Graph the line that passes through the points (9,2) and (3,4) and determine the equation of the line ( I need it with graph)
Answers
The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 and the graph is shown below .
In the question ,
it is given that
the required line passes through the points (9,2) and (3,4)
in order to find the equation of line we first need to find slope .
so , the slope(m) will be
m = (4-2)/(3-9)
m = 2/(-6)
m = -1/3
The equation of the line passing through the point (3,4) having slope -1/3 is
y - 4 = (-1/3)(x - 3)
3(y - 4) = -1(x - 3)
3y - 12 = -x + 3
x + 3y = 12 + 3
x + 3y = 15
the graph of the line is drawn below .
Therefore ,The equation of the line that passes through the points (9,2) and (3,4) is x + 3y = 15 .
Learn more about Equation Of Line here
https://brainly.com/question/15896978
#SPJ1
Related Questions
two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. what is the probability that the first card drawn is a diamond and the second card drawn is not a diamond? a) 0.1875 b) 0.1912 c) 0.0577 d) 0.0588 e) 0.7500 f) none of the above.
Answers
The correct answer is Option 'B'.
We are drawing cards without replacement,
So first card is a diamond is 13/52 and
Second not a diamond is 39/51
51 because we have picked 1 card in the first draw.
so final answer is
(13/52) *(39/51) = 0.1912.
Therefore, the probability that the first card drawn is a diamond and the second card drawn is not a diamond is 0.1912.
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain occurrences. The degree to which something is likely to happen is essentially what probability means.
Learn more about Probability at,
https://brainly.com/question/6317199
#SPJ4
What is the value of z where distance of between two point R(6, - 1, - 3) and S(3, 3, z) is 13?
Answers
Answer:
-15, 9
Step-by-step explanation:
Substituting into the distance formula,
[tex]\sqrt{(6-3)^2+(-1-3)^2+(-3-z)^2}=13 \\ \\ \sqrt{25+(3+z)^2}=13 \\ \\ 25+(3+z)^2=169 \\ \\ (3+z)^2=144 \\ \\ 3+z=\pm 12 \\ \\ z=-3 \pm 12 \\ \\ z=-15, 9[/tex]
what Is the inequality shown?
Answers
The inequality shown is -4 ≤ x ≤ 3.
We are given a diagram of the number line. The diagram shows the range of the inequality. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. Let the variable "x" represent all the values contained in the inequality. The minimum value contained in the inequality is -4. The maximum value contained in the inequality is 3. All the values between the minimum and maximum limits are included in the inequality. Hence, we can write the following inequalities :
-4 ≤ x
x ≤ 3
We can combine these into a single inequality.
-4 ≤ x ≤ 3
To learn more about inequalities, visit :
https://brainly.com/question/28823603
#SPJ1
the expressions 9x+7 and 7+9x are equivalent or not equivalent? The equation has_____
Answers
Answer:
Equivalent
Step-by-step explanation:
The equation is equivalent because they are just written the other way around although if you were to rewrite them both they would both be 9x+7
Expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
What is Expression?An expression is combination of variables, numbers and operators.
The expressions 9x+7 and 7+9x are equivalent because they have the same terms, although the order of the terms is different.
Let us check their equivalence.
9x+7 = 7+9x (commutative property of addition)
9x = 9x (subtract 7 from both sides and subtract 9x from both sides)
Both expressions simplify to the same thing, which means they are equivalent.
In terms of an equation, if we set these two expressions equal to each other, we get:
9x+7 = 7+9x
Simplifying this equation gives:
9x - 9x = 7 - 7
0 = 0
This means that the equation has an infinite number of solutions, since any value of x will satisfy.
Hence, expressions 9x+7 and 7+9x are equivalent and the equation has infinitely many solutions.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ2
Identify all of the roots of f(x) = x² + 2x + 2.
Answers
Answer: -1-1i and -1+1i
Step-by-step explanation:
A train traveled at the same speed for 9 hours. It went 320.55 miles in all. To the nearest hundredth of a mile per hour, how fast was the train going?
Answers
The train's speed was= 56.7 miles per hour
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
Entire distance = 210 miles + 130 miles = 340 milesTotal time = 3.5 hours and 2.5 hours = 6 hoursAverage speed = distance/ time = 340 miles/ 6 hours= 56.66666666666 miles per hourRounding to the nearest tenth= 56.7 miles per hourHence, The train's speed was= 56.7 miles per hour
learn more about unitary method click here:
brainly.com/question/24587372
#SPJ13
What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
Answers
The remainder of the division problem given by the image at the end of the answer is as follows:
How to obtain the remainder of a division problem?When a division does not result in an exact term, we have that the quotient is added to the remainder.
