In the figure to the right, EG = 12, EF = 2x – 3 and FG = x + 6. Find EF and FG.
Answers
Here the whole line segment measures 12.
Therefore, EG = 12or, EF + FG = 12 [Since, EF + FG = EG]or, 2x - 3 + x + 6 = 12Now, transpose -3 and 6 to the RHS
or, 2x + x = 12 - 6 + 3Now, do the addition and subtraction
or, 3x = 9Now, divide both sides by 3.
or, 3x/3 = 9/3or, x = 3Now, put the value of x in the values of EF and FG given.
Therefore, EF = (2x - 3) = 2 × 3 - 3 = 6 - 3 = 3FG = x + 6 = 3 + 6 = 9Answers:
EF is 3 and FG is 9.
Hope you could understand.
If you have any query, feel free to ask.
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Related Questions
Question 10 of 25 What is the recursive formula for this geometric sequence? -2,-16, -128, -1024,... A. ○ B. C. (a, D. 3₁ = :-2 an = 2n-1 = = -2 an = an-1.8 • a₁ = 8 an = an-1• (-2) (a₁ = -8 30 = 20-1.2 SUBMIT
Answers
Answer:
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
Step-by-step explanation:
a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r
here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
If CE= 7x+4
x+3 + 8x-9 = 7x+4
Answers
Explanation:
To find the x, you need to start by adding your “like” terms on each side of the equal sign. This means the parts that you can add together. So, on the left side, you would add 3 and -9 together, which will make -6. Then, you would add x and 8x together, which would make 9x. So your left side will look like “9x-6”. There is nothing you can add together on the right side, so now you move on to the second step: combining the terms on both sides. You can do this by knowing that the opposite of subtraction is addition, and it’s the same the other way. Let’s look at our equation now:
9x-6=7x+4
9x and 7x are “like terms” so we can subtract. So now we have:
2x-6=4
We still need to make x be by itself, so now we can move the -6 over to the 4. We add because the opposite of subtraction is addition. So now we have:
2x=10
When a number is next to a missing number, that means they are being multiplied, and the opposite of multiplication is division. So we can divide 10 by 2, which equals five. So, x=5 and we can add that to our other missing number, CE. Replace “x” with “5” and you will see that CE=39.
Given f (x) = 3 x minus 1 and g (x) = 2 x minus 3, for which value of x does g (x) = f (2)?
Answers
f ( x ) = 3x - 1
g ( x ) = 2x - 3
_____________________
g ( x ) = f ( 2 )
2x - 3 = 3(2) - 1
2x - 3 = 6 - 1
2x - 3 = 5
2x - 3 + 3 = 5 + 3
2x = 8
2x ÷ 2 = 8 ÷ 2
x = 4
There are 40 students trying out for a soccer team. After tryouts, 16 of these
students will make the soccer team and 4 of those who make the team will be
captains. What is the probability that Julie will be captain, given that she makes
the team?
Answers
The probability that Julie will be a captain, given that she makes the team, is 1/10.
To find the probability that Julie will be captain given that she makes the team, we need to consider the number of possible outcomes where Julie is a captain, and divide it by the total number of outcomes where she makes the team.
Given that there are 40 students trying out for the soccer team and 16 of them will make the team, the probability of Julie making the team is 16/40, which can be simplified to 2/5.
Out of the 16 students who make the team, we know that 4 of them will be captains.
Therefore, the probability of Julie being a captain among those who make the team is 4/16, which can be simplified to 1/4.
To calculate the probability that Julie will be a captain given that she makes the team, we multiply the probability of making the team (2/5) by the probability of being a captain among those who make the team (1/4):
(2/5) \(\times\) (1/4) = 2/20 = 1/10.
So, the probability that Julie will be a captain, given that she makes the team, is 1/10.
This means that out of all the students who make the team, there is a 1 in 10 chance that Julie will be selected as a captain.
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The graphs below show the sales of touchless thermostats, y, for the first 8 months last year. Both graphs show the same information.
Touchless Thermostat
Touchless Thermostat
Sales ($)
80,000
60,000
40,000
20,000
0
Sales
2
4
6
Months since
Start of the Year
Graph A
8
Sales ($)
40,000
30,000
20,000
10,000
0
Sales
To emphasize the slow increase in sales, it would be best for Samantha to use
Samantha should use this graph for her presentation because the sales
2
4 6 8
Months since
Start of the Year
Graph B
Samantha is preparing a presentation and wants to emphasize that the sales increased slowly over the first 8 months last year.
