Find an equation of the line passing through the given points . Use function notation to write the equation(-8,-3) and (-12,-2) f(x)=
Answers
Given
Two points (-8,-3) and (-12,-2)
we are to find the equation of the line
Solution
Steps to find the equation of a line from two points:
1. Find the slope using the slope formula. ...
2. Use the slope and one of the points to solve for the y-intercept (b). ...
3. Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.
Step 1
\(\begin{gathered} \text{Formula for Slope(M)} \\ M=\frac{y_2-y_1}{x_2-x_1_{}} \end{gathered}\)\(\begin{gathered} x_1=-8_{} \\ x_2=-12 \\ y_1=-3 \\ y_2=-2 \end{gathered}\)\(\begin{gathered} M=\frac{y_2-y_1}{x_2-x_1} \\ M=\frac{-2-(-3)}{-12-(-8)} \\ \\ \\ M=\frac{-2+3}{-12+8} \\ \\ \\ M=\frac{1}{-4} \end{gathered}\)Step 2
Now, the y-intercept is b
\(\begin{gathered} b=y_1-m.x_1 \\ b=\text{ -3 -(}\frac{-1}{4})(-8) \\ b=\text{ -3}-2 \\ b=-5 \end{gathered}\)Step 3
\(\begin{gathered} y=mx_{}+b \\ y=-\frac{1}{4}x-5 \end{gathered}\)The final answer
\(f(x)=-\frac{1}{4}x-5\)Related Questions
Please Help! I will give brainliest!
Answers
Answer:
D
Step-by-step explanation:
Wich statement best explains the relationship between the numbers divisible by 6, 2, and 3? what's the answer?
Answers
Answer:
oh! I once had this, the answer is a number that is divisible by 6 is also divisible by 2 and 3 because 2 and 3 are factors of 6.
For two n by n square matricies A and B,
suppose rankA = rankB = n-1.
Can rank(AB) become less than n-1 ?
(e.g. rank (AB) = n-2)
If so, I humbly ask you for an example.
Thank you very much.
Answers
No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.
According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.
If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.
Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.
However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.
Therefore, if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.
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What is the equation of the linear relationship that has a slope of 200 and a y-intercept of 100?
A. y = 100x + 200
B. y = 200x + 100
C. y = −200x + 100
D. y = −100x + 200
Answers
The solution is B. \(y = 200x + 100\) is a linear equation with a slope-intercept form.
How do linear and nonlinear differ?When a function is displayed in a graph, a linear function makes a straight line, but a nonlinear function, which is bent in some way, does not. Whereas the slopes of a non - linear function is changing constantly, the slopes of a linear model remains constant.
Why is a function linear?The graph of a linear function is a direct line. One regression coefficient and one predictor variables make up a linear function. The variables that are both independent and dependent are X and Y, respectively. The y interception, often known as the constant term a.
The slope-intercept form of a linear equation is \(y = mx + b\), where m is the slope and b is the y-intercept. Using the given values, we have:
slope \(= 200\)
\(y-\)intercept \(= 100\)
So, the equation of the linear relationship is:
\(y = 200x + 100\)
Therefore, the answer is B. \(y = 200x + 100\).
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(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answers
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
Simplify the expression using the order of operations agreements.
-8÷2+2×8=
Answers
Answer:
12
Step-by-step explanation:
PEMDAS is the order
P = parenthesis
E = exponent
M = *
D = division
A = +
S = -
so first 8*2 = 16
and then -8/2 = -4
and then -4 + 16
= 12
1. Division; -8 divided by 2 = -4
2. Multiplication; 2 times 8 = 16
3. Add; -4 plus 16 = 12
Therefore the answer is 12.
Which value of x makes this equation true? -3x+10=5x-8
Answers
Answer:
x= 2.25
Step-by-step explanation:
-3x +10= 5x -8
Bring all x terms to 1 side, constants to the other:
5x +3x= 10 +8
8x= 18
Divide both sides by 8:
x= 18 ÷8
x= 2.25
∴ The value of x is 2.25 to make the equation to be true.
You have 60 teaspoons of peppercorns. You need 0.25 teaspoons to make one serving of beef brisket. How many servings can you make?
Answers
Answer:
One Serving - 1/4 teaspoon
240 Serving - 60 teaspoon
plz mark as brainliest
Please help, been stuck on this for ages!
Answers
Answer:
\(\boxed {192 cm^{2}}\)
Step-by-step explanation:
Find the volume of separate cuboids :
Volume (top cuboid) :
⇒ V = 2 x 6 x (10 - 2)
⇒ V = 12 x 8
⇒ V = 96 cm²
Volume (lower cuboid) :
⇒ V = 8 x 6 x 2
⇒ V = 48 x 2
⇒ V = 96 cm²
Volume (prism) :
⇒ 96 + 96
⇒ 192 cm²
Type the correct answer in the box.
If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is
°.
Answers
Correct question is;
Type the correct answer in the box bellow: If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is ...........
Answer:
x = 35°
Step-by-step explanation:
We are told that;
cos x = sin(20 + x)°
and 0° < x < 90°
From trigonometric identities, we know that;
cos x = sin (90 - x)
Applying to our question gives;
sin (90 - x) = sin (20 + x)°
Comparing both sides, we have;
90 - x = 20 + x
Rearranging;
90 - 20 = x + x
70 = 2x
x = 70/2
x = 35°
Gerry had a coupon for $0.25 off a
frozen pizza. The grocery store
has a special triple coupon deal
and allows customers to use a
single coupon on up to five
items. By how much would his
total grocery bill change if Gerry used the coupon to buy five frozen
pizzas?
