use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).
Answers
The slope of the line is
[tex]\frac{-3-1}{6-3}=\frac{-4}{3}[/tex]
Substituting into point-slope form using the point (3,1),
[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]
Answer: The equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex] +5.
Step-by-step explanation:
Point-slope formula : (y - y1) = m(x - x1)
y = y coordinate of second point
y1 = y coordinate of first point
m = slope
x = x coordinate of second point
x1 = x coordinate of first point
slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]
m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]
now put values in point-slope formula : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)
y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4
y = [tex]\frac{-4x}{3}[/tex] +5
So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.
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Related Questions
Giving 20 points for the answer.
Answers
Answer:
B, A, C
Step-by-step explanation:
add the like terms together (ending in x2 with x2, ending in x with x etc )
Answer:
B A C
Step-by-step explanation:
combining like terms
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
Answers
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
[tex]P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124[/tex]
The probability of both a positive test and having the disease is given by:
[tex]P(A \cap B) = 0.939(0.038) = 0.035682[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750[/tex]
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Assume that the function f is a one-to-one function.
a. if f(3)=9, find ^-1 (9)
b. if f^-1(-8)=-9 , find f(-9)
Answers
Answer:
a. 3
b. -8
Step-by-step explanation:
let me know if you want an explanation
From this diagram, select the
pair of lines that must be
parallel if angle 1 is congruent to angle 8. If there is no pair of lines, select "none".
Answers
Answer:
Line L is parallel to Nangle 1 is equal to angle 4 ( vertically opposite angles)
if angle 1 is congruent to angle 8
then angle 4 is also congruent to angle 8
then slope of line L and n is equal
that is L is parallel to n
x2 +kx+12
What are two numbers that k could be so that each expression could be factored??
Answers
Answer:
K could be 7 or 8
Step-by-step explanation:
If K was to be 7, the equation would be x^2 + 7x + 12 = (x+3)(x+4)
If K was to be 8, the equation would be x^2 + 8x + 12 = (x + 2)(x + 6)
Help me please I beg you
Answers
You want to find the midpoint of (-4,8) and (4,-2).
Just plug the numbers in the formula and you get (4-4)/2 , (-2+8)/2 which equals 0/2 , 6/2 which tells you that the midpoint is (0,3).
Your answer should be (0,3)
Hope it helps!
Given market demand Qd=50-p, and market supply p=Qs+5.what would be the state of the market if market price was fixed at Birr 25 per unit?
Answers
The state of the market if market price was fixed at Birr 25 per unit is excess demand
Quantity demandedQd = 50 - p
p = Qs + 5
p - 5 = Qs
if market price was fixed at Birr 25 per unit?
Qd = 50 - p
= 50 - 25
Qd = 25
Qs = p - 5
= 25 - 5
Qs = 20
The state of the market if market price was fixed at Birr 25 per unit is excess demand (demand greater than supply) leading to an increase in price.
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I WILL GIVE BRAINLIEST
Which is true of dependent events?
ANSWER CHOICES:
The probability of all dependent events can be calculated using the OR formula P(A+B) =P(A) +P(B)-P(A and B) .
You can use a two-way frequency table to calculate the conditional probability of events that are dependent.
You can find the AND probability of dependent events using the formula P(A or B)= P(A) times P(B) .
The outcome of one event has no effect on the outcome of a second event.
Answers
Probability helps us to know the chances of an event occurring. The correct option is A.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Dependent events are those events in which the outcome of the first event affects the outcome of the second event. The statement that is correct about the dependent event is that the probability of all dependent events can be calculated using the "OR" formula P(A+B) =P(A) +P(B)-P(A and B).
Hence, the correct option is A.
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Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before. What does the result in part d mean?
Answers
Answer:
Total Miles he drives first day = 8 miles
Total Miles he drive second day = 12miles
Total Miles he drives third day = 18miles
Total Miles he drives fourth day = 27 miles
Step-by-step explanation:
This is a problem of linear equations in 1 variable:
The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
It is given in the question that ,
This week his goal is to drive bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before.
Let, on the first day, he drives x miles. On second day, he drives 1.5x. On the third day, he drives 1.5(1.5x) and on the fourth day, he drives 1.5(1.5(1.5x)).
So the equation is :
x +1.5x + 1.5(1.5x) + 1.5(1.5(1.5x)) = 65miles
x + 1.5x + 2.25x + 3.375x = 65miles
8.125x = 65 miles
x = 65/8.125 miles
x = 8 miles
so after solving the equation we get, on the first day Gavin drives 8 miles
similarly, on the second day he drives 12miles
on third day 18 miles
and on the fourth day 27miles
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A rectangular aquarium is 1m 20cm long, 90cm wide and 50cm deep. How many cubic centimeters of water can it hold
Answers
Answer:
540,000 cubic centimeters
Step-by-step explanation:
1 meter and 20 centimeters is equal to 120 centimeters.
