To form an isosceles triangle Jefferson should plot the third point at (4,2).
What is an isosceles triangle?Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.
Given, Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph.
the given points are,
(-2,-4) (4,-4)
Let, x₁ = -2, y₁ = -4
x₂ = 4, y₂ = -4
distance between (-2,-4) (4,-4) is given as,
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(4 - -2)² + (-4 - -4)²]
= √[(4 + 2)² + (-4+ 4)²]
= √[(6)² + (0)²]
= √[(6)²
= 6
now verifying with other options,
1). For points (-2, -9),
Distance between (-2, -4) and (-2, -9) = √[(-2 + 2)² + (-4 + 9)²] = √5
Similarly, distance between (4, -4) and (-2, -9) = √[(4 +2)² + (-4 + 9)²] = √61
side is not equal. So the triangle is not isosceles.
2). For a point (3, 1),
Distance between (3, 1) and (-2, -4) = √[(3 + 2)² + (1 + 4)²] = 5√2
Distance between (3, 1) and (4, -4) = √[(3 - 4)² + (1 + 4)²] = 26
side is not equal. So the triangle is not isosceles.
3). For a point (-2,0),
Distance between (-2, 0) and (-2, -4) = √[(-2 + 2)² + (-4 + 0)²] = 4
Distance between (-2, 0) and (4, -4) = √[(-2 - 4)² + (0 + 4)²] = 2√13
side is not equal. So the triangle is not isosceles.
4). For a point (4, 2),
Distance between (4, 2) and (-2, -4) = √[(4 + 2)² + (2 + 4)²] = 6√2
Distance between (4, 2) and (4, -4) = √[(4 - 2)² + (2 + 4)²] = 6
Sides are equal so the triangle formed is an isosceles triangle.
Therefore, the third coordinate is (4, 2).
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The complete question is,
Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. He has plotted the two points shown. Where should he plot the third point?
The point is on the graph is (-2,-4) (4,-4)
The options is
(-2,-9)
(3,1)
(-2,0)
(4,2)
can someone please give me 4 examples of problem of radical operation
Step-by-step explanation:
The answer is do ur homework ur self
Which expression is equivalent to g^2h√5g?
HELPP!!
One rental store charges a one time fee of $12 plus $3 per hour to rent a power washer. A
second rental store charges $15 plus $2 per hour to rent a power washer. For what number
of hours is the rental cost the same?
Answer:
3 hours
Step-by-step explanation:
First, we need to set up an equation with a variable representing the time.
12 + 3x = 15 + 2x
Then you solve.
12 + 3x = 15 + 2x
-2x-12 -2x-12
x = 3
Two people are working on a joint project. Each person i puts in some effort x i ∈[0,1], which costs x i 2, and the outcome of the project is worth 2x1x2 . The worth of the project is split equally between them, regardless of their effort. a. Find the Nash equilibria of the game. b. Determine whether there are effort levels that yield a total payoff higher than that of the Nash equilibrium (Hint: factor the total payoff function).
a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Nash Equilibrium & Total Payoffa. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.
In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:
pi = (2x1x2) / 2 = x1x2
By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:
dpi/dx i = x2 - xi = 0
Since xi is in the range [0,1], we have xi = x2.
Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b. Total Payoff: The total payoff of the project is given by:
pt = x1x2 + x1x2 = 2x1x2
By factoring the total payoff function, we get:
pt = 2x1x2 = 2x1x1 = 2x12
So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.
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12. Town A has 4.563 residents.
Town A has 127 more than
4 times the number of residents
of Town B. How many residents
does Town B have?
Answer: We can set up an equation to represent the given information:
4.563 = 4B + 127
where B is the number of residents in Town B.
To solve for B, we can first subtract 127 from both sides:
4.563 - 127 = 4B
Then divide both sides by 4:
B = (4.563 - 127) / 4
B = 1.140775
So Town B has approximately 1.140775 residents.
