The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
How to determine the best strategy for the proof?The theorem is given as
Theorem: The diagonals of a parallelogram bisect one another.
Also, we have the following given parameters
AD//BC; AB//CD;
AC and BD intersect at M.
The above means that:
Lines AD and BC are parallel lines, and AB and CD are parallel lines
The statement AC and BD intersect at M implies that
AM = MC and BM = MD.
The above means that we need to calculate the lengths of the above segments, and then make comparison
The lengths of the segments can be calculated using the distance formula
Other than that, the coordinate of the point M needs to be calculated
The option that satisfies the above conditions is (a)
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Find the distance to the oil platform from each end of the beach. Enter both values.
Answer:
3671.8, 3576.4
Step-by-step explanation:
The third angle of the triangle is 19°.
Let the first length be a. Then,
[tex] \frac{a}{\sin 85^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ a=\frac{1200\sin 85^{\circ}}{\sin 19^{\circ}} \approx 3671.8[/tex]
Let the second length be b.
[tex] \frac{b}{\sin 76^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ b=\frac{1200\sin 76^{\circ}}{\sin 19^{\circ}} \approx 3576.4[/tex]
While on a holiday in Montego Bay, Jamaica, Marilyn shops for souvenirs for friends. She
has budgeted C$120 for souvenirs.
a) How much does she have in Jamaican dollars to spend on souvenirs?
She spend J$10039.48 in Jamaican currency on souvenirs.
What is currency?The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service. The US dollar is the country's recognized unit of exchange. A currency is the standardization of money, including banknotes and coins, that is used or in circulation as a means of exchange. A currency can also be defined more broadly as a system of money that has been used often over time within a particular setting, particularly by residents of a country state.
Given Data
While on a holiday in Montego Bay, Jamaica, Marilyn shops for souvenirs for friends. She has budgeted C$120 for souvenirs.
She spend a certain amount in Jamaican currency is:
CD$120(83.6623)
J$10039.48
She spend J$10039.48 in Jamaican currency on souvenirs.
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. Which of the following expressions is a factor of the
expression x² - 6x + 8?
F. x-3
G. x-4
H. x-5
J. x-6
K. x-8
The correct answer is [G] x-4
x-4 is the expressions is a factor of the expression x² - 6x + 8.
What is a factor?The positive integers that can divide a number evenly are known as the factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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Hi, can you help me to solve this exercise please. If MK=6 ft, find the length “MKL to the nearest Tenth!
To find the arc length we need to know the angle subtended by the arc.
From the diagram we notice that angle MNK is of 180°.
We also notice that:
[tex]\begin{gathered} m\angle JNK+m\angle KNL=90 \\ 52+m\angle KNL=90 \\ m\angle KNL=90-52 \\ m\angle KNL=38 \end{gathered}[/tex]Then the angle subtended by the arc MKL is 218°.
Now that we know this we need to remember that the arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]in this case the radius is 3 ft (The radius is half the diameter) then we have that:
[tex]\begin{gathered} s=2\pi(3)(\frac{218}{360}) \\ s=11.4 \end{gathered}[/tex]Therefore the arc length is 11.4 ft.
(b) y = x²+2x9 dx = 11x¹⁰ + 10x¹, where 10 dy is the derived function. dx Find the value of p and the value of q.
The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.
Given that,
The expression y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.
Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.
We have to find the p and q values.
Take expression
y=[tex]x^{p} +2x^{q}[/tex]
[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]
[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]
Here,
we can see p=11 and
2q=10
q=5
Therefore, the p and q values are 11 and 5.
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The analysis of a data set last year produced a line of best fit with equation y = 2.108x - 0.3818. Data was collected from the same sample this year and produced a line of best fit with equation y= 2.107x + 1.7455. Explain the verticalchange in going from last year's data to this year's data.
The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.
A florist sells a dozen roses for $35.40. She sells individual roses for the same unit cost. How much would 18 roses cost?
Answer: 53.1
Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1
A school district has the following high school committee officers.• Committee A: Amber, Calipso, Juan• Committee B: Megan, Amber, Sam
For the given high school committee officers.
We need to find the sharing between the committee officers.
AS shown:
Amber is a common between A and B
Calipso is a common between A and C
Juan is a common between A and D
Sam is a common between B and C
So, the figure represents the situation will be option A
Can the angle measures of a triangle be 46°, 82°and 50°
Answer:Explanation:
No
The sum of the interior angles of a triangle is always 180°. in this case, the sum is:
Then,
46 + 82 + 50 = 178
Since 178 and 180 are distinct, 46°, 82°and 50° can't be the angle measures of a triangle.
