[tex]~~~~~~k = \dfrac{3n+2}{n+1}\\\\\implies k(n+1) = 3n+2\\\\\implies kn+k=3n+2\\\\\implies kn -3n= 2-k\\\\\implies n(k-3) = 2-k\\\\\implies n = \dfrac{2-k}{k-3}\\\\\implies n = -\dfrac{k-2}{k-3}~~~~~~~~;[k\neq 3][/tex]
After 3 hours,
Amelie has biked
15 miles
A professional
cyclist finished a
100-mile race in 4
hours
it took Emma
3 hours to bike 27
miles up to the top
of Mt. Evans
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Determine, which is the shorter path from A to B is: Around the two small semi circles or around the large semi-circle? Verify your answer by calculating the length of the path in each case.
A neutron star has a density of about kg/m3. what would be the approximate mass of a 1-centimeter cube (a cube 1 cm on all sides)? kg (1.3 quadrillion pounds) kg (1.3 trillion pounds) kg (1300 trillion pounds) kg (1.3 billion pounds)
Answer:
Step-by-step explanation:
5.9 1014 kg (1300 trillion pounds)
5.9 108 kg (1.3 billion pounds)
5.9 1017 kg (1.3 quadrillion pounds)
5.9 1011 kg (1.3 trillion pounds)
those are the options
Graph the inequality y ≤-3x - 3.
Answer: [tex]y\leq -3x-3[/tex] [tex]< --Graph[/tex]
In order to graph the equation "y ≤-3x - 3", we need to graph the inequality by finding the boundary line, then shading the appropriate area.
Aurelio is purchasing carpet tiles to cover an area of
his living room floor that is 8 feet wide by 10 feet
long. each carpet tile is a square 20 inches wide by
20 inches long. what is the minimum number of carpet
tiles that aurelio must purchase to cover this area of
his living room floor?
a. 5
b. 11
c. 21
d. 30
e. 84
Answer:d.33
Step-by-step explanation: To begin we convert his living room floor length and width to inches. 8 1 slash 3 feet = 100 inches
10feet= 120 inches
hence the area in square inches of the living room floor is 100 inches times120 inches = 12000 inches squared.
Each carpet tile has an area of 20 by 20 which = 400inches squared. dividing the area of the living room by 400inches of each carpet tile, would yield 30 carpet tiles needed to cover this area.
As per linear equation, the minimum number of carpet tiles that Aurelio must purchase to cover the area of his living room floor is 29.
What is a linear equation?A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.
Given, the room has a length of 10 feet = 12 × 10 inches = 120 inches
The width of the room is = 8 feet = 12 × 8 inches = 96 inches
Therefore, the area of the room is
= 120 × 96 square inches
= 11520 square inches
Length of each carpet tile is 20 inches
Width of each carpet tile is 20 inches
Therefore, the area of each tile is
= (20)² square inches
= 400 square inches
The number of tiles require
= (11520/400)
= 28.8
≈ 29
Therefore, 29 tiles will be required.
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Help me please given ABcd is a parallelogram
A circle is divided into 9 equal parts what is the angle measure of one of those parts?
Answer: 40°
40 * 9 =360° Each part has 40° angle
A job applicant estimates that his chance of passing a qualifying examination is , and his chance of being appointed if he does pass is . what is the probability that he will receive the job?
The probability that he will receive the job will be 1 / 6
The complete question is given below:-
A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
It is given that:
The chance of passing a qualifying examination is 2/3=P
and chance of being appointed, if he does pass, is 1/4=P'
Now, we are asked to find the probability that he will receive the job.
We are asked to find the probability that he will receive the job.
The probability is calculated as The probability that he qualify the exam×Probability that he is being appointed.
=P×P'
=(2/3)×(1/4)
=1/6
Therefore the probability that he will receive the job will be 1 / 6
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MATHH!!! find the surface area of the prism. pleaseee answer correctly and tell me how you got your answer.
Answer:232 inch^2
Step-by-step explanation:to solve, add the surface area of each side. Remember, there are 3 pairs of sides and the pairs have equal area. Area =length x length. So we have 2x(8x2)+2x(2x10)+2x(10x8) in square inches.
Please how to answer.
Answer:
Blue Rectangle: 135 mm²
Blue Triangle: 45 mm²
Not sure if you need this but the Total Square: 225 mm²
Step-by-step explanation:
Area of a rectangle: length x width
Area of a triangle: [tex]\frac{1}{2}[/tex] x base x height
First find the area of the blue rectangle.