Step-by-step explanation:
I earns 875,00 in five working days so how many days must I work in order to earn R3500,00
The number of days you will need to work in order to earn R3500,00 given the ratio of amount earned in 5 days is 20 days
How many days will I earn R350,000?If in 5 working days, you earn R87,500
Then, you will earn R350,000 in x working days
The task content can be solved using the concept of equivalent ratio;
Number of days : amount earned
5 : 87,500 = x : 350,000
5/87500 = x / 350,000
cross product
5 × 350,000 = x × 87500
1,750,000 = 87,500x
divide both sides by 87,500
x = 1,750,000 / 87,500
x = 20
Hence, you need to work for 20 days in order to earn R350,000
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Which point is a solution to the system of linear equations? y = −x + 2 x − 3y = 6
EASY POINTS 12 POINTS!
Find an ordered pair (x, y) that is a solution to the equation.
-x+2y=7
(x, y) = ????
Answer: y-int = (0,7)
x-int= (-7,0)
Step-by-step explanation:
-x+2y=7
2y=x+7
y-int = (0,7)
x-int= (-7,0)
on the graph, (1,4) (2, 4.5) (3, 5) etc
EASY POINTS!
What is the total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost?
$9.60
$172.93
$72.93
$159.60
Answer:
The total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost would be $159.60. To calculate this, multiply the original cost by 1.064, which is the amount of the sales tax in decimal form. For example, if the original cost was $150, then the total cost would be $150*1.064 = $159.60.
What is the area of a circle that has a circumference of 24¯?
Answer:
Below
Step-by-step explanation:
Circumf = pi * 2 r
Circumf/(2pi ) = r
area = pi r^2
= pi * (circumf/2pi)^2
= circumf^2 / 4 pi =
24^2 / (4 pi) = 45. 8 units^2
Answer:
45.84 units^2
If one wanted to find the probability of ten customer arrivals in an hour at a service station, one would generally use the _____ probability distribution.
a. Poisson
b. exponential
c. binomial
d. hypergeometric
To calculate the probability of arrival of ten customer in one hour at a service station then use of option a. Poisson probability distribution is more applicable.
Poisson probability distribution represents the discrete probability of any event.This represents the occurring of the independent event in a fixed interval of time.It is also called constant mean rate.Here arrival of ten customer in fixed time interval of one hour we have to calculate.It implies that the Poisson probability distribution is the best way to calculate the given situation.Therefore, the required probability for the given situation is Poisson probability distribution .
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A single card is drawn from a standard 52-card deck. What is the probability that the card is either a)a jack, or a five, or a king? b)a heart, or a club, or a spade? c)an ace, or a queen, or a heart? d)a seven, or a queen, or a heart, or a diamond?
Probability on cards.
(a) P(Jack or five or King) = 12/52 = 3/13
(b) P(heart or club or spade) = 39/52 = 3/4
(c) P(Ace or Queen or heart) = 19/52
(d) P(seven or Queen or heart or diamond) = 30/52 = 15/26
What is probability?Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceA single card is drawn from a standard 52-card deck. Find the probability that the card is either
a) a Jack, or a five, or a Jing?
b) a heart, or a club, or a spade?
c) an Ace, or a Queen, or a heart?
d) a seven, or a Queen, or a heart, or a diamond?
The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
The total number of events is n(S) = 52.
Let's count each number of favorable outcomes, then the probability of the event!
(a) The number of Jack is 4, five is 4, and King is 4. They are 12.
P(Jack or five or King) = 12/52 = 3/13
(b) The number of hearts is 13, clubs is 13, and spade is 13. They are 39.
P(heart or club or spade) = 39/52 = 3/4
(c) The number of hearts is 13, other Aces is 3, other Queens is 3. They are 19.
P(Ace or Queen or heart) = 19/52
(d) The number of diamonds is 13, hearts is 13, other seven is 2, other Queen is 2. They are 30.
P(seven or Queen or heart or diamond) = 30/52 = 15/26
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Solve the equation.
2x² +6=-34
The solutions are x =
and x =
The solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
How to evaluate for the solution of the equation2x² + 6 = - 36
2x² = - 36 - 6 { subtract 6 from both sides of the equation }
2x² = - 40
x² = -40/2 {divide through by the coefficient of x² which is 2}
x² = -20
we take the square root of both sides
x = ± √-20
√-20 = √20 x √-1 { -1 = I an imaginary number}
so;
x = √20i or x = -√20i
Therefore, the solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
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Please help me with this question.