Complete the following sentences.
for her presentation.
Y
on this graph.
Answers
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
How to determine the appropriate graph?
The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....
The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....
The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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4. (03.04)
Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x³ +1. Include the average rate of change in your answer. (10 points)
Answers
Answer:
39
Step-by-step explanation:
The given function to us is ,
\(\longrightarrow f(x) = 3x^3 + 1\\ \)
We need to find the average rate of change between \( x=1 \) and \( x=3\) .
We can calculate the average rate of change as ,
\(\longrightarrow A(x) =\dfrac{f(b)-f(a)}{b-a} \)
So that ,
\(\longrightarrow A(x) =\dfrac{f(3)-f(1)}{3-1}\\ \)
\(\longrightarrow A(x) =\dfrac{ \{ 3(3)^3 +1 -(3(1)^3+1)\}}{2}\\ \)
\(\longrightarrow A(x) = \dfrac{ 81 +1 - 3 -1 }{2}\\\)
\(\longrightarrow A(x) = \dfrac{78}{2}\\ \)
\(\longrightarrow\underline{\boxed{ A(x) = 39}} \)
On March 1, Anton purchased a new condominium. He pays a monthly maintenance fee of $975. His
monthly property taxes equal 14.7% of the monthly fee. How much will Anton pay in property taxes for
this calendar year?
Answers
Answer:
$143.33
Step-by-step explanation:
well 14.7% of 975 is 143.33 so I'm pretty sure thats the answer
Y =250x + 500
Solve for y
Answers
Answer:
y=500
Step-by-step explanation:
y= 250 * 0 + 500
Which of the following is the equation of a line with a slope of -5/9
Answers
Answer:
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Step-by-step explanation:
Please help me important question Please help me important question in image
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Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
Answers
Answer:
SSS
Step-by-step explanation:
Maurice has a bag containing 40 small wooden blocks.
There are 20 cubes, of which 5 are blue.
There are 20 spheres, of which 6 are blue
Maurice randomly selects a cube from the bag.
What is the probability that the cube he selects is NOT blue?
Answers
Answer: The probability that the cube Maurice selects is NOT blue is 0.75 or 75%.
Step-by-step explanation: The total number of cubes in the bag is 20, of which 5 are blue. Therefore, the number of cubes that are not blue is:
20 - 5 = 15
Maurice randomly selects one cube from the bag, so the total number of possible outcomes is 20. The probability of selecting a cube that is not blue is:
15/20 = 3/4 = 0.75
Therefore, the probability that the cube Maurice selects is NOT blue is 0.75 or 75%.
Answer:
Answer: The probability that the cube Maurice selects is NOT blue is 0.75 or 75%.
Step-by-step explanation: The total number of cubes in the bag is 20, of which 5 are blue. Therefore, the number of cubes that are not blue is:
20 - 5 = 15
Maurice randomly selects one cube from the bag, so the total number of possible outcomes is 20. The probability of selecting a cube that is not blue is:
15/20 = 3/4 = 0.75
Therefore, the probability that the cube Maurice selects is NOT blue is 0.75 or 75%.
Step-by-step explanation:
Find the area of this triangle.
Round to the nearest tenth.
10 cm
55°
12 cm
[? ]cm²
Enter
Answers
Answer:
Area = 49.15
Step-by-step explanation:
area = 0.5 * side a * side b * sin(Angle)
area = 0.5 * 10 * 12 * sin(55)
area = 60 * 0.8192
49.15
Events A and B are dependent. Find the missing probability.
P(A) = 0.6
P(B\A) = 0.2
P(A and B) = ???
Answers
Answer:
P(A and B) = 0.12
Step-by-step explanation:
Conditional Probability
Is a measure of the probability of the occurrence of an event, given that another event has already occurred. If event A has occurred, then the probability that event B occurs is given by:
\({\displaystyle P(B\mid A)={\frac {P(B\cap A)}{P(A)}}}\)
Where \(P(B\cap A)\) is the probability that both events occur and P(A) is the probability that A occurs.
We are given P(A)=0.6, P(B\mid A)=0.2, and it's required to find P(B\cap A). Solving for the required variable:
\(P(B\cap A)=P(B\mid A)*P(A)\)
\(P(B\cap A)=0.2*0.6=0.12\)
P(A and B) = 0.12
Chad baked 12 cookies with 2 scoops of flour. How many scoops of flour does
Chad need in order to bake 42 cookies? Solve using unit rates.
