Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
Distance Formula is used to calculate distance between two given points.
the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]
Mid point formula the mid point M(m₁,m₂,m₃) between the points A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])
To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.
Substituting the values in Distance formula we get
d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]
=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]
=[tex]\sqrt{1+25+49}[/tex]
=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]
to determine the midpoint M we will use mid point formula.
Substituting the values of the given points in the mid point formula we get
mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)
Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
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What is the solution of 4(x-5)+x=8 x-10-x ?
The value of x using the given equation is -5.
Define the solution of an equation.
A solution of an equation is defined as the set of all possible values of unknown variables that will make the equality hold.
Solving for the value of x
Given the equation, 4(x - 5) + x = 8x - 10 - x
4x - 20 + x = 8x - 10 - x
5x - 20 = 7x - 10
Rearranging the equation, we get,
7x - 10 - 5x + 20 = 0
2x + 10 = 0
x = -10 / 2
x = -5
Hence, the value of x on solving given equation is -5.
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Let g(x)=-x^2+6x+2. Find and simplify g(-3)
Helpppp
|x+3| horizontail stretch by a factor of 4
g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
How do we find the function that was used to create the graph?A graph contains information about which input corresponds to which output.An examination of this leads to the relationships that were used to create it.If a function's graph rises after a certain value of x, the function must have an increased output for inputs greater than that value of x.If we know that the function crosses the x axis at some point, we can use those as polynomial roots for some functions.So, we must write a function g whose graph represents a horizontal stretch of f(x)=|x+3| by a factor of 4.
f(x) = |x+3|Now perform horizontal stretch 4:
g(x) = |¼x + 3|Therefore, g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
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The correct question is given below:
Write a function g whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
g(x)=
How do you do these i need hellppp thank you
Step-by-step explanation:
16. [tex]PQ = \frac{IK}{2} ⟹ \frac{24}{2} [/tex]
[tex]PQ = 12[/tex]
I can't really solve no. 17
The profit from selling local ballet tickets depends on the ticket price. Using past receipts, the ballet company determines that the profit can be modeled by the function p = -15x2 + 600x + 60, where x is the price of each ticket. A) What unit price x should be charged to maximize revenue? B) what is the maximum revenue? C) between what two prices is a profit made?
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) The maximum revenue is 6060 dollars.
C) Two prices between which a profit is made are $19 and $21.
What are quadratic functions?f(x) = ax² + bx + c, where a, b, and c are numbers and are not equal to zero, is a quadratic function.A parabola is the shape of a quadratic function's graph.The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of the quadratic function, is where the parabola will open up. The vertex is the highest point on the graph or, if the parabola opens downward, the maximum value.Given:
profit function P(x)= -15x² + 600x + 60
The value of a is -15, which is negative, so the graph is opening downwards.
The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola f(x) is given by
x-coordinate of the vertex = -b/2a
y-coordinate of the vertex = f(-b/2a)
We have the x-coordinate of the parabola as:
⇒ -600 / 2(-15)
⇒ -600/-30 = 20
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) y-coordinate of the vertex is given by
f(20) = -15(20)² + 600(20) + 60
= 6060
The maximum revenue is 6060 dollars.
C) f(21) = -15(21)² + 600(21) + 60
= 6045
f(19) = -15(19)² + 600(19) + 60
= 6045
at $21, the profit is $6045
at $19, the profit is $6045
Two prices between which a profit is made are $19 and $21.
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A honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day. How many times more eggs can an army ant queen lay?
Answer:
An army ant queen can lay 299,742 more eggs
The army ant queen will lay 120 times more eggs than the honeybee queen.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day.
The ratio will be calculated as,
Army ant/honeybee queen = 300,000 / (2.5 x 10³)
Army ant/honeybee queen = 300,000 / 2500
Army ant = 120 x ( honeybee queen )
Therefore, the army ant queen will lay 120 times more eggs than the honeybee queen.
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A
Write an equation and solve the scenario
4) The sum of three consecutive even
numbers is 42. What is the smallest of
these numbers?
Step-by-step explanation:
Combine like terms on the right side,
42= 3x+6.
Subtract 6 from each side
36=3x
Divide each side by 3
x=12, which is our lowest integer.
The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.
Hope this helps.
Compare the following numbers using division. Which of the statements below
expresses the relationship between the numbers?
100 and 25
100 ÷ 25 = 4
25 is four times as large as 100.
100 is four times as large as 25.
100 is one-quarter as large as 25.
O100 is four more than 25.
Answer: 100 is four times as large as 25.
