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
Kazeer [188]
2 years ago
13

Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and

Mathematics
1 answer:
ruslelena [56]2 years ago
6 0

Two lines y_1,y_2 are perpendicular if their slopes are in a relation m_1=-\frac{1}{m_2}.

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}

The first slope of a line passing through PQ is

m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1

The second slope of a line passing through RS is

m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1

Now check if m_1=-\frac{1}{m_2} is true

-1=-\frac{1}{1}\implies -1=-1

This means the two lines <em>are</em> perpendicular.

Hope this helps.

You might be interested in
Simplify the exponential expression. (−8) 2 =
sweet-ann [11.9K]

Answer:

-16

Step-by-step explanation:

6 0
3 years ago
10 POINTS! PLEASE HELP!! The illustration shows a compact disc tray that holds five CDs. The radius of each compact disc is 9 cm
MariettaO [177]

We can see that there are 5 CDs, each of radius 9 cm

<u>Area occupied by 1 disc:</u>

Area of a circle = πr²

Area of disc = π(9)²

Area of disc = 3.14 * 81 = 254 cm²

<u>Area occupied by 5 discs:</u>

Area occupied by 5 discs = Area occupied by 1 disc * 5

Area occupied by 5 discs = 254 * 5

Area occupied by 5 discs = 1270 cm²

3 0
2 years ago
What is the derivative of x times squaareo rot of x+ 6?
Dafna1 [17]
Hey there, hope I can help!

\mathrm{Apply\:the\:Product\:Rule}: \left(f\cdot g\right)^'=f^'\cdot g+f\cdot g^'
f=x,\:g=\sqrt{x+6} \ \textgreater \  \frac{d}{dx}\left(x\right)\sqrt{x+6}+\frac{d}{dx}\left(\sqrt{x+6}\right)x \ \textgreater \  \frac{d}{dx}\left(x\right) \ \textgreater \  1

\frac{d}{dx}\left(\sqrt{x+6}\right) \ \textgreater \  \mathrm{Apply\:the\:chain\:rule}: \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx} \ \textgreater \  =\sqrt{u},\:\:u=x+6
\frac{d}{du}\left(\sqrt{u}\right)\frac{d}{dx}\left(x+6\right)

\frac{d}{du}\left(\sqrt{u}\right) \ \textgreater \  \mathrm{Apply\:radical\:rule}: \sqrt{a}=a^{\frac{1}{2}} \ \textgreater \  \frac{d}{du}\left(u^{\frac{1}{2}}\right)
\mathrm{Apply\:the\:Power\:Rule}: \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1} \ \textgreater \  \frac{1}{2}u^{\frac{1}{2}-1} \ \textgreater \  Simplify \ \textgreater \  \frac{1}{2\sqrt{u}}

\frac{d}{dx}\left(x+6\right) \ \textgreater \  \mathrm{Apply\:the\:Sum/Difference\:Rule}: \left(f\pm g\right)^'=f^'\pm g^'
\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(6\right)

\frac{d}{dx}\left(x\right) \ \textgreater \  1
\frac{d}{dx}\left(6\right) \ \textgreater \  0

\frac{1}{2\sqrt{u}}\cdot \:1 \ \textgreater \  \mathrm{Substitute\:back}\:u=x+6 \ \textgreater \  \frac{1}{2\sqrt{x+6}}\cdot \:1 \ \textgreater \  Simplify \ \textgreater \  \frac{1}{2\sqrt{x+6}}

1\cdot \sqrt{x+6}+\frac{1}{2\sqrt{x+6}}x \ \textgreater \  Simplify

1\cdot \sqrt{x+6} \ \textgreater \  \sqrt{x+6}
\frac{1}{2\sqrt{x+6}}x \ \textgreater \  \frac{x}{2\sqrt{x+6}}
\sqrt{x+6}+\frac{x}{2\sqrt{x+6}}

\mathrm{Convert\:element\:to\:fraction}: \sqrt{x+6}=\frac{\sqrt{x+6}}{1} \ \textgreater \  \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}}{1}

Find the LCD
2\sqrt{x+6} \ \textgreater \  \mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \  \frac{x}{2\sqrt{x+6}}+\frac{\sqrt{x+6}\cdot \:2\sqrt{x+6}}{2\sqrt{x+6}}

Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions
\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \  \frac{x+2\sqrt{x+6}\sqrt{x+6}}{2\sqrt{x+6}}

x+2\sqrt{x+6}\sqrt{x+6} \ \textgreater \  \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}
\sqrt{x+6}\sqrt{x+6}=\:\left(x+6\right)^{\frac{1}{2}+\frac{1}{2}}=\:\left(x+6\right)^1=\:x+6 \ \textgreater \  x+2\left(x+6\right)
\frac{x+2\left(x+6\right)}{2\sqrt{x+6}}

x+2\left(x+6\right) \ \textgreater \  2\left(x+6\right) \ \textgreater \  2\cdot \:x+2\cdot \:6 \ \textgreater \  2x+12 \ \textgreater \  x+2x+12
3x+12

Therefore the derivative of the given equation is
\frac{3x+12}{2\sqrt{x+6}}

Hope this helps!
8 0
2 years ago
Decrease 1000 Naira by 10%<br><br>​
AleksAgata [21]

Answer:

900

Step-by-step explanation:

1,000 degreased by 10%=900

hope this helps

have a great day/night

8 0
3 years ago
Jack bought 1 3/4 pounds of pork and 2 3/4 pounds of beef.
jolli1 [7]

Answer:

4 1/2 pounds of meat

Step-by-step explanation:

if you have 2 adding fractions with 3 quarters just add it like 1 1/2 + 2 1/2 and add half to your final answer

3 0
3 years ago
Other questions:
  • A square window has an area of 196
    15·1 answer
  • The heights of 200 adults were recorded and divided into two categories. Which two-way frequency table correctly shows the margi
    6·1 answer
  • Write 905 in unit form
    8·2 answers
  • The average of 16 and x is 3. Find x.
    13·2 answers
  • Factorise x squared + 4x -12
    9·2 answers
  • Question 7
    7·1 answer
  • Can someone help me solve this equation?<br><br> -11v-14=v-14
    7·2 answers
  • Rebecca is on a game show and must choose between door A, B, or C. One of the doors opens to the grand prize. What is the probab
    5·1 answer
  • Find the measurements of the square:<br> Area<br> 256ft2
    7·1 answer
  • Pls help. !!!!!!!!!!!!!!!!!! (Give steps if you can)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!