Find the perimeter of 6 regular octagons linked together side by side,if one side is 4.5 inches.
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also notice, the octagons on either edge, include 7 sides to the perimeter, whilst the octagons in between, only include 6 sides to the perimeter.
so, add all sides, excluding those borders, and that's the perimeter.
The shape has 38 equal sides, each side is 4.5 inches, so the perimeter is
4.5 × 38 = 171 inches
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This confuses me, can someone explain it?
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Find the slope of the graph of the function y=5x/x-2 at (3,15). Then find an equation for the line tangent to the graph at that point.
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The slope of the graph at the point (3,15) is -10. The equation of the tangent line at that point is y = -10x + 45.
Explanation:To find the slope of the graph, we need to differentiate the equation y=5x/(x-2). Using the quotient rule, the derivative of this equation is (5(x-2) - 5x)/(x-2)². Simplifying this further, we get -10/(x-2)². Now, substitute the x-coordinate of the point (3,15) into the derivative to find the slope at that point. Substituting x=3, we get a slope of -10/1 = -10.
To find the equation of the tangent line at the point (3,15), we use the point-slope form of a line, y - y1 = m(x - x1). Substituting the slope (-10) and the coordinates of the point (3,15) into this equation, we get y - 15 = -10(x - 3). Simplifying further, we get y - 15 = -10x + 30. Rearranging the equation, we get y = -10x + 45. Therefore, the equation of the tangent line to the graph at the point (3,15) is y = -10x + 45.
if I fail this I'm gonna fail the quarter. please help
Quadrilateral PQRS is shown below. Which of the following transformations of ΔPTS could be used to show that ΔPTS ≅ ΔQTR ?
A reflection over line segment QS
2) A reflection over line segment PR
3) A reflection over line m
4) A reflection over line l
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The transformation that would show triangle PTS is congruent to triangle QTR in quadrilateral PQRS is a reflection over the line segment PR, assuming PQRS is a parallelogram.
Explanation:The question involves identifying which transformation of triangle PTS would show that it is congruent to triangle QTR in quadrilateral PQRS. Without a diagram, it's difficult to provide a specific answer. However, the properties given refer to the symmetric treatment of the sides of a parallelogram and parallel lines. Based on the axioms provided, if PQRS is a parallelogram, then any reflection over the line connecting opposite corners (diagonals) would make two triangles inside the parallelogram congruent. This is because reflections over a line preserve the size and shape of a geometric figure while flipping it over the line. Since PTS and QTR share point T, reflect triangle PTS over the line containing this shared point, which is the line TR or line segment PR, assuming PQRS is a parallelogram.
Using this example, estimate the traffic flow for a roundabout presented below. the graphical model shows the number of cars per hour that are entering or leaving a roundabout. if the portion of the roundabout between a and b has an estimated traffic flow of from 6[e] to 8[a] cars per hour, what is the estimated traffic flow between c and a, and between b and c?
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We have three equations that we can use for this problem.
X1 − X3 = 35
X2 − X1 = 50 X3 – X2 = 15 To solve for C and A. We’ll take the first equation and put 23 for X1. X1 − X3 = 35 23 − X3 = 35 −X3 = 35 - 23 −X3 = 12 The estimated traffic flow for C and A is 12 cars per hour. Now, to solve for B and C, we’ll take the second equation and put 23 for X1 as well. X2−X1=50 X2− (23) =50 X2 = 50 + 23 X2 = 73 The estimated traffic flow for B and C is 73 cars per hour.
Josiah, the manager of a pet store, bought 72 oz of water conditioner to use in his fish tanks. His small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner. He made a sketch to show the line representing the different combinations of tanks he could put the water conditioner into. The x-axis represented the number of small tanks and the y-axis represented the number of large tanks. The manager labeled only the intercepts.
Which points did the manager label?
(0, 6) and (2, 0)
(0, 12) and (36, 0)
(6, 0) and (0, 2)
(0, 36) and (12, 0)
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Given that his small tanks would require 2 oz of conditioner and his large tanks would require 6 oz of conditioner and there are a total of 72 oz of water conditioners available.
The line representing the various combinations of tanks he could put the water conditioner into is given by 2x + 6y = 72.
Since, the manager labeled only the intercepts.