Step-by-step explanation:
[tex]100 \div25=4[/tex]
Hence, 100 is four times as large as 25.
Answer:
The answer is 100 is four times as large as 25
Step-by-step explanation:
Division compares numbers by telling you how many times larger the first number is then the second number. In this problem, 100/25=4.
Put another way, 25 x 4 = 100. Therefore,100 is four times as large as 25
Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.
How many times more did Samir walk?To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.
Solving gives:
= 3¹/₃ ÷ 1²/₃
= 10/ 3 ÷ 5/3
= 10/3 x 3/5
= 30/ 15
= 2 times more
In conclusion, Samir walked two times more.
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Answer:
Step-by-step explanation:
Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.
How many times more did Samir walk?
To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.
Solving gives:
= 3¹/₃ ÷ 1²/₃
= 10/ 3 ÷ 5/3
= 10/3 x 3/5
= 30/ 15
= 2 times more
In conclusion, Samir walked two times more.
Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
a. Find the volume of Spaceship Earth to the nearest cubic foot.
The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.
Volume refers to the amount of space occupied by a three-dimensional object.
Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.
The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (82.5 feet)^3
V = 4/3 π (561,5151.625 cubic feet)
V = 2,352,071.15 cubic feet
Rounding off to the nearest cubic foot,
V = 2,352,071 cubic feet
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A high school has 40 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players
weighing less than or equal to 246 pounds?
There are 91% of players weighing less than or equal to 246 pounds that the players' weights are given in the box plot.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that the box plot
Here, the total number of players = 40
And the minimum weight of players = 152 pounds
Third quartile (Q₃) = 246
In the box plot, approximately 10 of the 11 coverage intervals occur between 152 and 254.
So the approximate percentage of students that weigh 246 kg or less would be
⇒ (10 / 11)×100
⇒ 90.90
Therefore, there are 91% of players weigh less than or equal to 246 pounds.
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Find the position function x(t) of a moving particle with the given acceleration a(t) a(t)=3t
The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.
The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.
The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.
Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.
a(t) = 3t
d^2/dx^2=(3t)
x(t) = [tex]\int\limits {3t} \, dt[/tex]
= 3 *t^2 / 2
Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.
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Solve for x to the nearest tenth HELP
The value of x is 4.89 ≈ 5 units
Given,
The figure includes two right angled triangles.
Consider the first right angled triangle:
Hypotenuse = 7 units
Base = 3 units
Altitude = a
By using Pythagorean theorem, we can find a.
That is,
Hypotenuse² = Altitude² + Base²
7² = a² + 3²
49 = a² + 9
a² = 49 - 9
a² = 40
Altitude = [tex]\sqrt{40}[/tex] units
Now consider second right angled triangle:
Hypotenuse = [tex]\sqrt{40}[/tex] units
Altitude = 4 units
Base = x units
Apply Pythagorean theorem:
Hypotenuse² = Altitude² + Base²
([tex]\sqrt{40}[/tex])² = 4² + x²
40 = 16 + x²
x² = 40 - 16
x² = 24
x = [tex]\sqrt{24}[/tex]
Base, x = 4.89 ≈ 5 units.
Therefore, the value of x is 4.89 which is approximately equals to 5 units.
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2.For each of these cylinders dimensions find:
i. the volume
ii. the curved surface area
Give your answers in terms of π.
A. Base radius 3cm and height 8cm.
B. Base diameter 8cm and height 7cm.
5. A cylinder container is 65 cm in diameter. Water is poured into the container until it is 1 m deep.
how much water is in the container? Give your answer in litres.
2. For the given cylinders, we have that:
A. The volume is of 72π cm³ and the curved surface area is of 48π cm².
B. The volume is of 112π cm³ and the curved surface area is of 56π cm².
5. There are 330 liters of water in the container.
What is the volume of a cylinder?
The volume of a cylinder of radius r and height h is given as follows:
V = πr²h.
What is the curved surface area of a cylinder?
The curved surface area of a cylinder of radius r and height h is given as follows:
S = 2πrh.
For problem 2 item a, we have that the parameters are given as follows:
r = 3, h = 8.
Hence:
V = πr²h = 72π.S = 2πrh = 48π.The volume is of 72π cm³ and the curved surface area is of 48π cm².
For problem 2 item b, we have that the parameters are given as follows:
r = 8/2 = 4, h = 7.
Hence:
V = πr²h = 112π.S = 2πrh = 56π.The volume is of 112π cm³ and the curved surface area is of 56π cm².
For item 5, the parameters are given as follows:
r = 0.65/2 = 0.325m, h = 1m.