A long division problem is represented as follows:
q(x) + (r(x)/b(x))
In which the terms are listed as follows:
q(x) is the quotient.r(x) is the remainder.b(x) is the divisor.In this problem, the division is given as follows:
(x + 1)/x.
Separating the division into two terms, we have that:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Hence:
The quotient is of x.The remainder is of 1.Missing InformationThe division in this problem is:
(x + 1)/x.
More can be learned about the remainder of a division at https://brainly.com/question/25289437
#SPJ1
Answer: B. 1
Step-by-step explanation:
edge 2023
18. a rectangular page is to contain 42 square inches of printable area. the margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is . what should the dimensions of the page be so that the least amount of paper is used?
Answers
The page is in landscape mode with a width : height is 3: 2
Given that,
The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.
x = length of the horizontal side of the printable area
y = length of the vertical side of the printable area
XY = 42 inch²
y = 42/x
page height = y + 1 + 1
page width = x + 1 + 2
A = area of an entire sheet of paper
= (x+3)(y+2)
= (x+3)(42/x+2)
= x(42/x+2)+3(42/x+2)
= 42+2x+126/x+6
A = 2x+126/x+48
Extremes occur when A' = 0:
A' = 0 = 2 – 126/x²
1 = 63/x²
x² = 9*7
x = 3√(7), x has to be positive
y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)
What should the dimensions of the page be so that the least amount of paper is used?
page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)
page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)
So, the page is in landscape mode with width: height is 3: 2.
To learn more about dimensions click here:
braihttps://brainly.com/question/28815550
#SPJ4
If f(x)=4x^3+5, then what is the remainder when f(x) is divided by x−3?
Using Remainder theorem
Answers
Answer:
113
Step-by-step explanation:
Finding a remainder seems like you should be dividing. Remember everything is a shortcut for something else in math. So first you learn Long Division, but that's too much writing, so then you learn Synthetic Division, but there's an even shorter shortcut. It is called Remainder Theorem. If you just substitute 3 (because x-3 in the question) into the function, and you calculate it, you get the remainder.
f(x) = 4x^3 + 5
f(3) = 4(3)^3 + 5
f(3) = 4(27) + 5
= 108 + 5
= 113
See image.
Kermit and Miss Piggy are a part of a close group of 10 Muppets. Four of the Muppets are randomly selected to
do press for their next movie. What is the probability Miss Piggy will do press but Kermit will not?
A.4/15
B.1/15
C.1/24
D.None of the above
Answers
Answer:
d
Step-by-step explanation:
Because answer would be 4/10 or 5/10
An object is traveling at a steady speed of 10 and 1 tenth mi/h. How long will it take the object to travel 1 and 9 tenth mi? First round to the nearest integer to find the estimated answer. Then find the exact answer. (First Person To Answer Gets A Surpise!!)
Answers
Estimated Answer=1/2 hour
Exact Answer= 49/101 hour
Step-by-step explanation:
Steady speed of the object =10 and one tenth km/h = 10 1/10 km
Distance to be Covered=4 and nine tenths km = 4 9/10 km
To the nearest integer,
Steady speed of the object = 10 km/hr
Distance=5km
= 5/10 =1/2 hr
The estimated answer is 1/2 hr.
The exact time taken is 49/101 hours
Hudson goes to a store an buys an item that costs a dollars. He has a coupon for 20%
off, and then a 5% tax is added to the discounted price. Write an expression in terms
of a that represents the total amount that Hudson paid at the register.
Answers
An expression that represents the total amount (a) that Hudson paid is
a-a/10×2+{(a/10×2)/20}.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.So, the expression that represents the total amount Hudson paid:
We know that,
Hudson has a coupon for 20% off.A 5% tax is added to the discounted price.Then, the expression can be as follows:
a - (a/100×20) + {(a/100×20)/100 × 5}a - a/10 × 2 + {(a/10×2)/20}Therefore, an expression that represents the total amount (a) that Hudson paid is a - a/10 × 2 + {(a/10×2)/20}.
Know more about expressions here:
https://brainly.com/question/28934492
#SPJ13
Triangle DEF with coordinates D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH. If G has
coordinates (9, 3), what are the coordinates for H?
Answers
The coordinates for H are (9,2)
What are the coordinates?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
Here, we have
D(0, 0), E(3, 1), and F(3, 0) is similar to triangle EGH.
coordinates are (x,y) = (x+6,y+2)
F's coordinate is (3,0)
using the coordinates we get (9,2)
Hence, the coordinates of H are (9,2)
To learn more about the coordinates from the given link
https://brainly.com/question/26284611
#SPJ1
someone pls help this is the last question im begging you im gonna cry
Answers
Answer:
x = 10
Step-by-step explanation:
48 = x + 8 + 2x + x
48 = 4x + 8
-8 -8
40 = 4x
divide both sides by 4
10 = x or x =10
a haunted house claims that 80% of customers are scared speechless. if this is true, what is the probability that 60% or less out of a group of 50 customers will be scared speechless?
