Write a two-column proof for each case of Theorem 10.6 Case 3
Given: P lies outside
Prove: m< ABC = 1/2m AC
Answers
The measure of an inscribed angle is one-half the measure of the central angle.
What is the inscribed angle and the circumscribed angle?An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.
The measure of an inscribed angle is one-half the measure of the central angle. The measure of a circumscribed angle is 180 degrees minus the measure of the central angle.
Given: P lies outside
m ∠ABC = m ∠DBC – m ∠DBA ( Addition Postulate, Subtraction Property of Equality)
m ∠DBC = m 1/2(arc DC)
m ∠DBA = m 1/2(arc DA) (The measure of an inscribed ∠ whose side diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = m 1/2 (arc DC) – m 1/2(arc DA) (Substitution)
m ∠ABC = 1/2 [m(arc DC) – m(arc DA)] (Factor)
m(arc DA) + m(arc AC) = m(arc DC) (Arc Addition Postulate)
m(arc AC) = m(arc DC) – m(arc DA) (Subtraction Property of Equality)
m ∠ABC = m 1/2 (arc AC) (Substitution)
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Related Questions
Which equation models the line that passes through points (2, 5) and (3, 1)?
Answers
Answer: y = -4x + 13
Step-by-step explanation:
Given points (2, 5) and (3, 1)
First Step find the slope given the two points:
Use the slope formula [tex]m=\frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{1-5}{3-2} = -4[/tex] (Result)
Slope is equal to -4
Second step plug into y - y1 = m(x - x1) formula (Point Slope Formula)
For this I am using the first coordinate pair given (2, 5)
y - 5 = -4(x-2)
y - 5 = -4x + 8
y = -4x + 13
According to your company's safety regulations, the distance from the base of a ladder to a wall that it leans against should be at least one fourth of the ladder's total length. You are given a 20 -foot ladder to place against a wall at a job site. If you follow the company's safety regulations, what is the maximum distance x up the wall the ladder will reach, to the nearest tenth?
F 12 feet
G 19.4 feet
H 20.6 feet
J 30.6 feet
Answers
The maximum distance up the wall the ladder will reach = 19.4 ft
The total length of the ladder, L = 20 ft
Minimum distance of the base of the ladder to the wall, B = 1/4 x 20 = 5 ft
Now we need to find the maximum distance up the wall the ladder will reach. This is obtained when the base distance is the least.
i.e., when the base = 5 ft.
Now the ladder, the wall and the base distance between wall and ladder constitute a right triangle. In this right triangle, the ladder is the hypotenuse and the height of the wall up to which ladder reach, 'x' is its altitude with base = 5ft.
Then using Pythagoras theorem,
[tex]L^2 = B^2 +x^2[/tex]
⇒ [tex]x^2 = L^2 - B^2 = 20^2 - 5 ^2[/tex]
⇒ [tex]x^2 = 375[/tex]
⇒ [tex]x=\sqrt{375}[/tex] = 19.3649
When rounded to the nearest tenth, (i.e., only one decimal place),we get,
⇒ x = 19.4 ft
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What's 704 divided by 24? Make sure to give an explanation for Brainliest!
Answers
Answer:29.3 repeating
Step-by-step explanation:Just use
calculator
What is the x intercept of the line x = 3.5
Answers
Answer:
x=3.5
Y=None
Step-by-step explanation:
100 POINTS! ANSWER PLEASE! Order the following rational and irrational numbers from least to greatest. -2 3/5, square root of 20, 3.9, 10/3, 3 7/8
Answers
The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
What is the arrangement of the numbers in ascending order?It follows from the task content that the numbers given are rational and irrational numbers.
To order the numbers, they should be converted to decimal numbers as follows;
-2 3/5 = -2.6√20 = 4.473.9 = 3.910/3 = 3.333 7/8 = 3.875Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.
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Use each recursive definition to write an explicit formula for the sequence. a₋₁ = 1, a n =a n ₋₁ +4
Answers
The explicit formula for the given sequence is a(n) = 1 + 4(n - 1).
What is termed as recursive definition?A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.
The recursive formula for an arithmetic sequence is as follows.
a(1) = 1 and a(n) = a(n - 1) + 4.
Remember that this formula provides us with two types of data.
1 is the first term.Add 4 to obtain any term out of its previous term. To put it another way, this same common difference is 4.Let's look for a formal formula again for sequence.
Remember that we can use the standard explicit form to represent a sequence in which the first term is A & common difference is B: A + B(n - 1).As a result, the sequence's explicit formula is a(n) = 1 + 4(n - 1).Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = 1 + 4(n - 1).
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What is the value?
