -d)

Replacing

m2 = (0 - (-d) )/( (-c) - 0) = -d/c

m1 = m2,  so that both lines are parallel

-a/b = -d/c

-a*c = -d*b

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

step-by-step explanation: 4 cause 2+2=4