Answers
Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.
Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.
Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.
Then, by binomial distribution,
P(x≤30) =r=030nCr*pr*q(n-r)
Now we can substitute given values and find the desired probability,
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)
P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r
P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r
The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.
P(x≤30) = 0.000932
Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.
Learn more about binomial distribution probability here https://brainly.com/question/24756209
#SPJ4
professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78
Answers
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
Given that;
In his principles of microeconomics subject, Professor Elderman has utilized the same multiple-choice final exam for many years. He looks over the last ten years' worth of statistics and discovers that the scores have a mean of 76 and a standard deviation of 12.
µ = 76 , σ = 12 , n = 36
Using Normal Distribution;
For x = 70
z = (x - µ) / (σ/√n) = (70-76)/(12/√36) = -3.00
P( average greater than 70 ) = P(X>70)
= 1 - P(X<70)
= 1 - P(Z<-3.00)
= 1 - 0.0013
= 0.9987
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
To learn more about probability click here:
brainly.com/question/11234923
#SPJ4
Hamad lends $5,500 at a rate of 5 ½%. Find how long it will take for his investment to earn $205 in interest? Round to the nearest day
Answers
The time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
Define the term simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest does not really compound, therefore a borrower will only charge interest mostly on principal sum, and a borrower will never be required to pay further interest on the interest that has already incurred.The formula for calculating the simple interest is-
SI = PRT/100
In which,
SI = simple interest (= $205)P = principal amount ($5,500)R = rate of interest (5 ½%) = 11/2 %T= time in years.Put in formula.
205 = 5,500×11×T/200
T = 205×200 / 5,500×11
T = 0.67 years
T = 8.13 months = 253 days.
Thus, the time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
To know more about the simple interest, here
https://brainly.com/question/2294792
#SPJ4
Find side x to one decimal place
Answers
Answer:
10.8 cm
Step-by-step explanation:
To solve this answer, we should use sine law.
[tex]\frac{SinA}{a}[/tex]=[tex]\frac{SinB}{b}[/tex]
[tex]\frac{Sin40}{7}[/tex]=[tex]\frac{Sin81}{x}[/tex] (cross multiply)
xSin40 = 7Sin81
xSin = [tex]\frac{7Sin81}{40}[/tex]
x= [tex]\frac{7Sin81}{Sin40}[/tex]
x= 10.8 cm
Q1 Q2 Logic puzzles
Solve the problems.
3 paintings are for sale.
Painting A is three times the
price of painting B.
Painting B is half the price of
painting C.
Painting C costs £368.
What are the prices of paintings
A and B?
Painting A = £ I
Painting B = £
Answers
Step-by-step explanation:
so basically, because Painting C costs £368 and Painting B is half that cost, Painting B costs £184. And Painting A is three times that amount Painting A costs £552.
You're Welcome ♡.
What does the average rate of change represent in the context of the question? Use complete sentences.
Laura is planning to attend a soccer skills camp that will require her to complete different skills tasks in the fastest time possible. To get ready for the event, she is practicing and logging her time to complete each skills task.
The x-coordinate is the skills task number, and the y-coordinate is the time in seconds.
(1, 4), (2, 8), (3, 16), (4, 32)
Answers
The rate of change here represents the time in seconds it takes her to perform a certain number of skills task
What is the meaning of the average rate of change?The rate of change is defined as the rate at which one quantity is changing with respect to another quantity. Mathematically:
rate of change = change in y / change in x
Given that: The x-coordinate is the skills task number and the y-coordinate is the time in seconds
Thus, rate of change = time in seconds / skills task number
Therefore, the rate of change in this context represents the time in seconds it takes to perform a certain number of skills task
Learn more about rate of change on:
https://brainly.com/question/8728504
#SPJ1
write down the ratio 240kg:6kg give your answer in its lowest form
Answers
Answer:
40kg:1kg
Step-by-step explanation:
240kg:6kg
Both sides can be divided by 6 so we that to simplify
40kg:1kg
Hopes this helps please mark brainliest
240 : 6
answer = 1 : 4 the simplest form of 240 : 6
a random sample of size 36 is taken from a population with mean 50 and standard deviation 5. what is (the mean of the sample mean)?
Answers
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
Calculate the z-score of 51.5 using the formula:We substitute From the standard normal distribution table, the area to the left of 1.80 is0.9641Therefore it is 0.9461learn more about standard deviation here:
https://brainly.com/question/475676
#SPJ4
Carol wants to make a square garden with 81 plants. Each row and column will have the same number of plants. How many plants will be in each row and column?
