answer.
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
Sloan [31]
2 years ago
9

The angle measure of thre angle of a triangle are p, q and r. Angle measure of q is one third of p and r is the difference of p

and q.
Mathematics
2 answers:
Snowcat [4.5K]2 years ago
7 0

The angle measure of three angle of a triangle are p, q and r.

As, sum of angles of triangle is 180 degrees.

So, p+q+r=180

Angle measure of q is one third of p

q=\frac{1}{3}p

r is the difference of p and q

r=p-q

As, q=\frac{p}{3}

So, r=p-q=p-\frac{p}{3}

r=\frac{3p}{3}-\frac{1p}{3}

r=\frac{3p-1p}{3}

r=\frac{2p}{3}

As, p+q+r=180 and q=\frac{p}{3} and r=\frac{2p}{3}

So, we get

p+\frac{p}{3}+\frac{2p}{3}=180

To get rid of fraction, let us multiply the complete equation by 3

3*p+ 3* \frac{p}{3}+ 3*\frac{2p}{3}=3*180

3p+p+2p=540

6p=540

To solve for p, let us divide by 6 on both sides

\frac{6p}{6} =\frac{540}{6}

p=90

As, p=90

So, q=\frac{p}{3}

q=\frac{90}{3}

q=30

And, r=\frac{2p}{3}

r=\frac{2*90}{3}

r=\frac{180}{3}

r=60

So, p=90, q=30, r=60

The three angles of triangle are 90,30 and 60

alex41 [277]2 years ago
3 0

In this question, i think we have to determine all the three angles of a triangle.

Since the three angles of a triangle are p,q and r.

Since, angle measure of q is one third of p, which implies

q=\frac{p}{3}

Angle measure of r is the difference of p and q, which implies

r=p-q (Equation 1)

By using the angle sum property of a triangle which states that the sum of all the angles of a triangle is 180^{\circ}

p+q+r=180^{\circ}

Substituting the value of r from Equation 1,

p+q+p-q=180^{\circ}

2p=180^{\circ}

p=90^{\circ}

Since q=\frac{p}{3}

q=\frac{90}{3} = 30^{\circ}

Since, r=p-q

r =90^{\circ}-30^{\circ}=60^{\circ}

You might be interested in
Adrian Beltre hit 48 home runs during the 2004 Major League Baseball season, but only hit 19 home runs in the 2005 season. By wh
aliya0001 [1]

Answer:

60.42%

Step-by-step explanation:

Number of home runs hit by Adrian Beltre in 2004 = 48

Number of home runs hit by Adrian Beltre in 2005 = 19

To find:

Percentage decrease in home run production from 2004 to 2005.

Solution:

To find the percentage decrease, first of all we need to find the decrease in the number of home runs and then we will divide with the number of home runs in 2004 and then finally will multiply the result with 100 to get the percentage decrease.

Decrease in the number of home runs = Number of home runs in 2004 - Number of home runs in 2005 = 48 - 19 = 29

\text{Percentage of decrease in Home runs} = \dfrac{\text{Decrease in home runs}}{\text{Number of home runs in 2004}}\times 100\\\Rightarrow \text{Percentage of decrease in Home runs} = \dfrac{29}{48}\times 100 \approx \bold{60.42\%}

Therefore, by 60.42% Beltre's home run production has decreased from 2004 to 2005.

4 0
2 years ago
−4x+60<72 or 14x+11<−31 solve for x
gulaghasi [49]
The answer to your question is x = 8
5 0
2 years ago
Read 2 more answers
Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position
lakkis [162]
<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
</span>
<span>BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2  \\ BO^2=9+16  \\ BO^2=25  \\ BO=5.
</span>
{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8

Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
<span /><span>
</span><span>
</span>\sin \theta=-0.8 .





3 0
2 years ago
fifteen darts have landed on the dart board shown. each dart scores 3,5, or 7 points. in how many different ways can the fifteen
lukranit [14]

Answer:

The answer is "8".

Step-by-step explanation:

Let the number are a, b, c then value is as follows:

a= 3

b= 5

c= 7

The addition of equation ⇒ a+b+c =15....................(i)

multiply by the value ⇒ 3a + 5b + 7c = 75 ...............(ii)

let b= 15-a-c which  subtract from equation (ii)  

equation:

 ⇒ 3a + 5b + 7c = 75

⇒ 3a + 5(15-a-c) + 7c = 75

⇒ 3a +75-5a-5c+7c = 75

⇒ 3a -5a-5c+7c  = 75-75

⇒ -2a + 2c  = 0

⇒ 2(c-a)  = 0

⇒ (c-a)  = 0

⇒ c=a

if we put value in between 0 to 7 from it satisfies the two equations, with c=a and b = 15 - a - c. So, the correct answer is 8.

3 0
2 years ago
Scott wanted to bjy a sofa which originally cost $500.Store A was selling it for 20% off plus 6.5% sales tax.Store B was selling
USPshnik [31]

Answer:

Store A offers the least amount for the sofa

Step-by-step explanation:

Cost of sofa =$500

For store A

Discount =20% off

The amount of the discount is

=20/100*500

=0.2*500

=$100

6.5% sales tax

The amount of tax is

=6.5/100*500

=0.065*500

=$32.5

Total cost of the sofa

=500-100+32.5

=400+32.5

=$432.5

For store B

Discount =30% off

The amount of the discount is

=30/100*500

=0.3*500

=$150

Shipping fee $85

Total cost of sofa

=500-150+85

=350+85

=$435

3 0
2 years ago
Other questions:
  • Which compound most likely contains polar covalent bonds?<br> NaCl<br> AlF3<br> Br2<br> NF3
    7·2 answers
  • ) What is the difference between a sequence and a series? A sequence is an ordered list of numbers whereas a series is an unorde
    14·1 answer
  • How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2.x+ 2 6x – 4y = –10
    12·2 answers
  • The area of a rectangular plank is 4500 cm². The plank was broken into two pieces, one of which is a square and the other a rect
    11·2 answers
  • Which behavior can help increase savings?
    5·2 answers
  • A habitat of prairie dogs can support mmm dogs at most.
    9·1 answer
  • In a park, a sidewalk is built around the edge of a circular garden as shown below. The sidewalk is 5 feet wide, and the garden
    9·1 answer
  • Four numbers from the set 0 to 9, including 0 and 9, are used to create a personal identification number. Once a number is used,
    9·1 answer
  • Juan drove 126 miles in 3 hours. If he continued at the same rate, how long would it
    15·3 answers
  • Ben and Joel are raising money for their class trip by selling wrapping paper. Ben raised $43.50 by selling 12 rolls of solid pa
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!