Length = 15 mm
Width = 9 mm
Area = 135 mm²
Now find the area of the blue triangle:
Base = 6 mm (because the bottom is 15 total and you subtract the 9)
Height = 15 mm
Area = 45 mm²
Hope it helps!
A certain television is advertised as a 95-inch tv (the diagonal length). if the width of the tv is 77 inches, how tall is the tv? round to the nearest tenth of an inch.
The height of the television given the length of its diagonal and its width is 55.6 inches
What the height of the tv?The height of the television can be determined using Pythagoras Theorem.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
√95² - 77² = 55.6 inches
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Answer: 55.6
Step-by-step explanation: 55.6 that's what I put in and got it right
The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. the table used to place bets contains 38 numbers, and each number is assigned to a color and a range. what is the probability of winning when betting on two lines that touch each other on the table as in 1-2-3-4-5-6?
The probability of winning when betting on two lines that touch each other on the table is 6/38
How to determine the probability?The sample size is given as:
n = 38
The numbers on the range 1-2-3-4-5-6 is:
Range = 6
So, the probability is calculated as:
P = Range/n
This gives
P = 6/38
Hence, the probability of winning is 6/38
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5.) The price of gas last year was $1.75 per gallon. The price went up by 5%,
what is the new price for a gallon of gas?
Answer: 1.75•5%=0.0875
1.75+0.0875=$1.84
I’m pretty sure this is correct
Answer:
5% of 1.75 is 0.085.
So 1.75 + 0.085 is 1.8375.
Consider the given quadratic equations. Equations function it defines. Equation A y= 3x² - 6x + 21 Equation B y=3x² - 6x + 18 Equation C y= 3(x-1)2 +18 Equation Dy=3(x-1)² +21 Complete the following statement. equation. are equivalent , and of those, equation. is in the form most useful for identifying the extreme value of the function it define
Equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
Evaluation of the quadratic expressions
The quadratic expressions can be simplified as follows;
Equation A: y = 3x² - 6x + 21Equation C: y = 3(x - 1)² + 18Equation C is simplified as follows;
y = 3(x - 1)² + 18
y = 3(x² - 2x + 1) + 18
y = 3x² - 6x + 3 + 18
y = 3x² - 6x + 21
Thus, equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it defines.
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Peppers are sold in packs of 3 for $111,or in individual for $29 which is the best value
how to simplify 8x-6x
subtracting 6x from 8x. It's quite simple to deal with small two-part numbers like these. After subtracting 6x from 8x, you will get the answer 2x.
Quick Answer:
You simply 8x-6x by subtracting 6x from 8x, and then you will get the answer 2x
HAVE A NICE DAY
One number is 4 times another. Their difference is 27. How to get the other two numbers?
Answer:
x = 36; y = 9
Step-by-step explanation:
To solve this problem you need to set up two equations. The first equation comes from the first sentence "One number is 4 times another." This equation can be written as x = 4*y where x and y are the two numbers. The second equation comes from the second sentence "Their difference is 27." This equation can be written as x-y = 27. To find the numbers you need to rearrange one equation and plug it into the other.
Step 1: write equations
x = 4*y
x-y = 27
Step 2: rearrange
Not necessary here
Step 3: substitute in
x - y = 27
4y -y = 27
3y = 27
y = 9
Step 4: solve for x
x = 4*y
x = 4*9
x = 36
[tex]x[/tex] - one number
[tex]4x[/tex] - the other number
[tex]4x-x=27\\3x=27\\x=9\\\\4x=4\cdot9=36[/tex]
These numbers are 9 and 36.
Which triangles are similar please help lol
Answer:
triangles A and B are similar
Step-by-step explanation:
What is the period of f(x) = sin (8x)?
X/8
X/4
4
8
Answer: B- x/4
Step-by-step explanation:
The period is the horizontal distance needed for the values to repeat themselves.
how many pattern block trapezoids would create 4 hexagons?
Answer:
8
Step-by-step explanation:
2 pattern block trapezoids makes one hexagon
There are 4 hexagons so you have to multiply 2 by 4
you get 8
8 is your answer
The measure of an angle is 44.8°. What is the measure of its supplementary angle?
Answer:
Step-by-step explanation:
pls pls pls pls pls help me assap.
The quadrilaterals and their corresponding properties as shown in the given table are explained below.
How to Identify properties of Quadrilaterals?Property 1; All sides are Congruent means all sides are equal and only Square and Rhombus have this property.
Property 2; All angles are congruent means all angles are equal. Only Rectangle and Square have this property.
Property 3; Diagonals are perpendicular to each other. Only Square and rhombus have this property.
Property 4; Diagonals are congruent. This means the diagonals are equal and only Square and Rectangle have this property.