The x-intercept is the value of x when y = 0 and is given by
2x + 6(0) = 72
x = 72 / 2 = 36
Thus, the x-intercept is (36, 0)
The y-intercept is the value of y when x = 0 and is given by
2(0) + 6y = 72
y = 72 / 6 = 12
Thus, the x-intercept is (0, 12)
Therefore, the points labeled by the manager are: (0, 12) and (36, 0)
Find the value of sec θ for the point (7,6)
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Type the integer that makes the following addition sentence true:
+ 4 = 4
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I NEED HELP NOW PLEASE!!!!!!!!
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If y is the # of pages read and x the # days, so the equation becomes:
y = m.x + b where m is the rate of reading or the slope and b a constant. How to calculate m? and later b
Note that we can rewrite the given as:
x| 0 | 2 | 5 | 7 |
-|------|-----|-----|------|
y| 57 | 99|162 |204 |
m= (y₂-y₁)/(x₂-x₁) = Rise/Run
m= (204-162)/(7-5) = (162-99)/(5-2) = (99-57)/(2-0) = 21
Then
m = 21 and the function y = 21.x +b
We notice in the table that when x = 0; y = 57, then
57 = 0.x + b that means b = 5 and the final equation is:
y = 21.x + 57
karen sells clothes. after studing her constraints, she knows that she will make $10 profit on each jacket, j, she sells and $6 profit on each shirt, s, she sells. which equation or inequaltiy should she use to show her maximum profit , P?
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Hope this helps!
There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected by a biologist gives the model = 25.2 + 3.3x, where x is the number of chirps per minute and is the estimated temperature in degrees fahrenheit. what is the predicted increase in temperature for an increase of 5 chirps per minute?
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For an increase of 5 chirps per minute, the predicted increase in temperature is approximately 41.7 degrees Fahrenheit.
What is the predicted increase in temperature for an increase of 5 chirps per minute?In the given linear relationship model, the equation is:
T = 25.2 + 3.3x
Where:
T represents the estimated temperature in degrees Fahrenheit.
x represents the number of chirps per minute.
To find the predicted increase in temperature for an increase of 5 chirps per minute, you can simply plug in the value of x as 5 into the equation:
T = 25.2 + 3.3(5)
Now, calculate the result:
T = 25.2 + 16.5
T = 41.7
So, for an increase of 5 chirps per minute, the predicted increase in temperature is approximately 41.7 degrees Fahrenheit.
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An investor bought 400 shares of stock, some at $7.00 per share and some at $1.00 per share. If the total cost was $1450.00, how many shares of each stock did the investor buy?
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The investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
Explanation:To solve this problem, you can set up a system of equations. Let x be the number of shares bought at $7.00 per share and y be the number of shares bought at $1.00 per share.
From the information given, we know that:
x + y = 400 (equation 1)7x + y = 1450 (equation 2)To solve the system of equations, you can use the substitution method or the elimination method.
Using the elimination method, multiply equation 1 by 7 to make the coefficients of x in both equations equal:
7(x + y) = 7(400)7x + 7y = 2800 (equation 3)Now, subtract equation 2 from equation 3 to eliminate x:
(7x + 7y) - (7x + y) = 2800 - 14506y = 1350y = 225Substitute the value of y into equation 1 to find x:
x + 225 = 400x = 175Therefore, the investor bought 175 shares at $7.00 per share and 225 shares at $1.00 per share.
How many 7/8 yard long scarves can I make from 156 feet of fabric
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how many times does 7/8 go into 52? let's check.
[tex]\bf \cfrac{52}{\frac{7}{8}}\implies \cfrac{\frac{52}{1}}{\frac{7}{8}}\implies \cfrac{52}{1}\cdot \cfrac{8}{7}\implies \cfrac{52\cdot 8}{1\cdot 7}\implies \cfrac{416}{7} \\\\\\ \textit{7 goes into 416 \underline{59 times}, with a \underline{remainder of 3}}\implies 59\frac{3}{7}[/tex]
True or false. The equation csc^2x-1=cot^2x is an identity.
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Answer: true
Step-by-step explanation:
a pe x
which formula can be used to describe the sequence? 1.2, 3, 7.5, 18, 7.5, ...