In the given case- An inverse of a Laplace transform, which is the sum of two distinct components, is the sum of the inverse transforms of each term separately.
What does inverse Laplace transform refer to?
A Laplace transform that is the sum of two different terms has an inverse that is the sum of the inverse transforms of each term taken separately. A Laplace transform, which also has an inverse of the constant multiplied by the inverse of the function, is produced when a constant is multiplied by a function.
A given derivative function with a real variable (t) is transformed into a complex function with a variable (s) by the Laplace transform, which is an integral transformation. Assuming that f(t) complies with a number of later-explained conditions,
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Shannon planted t fewer trees than toby. Toby planted 6 trees . Choose the expression that shows how many trees Shannon planted
Shannon planted 6 - t trees.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
Shannon planted t fewer trees than toby.
Toby planted 6 trees.
Shannon planted.
= t - 6 trees.
Therefore, the result is 6 -t.
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7 Jon is using square ceramic tiles, each 20cm x 20cm, to cover a rectangular worktop in his greenhouse. He can fit exactly 6 tiles along the shorter edge of the worktop and 15 along the length. (a) How many tiles will he use, altogether, to cover the orktop? (b) What is the length of the worktop? Give your answer in metres (m). ............m
Answer:
(a) The number of tiles Jon will use to cover the worktop is 6 * 15 = 90 tiles.
(b) To find the length of the worktop, we first need to find the length of each tile, which is 20 cm = 0.2 m.
The length of the worktop is then 0.2 m * 6 tiles = 1.2 m.
The width of the worktop is 0.2 m * 15 tiles = 3 m.
So, the length of the worktop is 1.2 m and the width is 3 m.
A house was valued at $388,000. Over several years, the value decreased by 19%, giving the house a new value.
(a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal.
New value = x Old value
(b) Use your answer in part (a) to determine the new value.
New value: s
X
5
(a) New value = 0.81 * Old value
(b) New value = 0.81 * $388,000 = $313,480.
The First and third term of geometric progression
are 5 and 80 respectively. What is the 4th term
of geometric progress.
Answer:
±320
Step-by-step explanation:
You want the 4th term of the geometric progression that has first and third terms 5 and 80.
Common ratioThe general term of a geometric sequence is ...
an = a1·r^(n-1)
for first term a1 and common ratio r.
We are given the 1st and 3rd terms, so we can find the common ratio from ...
80 = 5·r^(3-1) . . . . . use a3 = 80, a1 = 5, n = 3
16 = r^2 . . . . . . divide by 5
±4 = r . . . . . . . . take the square root
Fourth termThe 4th term will be the product of the 3rd term and the common ratio:
a4 = a3·(±4) = 80·(±4) = ±320
The fourth term is -320 or +320.
Help need a answer asap
The polynomial
negative -19x^2+181x+14,420
represents the electricity generated (in gigawatts) by geothermal sources during 2002-2007. The polynomial
866x^2–78x+10,190 represents the electricity generated (in gigawatts) by wind power during 2002-2007. In both polynomials, x represents the number of years after 2002. Find a polynomial for the total electricity generated by both geothermal and wind power during 2002 - 2007
Step-by-step explanation:
To find the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007, we need to add the two given polynomials.
The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 would be:
negative -19x^2+ 181x + 14,420 + 866x^2 – 78x + 10,190
Simplifying, we get:
847x^2 + 103x + 24,610
So the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is 847x^2 + 103x + 24,610.
Write down the percentage multiplier to find 26% of an amount
pls do simple steps/working out :)
Answer:
To find 26% of an amount, you would use the percentage multiplier of 0.26.
Step-by-step explanation:
To use the multiplier, you would simply multiply the amount by 0.26.
For example:
26% of $100 = $100 x 0.26 = $26.
Alternatively, you can also express the percentage as a decimal by moving the decimal point two places to the left. In this case 26% is equal to 0.26
So, to find 26% of an amount you would multiply the amount by 0.26
For example:
26% of $100 = $100 x 0.26 = $26.
A rectangle is 3 feet wide and has an area of 438 square feet. What is the
perimeter of the rectangle?
