Generally speaking you can count on 2,000 steps equaling one mile.
How many steps in 1 mile?
The average person takes between 2,000 and 2,500 walking steps per mile as counted by a fitness band, or phone motion sensor. Running steps have a longer stride length, which means you may take between 1,000 and 2,000 steps per mile.A total of 10,000 steps equals 4 to 5 miles. The number of steps per mile varies from person to person and depends on your stride length. Knowing how many steps are typical for a mile, you can begin to envision how far you need to walk to log 10,000 steps per day.It also works in reverse. The miles might not seem so long if you realize how many you manage to log during your daily activities. Keep moving and you will make it to your daily goal.To learn more about mile refers to:
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A bag contains 5 black pencils and 3 yellow pencils. What is the
probability of drawing 1 black pencil and 2 yellow pencils without
replacement?
The probability of drawing 1 black pencil and 2 yellow pencils without replacement is 0.035714.
The probability of drawing 1 black pencil and 2 yellow pencils without replacement can be calculated by multiplying the individual probabilities of drawing each pencil.
The first step is to calculate the probability of drawing a black pencil which is 5/8. Then, the probability of drawing the first yellow pencil is 4/7 and the probability of drawing the second yellow pencil is 3/6.
To find the probability of drawing all three pencils, you multiply these three probabilities together:
5/8 × 4/7 × 3/6 = 0.035714.
This result represents the probability of drawing 1 black pencil and 2 yellow pencils in that order without replacement.
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The quadratic functions f(x) and g(x) are described in the table. x f(x) g(x) −2 4 64 −1 1 49 0 0 36 1 1 25 2 4 16 3 9 9 4 16 4 5 25 1 6 36 0 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 18 units Right by 18 units Left by 6 units Right by 6 units
Right by 6 units should f(x) be shifted to match g(x).
What is the quadratic functions?A quadratic function is a type of mathematical function that can be represented by an equation in the form of ax^2 + bx + c, where x is a variable, a, b, and c are coefficients, and a ≠ 0. Quadratic functions are commonly used in various fields including physics, engineering, and finance, to model various real-world phenomena.
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Kevin's bank offered him a 4. 5% interest rate for his mortgage. If he purchases 3 points, what will be his new rate?
The new interest rate for his mortgage would be 3.75%.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
Purchasing a point simply implies negotiating for a lower rate of interest, which involves paying 1% of the loan in lieu of 1% interest reduction.
A point implies a reduction in interest rate by 0.25% while 3 points would reduce the interest rate by 0.75%(0.25%*3)
New interest rate=4.5%-0.75%=3.75%
Thus, The new interest rate for his mortgage would be 3.75%.
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The sum of the squares of three positive numbers in an ap is 155. The sum of the numbers is 21. Find the number
at a point on the ground 50 meters from the foot of a tree, the angle of elevation of the top of the tree is 48 degrees. find the height of the tree to the newest hundredth of a meter.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
what is trigonometry ?The association between triangle line angle lengths and angles is examined in the mathematics discipline known as trigonometry. The application of geometry in astronomical inquiry gave rise to the area's first appearance in the 18th century, roughly in the third centuries BC. Exact approaches mathematics focuses on certain right triangle and how they could be applied to operations. In trigonometry, there are six well-known trigonometric functions. They are identified by their various names and buzzwords: sine, cosine, parallel, cotangent, hyperbolic tangent, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly of right triangles. The features of all geometric forms are studied in geometry.
given
Base = 50, Elevation Angle = 48
An angle's opposite or adjacent side is its tan.
Tan (48),
height/distance, = 50*tan (48),
height, or 55.5 feet.
When measured from a position on the ground 50 meters away from a tree, the height of the tree is 55.5 meters to the nearest hundredth of a meter.
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A and B are oppoite vertice of a regular ix-ide hape, the point C and D are the midpoint of two oppoite ide. The area of the regular ix-ided hape i 60. Determine the product of the length of the line AB and CD!
The product of AB and CD in a regular hexagon with an area of 60 is (40 / √3) / 2.
To find the product of the length of AB and CD in a regular hexagon, we have to initially calculate the length of one side of the hexagon and later use that information to find the length of AB and CD.
Let us say that the length of one side of the hexagon = s.
W.k.t the area of the hexagon = 60, so we can use the formula for the area of a regular hexagon:
Area = (3 * √3) / 2 * [tex]s^2[/tex]
Making this equal to 60 and solving s:
60 = (3 * √3) / 2 * [tex]s^2[/tex]
120 = 3 * √3 * [tex]s^2[/tex]
40 = √3 * [tex]s^2[/tex]
(40 / √3) = [tex]s^2[/tex]
Taking the square root of both sides:
s = (40 / √3)^(1/2)
Now that we found the length of one side of the hexagon, So we can use that to find the length of AB and CD.