Please help with the following question:
Using it's concept, the probabilities are given as follows:
a) Both go off on schedule: 0.30 = 30%.
b) Both go off on schedule: 0.2 = 20%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
From the text of the problem, the probability of A and not B is of 0.2, that is:
A x (1 - B) = 0.2.
We can multiply the probabilities as the events are independent.
In item a, the probability of neither is of 0.2, hence:
(1 - A) x (1 - B) = 0.2.
From the first equation, we have that:
A = 0.2/(1 - B).
From the second equation, we have that:
(1 - A) = 0.2/(1 - B).
Hence:
A = 1 - A
2A = 1
A = 0.5.
Then we can find B as follows:
(1 - A) x (1 - B) = 0.2.
1 - B = 0.2/0.5
1 - B = 0.4
B = 0.6.
The probability of both is:
A x B = 0.5 x 0.6 = 0.30 = 30%.
For item b, we consider that:
(1 - A) x B = 0.3.
We also have that:
A x (1 - B) = 0.2.
From the first equation:
B = 0.3/(1 - A).
Then, replacing on the second:
A x (1 - 0.3/(1 - A)) = 0.2
Which has a solution of:
A = 0.5, B = 0.4.
Hence the probability of both is:
0.4 x 0.5 = 0.2 = 20%.
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Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. Leave your answer in terms of π. A. 6π/5kmB. 6 kmC. 12π/5kmD. 2π km
Given:
The radius of the circle = 2.4 kilometers
The measure of the arc = 150°
The length of the arc is given by the formula:
[tex]A=\theta\cdot r[/tex]Note: we will convert the angle from degrees to radian
So, the length of the arc =
[tex](150\cdot\frac{\pi}{180})\cdot2.4=\frac{150}{180}\cdot2.4\cdot\pi=2\pi[/tex]So, the answer will be option D. 2π km
Given that tan x= - 10 and sin x is positive, determine sin(2x), cos(2x) and tan(2x) . Write the exact answer. Do not round
Answer:
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Given that tanx and sinx is negative, determine sin(2x), cos(2x), and tan(2x) Write the exact answer. Do not round: Answer Keyboard sin(Zx) cos(2x) Submit Ar
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PLEASE HELP- Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 25 gallons of fuel, the airplane weighs 2060 pounds. When carrying 45 gallons of fuel, it weights 2188 pounds. How much does the airplane weigh if it is carrying 60 gallons of fuel?
The linear function which can be used to represent the situation is y = 6.4x + 1900 and airplane weight if it is carrying 60 gallons of fuel is 2,284 pounds
How to find linear functiony = mx + b
where,
x = the number of gallons and y = the weight of the aircraft in pounds.Now, we can use the two sets of data points given to us to first solve for the slope m as:
m = (2188 - 2060) / (45 - 25)
= 128 / 20
= 6.4
y - yo = m(x - xo)
y - 2060 = 6.4(x - 25)
y - 2060 = 6.4x - 160
y = 6.4x - 160 + 2060
y = 6.4x + 1900
if it is carrying 60 gallons of fuelx = 60
So,
y = 6.4x + 1900
y = 6.4(60) + 1900
y = 384 + 1900
y = 2,284 pounds
Therefore, the weight of the airplane if it is carrying 60 gallons of fuel is 2,284 pounds
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The position, d, in metres of an object
in motion as it travels is given by:
d= (t + 2) (t + 1.2)
It is the time in seconds.
This is an equation of motion.
By looking at it, we can learn about
how the object started moving.
First, expand the brackets.
t2+2.4+3.2t
The initial height is the constant
(no t) term.
What is the initial height?
Answer:
2.4m
Step-by-step explanation:
The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.
[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]
A telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 25% of her calls, there is no answer or the line is busy. She sells subscriptions to 9% of the remaining calls. For what proportion of calls does she make a sale?
If a telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 25 % of her calls, there is no answer or the line is busy. She sells subscriptions to 9 % of the remaining calls. The proportion of calls she make a sale is: 189/ 25.
