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
blagie [28]
3 years ago
15

1) What is the equation of a line that is perpendicular to 2x+y=−4 and passes through the point (2, −8)

Mathematics
1 answer:
defon3 years ago
8 0

1.

Let\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2,\ then\\\\l\ \perp\ k\iff m_1m_2=-1.\\\\\text{We have}\ k:2x+y=-4\qquad subtract\ 2x\ from\ both\ sides\\\\k:y=-2x-4\to m_1=-2\\\\l:y=mx+b\\\\l\ \perp\ k\iff-2m=-1\qquad divide\ both\ sides\ by\ (-2)\\\\m=\dfrac{1}{2}\\\\l:y=\dfrac{1}{2}x+b\\\\\text{The line}\ l\ \text{passes throuth the point (2, -8).}\\\text{Susbtitute the coordinates of the point to the equation of the line }\ l:\\\\-8=\dfrac{1}{2}(2)+b\\\\-8=1+b\qquad subtract\ 1\ from\ both\ sides\\\\-9=b\to b=-9

\boxed{y=\dfrac{1}{2}x-9}


2.

If ΔABC is a right triangle, then we can use Pythagorean theorem.

The formula of a length of a line segment AB:

|AB|=\sqrt{(x_B-x_A)^2+(Y_B-y_A)^2}

A(1, -1), B(3, 2)

|AB|=\sqrt{(3-1)^2+(2-(-1))^2}=\sqrt{2^2+3^2}=\sqrt{4+9}=\sqrt{13}

(1) C(0, 2)

|AC|=\sqrt{(0-1)^2+(2-(-1))^2}=\sqrt{(-1)^2+3^2}=\sqrt{1+9}=\sqrt{10}\\\\|BC|=\sqrt{(0-3)^2+(2-2)^2}=\sqrt{(-3)^2+0^2}=\sqrt9=3

\sqrt{13} >\sqrt{10} > 3\\\\3^2+(\sqrt{10})^2\stackrel{?}{=} (\sqrt{13})^2\\\\L=9+10=19\\R=13\\L\neq R\\Not\ a\ Right\ Triangle

(2) C(3, -1)

|AC|=\sqrt{(3-1)^2+(-1-(-1))^2}=\sqrt{2^2+0^2}=\sqrt4=2\\\\|BC|=\sqrt{(3-3)^2+(-1-2)^2}=\sqrt{0^2+(-3)^2}=\sqrt9=3

\sqrt{13} > 3 > 2\\\\3^2+2^2\stackrel{?}{=}(\sqrt{13})^2\\\\L=9+4=13\\R=13\\L=R\\Right\ Triangle

(3) C(0, 4)

|AC|=\sqrt{(0-1)^2+(4-(-1))^2}=\sqrt{(-1)^2+5^2}=\sqrt{1+25}=\sqrt{26}\\\\|BC|=\sqrt{(0-3)^2+(4-2)^2}=\sqrt{(-3)^2+2^2}=\sqrt{9+4}=\sqrt{13}

\sqrt{26} > \sqrt{13}=\sqrt{13}\\\\(\sqrt{13})^2+(\sqrt{13})^2\stackrel{?}{=}(\sqrt{26})^2\\\\L=13+13=26\\R=26\\Right\ Triangle

You might be interested in
the equation y=12.21x +37.42 fits the scatterplot of the values for stock ABC over the past month with an r-value of 0.9871. how
Lynna [10]
I'm pretty sure you already solved this by now, but I'll say the answer anyway. This problem has already been solved by another as a verified answer. 

This is the concept of financial algebra, we are required to calculate the value of stock ABC which follows the model given by: 
y=12.21x+37.42
given that x=62 days, 
the value of th estock after 62 days will be given by: 
y=12.21(62)+37.42
y=757.02+37.42
y=794.44

ABC will be worth $794.44

I take no credit for this answer. It was solved by CastleRook. 
4 0
3 years ago
Solve (x – 4)2 = 5.<br><br> Plz hurry I need to finish this semester
mixas84 [53]
Answer: 6.5

6.5 -4 = 2.5

2.5 x 2 = 5
7 0
3 years ago
Read 2 more answers
Will GIVE BRAINIEST ANSWER!!!What is the slope of the line that is parallel to the y-axis and passes through the point (–1, 5)?
postnew [5]
If it's parallel to the y axis this means the slope will be any number over 0 with means it's D undefined
5 0
3 years ago
Read 2 more answers
-2n + 9 + 2n = 9 ? I need help
juin [17]

Answer:0n=0

Step-by-step explanation:

-2n+9+2n=9

-9 -9

———————

-2n+2n=0

-2n -2

———————

0n=0

5 0
3 years ago
Read 2 more answers
What does bounded mean
lakkis [162]

Answer:

a mathematical object that possesses a bound is bounded

Step-by-step explanation:

a lower bound is a value that is less than or equal to every element of set of data. a upper bound is a value that is greater than or equal to every element of set of data.

7 0
3 years ago
Read 2 more answers
Other questions:
  • I WILL MARK YOU BRAINLEST IF YOU HELP PLS HELP !!!!!!!!!!!!!!!!!!!!
    15·1 answer
  • What is the derivative of <br> (ln (7x))^(cos (5x))
    15·2 answers
  • HELP!!!
    7·1 answer
  • 5^3=? Can someone help me with this I am stuck lol
    12·2 answers
  • -4r&gt;16 I have to solve this for my math hw
    9·1 answer
  • Which list of elements is arranged in order of increasing atomic number?
    7·1 answer
  • How to find area of a triangle inside a rectangle
    9·2 answers
  • This is supposed to be a table btw
    15·1 answer
  • A footballer attempted 30 goals during a match and only makes 12. What fraction of the attempted goals did he make?
    10·2 answers
  • (-7,-5) m=0<br><br> In point slope form.<br> Please explain
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!