90.5=
1/81
4.5
3
Answers
Answer:181/2
Step-by-step explanation:
90.5 as a fraction is 181/2
Choose the letter of the correct answer.Write the chosen letter on a separate sheet of paper.
1.A number is divisible by 4 if the last_____.
A.digit of a number is divisible by 4
B.digit is even
C.two digit formed is divisible by 4
D.digit is zero
Answers
Answer:
C
Step-by-step explanation:
a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.
Here are five number cards.
2
5
7
8
One of the cards is removed and the mean aver
of the remaining four number cards is 6
Which card was removed?
Answers
The card with the number 7 was removed.
What are equations?An equation, in its most basic form, is a mathematical statement that shows that two mathematical expressions are equal.For example, 3x + 5 = 14 is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.So,
The sum of all the numbers on the cards is 2+5+7+8+9=31.One card is removed, for example, with the number x.Now the sum new would be =31-x. ... (1)6 is the average of the remaining four cards.So the sum of the remaining four cards is 6(4) = 24. ...(2)The sum of the remaining four cards is represented by(1) and (2). As a result, they should be equal to 31 - x = 24.Subtraction 31 from both sides yields -x = -7 or x = 7.Therefore, the card with the number 7 was removed.
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Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
0
2
8
10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter
Answers
Answer:
$3.90
Step-by-step explanation:
Expected Value formula
[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]
where:
[tex]x_i[/tex] is an outcome.[tex]P(x_i)[/tex] is the probability of the outcome.Given table:
[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]
Substitute the given values into the Expected Value formula:
[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]
Therefore, the expected value is $3.90.
So, on average, you would expect to receive $3.90 in winnings per game.
The length of a rectangle is four more than double the width. If the perimeter is 80 inches, find the dimensions.
The width is inches.
The length is inches.
Answers
Answer: width = 12 inches
length = 28 inches
Step-by-step explanation:
l = 4 + 2w
Perimeter = 2 ( l + w )
80 = 2 ( 4 + 2w + w )
80 = 2 ( 4 + 3w )
80 = 8 + 6w
80 - 8 = 6w
72 = 6w
w = 72 / 6
width = 12 inches
length = 4 + 2 (12)
= 4 + 24
= 28 inches
checking
Perimeter = 2 ( 28 + 12 )
= 2 (40)
= 80 inches
correct
Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week and is the answer going to be negative or positive
Answers
Answer:
Negative. Because he should run all seven weeks to get positive result.
Below are the graphs of functions over the interval [-4,4]. Find the following for each function:
The domain
Zeroes of the function(the values of x where the value of the function is 0)
Intervals where the function is positive and intervals where it is negative
Answers
For the given function, we have that:
The domain is [-4,4].The function has no zeros.The function is positive for x <= 0.The function is negative for x > 0.What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.
Hence, the domain is [-4,4] for the given function.
What are the zeros of a function?The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.
For this problem, the function does not cross the x-axis, hence it has no zeros.
When a function is negative and when it is positive?Looking at a graph, we have that:
It is positive if it is above the x-axis.It is negative if it is below the x-axis.Hence, for the given function:
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State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
A scalene triangle has at least two congruent sides.
Answers
A scalene triangle has at least two congruent sides is a FALSE statement.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
A scalene triangle is a triangle whose all sides are unequal.
Since congruent sides are the sides that are equal in length but in a scalene triangle, none of the sides are equal to each other.
Hence "A scalene triangle has at least two congruent sides is a FALSE statement".
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(- 3/4x - 8) - (- 17 + 2/8x)
Answers
Answer:
9-x
Step-by-step explanation:
Copy and complete the proof.
Given: MN ≅ PQ, PQ ≅RS
Prove: MN ≅ RS
Proof:
Answers
We conclude that MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.
What clearly does "triangle congruency" imply?Two triangles are said to be congruent if all three corresponding angles are equal and all three corresponding angles are equal in measure.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.If two triangles gratify the five congruence conditions, they are congruent.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
Given: MN ≅ PQ, PQ ≅RS
To Prove: MN ≅ RS
There is a rule that states that:If a = b, and b = c; then automatically a = c.This rule satisfies the above condition.
If MN ≅ PQ and PQ ≅RS, then MN ≅ RS automatically.Therefore, MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.
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please help asap (true or false question)
Answers
Answer:
The statement is true.
Step-by-step explanation:
Let us plug[tex]24=-4(8)-8[/tex] in 8 for [tex]x[/tex] and 24 for [tex]y[/tex] in our equation: [tex]24 =-4 (8) - 8[/tex].
Now we will solve in the order described by PEMDAS.
-4(8)=32
32-8=24
24=24
Thus, our statement is true.
Determine whether the polygons are always, sometimes, or never similar. Explain your reasoning. (Lesson 7-2).
An equilateral triangle and a scalene triangle
Answers
The given polygons that is an equilateral triangle and scalene triangle can never be similar ,as it is not possible to map equilateral triangle onto scalene triangle or vice-versa.
As given in question,
Given polygons are equilateral triangle and scalene triangle
An equilateral triangle never similar to scalene triangle.
Reason:
All sides of equilateral triangle are equal where as all sides of scalene triangle are not equal.Using transformation dilations and rigid it is not possible to map equilateral triangle onto scalene triangle or vice-versa.Therefore, the given polygons that is equilateral triangle and scalene triangle can never be similar.
The complete question is:
Determine whether the given polygons are always, sometimes, or never similar. Explain your reasoning.
An equilateral triangle and a scalene triangle
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4)
What would be the actual length, if the length of the model is 10 ft and the scale factor is greater
than one?
a) 10 ft
(b) 9.5 ft
c) 4yd
Answers
The actual length, if the length of the model is 10 ft and the scale factor is greater than one is Option(b) 9.5 ft.
What is Scale-Factor?Any geometric figure or object's size can be changed with respect to its original size by applying a scale factor, which is a numerical value. It is used to find the length, area, or volume that is missing from an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined.The image is magnified if the scaling factor (k > 1) is greater than 1.The image is shrunk if the scale factor is less than 1 (0 < k <1).The image doesn't change if the scaling factor is 1 (k = 1).There cannot be a zero scale factor.The basic formula to find the scale factor of a figure is as:
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given:
length of the model = 10 ft
Now we determine which actual length has a scale factor greater than one.
(a) Scale factor = (10/10)
Here, we can see that the scale factor is equal to 1.
(b) Scale factor = (10/9.5) = 1.05
Here, we can see that the scale factor is greater than 1.
(c) Scale factor = (10/12) = 0.83 ( 1 yard = 3 foot)
Here, we can see that the scale factor is less than 1.
Therefore, the actual length is 9.5 ft.
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What is the image point of (1,4)(1,4) after a translation left 5 units and down 5 units?
Answers
The image of the point after the translation is (-4, -1)
How to determine the image point after the translation?The point is given as
(1,4)
The translation is given as
Left 5 units and down 5 units
This is represented as
(x, y) = (x - 5, y - 5)
So, we have
(x, y) = (1 - 5, 4 - 5)
Evaluate
(x, y) = (-4, -1)
Hence, the image of the point after the translation is (-4, -1)
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The circle below is centred at O.
a) Work out the size of angle x.
b) Which of the circle theorems below allows
you to calculate this angle?
x
27°
Not drawn accurately
The angle at the circumference in a semicircle is a right angle
Opposite angles in a cyclic quadrilateral add up to 180°
The angle between the tangent and the radius at a point
on a circle is 90°
The perpendicular line from the centre of a circle to a chord
bisects the chord
Two tangents that meet at a point are the same length
Answers
Answer:
[tex]\textsf{a)} \quad x = 63^{\circ}[/tex]
[tex]\textsf{b)} \quad \boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Step-by-step explanation:
Part (a)The triangle inside the circle is an isosceles triangle, since two of its sides are the radius of the the circle (and therefore equal in length).
Therefore, its two base angles are 27°.
A tangent is a straight line that touches a circle at only one point.
The tangent of a circle is always perpendicular to the radius.
[tex]\implies x + 27^{\circ} = 90^{\circ}[/tex]
[tex]\implies x +27^{\circ}-27^{\circ}= 90^{\circ} - 27^{\circ}[/tex]
[tex]\implies x = 63^{\circ}[/tex]
Part (b)The circle theorem that allows the calculation of angle x is:
[tex]\boxed{\begin{minipage}{8.5 cm}\sf The angle between the tangent and the radius at a point \\on a circle is $90^{\circ}$.\end{minipage}}[/tex]
Sherry mccoy is a tax consultant. she charges $425 per diem for her services. if she worked 180 days last year, what was her gross income for the year?
Answers
With a rate of $425/day, Sherry McCoy's gross income for the year, working 180 days, is $76,500.
Gross income refers to the total salary or wages and other form of earnings before any deductions or taxes.
If as a tax consultant, Sherry McCoy charges $425 per diem for her services, then her rate is $425/day.
Rate is a ratio that compares two different quantities which have different units.
We will use this rate to find how much earnings she got if she worked for 180 days last year.
gross income = rate x time
gross income = $425/day (180 days)
gross income = $76,500
Hence, working 180 days last year, Mary has a gross income of $76,500.
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if caleb pick 2 grapes in 15 minutes how many would he pick in 2 hours
Answers
Answer:16
Step-by-step explanation:
Write an equation in slopeintercept form that describes the line containing the points (-1,0) and (2,4) .
Answers
The equation in slope-intercept form y = 4/3 x + 4/3 contains the points (-1 , 0) and (2 , 4).
An equation of a line in slope-intercept form is given by the formula y = mx+ b, where m is the slope of the line and b is the y- intercept.
If you know two points on a line, you can use them to write the equation of the line in slope-intercept form.
First is to find the slope of the line using the two given points.
let Point 1(-1 , 0) and Point 2(2 , 4)
slope = m = (y2 - y1) / (x2 -x1)
m = (4 - 0) / (2 - -1)
m = 4/3
Next, use the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = 4/3 x + b
Using Point 1,
0 = 4/3 (-1) + b
0 = -4/3 + b
b = 4/3
Finally, set up the equation of the line in slope-intercept form.
y = mx+ b
where m = 4/3 and b = 4/3
y = 4/3 x + 4/3
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PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
Answers
3x+21+4=40
3x+25=40
-25 -25
3x=15
Divide by 3.
x=5
Hope this helps.
Answer:
x = 5
Step-by-step explanation:
3(x + 7) + 4 = 40 ( subtract 4 from both sides )
3(x + 7) = 36 ( divide both sides by 3 )
x + 7 = 12 ( subtract 7 from both sides )
x = 5
As a check
substitute x = 5 into the left side of the equation and if the value obtained is equal to the right side (40) then it is a solution
3(5 + 7) + 4
= 3(12) + 4
= 36 + 4
= 40
left side = right side
then x = 5 is the solution to the equation
Each sequence has eight terms. Evaluate each related series. -3.5,-1.25,1,. . . . . . , 12.25
Answers
An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.
First term a=-3.5,
Common difference d=2.25,
Number of terms n=8
Solution:
Here first term a=-3.5,
Common difference d=2.25
We know that,
f(n)=a+(n-1) d
f (8)=-3.5+(8-1)(2.25)
=-3.5+(15.75)
=12.25
We know that,
Sn=n2[2a+(n-1)d]
∴S8=82⋅[2(-3.5)+(8-1)(2.25)]
=4⋅[-7+(15.75)]
=4⋅[8.75]
=35
Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.
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Write an equation of a parabola with the given information.
vertex (3,2) , focus (4,2)
Answers
The equation that defines the parabola with vertex at the point (3, 2) and focus at (4, 2) is:
(Y - 2)² = 16(X - 3)
A parabola is a quadratic function that can move on any axis, it is composed of:
vertexfocal axisdirectrixThe equation that defines a parabola can be given by:
(x - h)² = 4p(y - k)(y - k)² = 4p(x - h)This will depend on its aperture
In this case we have the vertex of the parabola at the point (3, 2) and the focus at the point (4, 2) this is displaced on the x-axis to the right, so the parabola is of the form X = Y²
(y - 2)² = 4p(x - 3)
Focus
f = (0 + p, 0)
0 + p = 4p = 0 + 4p= 4(y - 2)² = 4*4(x - 3)
(Y - 2)² = 16(X - 3)
Y² - 4Y + 4 = 16X - 48
X = Y²/16 - Y/4 + 13/4
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help me please i need math
Answers
Based on the information given, the area of the trapezoid will be 89.7cm².
How to calculate the area?It should be noted that the formula for calculating the area of a trapezoid will be:
= (a + b)/2 × h
where a = 8
b = 13
h = 7.8
Area = (13 + 8)/2 × 7.8
= 21/2 × 7.8
= 11.5 × 7.8
= 89.7cm²
Therefore, based on the information given, the area of the trapezoid will be 89.7cm².
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Explain a strategy you use to identify a pattern.
Answers
A good way to find patterns in data is to arrange it in tabular form, which acts as an "input-output" machine.
What strategy do you use to identify a pattern?A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements. Any kind of event or object can be connected to the Pattern.
A pattern is referred to as a rule or a way in which a group of numbers is related to one another. Sometimes a pattern is also referred to as a sequence.
Putting data into a tabular format, which functions as an "input-output" computer, is a useful way to find patterns. It will process an input value, return an output value, and take another value as an input.
The table's process column will make it easier to comprehend how input and output are related.
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if g(x)=3x+7 what is g(4b) show your thinking
Answers
Answer: g(4b)=12b+7
Step-by-step explanation:
g(x)=3x+7
g(4b)=3(4b)+7
g(4b)=12b+7