[tex]120 \times 90 \times 50 = 540000[/tex]
Algebra 2 point slope form help
Answers
The slope of the line is
[tex]\frac{-1-4}{-1-0}=5[/tex]
So, the equation of the line in point-slope form is [tex]\boxed{y+1=5(x+1)}[/tex]
hey
can someone solve this 4 me
Answers
Answer:
∠a = 50°
∠b = 130°
∠c = 130°
Explanation:
Following Vertical Angles Theorem:
∠(2a - 50) = ∠a2a - 50 = a2a - a = 50a = 50A straight line has 180° angle measure, ∠c and ∠a lies on a straight line
∠c + ∠a = 180°∠c + 50° = 180°∠c = 180° - 50°∠c = 130°Also, following vertical angle theorem:
∠b = ∠c∠b = 130°Mark divided a basket of apples evenly into small bags. The number of bags was equal to the number of apples in each bag. Which could be the total number of apples?
A. 25 B. 27 C. 20 D. 18
Answers
There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.
What is a Perfect Square ?A perfect square is a number which can be written as the product of an integer with itself.
It is given that Mark divided a basket of apples evenly into small bags.
Let there be n no. of bags and therefore n number of apples in each bag
Then the total number of apples will be
n * n
n²
The value of total number of apples should be a perfect square,
In the option given only 25 is the perfect square
Therefore the equation can be made as
n² = 25
n = 5
There are 5 bags and each bag has 5 apples and total there are 25 apples.
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pls help with thisc...................................
Answers
Answer:
D
598*47+38=
28106+38=
28134
Mary Lou received $5,000 from her grandparents for her college education 8 years prior to her enrolling in college. Mary Lou invested the money at 5.5% compounded semiannually. How much money would she have in her savings account when she is ready to enroll in college? A: The balance in her account would be $__________ when she is ready to enroll in college. (Round your answer to the nearest cent.)
Answers
Answer:
The total amount , principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
Step-by-step explanation:
Compound interest is based on the principal amount and the interest that accumulates on it in every period.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.055/2)^(2)(8)
A = 5,000.00(1 + 0.0275)^(16)
A = $7,717.55
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
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Suppose that the speed at which cars go on the freeway is normally distributed with mean 65 mph and
standard deviation 6 miles per hour. Let X be the speed for a randomly selected car
b. If one car is randomly chosen, find the probability that it is traveling more than 63 mph.
Answers
Answer:
B) the probability that is traveling more than 63 mph is 0.6293 (or 62.93%)
Step-by-step explanation:
Given:
Normally DistributedMean (μ) = 65 mphStandard Deviation (σ) = 6 miles per hourFinding the Probability:
If one car is randomly chosen, we want the probability that is traveling more than 63 mph is,
P(X > 63)
To find the value of z,
z = x - μ / σ
z is the standard scorex is the observed valueμ is the mean of the sampleσ is the standard deviation of the samplez = 63 - 65 / 6
z = -2 / 6
z = -1 / 3 which is approximately -0.33
Using Z table (attached below):
z = -0.33to find this on the table
on the vertical side under z go to -0.3on the horizontal next to z, go to .03The area under the curve is 0.3707
P(z > 63) = 1 - P(z < 63)
= 1 - 0.3707
= 0.6293
Hence the probability that is traveling more than 63 mph is 0.6293
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Solve for the values of x and y.
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 6 \:\: units[/tex]
[tex]{\qquad \tt \rightarrow \: y = 20° } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Two sides and their opposite angles of a Triangle are given equal.
[tex]\large \textsf{ For x :} [/tex]
[tex]\qquad \tt \rightarrow \: 2x - 1 = x + 5[/tex]
[tex]\qquad \tt \rightarrow \: 2x - x = 5 + 1[/tex]
[tex]\qquad \tt \rightarrow \: x = 6 \: \: units[/tex]
[tex] \large\textsf{For y :} [/tex]
[tex]\qquad \tt \rightarrow \: 3y - 10 = y + 30 [/tex]
[tex]\qquad \tt \rightarrow \: 3y - y = 30 + 10[/tex]
[tex]\qquad \tt \rightarrow \: 2y = 40[/tex]
[tex]\qquad \tt \rightarrow \: y = 20 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Im stuck on this to could you guys explain how you do this
Answers
The required equation of a line is y = -3x- 1
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Using the coordinate point (0, -1) and (-1, 2)
Slope = 2-(-1)/-1-0
Slope = 3/-1
Slope =-3
Since the line crosses the y-axis at (0, -1), hence the value of b is -1
Determine the equation
y = mx + b
y = -3x + (-1)
y = -3x- 1
Hence the required equation of a line is y = -3x- 1
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need answers right now
Answers
Volume = 10×5.2×6 = 312 centimeters3
Which of the following is a solution to this inequality?
y<2/3x+2
O (0, 3)
O (-3, 1)
O (3,5)
O (1, 2)
Answers
Answer: D
Step-by-step explanation:
We can substitute in each of the coordinate pairs.