Property 5; Exactly One pair of parallel sides is given by Only Trapezoid.
Property 6; Two pairs of opposite sides are congruent. Only Parallelogram, Rectangle, Rhombus and Square have this property.
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It is the middle of the heatwave, and you AC unit has broken. You have 2 companies that come highly qualified. Company A charges $200 to come out plus $50 per hour to look at your AC and determine what is wrong. Company B charges $125 plus $75 an hour for the same exact service.
After how many hours (x) will both companies charge you the same amount(y)?
By solving a linear equation, we will see that after 3 hours, both companies will charge the same amount.
After how many hours will both companies charge you the same amount?
We know that company A charges $200 plus $50 per hour. So if they work for x hours, they charge:
A(x) = $200 + $50*x
And company B charges $125 plus $75 per hour, so if they work for x hours, they charge:
B(x) = $125 + $75*x
We want to find the value of x such that A(x) = B(x), then we want to solve the linear equation:
$200 + $50*x = $125 + $75*x
$200 - $125 = $75*x - $50*x
$75 = $25*x
$75/$25 = x = 3
This means that after 3 hours, both companies will charge the same amount.
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John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the
function v= 20,000(0.84), where t is the number of years from the time of purchase. One of the factors John is using to make his decision is
the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this
context?
The reasonable domain of the function is [0,4)
How to determine the domain?The function of the car value is given as:
V(x) = 20000 * (0.84)^x
When the car reaches half its value, we have:
V(x) = 10000
Substitute V(x) = 10000 in V(x) = 20000 * (0.84)^x
10000 = 20000 * (0.84)^x
Divide both sides by 20000
0.84^x = 0.5
Take the logarithm of both sides
x log(0.84) = log(0.5)
Divide both sides by log(0.84)
x = 4
This means that the maximum value of x is 4
Hence, the reasonable domain of the function is [0,4)
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X-7/20=5/16 solve for x
x = 53/80 = 0.6625
if isn't right I have another equation
Answer:
13.25
Step-by-step explanation:
[tex]x - 7 \div 20 = 5 \div 16[/tex]
by cross multiplying
16(x-7)=5(20)
16x-112=100
16x=100+112
16x=212
x=212 /16
×=13.25
if the question is this
i need help grades are do today sorry for the trouble
Answer:
13
Step-by-step explanation:
[tex]Sin = \frac{opp}{hyp} \\cos= \frac{adj}{hyp} \\tan = \frac{opp}{adj}[/tex]
=> get the length of the diag on bottom
[tex]tan x = \frac{3}{4} x = 36.87[/tex] degree
[tex]sin(36.87)=\frac{3}{y}[/tex]
y is about 5
=> calculate max length of stick
[tex]tan\left(x\right)\:=\frac{5}{12}, x= 22.62degree[/tex]
[tex]sin\left(22.62\right)\:=\:\frac{5}{x}[/tex]
which is 13
Which table represents a linear function?
use the information given to answer the question. write your answer as a decimal rounded to the nearest tenth
Answer: The value of x is 3.5
Explanation:
Equation:
y = 2x - 7
When the equation's Line intersects the x-axis, the value of y shall be always 0
Insert y = 0, to find x intercept
⇒ 0 = 2x - 7
⇒ 2x - 7 = 0
⇒ 2x = 7
⇒ x = 3.5
So coordinates: (x, y) → (3.5, 0)
i NEED HELP ASAP
A(n) sampling method is one that is representative of the population, selected at random, and large enough to provide accurate data.
A sample is one that is representative of the population, selected at random, and large enough to provide accurate data.
What is a sample?A sample is a smaller group that is representative of the population. A sample is sometimes necessary because it might not be feasible or cost effective to access the whole population.
For example, if a researcher is studying the impact of inflation on US families. It is not feasible to reach the whole of the families in the US. So, the researcher would use a representative group of US families. This is known as a sample.
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Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x3 + 2. include the average rate of change in your answer.
Answer:
147
Step-by-step explanation:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\ \\\frac{f(5)-f(3)}{5-3}\\ \\\frac{(3(5)^3+2)-(3(3)^3+2)}{2}\\ \\\frac{(3(125)+2)-(3(27)+2)}{2}\\ \\\frac{(375+2)-(81+2)}{2}\\ \\\frac{377-83}{2}\\ \\\frac{294}{2}\\ \\147[/tex]
Recall that if a function [tex]f[/tex] is continuous over the interval [tex][a,b][/tex], then its average rate of change is [tex]\frac{f(b)-f(a)}{b-a}[/tex].