ProportionGiven data ;
Calls without answer or line busy = 25%
Subscription sold out of remaining calls = 9%
Now let determine the proportion of calls she make a sale :
Proportion = 9 % × ( 100 % - 25 %)
Proportion = 9 % × 75 %
Proportion = 7.56 %
Since we were told the proportion of calls she make a sale we would have to convert the percentage into fraction :
Proportion :
Proportion = 7.56 %
Proportion = 189 / 25
Therefore we can conclude that the proportion is 189 / 25.
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Your teacher wants to put a garden in her backyard with a fence around it. The width needs to be the same size as the shed which is 8ft. If she bought 50 feet of fence and wants the largest garden she can make, what should the length of the garden be? Justify your thinking.
Th length of the garden when the teacher bought 50 feet of fence is 17 feet.
How to calculate the value?From the information, the width needs to be the same size as the shed which is 8ft and she bought 50 feet of fence and wants the largest garden she can make,
It should be noted that perimeter is calculated as:
= 2(Length + Width)
In this case, the perimeter is 50 feet.
2(Length + Width) = 50
2(Length + 8) = 50
2L + 16 = 50
2L = 50 - 16
2L =34
Divide
L = 34/3
L = 17 feet.
The length is 17 feet.
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Can someone help with this question?
The slope of the line is 2 / 3.
How to find the slope of a line?The slope of a line can be found as follows:
The slope of a line is change in y with respect to change in x.
In other words, the slope of a line is rise over run.
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Using (0, 3)(-3, 1)
Hence,
x₁ = 0
x₂ = -3
y₁ = 3
y₂ = 1
Therefore,
slope = 1 - 3 / -3 - 0
slope = -2 / -3
slope = 2 / 3
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Many people use mobile apps and online software to manage and create personalized budgets. Suppose your task is to develop an online tool for personal budgeting. What information would be included or entered? What types of features would the tool have?
The information that would be included or entered into the application or online tool for personal budgeting should include but not be limited to:
ExpensesExpense CategoriesAuto Expense summationExpense forecastingExpense reporting etc.IncomeIncome categoriesAuto Income summationIncome forecastingIncome reporting etc.The features that the tool will have are:
Item-by-item analysisCalendar Reporting AnalysisEmail and Password for login and User RegistrationCloud functionality so that you are able to back up and retrieve information.Learn more about Budgeting:
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[tex] \rm \int_0^ \infty \frac{1}{(1 + {x}^{ \phi} {)}^{ \phi} } dx \\ [/tex]
Recall that [tex]\phi = 1 + \frac1\phi[/tex].
In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have
[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]
Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to
[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]
Finally, substitute [tex]u=1-z[/tex].
[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]
What is the slope of a line perpendicular to the line whose equation is 4x-3y=-3 simple answer
Answer:
3=-4x+3y or -4x+3y=3
Step-by-step explanation:
it perpendicular
)) 24 cups 5) 3 cups
Answer: 12 cups
Explanation
Anna needs 6 pint of milk to produce yoghurt
1 pint = 2 cups
let cups of milk be x
1 pint of milk will give 2 cups
6 pints of milk will give x cups of milk
1 pint = 2cups
6 pints = x cups
Cross multiply
1 * x = 2 * 6
x = 12 cups
Therefore, Anna will need 12 cups of milk to produce a yoghurt.
The quantity of six and a number, times
five
In geometry,you can use deductive rules to
A
b
c
d
In geometry, you can use deductive rules to prove conjectures.
What is geometry?Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.
Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.
Given Data
In geometry, you can use deductive rules to
In geometry, you can use deductive rules to prove conjectures.
In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.
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Mai, Bill, and Dante have a total of $105 in their wallets. Dante has 3 times what Mai has. Bill has $10 more than Mai. How much does each have?
Answer:
Mai 19
Bill 29
Dante 57
Step-by-step explanation:
assume
mai = X
Bill = Y
Dante = Z
X + Y + Z = 105
Z = 3X
Y = 10 + X
then
X + Y + Z = X + 3X + 10 + X
5X + 10 = 105
5X = 95
X = 19
Y = 29
Z = 57
line m || line n m<4 = 72°
what is the measure of angle 5?
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle 4[/tex] and [tex]\angle 5[/tex] are supplementary since they are consecutive interior angles.
The sum of two integers is 236. If one of the integers is-122, determine the other.
Answer: 114.
Step-by-step explanation: This would be an equation to set up. We have all three parts of the equation: The sum of the two numbers (236), one of the integers (122), and then an unknown number, (let's call it x). Since 236 is the total, 122 is one of the numbers, we need to look for the unknown number, x. Then we would set it up as 122+x=236. Subtract 122 to both sides, to get 114.
