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
insens350
6 days ago
9

Q is in the interior of angle ROS S in the interior of angle QOP. P is in the interior of angle SOR. S is in the interior of ang

le ROT and the measure of angle ROT is 160° the measure of angle SOT is 100° and the measure of angle ROQ to equals the measure of angle QOS equals the measure of angle POT

Mathematics
1 answer:
PIT_PIT [3.9K]6 days ago
3 0

∠ROT=160°

∠SOT=100°

Now we calculate ∠SOR as follows: ∠SOR = ∠ROT - ∠SOT

∠SOR = 160° - 100°

∠SOR = 60°

It is stated that the angles ROQ, QOS, and POT all have the same measure.

Thus, ∠SOQ + ∠QOR = 60°

Since ∠SOQ equals ∠QOR, we can express this as:

2∠SOQ = 60°

From which we find ∠SOQ = 60° ÷ 2

∠SOQ = 30°

Also, ∠POT = ∠SOQ = ∠ROQ = 30°


You might be interested in
If g(x)=4x^2-16 were shifted 5 units to the right and 2 down, what would the new equation be?
lawyer [4008]
Try this method:
When a graph shifts right, replace 'x' with 'x' minus the number.
When it shifts down, subtract the number from 'y'.
So the final equation becomes: y = 4(x - 5)² - 18.
The answer is A.
4 0
13 days ago
Read 2 more answers
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the sh
lawyer [4008]

Answer:

The detailed work and solution can be found in the attachment

Step-by-step explanation:

7 0
2 days ago
True or False: Like the edges of a filled-in area, the endpoints of a polygon do not need to conform to snap points.
PIT_PIT [3919]

Answer:

The response is "False."

Explanation:

In geometry, an area refers to the space that an object occupies. A filled area consists of lines that connect to create an "edge."

These connecting lines help define the shape or area of the object and are known as "snap points." Keep in mind that "polygons" are made up of line segments that connect at their endpoints to form a closed shape. Consequently, it must adhere to "snap points."

This clarifies the response.

8 0
11 days ago
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to th
Svet_ta [4321]

Answer:

y>\frac{2}{3}x+3

Step-by-step explanation:

Step 1

Calculate the slope of the dashed line

The slope between two points is computed with the formula:

m=\frac{y2-y1}{x2-x1}

We consider

(-3,1) and (0,3)

and substitute into it:

m=\frac{3-1}{0+3}

m=\frac{2}{3}

Step 2

Determine the equation of the dashed line in slope-intercept form:

y=mx+b

The equation we established is:

m=\frac{2}{3}

b=3 ---> associated problem

Substituting yields:

y=\frac{2}{3}x+3

Step 3

Establish the inequality corresponding to the graph

Given that it is represented by a dashed line, the area to the left of this line is shaded.

Thus,

y>\frac{2}{3}x+3

Refer to the attached diagram for enhanced understanding of the problem.

8 0
9 days ago
Read 2 more answers
A rectangular schoolyard is to be fenced in using the wall of the school for one side and 150
lawyer [4008]

Answer:

Part 1) The equation is A(x)=150x-2x^2

Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

P=2x+y

P=150\ m

thus

150=2x+y

y=150-2x -----> this is equation A

The area of the rectangular school yard is

A=xy ----> this is equation B

Substituting equation A into equation B yields

A=x(150-2x)

A=150x-2x^2

Change to function notation

A(x)=150x-2x^2

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

A(40)=150(40)-2(40^2)

A(40)=2,800\ m^2    

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

A(x)=150x-2x^2

This forms a vertical parabola opening downwards

The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

The y-coordinate of the vertex denotes the maximum area

The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

The x-intercepts are located at x=0 m and x=75 m

The domain for A is the range -----> (0, 75)

All real numbers greater than zero and less than 75 meters

5 0
11 days ago
Other questions:
  • If  BD BC, BD = 5x – 26, BC = 2x + 1, and AC = 43, find AB.
    5·1 answer
  • The height of a rocket a given number of seconds after it is released is modeled by h (t) = negative 16 t squared + 32 t + 10. W
    13·2 answers
  • Given angle A, how can you construct an angle whose measure is 1/4 m of angle A?
    10·2 answers
  • Sari estimated the quotient of 120.78 ÷ 9.9 to be 12. She said that her estimate is slightly greater than the actual answer. Is
    13·2 answers
  • A 22.5 ounce candle burns at the rate of one ounce every 5 hours. write an equation for the amount of candle left
    12·1 answer
  • When Joanne checked her Work by substituting the value of the variable back into the equation she got an answer of 12.34 equals
    6·2 answers
  • If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, and , which condition needs to be met to prove ?
    14·2 answers
  • Tiffany sells two kinds of homemade tomato sauce. A quart of her Tuscan sauce requires 6 tomatoes and 1 cup of oil. A quart of h
    10·2 answers
  • A train travelled a distance of 6,000km from Lahore to Karachi in 22 hours. And during travel from Karachi to Lahore the train g
    11·1 answer
  • Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!