Answer: The distance formula is a mathematical formula used to find the distance between two points in a plane. One way to find the distance formula is by using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The distance formula can be derived from the Pythagorean theorem by considering the two points as the two endpoints of a line segment. The formula is as follows:
Distance = √(x2 - x1)^2 + (y2 - y1)^2
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this formula, the difference in the x-coordinates is squared and the difference in the y-coordinates is also squared. Then, these two values are added and the square root of the result gives the distance between the two points.
For example, if we have two points (x1, y1) = (2, 3) and (x2, y2) = (5, 8), we can use the distance formula to find the distance between these two points:
Distance = √((5 - 2)^2 + (8 - 3)^2)
Distance = √(3^2 + 5^2)
Distance = √(9 + 25)
Distance = √(34)
Distance = 5.83
Therefore, the distance between the two points is 5.83 units.
Step-by-step explanation:
(3x3y)(-14x2y2z) can someone solve this
Answer:
-252 y^3 z
Step-by-step explanation:
easy qs no need steps
Pls answer................
Answer:
m<C = 43°
Step-by-step explanation:
m<P = m<A = 45°
m<B = (5x + 2)°
m<Q = 6x - 16
m<Q = m<B
6x - 16 = 5x + 2
x = 18
m<B = m<Q = 5 × 18° + 2° = 92°
m<A + m<B + m<C = 180°
45° + 92° + m<C = 180°
m<C = 43°
please helpppp me!!!
Answer:
K = Fr^2/q1q2
first one option A is the correct
How would the following triangle be classified?
Answer:
scalene acute as its all sides length are not equall and its all angle are less than 90 degrees
Mr. Vivaldi is getting ready for the spring orchestra concert.
x+6y=-5
2x+12y=-10
Solve the system using elimination method
Answer:
The system has infinitely many solutions---------------------------------------
Given system:
x + 6y = - 52x + 12y = - 10First simplify the second equation by dividing all terms by 2:
x + 6y = - 5We got the same equation as the first one. It means the two lines overlap, so there are infinitely many solutions.
If we use elimination method, we will subtract the two equations then end up with equation 0 = 0.
(04.03 LC)
Which of the following fractions compares BC to BD?
O
213
O
5/2
-3-
-24
2
O
1
O
-1-
B
T
C
2
D
3 4
5
6
The fraction compares BC to BD is 2/3. Therefore, option A is the correct answer.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Given that, the coordinate points are B(0,1), D(3 ,1) and C(2, 1).
Here, BC is
BC=√[(2-0)²+(1-1)²]
BC=2 units
BD is
BD= √[(3-0)²+(1-1)²]
BD= 3 units
The fraction compares BC to BD is 2/3
Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which of the following fractions compares BC to BD? coordinate plane with segment BD at B(0,1) and D(3 ,1); point C is on segment BD and (2, 1).
Answer choices:
A) 2/3
B) 5/2
C) 2/5
D) 3/2
Answer:
2/5
Step-by-step explanation:
d = √[(x2 - x1)² + (y2 - y1)²]
For segment BD:
BD = √[(5 - 0)² + (1 - 1)²]
= √[5² + 0²]
= √25
= 5
For segment BC:
BC = √[(2 - 0)² + (1 - 1)²]
= √[2² + 0²]
= √4
= 2
(Answer accurately to a spreadsheet!)
You run a table at a flea market for 7 days. You sell sunglasses for $5.00 per pair. You buy them for $1.25 per pair. These are your sales for the week: Day 1, 8 pair. Day 2, 7 pair. Day 3, 15 pair. Day 4, 12 pair. Day 5, 31 pair. Day 6, 20 pair. Day 7, 35 pair. How much were your sales each day? What were your total sales for the week? What was your daily average of sales? What
was your total cost? How much profit did you make?
Answer:
Day 1: 8 pairs x $5.00/pair = $40.00
Day 2: 7 pairs x $5.00/pair = $35.00
Day 3: 15 pairs x $5.00/pair = $75.00
Day 4: 12 pairs x $5.00/pair = $60.00
Day 5: 31 pairs x $5.00/pair = $155.00
Day 6: 20 pairs x $5.00/pair = $100.00
Day 7: 35 pairs x $5.00/pair = $175.00
Total sales for the week: $40.00 + $35.00 + $75.00 + $60.00 + $155.00 + $100.00 + $175.00 = $605.00
Daily average of sales: $605.00 / 7 = $86.43
Total cost: 8 pairs + 7 pairs + 15 pairs + 12 pairs + 31 pairs + 20 pairs + 35 pairs = 128 pairs x $1.25/pair = $160.00
Profit: $605.00 - $160.00 = $445.00
So your total sales for the week were $605.00, your daily average of sales was $86.43, your total cost was $160.00 and your profit was $445.00
. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
volume of the cylinder.
