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
jonny [76]
2 years ago
13

P, Q & R form a right-angled triangle.

Mathematics
1 answer:
kvasek [131]2 years ago
5 0

Answer:

∠RPQ = 27

Step-by-step explanation:

In ΔSRQ,

∠R = 90

∠SQR = 36°

∠R + ∠SQR + ∠RSQ = 180    {Angle sum property of triangle}

90 + 36 + ∠RSQ = 180

126 + ∠RSQ = 180

         ∠RSQ = 180 - 126

        ∠RSQ = 54°

∠PSQ +∠RSQ = 180   {Linear pair}

∠PSQ + 54 = 180

 ∠PSQ = 180 - 54

∠PSQ = 126

In ΔPSQ,

SQ = PS ,

So, ∠SQP = ∠SPQ    {Angles opposite to equal sides are equal}

∠SQP = ∠SPQ   =x

∠PSQ + x +x = 180  {Angle sum property of triangle}

126 + 2x = 180

2x = 180 - 126

2x = 54

x = 54/2

x = 27

∠RPQ = 27°

You might be interested in
All of these ODEs model a system with a spring, mass and dashpot.
Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

This differential equation will have a characteristic equation of the form:

a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

  • If the discriminant is greater than zero, the solution is over-damped

  • If the discriminant is less than zero, the solution is under-damped

  • If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

-3y''-3y+3y=0

Which has characteristic equation of the form:

-3r^2-3r+3=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-3\\b=-3\\c=3

So:

Disc=(-3)^2-4(-3)(3)=9-(-36)=45

In this case:

Disc=45>0

Therefore the solution is over-damped.

Now, given the differential equation:

-2y''-4y'+1y=0

Which has characteristic equation of the form:

-2r^2-4r+1=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-2\\b=-4\\c=1

So:

Disc=(-4)^2-4(-2)(1)=16+8=24

In this case:

Disc=24>0

Therefore the solution is over-damped.

Finally, given the differential equation:

1y''+7y'+5y=0

Which has characteristic equation of the form:

1r^2+7r+5=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=1\\b=7\\c=5

So:

Disc=(7)^2-4(1)(5)=49-20=29

In this case:

Disc=29>0

Therefore the solution is over-damped.

6 0
3 years ago
PLEASE HELP ASAP!!!! 15 POINTS! AND I WILL GIVE BRAINLIEST!!!!
pochemuha

Answer:

9

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What are the sides of each figure
Naya [18.7K]
The question to that answer is 10
8 0
2 years ago
Write an equation of the line that passes through point p and is perpendicular to the line with the given equation
goldenfox [79]
Do you have the specific point??

Remember, if 2 lines are perpendicular, their slopes are opposite reciprocals. So if one line has a slope of 4, the other line should have a slope of -1/4.

Hopefully your equation is in y=mx+b form. If so,

make sure you know slope (m) and the y-intercept. After this is done, plug in the points from p for y and x, and make sure to turn m into -1/m. Solve for b, and your new equation should be y=(new slope)x+(new y-intercept)
5 0
3 years ago
0.175 as a percentage
Paul [167]

Answer: 17.5%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 0.175 × 100 = 17.5% (answer).

➥ The ease way:

1) Move the decimal point two places to the right: 0.175 → 1.75 → 17.5.

2) Add a % sign: 17.5%

Answer: 17.5%

3 0
2 years ago
Read 2 more answers
Other questions:
  • What is the midpoint of FB?<br><br>Point A<br>Point G<br>Point H<br>Point L
    8·2 answers
  • Write the expression in factored form 100m^2-121
    7·1 answer
  • The equation of a line is given below.
    7·2 answers
  • the lines are below are parallel . if the slope of the green line is - 2/3 , what is the slope of the red line?
    12·1 answer
  • A chef has 1/2 a pound of flour to divide equally into two containers. How much flour will be in each container?
    15·1 answer
  • write an equation in point-slope form and slope-intercept form for a line that passes through point(4,-1) and has a slope of -3
    5·1 answer
  • Please help me quick I will make a new question but it''s giving you about 98 points!!!1
    13·1 answer
  • find the exact value given that sin A= -4/5 with A in quadrant IV, tan B=7/24 with b in quadrant III, ; cos C= -5/13 with c in q
    11·1 answer
  • (3,-2) (4,5)<br> m = [?]
    6·2 answers
  • I need helpppppp please
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!