AB = the length of one side of the hexagon times the square root of 3, CD = the length of one side of the hexagon divided by 2.
So,
AB = s * √3
CD = s / 2
Now, we can find the product of AB and CD by multiplying them together:
AB * CD = s * √3 * s / 2
AB * CD = (s^2 * √3) / 2
AB * CD = (40 / √3) / 2
So the product of AB and CD in a regular hexagon with an area of 60 is equal to (40 / √3) / 2.
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21.1.4 Quiz: Thinking Chronologically
Question 5 of 5
Which timeline correctly organizes the founding of important world religions?
O A
B.
О с.
O D.
World Religions
Christianity was founded about 2,000 years ago.
• Islam was founded about 1,400 years ago.
.
Hinduism was founded about 3,500 years ago.
.
• Buddhism was founded about 2,500 years ago.
• Judaism was founded about 4,000 years ago.
·
← PREVIOUS
Buddhism
Judaism
Christianity
Hinduism
Judaism
Buddhism
Judaism
Islam
Christianity
Christianity
Islam
Christianity
Islam
Islam
Hinduism
Judaism
Hinduism is one of the suggested timelines for the foundation of significant world religions. Islam Buddhism Christianity The right answer is C.
Whose faith is the most popular worldwide?With more than two billion adherents, Christianity is the largest of the world's main religions. Christianity, which has been around for around 2,000 years, is founded on the life and teachings of Jesus. Faith and reason have always been seen as the basis of religious beliefs. There are reportedly 10,000 different religions in the globe, although almost all of them have localised, insignificant followings.
Which seven world religions are there?JUDAISM.
CHRISTIANITY.
ISLAM.
HINDUISM.
BUDDHISM.
SIKHISM.
ANIMISM.
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if f(x) = f(xf(xf(x))), where f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and \" f '(6) = 6\" , find f '(1).
The value of the composite function F(1) is 6.
Composite function;
When the result of one function is utilized as the input for another, this is known as a composite function.
Composite function;
F(x) = f(xf(xf(x)))
Also, we have
f(1) = 4, f(4) = 6, f '(1) = 4, f '(4) = 5, and f '(6) = 6,
Substitute 1 for x in the equation F(x) = f(xf(xf(x)))
So, we have
F(1) = f(xf(xf(1)))
From the question
f(1) = 4
So, we have
F(1) = f(xf(4))
From the question
f(4) = 6
So, we have
F(1) = f(6)
As a general rule
If f '(4) = 5 then f(6) = 6
So, we have
F(1) = 6
Hence, the value of the function F(1) is 6
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Which would cause a shift in the supply curve?
The supply curve shifts as a result of every factor but a change in market price. The movement along the supply curve and the change in price are correlated.
What is meant by supply curve?The supply curve can change depending on a number of variables, such as shifts in production costs (such as raw material and labor prices), advancements in technology, the level of competition and the number of sellers/producers, as well as the regulatory and tax environment.
Although a shift in the quantity supplied or along the supply curve for a given commodity or service is frequently brought about by a change in price, the supply curve itself does not alter as a result.
Input prices, weather conditions, technological advancements, as well as governmental taxes, regulations, and subsidies, can all modify the supply curve for goods and services, resulting in a different quantity being delivered for a given price.
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Line G has a slope of 5/4. Line H is perpendicular to line G, what is the slope of line g.
Answer:
-4/5
Step-by-step explanation:
Since Line H is perpendicular to Line G, its slope is the negative reciprocal of the slope of Line G.
Line G: m = 5/4
Line H: m = -4/5
Show that each term in the following equation has units of lb/ftº. Consider u as velocity, y as length, x as length, p as pressure, and u as absolute viscosity
The equation [tex]p*u*(dy/dx)[/tex]has units of[tex]lb/ftº[/tex], which is derived by multiplying the units of each of the three terms in the equation: [tex](lb/ft²)(ft/s)(1/ft).[/tex]
[tex]p*u*(dy/dx)[/tex]
[tex]lb/ftº = (lb/ft²)(ft/s)(1/ft)[/tex]
[tex]= (lb/ft²)(ft/s)(ftº)= lb/ftº[/tex]
1. The first term in the equation is pressure, p, which is measured in units of [tex]lb/ft².[/tex]
2. The second term is absolute viscosity, u, which is measured in units of ft/s.
3. The third term, [tex](dy/dx)[/tex] is the derivative of y with respect to x, and has units of 1/ft.
4. Multiplying the three terms together gives a result of[tex](lb/ft²)(ft/s)(1/ft)[/tex]which is equal to[tex]lb/ftº.[/tex]
The equation[tex]p*u*(dy/dx)[/tex] has units of [tex]lb/ftº[/tex], which is derived by multiplying the units of each of the three terms in the equation: [tex](lb/ft²)(ft/s)(1/ft).[/tex]
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which of the following statistics are unbiased estimators: a) all these (sample mean, sample proportion, and sample variance) b) the sample proportion c) the sample variance d) the sample mean
All these (sample mean, sample proportion, and sample variance) are the statistics are unbiased estimators.
What is meant by unbiased estimator?The difference between an estimator's expected value and the actual value of the parameter under consideration is known as bias in statistics. Unbiased estimators or decision rules are referred to as unbiased. "Bias" is a statistical term for an estimator's objective property.An estimator's expected value must exactly match the population parameter's value in order for it to be considered impartial. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator has bias if this difference is not zero.Given a straightforward random sample, the sample mean is an unbiased estimator of the population parameter because, over a large number of samples, it does not consistently overestimate or underestimate the true population mean.Learn more about unbiased estimator refer to :
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Find sn for the arithmetic series where a1=5 , An= -13 , n=10
The sum of the first 10 terms of the arithmetic sequence is given as follows:
-40.
How to obtain the sum of an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The sum for the first n terms of an arithmetic sequence is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In which:
[tex]a_1[/tex] is the first term.[tex]a_n[/tex] is the nth term.The parameters for this problem are given as follows:
[tex]n = 10, a_1 = 5, a_n = -13[/tex]
Hence the sum is given as follows:
S = 5 x (5 - 13)
S = -40.
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PLEASE HELP!!!! I WILL GIVE BRAINLIEST
Answer:
Below
Step-by-step explanation:
Work your way through this to make sure you understand:
The 'b' part at the bottom means you have to make SURE that BOTH of the answers actually WORK In the equation.... ONE MAY not...you have to try them both to see if one is 'extraneous' (which means 'does not work')
the sales tax on a 30,000 purchese was $2.40. What was the sales tax rate for this purchese?
(1 point) write the system of equations −5x 2y 2z=23x 2y 5z=2−3x 4y 2z=−3 as a matrix equation, that is, rewrite it in the form ⎡⎣⎢a11a21a31a12a22a32a13a23a33⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢b1b2b3⎤⎦⎥
the system of equations can be rewritten as a matrix equation as follows: ⎡-5 2 -2 3 -3 4 2 0 0 0⎤ ⎢x y z⎤= ⎡23 2 -3⎤
We have a system of equations in the form ax2 + by2 + cz = d, ex2 + fy2 + gz = h, and ix2 + jy2 + kz = l. To rewrite this system of equations as a matrix equation, we need to arrange the coefficients of the variables into a 3x3 matrix. This matrix is referred to as the coefficient matrix. For example, the coefficient matrix of our system of equations is:
⎡a11a21a31a12a22a32a13a23a33⎤ = ⎡-5 2 -2 3 -3 4 2 0 0 0⎤
Next, we need to arrange the variables in a separate matrix. This matrix is referred to as the variable matrix. The variable matrix for our system of equations is:
⎡xyz⎥=⎡x y z⎤
Finally, we need to arrange the constants of the equations in a separate matrix. This matrix is referred to as the constant matrix. The constant matrix for our system of equations is:
⎡b1b2b3⎤=⎡23 2 -3⎤
Therefore, the system of equations can be rewritten as a matrix equation as follows:
⎡-5 2 -2 3 -3 4 2 0 0 0⎤⎡x y z⎤=⎡23 2 -3⎤
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Find the horizontal asymptote of f of x equals quantity x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2}+3x+6 }{x^{2} +1}[/tex]
Here degree of numerator = degree of denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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The horizontal asymptote will be y = 2
What is Horizontal asymptote?
A graph's horizontal asymptote is a horizontal line y = b along which the graph approaches as the inputs approach or ∞ or –∞. A graph's slant asymptote is a slanted line y = mx + b along which the graph approaches the line as the inputs approach or ∞ or –∞
What is Square?
A square is a regular quadrilateral, which implies it has four equal sides and angles. It can alternatively be defined as a rectangle having two neighboring sides of identical length.
f (x) = [tex]\frac{2x^{2} +3x+6}{x^{2} +1}[/tex]
Here the degree of numerator = degree of the denominator
Hence the equation of horizontal asymptote y = 2/1
=2
Hence the equation of horizontal asymptote y=2
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simplify each expression by adding or subtracting {5a2+5-a} + {6-2a+4a4}
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
5a² + 5 - a + 6 - 2a + 4a⁴
Combine like terms.