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This is a geometric sequence with common ratio of 2.5, because
3/1.2 = 2.5
7.5/3 = 2.5
18.75/7.5 = 2.5
The 1st term is a₁ = 1.2(2.5)⁰
The 2nd term is a₂ = 1.2(2.5)¹
The 3rd term is a₃ = 1.2(2.5)²
and so on
Therefore the sequence obeys the formula
f(x) = 1.2(2.5)ˣ⁻¹
Answer: [tex]f(x) = 1.2(2.5)^{x-1}[/tex]
Answer:
Option A) [tex]1.2(2.5)^{x-1}[/tex]
Step-by-step explanation:
We are given a series:
[tex]1.2, 3, 7.5, 18.75, ...[/tex]
We know that the given series is a geometric series as
[tex]\displaystyle\frac{3}{1.2} = \frac{7.5}{3} = \frac{18.75}{7.5} = 2.5[/tex]
Geometric Series:
A geometric series is a series with a constant ratio between successive terms. The first term is represented by aIn the given series a = 1.2The common ratio is denoted by rFor the given series r = 2.5The [tex]n^{th}[/tex] term of a geometric series is given by:
[tex]a_n = a(r)^{n-1}[/tex]
[tex]a_1= 1.2\\a_2 = 1.2(2.5)^{2-1} = 3\\a_3 = 1.2(2.5)^{3-1} = 7.5\\a_4 = 1.2(2.5)^{4-1} = 18.75[/tex]
Thus, the general term of the given series can be formulated with the help of [tex]f(x) = 1.2(2.5)^{x-1}[/tex]
Option A) [tex]1.2(2.5)^{x-1}[/tex]
What should be done so that the expression will have a value of 10? 4 + 4 2 - 5 × 2
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Answer: D NOTHING NEEDS TO BE DONE
Step-by-step explanation: and ANY ONE WHO NEEDS THIS ANSWER LOOK IN THE COMMENTS ON THE QUESTION SO YOU KNOW WHAT IM TALKING ABOUT
there are 500 seventh grade students at heritage middle school. sixty percent of them play a musical instrument. how many seventh grade students play a musical instrument
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Which expression shows the result of applying the distributive property to 3(2x−6) ?
A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3
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Hope this helps!
answer
B. 6x−18
Francois baked just enough cookiesto fill all the orders at his bakery. While the cookies were cooling, a kitchen assistant knocked over a cooling rack and spilled 12 percent of the cookies onto the floor. Francois had to bake 36 more cookies to replace them.
How many cookies were ordered in total? And please explain.
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12% of cookies is same as = 36 cookies
Then
100% of cookies is the same as = (36/12) * 100
= 3 * 100
= 300
So 300 cookies were ordered in total.
Hope this helped ☺
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?. .a. y = 2x – 2. b.y = 2x + 2. c.y = x + 2. d. y = x – 2
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the equation for a line is y = m x + b
using the first set of coordinates (0,2)
2 = m * 0 + b
b = 2
using the second set of coordinates (4,6)
6 = 4 m + 2
4 m = 4
m = 4 / 4
m = 1
use those numbers into the line equation
y = x +2
Answer is C
Answer:
The equation of line is y = x + 2 .
Option (c) is correct .
Step-by-step explanation:
The equation of line is represented by
[tex](y-y_{1}) = \frac{(y_{2}-y_{1})}{x_{2}-x_{1}} (x-x_{1})[/tex]
As given
Line CD passes through points (0, 2) and (4, 6).
[tex](y-2) = \frac{(6-2)}{4-0}(x-0)[/tex]
[tex](y-2) = \frac{4}{4}(x-0)[/tex]
y -2 = x
y = 2 + x
Therefore the equation of line is y = x + 2 .
Option (c) is correct .
A and b alternate rolling a pair of dice, stopping either when a rolls the sum 9 or when b rolls the sum 6. assuming that a rolls first, find the probability that the final roll is made by
a.
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The probability of the player for final roll is 25%.
Given data:
To find the probability that the final roll is made by player A, we need to consider the possible outcomes of the game. There are two possible scenarios:
Player A rolls a sum of 9 before player B rolls a sum of 6.
Player B rolls a sum of 6 before player A rolls a sum of 9.
Let's calculate the probability for each scenario and determine the probability that the final roll is made by player A.
Scenario 1:
Player A rolls a sum of 9 before player B rolls a sum of 6.
The probability of rolling a sum of 9 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 9 is 4, as there are four ways to get a sum of 9: (3, 6), (4, 5), (5, 4), and (6, 3).
The total number of possible outcomes when rolling two dice is 36 (6 possible outcomes for each die).
Therefore, the probability of player A rolling a sum of 9 before player B rolls a sum of 6 is 4/36 = 1/9.
Scenario 2:
Player B rolls a sum of 6 before player A rolls a sum of 9.