Answers
Answer:
7
Step-by-step explanation:
Set up a proportion
12 cookies / 2 cups = 42 cookies / x Notice that cookies are on the top and cups are on the bottom of each proportion.
12/2 = 42/x Cross multiply
12x = 84 Divide by 12
x = 84/12
x = 7
He will need 7 cups to make 42 cookies.
en la feria del condado, la calabaza con la cinta roja pesaba 108 libras menos que la calabaza con la cinta azul. cuanto pesaba la calabaza con la cinta azul?
Answers
Answer:
sorry i dont know
Step-by-step explanation:
Divide (do not round): 429.6 :
1000 =
Help please
Answers
= 0.4296
Answer:
429.6 : 1000 = 0.4296
you can count how many zeros are there and than move the dot that many times (in this case 3)
HELPP DONT SEND A FILE WHATS the surface area explain step by step too
Answers
Answer:6
Step-by-step explanation:
In a right-angled triangle the ratio of the two smaller angles is 3:2. Find the sizes of each of the angles.
Answers
Answer:
36° , 54° , 90°
Step-by-step explanation:
since the triangle is right then one angle is 90°
the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )
the sum of the 3 angles in the triangle is 180° , that is
3x + 2x + 90 = 180
5x + 90 = 180 ( subtract 90 from both sides )
5x = 90 ( divide both sides by 5 )
x = 18
Then
3x = 3 × 18 = 54°
2x = 2 × 18 = 36°
the 3 angles measure 36° , 54° , 90°
Poindexter's uncle is building a house on land that has been devastated by hurricanes 160 times in the past 200 years. However, there hasn't been a major storm there in 13 years, so his uncle says this is a safe investment. His nephew argues that he is wrong because a hurricane must be due soon. What are the fallacies in the reasoning of both men?
Answers
Both men are committing fallacies in their reasoning. The occurrence of a hurricane on that land cannot be predicted with certainty, and making decisions based on fallacious reasoning can lead to poor outcomes.
What are the fallacies in the reasoning of both men?A fallacy refers to the statement in an argument that makes an error in logic. Fallacies are very dangerous because they lead to incorrect thinking about certain topics and may lead to an incorrect conclusion about that topic most of the time.
The fallacy in Poindexter's uncle's reasoning is known as the fallacy of induction. This fallacy occurs when someone assumes that because a certain event has happened in the past, it is likely to happen again in the future. While it is true that the land has been hit by hurricanes 160 times in the past, it doesn't necessarily mean that it will happen again in the near future.
On the other hand, Poindexter's nephew is committing the fallacy of the Gambler's Fallacy. This fallacy occurs when someone assumes that because something hasn't happened in a while, it is more likely to happen soon. In this case, the nephew assumes that a hurricane must be due soon simply because it hasn't happened in the past 13 years. However, the occurrence of a hurricane is not influenced by the time that has passed since the last one. Each hurricane is a unique event that is not influenced by previous occurrences.
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How many lines can be constructed perpendicular to AC that pass through point D?
Answers
Answer:
1
Step-by-step explanation:
This is the answer by definition.
What is the answers to Part A, B, and C ?
Answers
Part a: The data points appear to follow an exponential pattern. This is because the balance is increasing at a rate that is proportional to the current balance.
How to explain the informationPart b: The equation of the best fit is y = 50(1.06)^x. This can be found using a variety of methods, including graphing the data points and fitting a curve to them, or using a statistical software package.
Part c: When x = 32, y = 50(1.06)^32 = $2,499.82.
Years since 1990, x 0 5 10 15 20 25 30
Balance, y $50 $62.31 $77.65 $96.76 $120.59 $150.27 $187.27 $2,499.82
The equation of the fitted curve is y = 50(1.06)^x.
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What is the median of this data set?
{13, 8, 12, 8, 12, 3}
Enter your answer in the box.
Answers
{13, 8, 12, 8, 12, 3}
3, 8, 8, 12, 12, 13
median — (8 + 12) : 2 = 20 : 2 = 10
\(\huge\text{Hey there!}\)
\(\large\text{The word \underline{median} means the number in the CENTER (the \bf middle}\\\large\text{number).}\\\\\\\large\text{To find your median you have to put your numbers from least}\\\large\text{(smallest) to greatest (biggest).}\)
\(\large\text{Your data slot: \textsf{13, 8, 12, 8, 12, \& 3}}\)
\(\large\text{Conversion: \textsf{3, 8, 8, 12, 12, \& 13}}\)
\(\large\text{Finding your result: }\large\boxed{\rm{\dfrac{8+12}{2}}}\\\\\large\boxed{= \rm{\dfrac{20}{2}}}\\\\\\\large\boxed{= \rm{\dfrac{20\div2}{2\div2}}}\\\\\\\large\boxed{\rm{= \dfrac{10}{1}}}\\\\\\\large\boxed{= 10\div 1}\\\\\\\large\boxed{\rm{= 10}}\)
\(\huge\text{Therefore, your answer is: \boxed{\mathsf{10}}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
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Please help
Find the value of x
Answers
Answer:
75
Step-by-step explanation:
60+55+x=180
All triangles equal 180 so if you add 60 and 55 you get 105 then subtract that from 180 to get 75.