Answer:
Area is 438 Square Feet
Perimeter is 298
Step-by-step explanation:
Area is 438 Square Feet
Area= L x W
438 = L x 3
438 divided by 3 = 146
L=146
Perimeter is 2 (L x W)
2 (146x3)
Perimeter is 298
In a large IT company, 75% of programmers are male while 36% know Python. Twenty-seven percent of the programmers are male and know Python.
a- If a randomly selected programmer turns out to be male, what is the probability that he knows Python? Round your answer to four decimal places.
b- Are "being male" and "knowing Python" independent? Justify your answer using relevant probabilities.
Are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that In a large IT company,
75% of programmers are male while 36% know Python.
27% of the programmers are male and know Python.
We need to find the probability that he knows Python
P(M)=0.75
P(P)=0.36
P(MUP)=0.27
The probability that he knows Python is 0.36-0.27=0.09
Independent events are those events whose occurrence is not dependent on any other event.
Hence, are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python
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In a scientific study there are 10 guinea pigs, 4 of which are pregnant. If 3 are selected at randorm without replacement, find the probability that all are pregnant. Enter your answer as a fraction or a decimal rounded to 3 decimal places.
P (3 are all pregnant) =
The probability that all 3 selected guinea pigs are pregnant is 0.033.
Let's consider the event "A" as "3 guinea pigs selected are all pregnant". The number of ways to choose 3 guinea pigs from the 4 pregnant ones is C(4,3) = 4. The total number of ways to choose 3 guinea pigs from the 10 is
C(10,3) = 120.
The probability of event "A" is given by
P(A) = C(4,3) / C(10,3) = 4 / 120 = 1/30.
Therefore, the probability that all 3 guinea pigs selected are pregnant is 1/30 or 0.033 rounded to 3 decimal places.
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Need help ASAP will reward
Answer: 24.35333333
Step-by-step explanation:
If x and y are positive integers x/y=2, and (x^2+y^2)=z, which of the following cannot equal z?
Step-by-step explanation:
I'm not sure if there were answer choices, but the smallest possible positive integers for x/y=2 is x=2 and y=1
If we plug those in to the other equation
(x^2+y^2)=z
(2^2+1^2)=z
(4 + 1) = z
5=z
Indicating that any number less than 5 cannot equal Z
Find the area of the sector of the circle with central angle of 195° and radius of 7 cm. Use 3.14 for pi(π) and round to the nearest hundredth.
Group of answer choices
23.81 cm2
166.68 cm2
27.86 cm2
83.34 cm2
Answer:
A ≈ 83.34 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{195}{360}[/tex] ( r is the radius of the circle )
= 3.14 × 7² × [tex]\frac{13}{24}[/tex] ( cancelling by 15 )
= [tex]\frac{3.14(49)(13)}{24}[/tex]
≈ 83.34 cm² ( to the nearest hundredth )
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.) 1 0 1 0 1 0 0 0 0 (x1, x2, x3) =
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
The matrix is:
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
The system of equations' equivalent augmented matrix is
[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]
The following matrix has been reduced and transformed into a set of equations.
x(1) + x(3) = 0
Subtract x(3) on both side, we get
x(1) = -x(3)
x(1) = -t
x(2) = 0
Let x(3) = t
[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
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The complete question is:
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
(x1, x2, x3) =
What will it cost to make 1,580 copies if the cost of 50 copies is $2.05
Answer:
=$64.78
Step-by-step explanation:
If. 50 copies. = $2.05
than. 1,580 copies = ?
1580/50 × $2.05
=3239/50
=64.78
Therefore if the cost of 50 copies is $2.05 than the cost of 1,580 copies is $64.78.
Answer:
$64.78
Step-by-step explanation:
Proportions:
50 copies >>>> $2.05
1580 copies >>>> $C
C = 1580"2.05/504
C = 64.78
18. 60 minutes is 20% of
minutes.
Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
Answer:
16.625 miles
Step-by-step explanation:
The time elapsed between 4:45 pm and 12 noon is 4 hours and 45 minutes
45 minutes is equivalent to 45/60 = 0.75 hour
Total elapsed time = 4.75 hours
At a speed of 3.5 mph the distance that can be covered
= 3.5 x 4.75 = 16.625 miles