5a² + 11 - 3a + 4a⁴
4a⁴ + 5a² - 3a + 11
Answer:
4a⁴ + 5a² - 3a + 11
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
Let's simplify the expression,
→ (5a² + 5 - a) + (6 - 2a + 4a⁴)
→ 5a² + 5 - a + 6 - 2a + 4a⁴
→ (4a⁴) + (5a²) + (-a - 2a) + (5 + 6)
→ 4a⁴ + 5a² + (-3a) + (11)
→ 4a⁴ + 5a² - 3a + 11
Therefore, this is the answer.
this was a question on my homework assignment from school but I don't know how to solve this without the height of the cone from top to bottom.
Answer: [tex]\sqrt{585}[/tex] units or [tex]3\sqrt{65}[/tex] units
Step-by-step explanation:
The formula for volume of a cone is π[tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]. You can find the height by plugging in 72π for volume and 3 for radius.
diameter = radius x 2, so 6/2=3 units for radius.
72π = π([tex]3^{2}[/tex])([tex]\frac{h}{3}[/tex])
72=9*[tex]\frac{h}{3}[/tex]
8 = [tex]\frac{h}{3}[/tex]
h = 24 units
The formula for slant height is [tex]\sqrt{{r}^2 + {h}^2 }[/tex]
Plug in 3 for r and 24 for h. You should get [tex]\sqrt{(9+576)}[/tex]=[tex]\sqrt{585}[/tex] or 3[tex]\sqrt{65}[/tex] as your answer.
Question: Which function is best represented by this graph?
Responses: f(x)=x2+2x−1 f(x)=x2−2x−1 f(x)=x2+2x f(x)=x2−2x
The quadratic function best represented by the graph is given as follows:
f(x) = x² + 2x.
How to model the quadratic function?The quadratic function of roots x* and x** is given by the rule presented as follows:
y = a(x - x*)(x - x**).
In which a is the leading coefficient.
The roots are given on the graph by the values of x when the graph crosses the x-axis, hence they are given as follows:
x* = -2, x* = 0.
Hence:
y = a(x + 2)(x)
When x = -1, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a(-1 + 2)(-1)
-a = -1
a = 1.
Meaning that the function is defined as follows:
f(x) = x² + 2x.
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A student is buying single-serve breakfast meals for the next 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl. How many different selections could the student make?
The student has 36 different combinations of breakfast options to choose from (4 options x 9 days).
To determine this:
The student has four different options for breakfast each day for 9 days, so the number of different selections could be calculated as 4 options x 9 days = 36 different selections.
This means that the student has 36 different combinations of breakfast options to choose from, as they can choose one option each day for 9 days. The options are meat bowl, vegetarian bowl, cereal bowl, and taco bowl, and they can choose any combination of these options for their 9 days of breakfast.
For example, they can choose a meat bowl on day 1, a vegetarian bowl on day 2, a cereal bowl on day 3, a taco bowl on day 4, and so on, or they can choose the same option every day, or they can mix and match their options in any combination they like.
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there are nine different positions on a baseball team. if a team has 15 players how many different line-ups can the team make? (assume every player can play every position.) the team can make different line-ups. baseball games consist of nine innings. a team wants to change its line-up every inning. if no game goes to extra innings, and a season consists of 66 games, how many complete seasons can the team play without repeating a line-up?
There are 18 seasons and the number of different line-ups the team can make is 24310
A) We are given the team has 17 players and there are 9 different positions in the team.
This is a combination question and thus, the number of different line-ups the team can make is;
C(17, 9) = 24310
B) We are told the basketball games consist of 9 innings.
Thus,
Number of games you can fill = 24310/9 = 2701.1111
And then we are told a season consists of 147 games.
Thus;
The number of complete seasons can the team play without repeating a line-up = 2701.1111/147 ≈ 18 seasons.
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If I paid $625 interest on $5000 that I borrowed at 5%, how many years did I borrow it? *Remember, I = P x R x T help fast
What are your tips for memorizing the functions sin, cos, tan, cot, csc, and sec?
The nonsense syllables Oh, Ah, and Oh-Ah (i.e. /o o. /) for O/H, A/H, and O/A can also be memorized as a substitute for the letters Sin, Cos, and Tan. For these letters, longer mnemonics like "Oscar Has A Hold On Angie" and "Oscar Had A Heap of Apples" can be used.
