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
Joseph is building a cone using modeling clay. The cone has a radius of 6 cm and a height of 12 cm. Joseph adds additional clay,
dmitriy555 [2]
<span>Cone Volume = (<span>π<span> • r² •<span> h) ÷ 3

Original cone = (3.14 * 6^2 * 12) / 3
</span></span></span></span>
<span><span>Original cone = 452.16 </span> cc

</span>Larger cone =  <span>(3.14 * 6^2 * 18) / 3 = </span> <span> <span> <span> 678.24 </span> </span> </span> cc

Difference = <span>(678.24 -452.16) = </span> <span> <span> <span> 226.08 </span> </span> </span> cc


3 0
3 years ago
Read 2 more answers
What is the polar form of 7 StartRoot 3 EndRoot minus 7 i?
ololo11 [35]

Answer:

14(cos(330 degrees) + i sin(330 degrees))

option D

Step-by-step explanation:

edge 2020

3 0
3 years ago
What is 2/15 divided by 4/15
Yanka [14]
The answer is 1/2 or 0.5
4 0
3 years ago
Read 2 more answers
Which pair of triangles is congruent?
daser333 [38]
You are only showing one pair of triangles
4 0
3 years ago
Find (2x+4) (x-4) using the table of products. write your answer in standard form.​
ValentinkaMS [17]

Answer:

2x^2-4x-16

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is the product?<br><br> (6r − 1)(−8r − 3)
    9·2 answers
  • Which function has an inverse function?
    5·2 answers
  • Which expression is equivalent to the following function?
    10·2 answers
  • How do I solve this algebra problem: 2(4a-12)+3a=6a+1
    10·2 answers
  • I WILL GIVE BRAINLIEST!!!
    6·1 answer
  • Please help with this math question will mark you brainiest
    11·1 answer
  • What happened to the tutor option :(
    8·1 answer
  • Factor the expression using the GCF.<br><br> 50x−60
    15·1 answer
  • Question 4
    10·1 answer
  • The length of the diagonal of a rectangle is 140−−−√ inches.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!