Please help me with the following question.
If one order is selected, the probability of getting an order that is not accurate is 0.236.
What is probability in maths?Probability is a measure of the likelihood of an event occurring. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Scientific probability is built on the basis of probability theory.
The calculation is;
P(Not accurate ) is equal to [n(Not accurate) + (Not accurate)- n] /Total
Thus, we have;
P(Not accurate) is calculated as follows:
(60 + 32 + 12 + 38 + 122 + 12 - 12)/(280 + 245 + 122 + 331 + 60 + 32 + 12 + 38).
P(Not accurate) = 264/1120
P(Not accurate ) = 0.236
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What is the standard form of the equation of a quadratic function with roots of 3 and −1 that passes through (1, −10)?
y = 2.5x2 − 5x + 7.5 y = 2.5x2 − 5x − 7.5 y = −2.5x2 − 5x + 7.5 y = −2.5x2 − 5x − 7.5
The quadratic equation with the given zeros is:
y = 2.5*x^2 - 5x - 7.5
How to find the quadratic equation?
For a quadratic equation with the zeros h and k, and a leading coefficient a is:
y = a*(x - h)*(x - k)
Here we know that the zeros are 3 and -1, replacing these values we will get:
y = a*(x - 3)*(x + 1)
Finally, we also know that the quadratic goes through (1, -10)
Replacing these values we will get:
-10 = a*(1 - 3)*(1 + 1)
-10 = a*(-2)*2
-10 = -4a
10/4 = a
5/2 = a = 2.5
Then the quadratic equation is:
y = 2.5(x - 3)*(x + 1)
Expanding that we will get:
y = 2.5*(x^2 - 3x + x - 3)
y = 2.5*x^2 - 5x - 7.5
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A can of soda can be modeled as a right cylinder. Ajay measures its height as 8.9 cm
and its radius as 1.9 cm. Find the volume of the can in cubic centimeters. Round your
answer to the nearest tenth if necessary.
Answer:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
So, using the given measurements, we can substitute in the values and solve for the volume:
V = π(1.9 cm)^2(8.9 cm) = 301.958 cm^3
Rounded to the nearest tenth, the volume of the can is 301.9 cm^3.
Step-by-step explanation:
Three numbers sum to 117. The second number is 10 less than the first. The third number is 2 more than half the first. What are the three numbers?
Answer:
Step-by-step explanation:
The three numbers are 50, 40, and 27.
We can solve this equation by setting up a system of equations.
Let x be the first number, y be the second number, and z be the third number.
x + y + z = 117
y = x - 10
z = (1/2)x + 2
Substituting the equation for y into the first equation, we get:
x + (x - 10) + (1/2)x + 2 = 117
2x - 8 = 117
2x = 125
x = 62.5
Substituting this value of x into the other equations, we get:
y = x - 10 = 62.5 - 10 = 52
z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5
Rounding these values, the three numbers are 50, 40, and 27.
The fourth grade is going on a field trip and taking two buses. One bus has 3 rows of seats with 9 deatd in each row the other bus has four times as many seat as the first bus. How many seats are there in both buses?
The number of seats in the two buses are: first bus includes 27 seats and second bus includes 108 seats.
What is proportion?An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometres per hour is equal to the time it needs to travel 500 kilometres in five hours. Example: 100 km/hr = 500 km/5 hour.
Given that:
Three rows of nine seats each make up one bus, hence the first bus's seating arrangement is as follows:
3 x 9 = 27.
Since the other bus has four times as many seats as the first bus, the second bus's seat count is as follows:
4 x 27 = 108.
Hence, the number in the two buses are first bus includes 27 seats and second bus includes 108 seats.
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Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 3.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
A button hyperlink to the SALT program that reads: Use SALT.
