1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anastaziya [24]
3 years ago
14

Math help Please!!!!

Mathematics
2 answers:
GalinKa [24]3 years ago
5 0

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 y=-\dfrac{3}{2}x-\dfrac{7}{2}. Here the slope of the given line is  m_1=-\dfrac{3}{2}. If m_2 is the slope of perpendicular line, then

m_1\cdot m_2=-1,\\ \\m_2=-\dfrac{1}{m_1}=\dfrac{2}{3}.

Answer 1: \dfrac{2}{3}

Part B. The slope of the line y=−2x+3 is -2. Since -\dfrac{3}{2}\neq -2\quad \text{and}\quad \dfrac{2}{3}\neq -2, then lines from part A are not parallel to line a.

Since -2\cdot \left(-\dfrac{3}{2}\right)=3\neq -1\quad \text{and}\quad -2\cdot \dfrac{2}{3}=-\dfrac{4}{3}\neq -1, 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 y=\dfrac{x}{4}+5 is \dfrac{1}{4}. 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 \vec{p}_1=(-c-0,0-(-d))=(-c,d)\quad \text{and}\quad \vec{p}_2=(0-b,a-0)=(-b,a). These vectors are collinear, then

\dfrac{-c}{-b}=\dfrac{d}{a},\quad \text{or}\quad -\dfrac{a}{b}=-\dfrac{d}{c}.

Answer 5: -\dfrac{a}{b}=-\dfrac{d}{c}.

Harlamova29_29 [7]3 years ago
3 0

Answer:

(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

You might be interested in
What are the numbers for Pi <br> (Urgent)
bagirrra123 [75]
Pi is many numbers since it goes on and on so the rounded number for pi is 3.14
6 0
3 years ago
Read 2 more answers
Given the Coordinate Rule (x + 2, y - 3), where would point (4, 7) translate to?
GaryK [48]

Answer:

(6,4)

Step-by-step explanation:

(x+2,y-3)

=(4+2,7-3)

=(6,4)

3 0
3 years ago
Read 2 more answers
Ben needs to mix 1.5 cups of lemonade concentrate with 4 cups or water to make lemonade. He has 6 cups of concentrate. How much
lubasha [3.4K]

Answer:

<u>24</u>

Step-by-step explanation:

To get your answer, you need to multiply 1.5 and 6.

<u>1.5 x 6 = 9</u>

Then you multiply 4 and 6.

<u>4 x 6 = 24</u>

Which is your final answer.

<h3><em>I hope this helps you! Good Luck!</em></h3>
4 0
3 years ago
A landscaper is selecting two trees to plant. He has five to choose from. Three of the five are deciduous and two are evergreen.
ICE Princess25 [194]

Answer:

The probability that he chooses trees of two different types is 30%.

Step-by-step explanation:

Given that a landscaper is selecting two trees to plant, and he has five to choose from, of which three of the five are deciduous and two are evergreen, to determine what is the probability that he chooses trees of two different types must be performed the following calculation:

3/5 x 2/4 = 0.3

2/5 x 3/4 = 0.3

Therefore, the probability that he chooses trees of two different types is 30%.

4 0
2 years ago
Read 2 more answers
The lowest number is 11 the range is 13 and the median is 17 what are the 3 numbers
11Alexandr11 [23.1K]

Answer:

11, 17, and 28.

Step-by-step explanation:

x, y, z\\

Lowest number is x

Median is y

Highest number is z

x=11\\y=17\\\\z-x=17\\z-11=17\\z-11+11=17+11\\z=28\\\\x=11\\y=17\\z=28\\\\11, 17, 28

3 0
3 years ago
Other questions:
  • Express the sum in the simplest form.
    5·1 answer
  • Solve x^2=121 please solve this quickly
    5·1 answer
  • Given that 2x + 7 = 27 and 3x + 1 = 28, does 2x + 7 = 3x + 1
    15·2 answers
  • What does (r−c)(5) mean about George's new store?
    10·1 answer
  • What is the measure angle of N???
    9·1 answer
  • HELP PLEASE MATH :((((
    6·1 answer
  • What is the number between 0.25 and 0.125
    14·2 answers
  • What does 3/5 + 2/5=
    13·2 answers
  • Help help help.
    6·1 answer
  • Find the perimeter. Simplify your answer.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!