Hence the volume is:
V = πr²h = π(0.325)² = 0.33 m³.
Each m³ has 1000 liters, hence:
0.33 x 1000 = 330 liters.
There are 330 liters of water in the container.
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Leroy won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Leroy
a bucket of fish to divide evenly among 5 dolphins. Each dolphin gets 4 fish.
Which equation can you use to find the number of fish f in the bucket before Leroy feeds the
dolphins?
F/5=4
5f=4
F-5=4
F+5=4
Answer:
A. F/5 = 4
Step-by-step explanation:
F is the total of fish so F is divided by the total of dolphins, which is 5
so F/5 = 4
Answer:
F/5=4
Step-by-step explanation:
F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.
find the L in the cone.
We can use the pythagorean theorem to answer this question.
We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.
So, we can build the equation:
[tex]7^2+7^2 = l^2[/tex]
[tex]98 = l^2[/tex]
[tex]\sqrt{98} = l[/tex]
Determine if the conjecture is valid by the law of detachment. given: if tommy made enchiladas tonight, then tommy must have an oven. tommy has an oven. conjecture: tommy made enchiladas tonight.
By determining the conjecture is not valid by the law of detachment.
A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.
Hypothesis: Tommy makes cookies tonight.
Conclusion: Tommy must have an oven.
Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.
Hence, the hypothesis is unfounded.
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There are 4 white and 8 red roses in bouquet. Find the ratios.
Answer:
4/12
Step-by-step explanation:
If the ratio 4:8 is a part-to-part ratio, it means that there are 4 of something and 8 of something else with a total of 12. To convert a part-to-part ratio such as 4:8 as a fraction, you make the left side of the colon the numerator and the total the denominator: 4:8 → 4/12
For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.5 th term
The 5th term of the given geometric sequence is 768.
A geometric sequence is a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a(n-1) . r
Where:
a(n) = nth term
r = ratio
The given geometric sequence is:
3,12,48,192, . . .
Find the ratio
r = a(n)/a(n-1)
= a(2)/a(1) = 12/3 = 4
Use the formula for the nth term.
a(n) = a(1) . r^(n-1)
In the given sequence a(1) = 3.
Substitute a(1) = 3, r = 4, and n = 5:
a(5) = 3 . 4⁵⁻¹
= 3 . 4⁴ = 768
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Type the integer that makes the following addition sentence true:
_____+ –3 = –4
The integer that makes the expression, (____ + -3 = -4), true is -1.
According to the question,
We have the following expression:
__ + (-3) = -4
Now, let's take the integer to be filled in the blank as x.
Now, putting x in the given expression:
x + (-3) = -4
x = -4+3 (3 was negative on the left hand side. So, it is positive on the right hand side.)
x = -1
(More to know: when two numbers are given with two different signs then the smaller number is subtracted from the larger number but the sign remains of the number which is larger.)
Hence, the integer that makes the given addition sentence true is -1.
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Austin makes $10 an hour working as a cashier at a bookstore. His employer requires him to work at least 10 hours per week and his current school schedule limits him to a maximum of 25 hours per week.
1. Write an equation that represents Austin's gross pay where x represents the number of hours he works per week and f(x) (as in functions) represents his gross pay.
2. What is the domain and range in this situation?
The linear function is:
f(x) = $10*x
Where the domain is: [10, 25]
And the range is: [$100, $250]
How to write the equation that models Austin's gross pay?Here we know that x represents the number of hours that he works per week, and we also know that he wins $10 per hour, then if he works x hours, the amount that he wins is x times $10, so the equation is just:
f(x) = $10*x
Now we also want to get the domain and range for this function. We know that he needs to work at least 10 hours and at maximum of 25 hours, so we have the restrictions:
10 ≤ x ≤25
So the domain is D: [10, 25]
To find the range we evaluate in the values of the domain, the minimum of the range is f(10) = $10*10 = $100
The maximum of the range is f(25) = $10*25 = $250
Then the range is R: [$100, $250]
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Circle J has a radius of 10 units, ®K has a radius of 8 units, and BC = 5.4 units. Find the measure.
AB
Circle J has a radius of 10 units and BC = 5.4 units then the measure of AB is 14.6 units.
What is meant by the radius of a circle?A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
Since AC is the diameter of circle J and the radius is 10, AC = 2(10) or 20 units.
AB + BC = AC
Where the value of BC = 5.4, we get
substitute the value of BC in the above equation, then we get
AB + 5.4 = 20
subtract 5.4 from both sides
AB + 5.4 - 5.4 = 20 - 5.4
simplifying the above equation,
AB = 14.6
Therefore, the measure of AB is 14.6 units.