(a) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
(b) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
(c) What is the probability that for 34 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
The probabilities regarding the total time of the 34 jets are given as follows:
a) Less than 320 minutes: 0.9306 = 93.06%.
b) More than 275 minutes: 0.8238 = 82.38%.
c) Between 275 and 320 minutes: 0.7544 = 75.44%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a total of n observations, the mean is of [tex]n\mu[/tex], while the standard deviation is of [tex]\sigma\sqrt{n}[/tex]The mean and the standard deviation for the total time of the 34 jets is given as follows:
[tex]\mu = 8.6 \times 34 = 292.4[/tex][tex]\sigma = 3.2\sqrt{34} = 18.66[/tex]The probability that the mean is less than 320 minutes is the p-value of Z when X = 320, hence:
Z = (320 - 292.4)/18.66
Z = 1.48
Z = 1.48 has a p-value of 0.9306.
The probability that the mean is more than 275 minutes is one subtracted by the p-value of Z when X = 275, hence:
Z = (275 - 292.4)/18.66
Z = -0.93
Z = -0.93 has a p-value of 0.1762.
1 - 0.1762 = 0.8238.
The probability of a value between these two amounts is given as follows:
0.9306 - 0.1762 = 0.7544.
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5. There are two tall buildings across the street from each other. The floors of the two
buildings are different heights. You are standing on the 10th floor of building A. Across the
street a friend is standing on the 12th floor of building B. Your feet are at exactly the same
height above the ground. If you go to the 15th floor, what floor will be directly across from
your feet in the other building?
According to the information, when I am on the 15th floor of building A, my friend is on the 18th floor of building B.
How to find which floor of building B is my friend?To find the floor number where my friend is in building B while I am on the 15th floor of building A, we must perform the following mathematical operation:
Rule of three
10A - 12B15A - ?B15 * 12 / 10 = 18Based on the above, we can infer that to find the number of the floor where my friend is, we must follow a rule of three. This gives us 18 as a result, that is, he is on that floor number in building B, while I am on 15 in building A.
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Some students collected the data below month and average temperatures. They will graph the data. What is the y-intercept? Your answer should be an ordered pair/
The y intercept of the data collected is 42°C
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the average temperature and x represent the month. x = 0 represent the month January.
From the table, at January, the average temperature is 42°C. Hence the y intercept is 42°C.
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What is the equation of the midline of the sinusoidal function
Answer: y = 0
Step-by-step explanation:
A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. For y = sin x, the midline is y = 0 (the x-axis). The midline is parallel to the x-axis and is located halfway between the graph's maximum and minimum values.
A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
How much of the $14000 did the bank loan out at 7%
The required loan out of 14000 which is on 7% interest is given as $3800.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let part of the loaned amount at 7 % interest be x and another part with 17% interest be y,
A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year, and the interest received in one year totaled $2000,
According to the question,
x + y = 14000
x = 14000 - y - - - - - (1)
and,
0.07x + 0.17y = 2000 - - - - (2)
Put x from equation 1 in equation 2
Gives,
y = 10200
Now,
x = 14000 - 10200
x = 3800
Thus, the required loan out of 14000 which is on 7% interest is given as $3800.
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Find the equation of a line that is parallel to y=13x−5 and passes through the point (3,−2).
Give your answer in the form y=mx+b.
Answer:
y = 13x - 41
Step-by-step explanation:
Parallel lines always have the same slope since
[tex]m_{2}=m_{1}[/tex]
Thus, the slope of the second line is m = 13.
We can find the y-intercept of the line by plugging in the points for x and y, 13 for m, and solving for b:
[tex]-2=13(3)+b\\-2=39+b\\-41=b[/tex]
what is the value of the expression below?
[9.75+(1/2)^2]÷2
Answer:
5
Step-by-step explanation:
{9.75 + [tex]\frac{1}{2} ^{2}[/tex]] ÷ 2
[9.75 + [tex]\frac{1}{4}[/tex]] ÷ 2 1/4 = .25
(9.75 + .25) /2
10/2 = 5
Expand (2d - 5e)(2d - 5e)
Answer:
expanded from:4d²-20de-25e²
The mean distance of Earth from the Sun is 9.29 10^7 miles. Assuming that the orbit of the Earth
around the Sun is circular and that 1 revolution takes 365 days, find the linear speed of the Earth.
Express your answer in miles per hour.