Similarly, the probability of rolling a sum of 6 with two dice is given by the number of favorable outcomes divided by the total number of possible outcomes.
The number of favorable outcomes for a sum of 6 is 5, as there are five ways to get a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1).
Therefore, the probability of player B rolling a sum of 6 before player A rolls a sum of 9 is 5/36.
Now, calculate the probability that the final roll is made by player A by adding the probabilities of both scenarios:
Probability that the final roll is made by player A = Probability of Scenario 1 + Probability of Scenario 2
= 1/9 + 5/36
= 4/36 + 5/36
= 9/36
= 1/4
Hence, the probability that the final roll is made by player A is 1/4 or 25%.
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f(x) = 2x^2 + 3 and g(x) = x^2 - 7, find (f-g)(x)
A) 3x^2 - 10
B) x^2 - 4
C) x^2 + 10
D) 3x^2 - 4
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Let's solve for a.y=2x2+3andgxStep 1: Flip the equation.3adgnx+2x2=yStep 2: Add -2x^2 to both sides.3adgnx+2x2+−2x2=y+−2x23adgnx=−2x2+yStep 3: Divide both sides by 3dgnx.3adgnx3dgnx=−2x2+y3dgnxa=−2x2+y3dgnx answer :a=−2x2+y3dgnx
A culture of 2.4×10^11 bacteria is in petri dish A. A culture of 8×10^9 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
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The number of bacteria in petri dish A is 30 times greater than the number in petri dish B. This is calculated by dividing 2.4 × 10^11 by 8 × 10^9.
To determine how many times greater the number of bacteria in petri dish A is compared to petri dish B, we need to divide the number of bacteria in petri dish A by the number in petri dish B.
Given:
Petri dish A: 2.4 × 10^11 bacteriaPetri dish B: 8 × 10^9 bacteriaThe calculation is:
2.4 × 10^11 / 8 × 10^9 = 3 × 10^1 = 30
Therefore, the number of bacteria in petri dish A is 30 times greater than in petri dish B.
Use the chain rule to find dz/dt. z = xy9 − x2y, x = t2 + 1, y = t2 − 1
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[tex]\dfrac{\mathrm dz}{\mathrm dt}=(y^9-2xy)(2t)+(9xy^8-x^2)(2t)[/tex]
[tex]\dfrac{\mathrm dz}{\mathrm dt}=20t^{19}-144t^{17}+432t^{15}-672t^{13}+504t^{11}-336t^7+282t^5-112t^3+18t[/tex]
The value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
According to chain rule:
[tex]\frac{dz}{dt} = \frac{\delta z}{\delta x} \frac{dx}{dt} + \frac{\delta z}{\delta y} \frac{dy}{dt}[/tex]
Given the following expressions
z = xy⁹ − x²y,
x = t² + 1
y = t² − 1
Get the differentials in the equation
[tex]\delta z/\delta x = y^9-2xy\\dzx/dt = 2t\\\delta z/\delta y =9xy^8-x^2\\dy/dt = 2t[/tex]
Substitute the differentials into the formula
[tex]\frac{dz}{dt} = (y^9-2xy)(2t)+(9xy^8-x^2)(2t)\\\frac{dz}{dt} = 2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
Hence the value of dz/dt using the chain rule is [tex]2t[(t^2-1)^9 -2(t^4-1)]+2t[9(t^2+1)(t^2-1)^8-(t^2+1)^2][/tex]
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0.09 is 10 times as much as
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Hope I was able to help, if you need any more help, please let me know.
121 bricks in 16.5 minutes 22 brings in m minutes
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121/16.5 = 22/m
121m = 16.5 * 22
11m = 16.5 * 2
11m = 33
m = 3
3 minutes.
What is 20% of 1630?
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What Number=20%(1630)
Wn=20%(1630)
Wn=326
Answer=326
Hope this helps! :)
Monica wants to make sure that her sentences are easily understood. how long should she make them?
a. an average of 28 words
b. no more than 8 words
c. at least 30 words
d. an average of 20 words
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How to write one hundred seventy five and one hundred fifty five thousandth in standard form
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one hundred fifty fice thousand__1075
what is the prime factorization of 720
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There are eight rooms in Fern's home . Two of them are used for her office space. What percentage of the home's rooms is not used for the office space?
Please help me will pick brainliest answer with more info!!!
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# of non-office rooms/total rooms
or
6/8
In percentage, this is 75%
Hope this helps!