What is meant by function?A mathematical formula, rule, or legislation that establishes the link between the independent variable and the dependent variable (the dependent variable). At its most basic level, management is a discipline made up of the following five general tasks: organizing, staffing, leading, and controlling. A corpus of theories and practices on how to be a great manager includes these five functions. The eight categories are power, quadratic, rational, exponential, logarithmic, sinusoidal, polynomial, and linear. When examining a graph, one method is to perform a "vertical line test" to see if a relationship is indeed a function. The vertical line test can be used to determine if a graph accurately depicts a function. If a vertical line is drawn over it and is moved so that it only ever touches it once, the graph is said to be a function. If the vertical line crosses the graph multiple times, it is not a function.To learn more about function, refer to:
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What is the range of exponential function g?
A. g ( x ) < 0
B. g ( x ) > - 6
C. all real numbers
D. g ( x ) < 10
The range of exponential function g is g(x) > -6.
What is Exponential Function?The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be more significant than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given the graph of an exponential function,
the graph shows that It starts out as a horizontal line and then grows slowly before accelerating.
the horizontal line is parallel to the x-axis,
from the graph, we find that the function grows from -6,
so the function is f(x) > -6.
Hence option B is correct.
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a boy weighs 88kg which is 10% higher than his normal weight. What is his normal weight.
If the boy weighs 88kg and it is 10% higher than his normal weight, we can use the following formula to find his normal weight:
Normal weight = Current weight / (1 + 10%)
10% of the boy's weight is 0.10 * 88kg = 8.8kg
So, Normal weight = 88kg / (1 + 8.8kg) = 88kg / 1.10 = 80kg
Therefore, the boy's normal weight is 80kg.
1)The time (in minutes) that it takes a mechanic to change oil has an exponential distribution with mean 20.
a) Find P(X < 25), P(X > 15), and P(15 < X < 25)
b) Find the 40th percentile
a) P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859 and The 40th percentile is : 10.2165
What is exponential distribution?The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a certain event occurs. It refers to a system in which things proceed continuously and separately at such an average speed that is constant.
Let X = The time (in minutes) that it takes a mechanic to change oil
We have,
X = Exp (mean = 20)
The distribution function of X is: F(x) = P (X < x) = 1 - e{-x/20}
a) Consider, P (X < 25) = F(25)
= 1 - e{-25/20}
= 0.7135
Consider, P( X > 15)
= 1 - P (X < 15)
= 1 - 1 - e{-15/20}
= 0.4724
Consider, P(15 < X < 25)
= P (X < 25) - P (X < 15)
= 1 - e{-25/20} - 1 - e{-15/20}
= 0.1859
Hence,
P(X<25) = 0.7135 P(X>15) = 0.4724 P(15<X<25)=0.1859
b) We want to find x such that P(X<x) =0.40
Consider, P (X < x) = 0.40
1 - e{-x/20} = 0.40
x = 10.2165
Hence, The 40th percentile is : 10.2165
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don't quite understand. can someone explain pls?
The two column proof showing that m∠AKG = m∠HKB is as below and explained.
How to interpret two column proof?A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.
The two column proof showing the vertical angles are explained below.
Statement 1: Segment GH Intersects Segment AB at K
Reason 1: Given
Statement 2: m∠AKG + m∠GKB = 180°
m∠GKB + m∠HKB = 180°
Reason 2: Definition of supplementary angles
Statement 3: m∠AKG + m∠GKB = m∠GKB + m∠HKB
Reason 3: Substitution property
Statement 4: m∠AKG = m∠HKB
Reason 4: Subtraction property
Now, supplementary angles are defined as angles that sum up to 180 degrees and that is why m∠AKG + m∠GKB = 180° and m∠GKB + m∠HKB = 180°
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How do you simplify 2 + square root of 60 all divided by 4?
The simplified expression is [1 + √15]/2
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2 + √60]/4
So, we have
2 + 2√15]/4
Divide
1 + √15]/2
Hence, the expression is [1 + √15]/2
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below is a sketch of the region bounded by the line y=4−2x, the line y=0, and the line x=0
[tex]y = 4-2x , y = 0 , x = 0[/tex] The region is a triangle with the upper right corner at (2, 4).
1. Start by drawing the three lines: the line [tex]y=4−2x[/tex], the line y=0, and the line x=0.
2. Find the coordinates of the upper right corner of the region. To do this, we need to find the point where the two lines y=4−2x and x=0 intersect. We can solve this by setting y=4−2x and x=0, which gives us the point (0, 4). This is the upper right corner of the region.
3. The region is a triangle with the upper right corner at (2, 4).
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