The linear speed of the Earth is 6.66×10⁴mi/hr
What is Speed?Speed is a measure of how fast an object is moving
The formula for linear speed is v=rw
where the radius, , is the distance from the Earth to the Sun which is 9.29×10⁷miles and the angular speed is w=1 rev/365 days
Solving for the speed
=9.29×10⁷×1 rev/365 days
=9.29×10⁷×(1 rev/365 .2π rad/1 rev. 1 day/24 hr)
=9.29×10⁷×(2π rad/365.24hr)
v=66633.32mi/hr
Hence, the linear speed of the Earth is 6.66×10⁴mi/hr
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you can perform 6 push ups in 24 seconds. wrote and graph an equation that represent the relationship between time and number of push up. at this rate how many pushups can you perform in 2 minutes
At the given rate, I can perform 480 pushups.
Your goal should be to complete 100 push-ups in 2 minutes (this is a standard for elite soldiers).
White defines that as 10 to 20 push-ups if your max is 25 reps, 2 sets of 10 to 20 if your max is 25 to 50 reps, and 2 to 3 sets of 10 to 20 if your max is greater than 50 push-ups. "If you're doing a lot of sets and hitting a lot of volume, I'd try to do them every other day.
24/6 = 4
meaning they are doing 4 push ups per second, this is your slope
the equation of your line is y = 4x, you can graph this using a table of values
2 minutes = 120s
y = 4(120)
y = 480 push ups
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Find the number next in the sequence: 1,4,9,16,25
Answer:
Step-by-step explanation:
1+3=4, 4+5=9, 9+7=16, and 16+9=25.
The numbers added are in odd numbers from least to greatest.
So the next number is supposed to be 25+11=36.
James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours. How many hours will James have to work each week?
Please help me with the formula
The number of hours that James have to work each week will be 25 hours.
How to calculate the number of hours?The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge.
In this case, James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours.
The number of hours that James have to work each week will be:
= 5(38) - 3(15 - 4)
= 5(38) - 3(11)
= 5(38 - 33)
= 5 × 5
= 25 hours
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What is the area (in square centimeters) of a rectangle that is 6.5 centimeters long and 2.4 centimeters wide?
Answer:
Area = 15.6 cm²
Step-by-step explanation:
Area of a rectangle = long * wide
Then:
Area of a rectangle = 6.5 cms * 2.4 cm
Area of a rectangle = 15.6 cm²
3x-2y=4 4x-y=13 simultaneous equations
Answer:
To solve the simultaneous equations 3x - 2y = 4 and 4x - y = 13, we can use elimination or substitution. To solve by elimination, we can subtract 3x - 2y from both sides of the first equation, and 4x - y from both sides of the second equation, resulting in -2y = -12 and -y = 9. Then we can add the two equations together which gives us -3y = -3. Dividing both sides by -3 gives us y = 1. We can then substitute this value for y into either of the original equations and solve for x. In this case, if we substitute 1 for y in the first equation, we get 3x - 2(1) = 4, which simplifies to 3x = 6. Dividing both sides by 3 gives us x = 2. Therefore, the solution to the simultaneous equations is x = 2 and y = 1.
Step-by-step explanation:
see above
Answer:
[tex]x= -2 , y=5[/tex]
Step-by-step explanation:
[tex]3x + 2y = 44x - y = -13[/tex]
Take either of the equations and choose which to make the subject. i shall choose the second equation and make -y the subject of the formula.
[tex]4x - y = -13[/tex]
lets take -y to the other side because we want -y to be positive, ie (+y)
[tex]4x = y - 13 ,[/tex] take -13 to the other side,
[tex]y= 4x + 13[/tex]
now that we have that we take the other equation and substitute what y is into the equation, i.e
[tex]3x + 2( 4x + 13) = 43x + 8x + 26= 411x + 26 = 4[/tex]
we take +26 to the other side,
[tex]11x = 4 - 26[/tex]
[tex]11x = -22[/tex][tex],[/tex] divide both sides by 11, x becomes
[tex]x = -2[/tex]
now that we know what x is we substitute it into the formula,
[tex]4(-2) - y = -13-8 - y = -13y = -8 + 13y = 5[/tex]
The conjugate of x-14 is?
Step-by-step explanation:
the conjugate is where we change the sign in the middle of the two terms
so we change the - to a +
x + 14 is our answer