A) We get 3 < (2/3)(0)+2, which is false.
B) We get 1 < (2/3)(-3)+2, which is false.
C) We get 5 < (2/3)(3)+2, which is false.
D) We get 2 < (2/3)(1)+2, which is true.
I need this answered fast pleasee
Suppose you and your friends form a band and you want to record a demo. Studio A rents for $75 plus $75 an hour and Studio B rents for $150 and $50 an hour. Let t = the number of hours and c = cost.
Part A Write a system of equations to represent the cost at each studio.
Part B Solve the system of equations from Part A. Explain your method.
Part C Explain what the solution to the system means in terms of where your band will rent a studio.
Answers
The descriptive answer of different part is described below.
What is Linear Equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.
Here, Studio A rents for $75 plus $75 an hour .
Studio B rents for $150 and $50 an hour.
Let t = the number of hours and c = cost.
Part A
Studio A: c = 75 +75·t
Studio B: c = 150 +50·t
Part B
We solve the system of equation using substitution method, where we substitute c in the first equation with 150 +50t.
150 +50·t = 75 +75·t, subtract 75 and 50t from both sides
150 -75 = 75t -50t, combine likes terms
75 = 25t, divide both sides by 25
3 = t
Now we know that t = 3 so we find c by substituting t with 3 in the second equation.
c = 150 +50·t
c = 150 +50·3
c = 300
The solution of the system of equations is c = 300 and t = 3
Part C:
The solution of the system of equation tells us that if we rent either studio A or B for 3 hours will pay the same price $300.
The price will be different if we rent studio A then studio B if we rent it for a different amount of time than 3 hours.
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Need help with this please!! :)
Answers
2x+3y=7
2x - 3y = 4
Its asking me to find x
Answers
Trevor uses 2 ounces of almonds in each bag of trail mix he makes
Answers
The line on the graph which represents the same relationship between quantities. is line B; y = 2x
Line graphNumber of almonds = 2 ounces
Bags of trail mix = x
Total mix = y
The equation:
y = 2 × x
y = 2x
Complete question:
Trevor uses 2 ounces of almonds in each bag of trail mix he makes.
Bags of Trail Mix Almonds (oz.)
6 Line on the graph represents the same relationship between quantities.
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Which rational number is equivalent to 5.5?
Answers
Answer:
11/2
Step-by-step explanation:
Multiply by 2/2 to remove the decimal.
PLEASE HELP IF YOU DO YOU BELIEVE IN JESUS THANK YOU SO MUCH
These steps outlined were used to construct the perpendicular bisector of
Answers
Answer: ZT = ZS
Step-by-step explanation: ZT = ZS must be true under all circumstances. This is because a perpendicular bisector of a line cuts the line into two equal pieces. It is the midpoint of the entire line. Thus, ZT is the same as ZS since the line is equally cut in half and thus are the same.
The table has data reflecting the measured population of Complete the descriptors of the regression equation for
North Carolina in terms of years since 1920
this data
The data is best modeled by
function
The value of a is
and the value of c is
the value of b is
Answers
The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively
The function typeFrom the table, we can see that as the number of years increases, the population increases.
This implies that the function can be best modeled by a linear regression.
The values of a, b and cA linear regression equation is represented by
ax + by = c
Next, we enter the data in a statistical calculator.
From the statistical calculator, we have the following summary:
Sum of X = 225Sum of Y = 27.505Mean X = 37.5Mean Y = 4.5842Sum of squares (SSX) = 3937.5Sum of products (SP) = 231.4875The regression equation is then represented as:
y = bx + a
Where:
b = SP/SSX = 231.49/3937.5 = 0.05879
a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952
So, we have:
y = 0.05879x + 2.37952
Approximate
y = 0.06x + 2.4
Multiply through by 100
100y = 6x + 240
Rewrite as:
-6x + 100y = 240
Hence, the values of a, b and c are -6, 100 and 240, respectively
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Answer:
The data is best modeled by an exponential function.
The value of a is 2.653, the value of b is 1.01, and the value of c is not used
Step-by-step explanation:
EDGE answers
Part A
Which shapes can you use to model the log and the board?
Answers
Answer:
A cylinder
Step-by-step explanation:
Hope this helps :)
If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018? Be careful to treat the year 2000 as the beginning; let x be the number of years since the year 2000.
The answer is not 2,100
Answers
The population at the end of the year 2018 will be 2150.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018.
The population will be calculated as the year 2000 is also considered:-
P = Total years x Increase per year
P = 19 x 50
P = 2150
Therefore the population at the end of the year 2018 will be 2150.
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The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000.
A 2-column table with 5 rows. The first column is labeled years after 2000, x with entries 0, 3, 4, 7, 10. The second column is labeled population, P with entries 10,5000; 14,000; 15,500; 20,500; 27,000.
For which year would this model most likely be sufficient to make a prediction of the population?
1950
2005
2025
2050
Answers
Answer:
B: 2005
Step-by-step explanation:
Worked on edge 2022