Answers
Answer: Row: 9 Column: 9
Step-by-step explanation:
Carol wants a square garden that means the amount of plants must be square, which it is so the square root of 81 is 9 so the square is 9 by 9
Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
x
x + 1
x + 2
2x
Answers
She should use (b) x + 1 to represent her second number
How to determine the representation of the second number?From the question, we have the following statements that can be used in our computation:
She uses x to represent her first numberThe numbers are consecutive numbersAs a general rule
Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other
Take for instance:
2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers
Recall that she uses x to represent her first number
This means that the next number is
Next number = First number + 1
Substitute the known values in the above equation, so, we have the following representation
Next number = x + 1
Hence, the second number is (b) x + 1
Read more about Consecutive numbers at
https://brainly.com/question/10853762
#SPJ1
At the local petting zoo, 65% of the goats are female. A researcher selects a sample of five and the goats and notes that three are female. What are p nd p^(p-hat) for female goats?
Answers
The values of p and ρˆ (p-hat) in the sample are
p = 0.65 and ρˆ (p-hat) = 0.4
How to determine the values of p and ρˆ (p-hat)?From the question, we have the following parameters that can be used in our computation:
Proportion of female goats = 65%
Sample = 5
Female = 3
The proportion of female represents the variable p
So, we have
p = Proportion of female = 65%
This gives
p = 65%
Express as decimal
p = 0.65
The variable ρˆ (p-hat) is then calculated as
ρˆ = x/n
In this case,
x = Female = 2
n = Male + Female = 2 + 3 = 5
So, we have
ρˆ = 2/5
Evaluate
ρˆ = 0.4
Hence, the values are 0.48 and 0.44, respectively
Read more about p values at
brainly.com/question/4621112
#SPJ1
10) Determine the value of 10 - t when t = 4.
11) Determine the value of 12 + m when m = 6.
12) Determine the value of a + 5.2 when a = 1.9.
13) Determine the value of 3.4 - b when b = 2.1.
Answers
Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go
Pack of 25 envelopes for £3.19
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Answers
Betsie should buy the 250 envelopes from the shop Letter2go.
As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.
Given, that Betsie is going to buy 250 envelopes.
the cost of envelopes in two shops:
Value World:
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go:
Pack of 25 envelopes for £3.19
Now, if we see the cost of envelopes in shop 1 i.e. Value World
Cost of Pack of 10 envelopes = £1.99
Also, 1 pack is free for 2 packs
1 pack = £1.99
2 packs = 2×£1.99 = £3.98
Also, with 2 packs Betsie get 1 pack free
so, Betsie gets 3 packs for £3.98.
1 pack = 10 envelopes
3 packs = 30 envelopes.
Hence, In shop Value World:
30 envelopes = £3.98
1 envelope = £3.98/30
250 envelopes = (3.98/30)×250
So, 250 envelopes will cost £33.17 in Shop Value World.
And in shop Letter2go:
25 envelopes = £3.19
1 envelope = £3.19/25
250 envelopes = (3.19/25)×250
So, 250 envelopes will cost £31.9 in Shop Letter2go.
Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.
So, Betsie should buy the 250 envelopes from the shop Letter2go.
Learn more about Unitary Method here https://brainly.com/question/23423168
#SPJ1
Please help, I'm struggling.
Answers
I think you would just add 8 + 5, because if NO is the same length as MN, then the length from MN is 5 and NP makes up the rest of the line.
Answer: MP = 13
HELP ASAP !!!! Use the equation one fourth plus s equals 18 over 20 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
Answers
a. The two numbers between which the solution to the equation lies are 0 and 1.
b. The value of the variable "s" is 13/20.
How to solve Algebra Word Problems?The equation given to us is one fourth plus s equals 18 over 20. This can be expressed as;
¹/₄ + s = ¹⁸/₂₀
s = ¹⁸/₂₀ - ¹/₄
s = (18/20) - (5/20)
s = (18 - 5)/20
s = 13/20
The solution is a rational number. A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
We can determine two rational numbers such that the solution is in between them. A rational number smaller than the solution is 0. A rational number larger than the solution is 1. Hence, the solution lies between 0 and 1.
Read more about Algebra Word Problems at; https://brainly.com/question/28339921
#SPJ1
A factory produces 270000 000 sweets every
week. How many sweets does the factory
produce in a year? Give your answer in
standard form
Answers
The factory produced 1.404 x 10⁶ sweets in a year
How to calculate the number of sweets the factory produce in a year?
Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation
Given that: The factory produces 270000000 sweets every
week.
To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:
Number of sweet in a year = Weekly production x 52
= 270000000 x 52 = 14040000000 sweets
To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The number of steps will then be used as the power of 10:
14040000000 = 1.404 x 10⁶
Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets
Learn more about standard form on:
https://brainly.com/question/29229819
#SPJ1