Mary has 65 roses and 104 tulips. What is
the greatest number of bouquets they can be
divided into if there will be the same number
of roses in each bouquet and the same
number of tulips in each bouquet?
The greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet is 5.
Given that:-
Number of roses Mary has = 65
Number of tulips Mary has = 104
We have to find the greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet.
HCF (65, 104) = 13
Hence, the groups of 13 roses and 13 tulips will together make a bouquet.
From 65 roses, 65/13 = 5 bouquets can be made.
From 104 tulips, 104/13 = 8 bouquets can be made.
Min (5,8) = 5.
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I need help with this problem
We have the following function:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4}))+15[/tex]a) The initial height occurs at t=0. By substituting this value into the function, we get
[tex]H(0)=10\sin (2\pi(0-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(0)=10\sin (-2\pi\frac{1}{4})+15 \\ H(0)=10\sin (-\frac{2\pi}{4})+15 \\ H(0)=10\sin (-\frac{\pi}{2})+15 \end{gathered}[/tex]since sin(-Pi/2) is equal to -1, we have
[tex]H(0)=-10+15[/tex]Then, H(0)= 5, so the height is 5 feets.
b) The car will make a full rotation when the argument is shifted 2Pi:
[tex]H(t)=10\sin (2\pi(t-\frac{1}{4})+2\pi)+15[/tex]at this point H(t) must be equal to 5 feets. Then, we have
[tex]5=10\sin (2\pi(t-\frac{1}{4})-2\pi)+15[/tex]and we must find t. If we move +15 to the left hand side, we obtain
[tex]\begin{gathered} 5-15=10\sin (2\pi(t-\frac{1}{4})-2\pi) \\ \text{then} \\ 10\sin (2\pi(t-\frac{1}{4})-2\pi)=-10 \end{gathered}[/tex]By moving the coefficient 10 the the right hand side, we get
[tex]\begin{gathered} \sin (2\pi(t-\frac{1}{4})-2\pi)=-\frac{10}{10} \\ \sin (2\pi(t-\frac{1}{4})-2\pi)=-1 \end{gathered}[/tex]we can note that when
[tex]\sin \theta=-1\Rightarrow\theta=-90=-\frac{\pi}{2}[/tex]this implies that the argument of our last result is
[tex]2\pi(t-\frac{1}{4})-2\pi=-\frac{\pi}{2}[/tex]By moving 2Pi to the right hand side, we have
[tex]\begin{gathered} 2\pi(t-\frac{1}{4})=-\frac{\pi}{2}+2\pi \\ 2\pi(t-\frac{1}{4})=\frac{3\pi}{2} \end{gathered}[/tex]Now, by moving 2Pi to the right hand side, we have
[tex]t-\frac{1}{4}=-\frac{\frac{3\pi}{2}}{2\pi}[/tex]which gives
[tex]t-\frac{1}{4}=\frac{3}{4}[/tex]so, t is given by
[tex]\begin{gathered} t=\frac{3}{4}+\frac{1}{4} \\ t=1 \end{gathered}[/tex]That is, n 1 minute, the car will take one full rotation.
c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get
[tex]H(\frac{1}{2})=10\sin (2\pi(\frac{1}{2}-\frac{1}{4}))+15[/tex]which gives
[tex]\begin{gathered} H(\frac{1}{2})=10\sin (2\pi(\frac{1}{4}))+15 \\ H(\frac{1}{2})=10\sin (\frac{\pi}{2})+15 \\ H(\frac{1}{2})=10(1)+15 \\ H(\frac{1}{2})=25 \end{gathered}[/tex]that is, the maximum height is 25 feets
In the figure shown, &, //&₂. If m26=146°, what is the measure of 21 in degrees?
Answer:
angle 1 = 34 degrees
Step-by-step explanation:
Angle 2 and angle 6 are corresponding, therefore they are congruent and have a measure of 146 degrees.
angle 1 and angle 2 form supplementary angles so:
angle 1 = 180-angle 2
angle 1 = 180 - 146
angle 1 = 34 degrees
Isabelle is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $9, and her grandmother has pledged $1 per mile. If Isabelle walks a certain distance, the two donors will end up owing the same amount. How much will each donor owe?
Answer:
9 mileds
Step-by-step explanation: