Answers
The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.
In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.
Let's start the proof:
1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.
2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.
3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.
4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).
5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.
6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.
7. Now, we need to show that arc DE + arc FG = 360∘.
8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.
9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.
10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.
11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.
12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.
13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.
14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.
15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.
16. Simplifying, we have 90∘ = 180∘, which is a true statement.
17. Therefore, we have proven that m∠D + m∠F = 180∘.
Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
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Related Questions
Brainliest if correct What kind of coin is coin B And coin C
Answers
Answer:
coin B
Better Date 2000 American Silver Eagle 1 Troy Oz .999 Fine Silver BU Unc
Coin C
1923 United Kingdom Great Britain GEORGE V Silver Florin 2 Shillings Coin i63027
you can get those coins from ebay
What is the area?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
1247/90 km² or 13 77/90 km²---------------------------
Given is the parallelogram.
Area of a parallelogram:
A = bhSubstitute the values and find the area:
A = 3 2/9 × 4 3/10 = Convert to fraction 29/9 × 43/10 = Multiply 29*43/90 = 1247/90 = Fraction 13 77/90 Mixed numberdoes x*x*x*x*x = 5x?
I'm not really sure so it would help.
Answers
Answer:
Step-by-step explanation:
no ,x*x*x*x*x=x^5
x+x+x+x+x=5x
in multiplication those who have same base we add their power.
in addition those variables which have same base(or are like term) we add them.
Which of these are characteristics of good experimental design? Check all that apply. Good experimental design uses different methods for trials in an experiment. Good experimental design allows scientists to replicate experiments. Good experimental design tests only one variable at a time. Good experimental design plans how to record data so the data can be published. Good experimental design involves only one trial in an experiment. Good experimental design includes logging every step and data point of the experiment.
Answers
Answer:21
Step-by-step explanation:9+10
Answer:
B,C,D.F
Step-by-step explanation:
Round to the nearest thousands 34,385
need help
Answers
Answer:34,000
Step-by-step explanation:
Answer:
its 34,000 because it below 5
Step-by-step explanation:
brainliest please
Rewrite the equation in simplified slope-intercept form: 77-y=5x
Answers
The equation of the line in slope - intercept form is -
y = - 5x + 77.
What is the equation of a straight line in slope - intercept form?The equation of a straight line in slope - intercept form is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is the equation as -
77 - y = 5x
We have the equation in the slope - intercept form as -
77 - y = 5x
y = 77 - 5x
y = - 5x + 77
Therefore, the equation of the line in slope - intercept form is -
y = - 5x + 77.
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The pie chart shows student participation in fundraisers
at Mountain View Middle School.
Mountain View Middle School
Fundraisers
Which describes a bar diagram showing the percent of
students who participated in dances?
1 shaded square out of 10 squares
2 shaded squares out of 10 squares
3 shaded squares out of 10 squares
4 shaded squares out of 10 squares
20
Carnival
Car Wash
Bake Sale
Talent Show
10
50
5
15
Dances
Answers
Answer:
Step-by-step explanation:
If you add all of the numbers up, you get 100. Dances are colored purple, and that is 20. 20/100 simplified is 1/5. 1/5 is equivalent to 2/10. Therefore, the answer is 2 shaded squares out of 10 squares.
See question in screenshot below:
Answers
The measure of the length x, using the trigonometric ratios, is given as follows:
x = 277.05.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine = opposite side/hypotenuse.Cosine = adjacent side/hypotenuse.Tangent = opposite side/adjacent side = sine/cosine.The measure of x is divided into two parts, as follows:
Part 1: Adjacent to the angle of 41º.Part 2: Adjacent to the angle of 38º.The total measure is given by the sum of each of these two measures.
The measure of the first part is obtained as follows:
tan(41º) = 114/x1
x1 = 114/tan(41º)
x1 = 131.14.
The measure of the second part is obtained as follows:
tan(38º) = 114/x2
x2 = 114/tan(38º)
x2 = 145.91.
Hence the total measure of x is obtained as follows:
x = x1 + x2 = 131.14 + 145.91 = 277.05.
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A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answers
Answer:
Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)
Evaluate
(y + z)^2when y = -8, z =19
Answers
Answer:
Substitute the value of the variable into the expression and simplify.
121
Step-by-step explanation:
Step-by-step explanation:
(y + z)^2
substitute in the given
y = -8, z = 19
(-8 + 19)^2
(11)^2
121
Hope this helps :)
A packet has 54 sheets of paper. Suraj uses 4/9of the sheets. How many sheets has he used?
Answers
Answer:
Step-by-step explanation:
54(4/9)
216/9
24 sheets
Answer:
Suraj used 24 sheets of paper
Marama is planting a rectangular garden in her backyard. She is planning to fence the garden with 28 feet of wired fencing. The garden's area can be represented by the function A(t) = -t2+ 14t where t is the length of a side. What are all of the appropriate values of the domain for the graph of this function? Explain your answer in terms of the situation. Use words, numbers, and/or pictures to show your work.
Answers
The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.
To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.
The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.
We are also told that Marama plans to fence the garden with 28 feet of wired fencing.
Now, let's break down the problem and find the appropriate values for the domain.
We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:
\(Perimeter = 2t + 2w\),
where t is the length of one side (the width) and w is the length of the other side (the width).
The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:
\(2t + 2w = 28\).
Simplifying this equation, we have:
\(t + w = 14\).
We can express w in terms of t as \(w = 14 - t\).
The area of a rectangle is given by the product of its length and width:
\(Area = t \times w\).
Substituting the expression for w from step 2, we have:
\(A(t) = t \times (14 - t)\).
Simplifying further:
\(A(t) = 14t - t^2\).
To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.
We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).
This shows that the value of t can range from 0 to 14, inclusive.
Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).
To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):
^
|
A(t)|
|
|_______________________________
0 t 14
The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.
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Find the sum. (6p+ 15) + (10p-9) O A. 16p+ 6 O B. 6p+ 6 O C. 16p - 6 O D. 16p+24
Answers
Given the expression (6p+15)+(10p-9)
Expand the parenthesis
\(\begin{gathered} (6p+15)+(10p-9) \\ =\text{ 6p+15+10p-9} \end{gathered}\)
Collect the like terms
\(=6p+10p+15-9\)Evaluate the resulting expression:
\(16p+6\)Hence the sum required is 16p+6. Option A is correct
A train leaves Station A traveling west at 60 miles per hour for 7 hours, and then continues to travel west on the same track for 3 hours at 55 miles per hour, where it stops at Station B. How far is Station A from Station B?
Answers
Answer: 585 miles
Step-by-step explanation: 60 x 7 for the first 7 hours = 420 miles, then 3 x 55 for the last 3 hours = 165 add them together, 420+265 you get= 585
60 miles per hour x 7 hours = 420 miles
55 miles per hour x 3 hours = 165 miles
Total miles = 420 + 165 = 585 miles
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answers
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Suppose a mom uses the following formula for the cost, C, in dollars of acamping trip if there are n campers going on the trip.C = 15n + 75a. solve for n in the formula above to obtain a formula expressing n as a function of C n=______b. how many campers can go if her budget is 225 dollars =_____campers
Answers
a)
To solve for n, we gotta take n to one side and everything else to another, like this:
\(\begin{gathered} C=15n+75 \\ 15n=C-75 \\ n=\frac{C-75}{15} \end{gathered}\)b)
Given a budget of 225 dollars, it means C = 225.
We need to figure out n, which we already have (the formula) from part (a) above.
So, let's use that and plug in C = 225.
Thus:
\(\begin{gathered} n=\frac{C-75}{15} \\ n=\frac{225-75}{15} \\ n=\frac{150}{15} \\ n=10 \end{gathered}\)Thus, she can take 10 campers
What are the mathematical names for these shapes?
Answers
The mathematical names of the given figures are:
a. square pyramid
b. sphere
c. cube
d. triangular pyramid
What are Mathematical Names of Shapes?A pyramid has four triangular faces and a base that is usually a square. For example, figure A in the diagram is a square pyramid.A sphere is a three-dimensional shape that has a round, ball-like shape. Figure B is an example of a sphere.A cube is a three dimensional shape that has 6 square surfaces. An example of a cube is the shape in figure C. The shape in figure D is a triangular pyramid having a triangular base.Thus, the mathematical names of the given figures are:
a. square pyramid
b. sphere
c. cube
d. triangular pyramid
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a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
Answers
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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A restaurant has 100 tables and 28 of the tables seat 2 people and 72 of the tables seat 4. What percentage of the tables seat 4 people?
Answers
What kind of triangle is shown
Please help me my minds not working today
Answers
Answer: acute equilateral
Step-by-step explanation:
Guess the rule and add the next number in the sequence.
6, 8, 12, 18, 26,
Answers
Answer:
The rule: Adds twice as much as the previous number added
Next number: 38
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
The rule is every time you add 2 so 6 plus 2 equals 8 them you would do 8+4=12. your counting by 2 as u go up the line.
The question is attached above/below
Answer it Thanks
Answers
\( :) \)
Write a function rule for
Answers
Answer:
x^2
Step-by-step explanation:
1^2=1
2^2=4
3^2=9
If the prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5, what would you need to multiply it by to get the prime factorization of 3000?