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Work out the mean of these numbers 2 √18 √50 Give your answer in the form a√2 where a is an integer.
answer in the form a√2 where a is an integer. √18 √50= 4 root 2
Solution:
Mean
Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate the mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.
Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations
Observation :
An observation is a fact or figure we collect about a given variable. It can be expressed as a number or as a quality. An example of a number is the observation "25" for the age of a mother at the birth of her first child.
Using mean formula
Mean = {Sum of Observation} ÷ {Total numbers of Observations}
= [tex]\sqrt{18} +\sqrt{50}[/tex]
=[tex]3\sqrt{2} + 5\sqrt{2}\\ = 5\sqrt{2}[/tex]
sum of observation is 8[tex]\sqrt{2}[/tex]
total number of observation = 2
[tex]8\sqrt{2} /2\\=4\sqrt{2}[/tex]
Answer in the form a√2 where a is an integer. = 4 [tex]\sqrt{2}[/tex]
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ans = [tex]4\sqrt{2}[/tex]
Wright a variable expression for the word phrase, "the product of a number z and 7" A: 7 - z
B: 7 + z
C: 7z
D: 7 ÷ z
The variable expression for the word phrase, "the product of a number z and 7", is C. 7z.
A variable expression is defined as a mathematical phrase that contains variables and numbers combined together with any mathematical operations. The most common variable used to denote something is the variable x.
Given the word phrase "the product of a number z and 7"
let z be the variable denoted for a number
and a product of a number z and 7 can be written as:
7z
Therefore, the variable expression for the word phrase "the product of a number z and 7" is 7z.
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-5+9-4-(-4)+(-9)-12+7
Answer:
Step-by-step explanation:
if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )
and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )
so -(-4) = 4 and +(-9) = -9
-5+9-4+4-9-12+7=-10
I hope this helps
Physical science
If a car travels 625 meters 15 seconds, how fast is it going?
Determine whether each infinite geometric series converges or diverges. If the series converges, state the sum. 2/3 + 4/9+8/27+ ......
The given infinite geometric series 2/3+4/9+8/27+ ...... is convergent and the sum is 2
The given geometric series is:
2/3 + 4/9 + 8/27 + ......
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 2/3
a(2) = 4/9
a(3) = 8/27
Hence, the common ratio is
r = a(2) / a(1) = (4/9) / (2/3) = 2/3
An infinite geometric series is convergent if 0 < | r | < 1.
Since r = 2/3, then the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 2/3 and r = 2/3 into the formula:
S = (2/3) / (1 - 2/3)
= (2/3) / (1/3)
= 2
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Solve-2x - 7> 5x+14.
Ο A. * < -3
OB. x>-5
O C. x < -5
OD. x>-3
Answer:
D.
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 2x - 7 > 5x + 14 \\ - 2x - 5x < 14 + 7 \\ - 7x < 21 \\ x < \frac{21}{ - 7} \\ x > - 3[/tex]
What is 5/9 + 2/3 ? I need to show all my work
Answer:
1.2
Step-by-step explanation:
Answer:[tex]2/3+5/9= \frac{2x3}{3x3} + 5/9 =6/9 +5/9+\frac{6+5}{9} = 11/9[/tex]
Step-by-step explanation: answer : 11/9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two thirds plus five ninths is eleven ninths.Hope this helps u ; )
PLEASE HELP
PLEASE SHOW HOW U CHECKED UR WORK
also show regular work
pls i need help
Answer:
Step-by-step explanation:
3
2
−
2
3
y+
3
1
y+4=0
Combine −
2
3
y and
3
1
y to get −
6
7
y.
3
2
−
6
7
y+4=0
Convert 4 to fraction
3
12
.
3
2
−
6
7
y+
3
12
=0
Since
3
2
and
3
12
have the same denominator, add them by adding their numerators.
3
2+12
−
6
7
y=0
Add 2 and 12 to get 14.
3
14
−
6
7
y=0
Subtract
3
14
from both sides. Anything subtracted from zero gives its negation.
−
6
7
y=−
3
14
Multiply both sides by −
7
6
, the reciprocal of −
6
7
.
y=−
3
14
(−
7
6
)
Multiply −
3
14
times −
7
6
by multiplying numerator times numerator and denominator times denominator.
y=
3×7
−14(−6)
Do the multiplications in the fraction
3×7
−14(−6)
.
y=
21
84
Divide 84 by 21 to get 4.
y=4