Answer:
x = 65
Step-by-step explanation:
= 60 +55 =115 ( exterior < property)
x = 180 -115 = 65 (linear pair)
fraction that is equivalent to 3/9 and has a denominator of 3."
Answers
, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: The fraction 3/9
Now we can simplify the fraction further by dividing both the numerator and denominator by 3
let p=3/9
then p=3/3 / 9/3
p= 1/3
Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3
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If it costs $1.40 per square foot to install the garden, what is the cost for plan A? Plan B?
Answers
Answer:
Step-by-step explanation:
I NEED HELP PLEASE
Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. If it takes approximately ten minutes to serve each customer, find the mean use at least four digits after the decimal if rounding...)
and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) (use at least four digits after the decimal if rounding...) What is the probability that the total service time will exceed 2.5 hours? (use at least four digits after the decimal if rounding...)
Answers
The answer of this question is found to be 0.0012.
The mean total service time is 10 minutes times lambda (the average number to turn up during the hour)
Lambda is 7, since the average rate is 7 per hour and your time window is 1 hour.
mean service time = 7 × 10 = 70 minutes.
For a poisson process, lambda is both the mean and variance of the arrivals.
So the variance = 10² × lambda = 700, since we want the variance of the service time, rather than the variance of the arrival rate.
This is because:
σ(aX) = a × σ(X).
and σ = sqrt(variance)
σ(service time) = 10 σ(arrival time)
variance(service time) = (10 × σ(arrival time))²
variance(service time) = 100 × variance(arrival time) = 100 × lambda = 100 × 7
mean(servicetime) = 70
variance(servicetime) = 700
2.5 hour = 150 min
Z = \(\frac{(S - 70)}{\sqrt{700} }\) follow N(0,1)
P(S > 150) = P( \(\frac{(S - 70)}{\sqrt{700} }\)> \(\frac{(150 - 70)}{\sqrt{700} }\))
=P(Z > -2.5512)
=0.0012
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Simplify 5x + 3x + 2 +4
Answers
Hi
add "x" with "x" and numbers with numbers
5x+3x+2+4 = 8x+6
Answer: \(8x+6\)
Add
\(5x+3x=8x\\2+4=6\\8x+6\)
Given P(A) = 9⁄25, P(B) = 21⁄50 and P(A ∩ Bc ) = 4⁄25. Find P(A ∩ B).
A) 0.94
B) 0.24
C) 0.21
D) 0.20
E) 0.36
F) None of the above.
Answers
Last year, there were 43 scienceprojects submitted to the student sciencefair. This year, there was 52 submitted.Find the percent change. Round to thenearest tenth.
Answers
Answer:
An increase of 20.9%
Explanation:
Number of projects submitted last year = 43
Number of projects submitted this year = 52
To calculate the percentage change, we use the formula:
\(\text{Percent change =}\frac{\text{Final Value-}Initial\text{ Value}}{\text{Initial Value}}\times100\)Substituting our values, we have:
\(\begin{gathered} \text{Percent change =}\frac{52-43}{\text{4}3}\times100 \\ =\frac{9}{43}\times100 \\ =0.2093\times100 \\ =20.9\% \end{gathered}\)The percent change is an increase of 20.9% (correct to the nearest tenth).
In Houston, Texas, it is 92 degrees Fahrenheit. The temperature is expected to drop 2.5 degrees each hour. In Chicago, Illinois, it is 80 degrees Fahrenheit, and the temperature is expected to drop 1 degree each hour. Which inequality shows the number of hours, x, it will take for the temperature in Chicago to be greater than the temperature in Houston?
A. 92 – 2.5x > 80 – x
B. 92x – 2.5 x + 80
D. 92 – 2.5x < 80 – x
Answers
Answer:
the answer is d i took the test and got it right
Step-by-step explanation:
i have none