Answers
To get the Prime factorization of 3000 we need to multiply by 5.
What is Prime Factorization:When the number is factored using prime numbers, or primes, the process is known as prime factorization. The easiest method to determine the prime factors of a given number is to keep dividing the given number by the prime factors until we will get 1.
For example, the Prime factorization of 45 is given below
=> 45/5 = 9, 9/3 = 3, 3/3 = 1
=> 45 = 5 × 3 × 3
Here we have
The prime factorization of 600 is 2 x 2 × 2 × 3 × 5 × 5
Let us assume that on multiplying with p,
we will get the factorization of 3000
=> 2 x 2 × 2 × 3 × 5 × 5 × p = 3000
=> p = \(\frac{3000}{2\times 2 \times 2 \times 3 \times 5 \times 5}\)
Her 2 x 2 × 2 × 3 × 5 × 5 = 600
=> p = \(\frac{3000}{600}\)
=> p = 5
Therefore,
To get the Prime factorization of 3000 we need to multiply by 5.
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Kecia made a password that consists of 4 digits, 0-9. None of the digits are the same. How many possible passwords did Kecia choose from? (HOW DID YOU GET YOUR ANSWER PLEASE SHOW YOUR WORK!!)
A. 70%
B. 5040
C. 5.2
D. 4(2X+4)
E. 300%
F. 2.5
G. 5267
H. 4X(2X-4)
I. 299%
J. .4
Answers
Answer:
There are 9 possible numbers for the first number. There are 8 possible numbers for the second number since one number has been picked. For the third number there are 7 possible numbers.
9*8*7=5040
Step-by-step explanation:
Mr. Apollo’s art class is designing tiles for a mosaic.
The class worked in groups, and each group selected a color and a set of shapes to use.
Match the shape names of all of the shapes in each group by dragging them to the correct color in the table.
Names may be used once, more than once, or not at all.
Set 1 has 4 blue rectangles, Set 2 has 4 red triangles, Set 3 has 4 green kites and Set 4 has 3 yellow trapezoids.
Rectangle returned to the choices list. Parallelogram
Rhombus
Square
Trapezoid
Rectangle
Triangle
Right Triangle
Isosceles Trapezoid
Obtuse Triangle
Blue
Red
Green
Yellow
Answers
To complete this task classify the shapes by considering both the color and the features of the shape.
How to classify a shape?Identify the shape. For example, a triangle has 3 sides and if one of the sides has a 90° angle, the triangle is a right triangle.Assign the name to the shape.Identify the color.Match the shape to set 1, 2 or 3. For example if the right triangle is red, this will belong to set 2.Note: This question is incomplete because the shapes are not given; due to this, the answer is based on general knowledge.
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List the angles in order from smallest to largest 2.8 3.2 and 3
Answers
Answer:
2.8, 3, 3.2 jhgfdsdrftggggggbhjn
Use the Laws of logarithms to rewrite the expression
Answers
The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)
Rewriting the expression using the laws of logarithmsFrom the question, we have the following parameters that can be used in our computation:
log₃(x²∛y²)
The product law of logarithms states that
log(ab) = log(a) + log(b)
Using the above as a guide, we have the following:
log₃(x²∛y²) = log₃(x²) + log₃(∛y²)
The power law of logarithms states that
log(aᵇ) = blog(a)
Using the above as a guide, we have the following:
log₃(x²∛y²) = 2log₃(x) + 2/3log₃(y)
This means that the values of A and B are A = 2 and B = 2/3
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Find m\angle Am∠Am, angle, A.
Round to the nearest degree.
Answers
Answer:
m∠A = 106°
Step-by-step explanation:
All three sides of the triangle are given in the question.
To find the measure of included angle A between two sides we will apply cosine formula,
BC²= AB² + AC² - 2(AB)(AC)cosA
(13)² = (10)² + (6)² - 2(10)(6)cosA
169 = 100 + 36 - 120cosA
cosA = \(\frac{-169+136}{120}\)
cosA = -0.275
A = \(\text{cos}^{-1}(-0.275)\)
A = 105.96°
A ≈ 106°
Therefore, m∠A = 106° will be the answer.
What is the translation from
a) shape X to shape Z?
b) shape Z to shape X?
Answers
The translation form of each shape is given as follows:
a) X to Z: (x, y) -> (x + 5, y + 2).
b) Z to X: (x, y) -> (x - 5, y - 2).
What are the translation rules?The four translation rules are defined as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the composition of translations, we add the coordinates, hence:
-2 + 7 = 5.5 - 3 = 2.Hence the rule from X to Z is given as follows:
(x, y) -> (x + 5, y + 2).
From Z to X, we have the inverse rule, hence:
(x, y) -> (x - 5, y - 2).
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