Answers
Multiply.
0.25 * 5 = $1.25 in savings
So whatever the original price was for each frozen pizza, you multiply that by 5 and subtract that by the total savings.
Best of Luck!
Answer:
1.25
Step-by-step explanation:
0.25*5
a ravi sells two wrist watches for rs 2400 each gaining 20% on one and losing 20% on the other calculate his overall gain or loss
Answers
refer to this attachment
gamsahaeyo
A Candy store keeps track of its sales during the month of January. Thegraph shows the number of sales for the first, second, third, and fourthweeks of the month. Which data could the graph represent the graph? *
Answers
Solution
For this case we can discard options 3 and 4 since are increasing values with week
Therefore the best option is:
Option 1
Since in option 2 the distance in the y value from week 1 and 2 is larger compared to waht we can see in the figure given
Explain the Central Limit Theorem for the distribution of sample means.
Answers
Answer:
I means that approximates a normal distribution as the sample size gets larger.
Step-by-step explanation:
in an experiment to learn whether substance m can help restore memory, the brains of 20 rats were treated to damage their memories. first, the rats were trained to run a maze. after a day, 10 rats (determined at random) were given substance m and 7 of them succeeded in the maze. only 2 of the 10 control rats were successful. the two-sample z test for the difference in the true proportions. Gives z= 2.25, P< 0.02
Answers
The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
What is probability ?
Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.
Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.
This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).
In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.
Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.
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Felip bought 5 pounds of sugar for $3. How many pounds of sugar did he get per dollar?Round your answer to the nearest hundredth of necessary
Answers
Since the total amount of money spent to buy 5 pounds of sugar was 3 dollars, then, divide the number of pounts (5) over the number of dollars (3) to find hoy many pounds per dollar did Felip get.
\(\frac{5}{3}=1.666\ldots\)Therefore, to the nearest hundredth, Felip got 1.67 pounds of sugar per dollar.
Find the perimeter
write the process plz
Answers
Answer:
118 cm
Step-by-step explanation:
the bottom is 30 cm (22+8)
the right side is 13 cm (29-16)
30+29+8+16+22+13 = 118
Answer:
118cm
Step-by-step explanation:
29+8+16+22+(22+8)+(29-16)
Solve the equation.
3(x−9)=30
Answers
Answer:
x = 19
Step-by-step explanation:
3(x - 9) = 30
Divide both sides by 3 to isolate the binomial.
x - 9 = 10
Add 9 to both sides to isolate x.
x = 19
Check your answer by plugging x = 19 back into the equation.
3(x - 9) = 30
3(19 - 9) = 30
Subtract.
3(10) = 30
Multiply.
30 = 30
Your answer is correct.
Hope this helps!
Answer:
x = 19
Step-by-step explanation:
First, we must distribute 3(x-9) = 30
\(3x - 27 = 30\)
Now, that we've distributed this equation, we can proceed.
Secondly, since there is a subtraction sign in front of 27, we must do the opposite, addition.
Add 27 to 27 and 30:
\(3x - 27 = 30\)
\(-27 + 27 = 0\)
\(30 + 27 = 57\)
Furthermore, -27 + 27 is 0, so it cancels itself out. Also, since we added 30 and 27 and got 57, replace 30 with 57.
\(3x = 57\)
Lastly, divide 57 by the number in front of coefficient, 3.
\(57/3=19\)
Therefore, \(x=19.\)
**TO MAKE THIS MORE UNDERSTANDING, THIS IS HOW YOUR EQUATION SHOULD LOOK WHILE SOLVING**
Solve the following:
NO BOTS OR PEOPLE WANTING POINTS!
Answers
What are the domain and range of the function f(x)= Squrt x-7+9
Answers
Answer:
domain: x ≥ 7range: f(x) ≥ 9Step-by-step explanation:
The domain is the set of values of x for which the function is defined. Those are the values of x that make the square root argument non-negative:
x -7 ≥ 0
x ≥ 7
__
Since the square root cannot be negative, the sum of it and 9 cannot be less than 9. The range is ...
f(x) ≥ 9
Answer:
domain: x ≥ 7
range: f(x) ≥ 9
HELP PLEASEEE
A party rental company has chairs and tables to rent. There were two customers who rented both chairs and tables last week. The table below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.
Answers
By setting up the equation, we get the system of linear equations are
9x + 7y = 77
3x + 5y = 49
solving these equation Cost to rent a chair = $1.75
cost to rent a table = $8.75
What is system of linear equation?A system of linear equations is a collection of one or more linear equations involving the same variables.
What are the method to solve system of linear equations?There are several methods for solving systems of linear equations, including:
Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.
Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.
Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.
etc.
To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.
First, solve the first equation for y:
9x + 7y = 77
7y = -9x + 77
y = (-9/7)x + 11
Now substitute this expression for y into the second equation:
3x + 5((-9/7)x + 5(11) = 49
3x - (45/7)x + 55 = 49
solving for x :
x = 1.75
Now substitute this value for x back into the first equation to find y:
y = 8.75
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Makesha lost 58.5 pounds in 18 weeks. Find her rate of loss in pounds per week.
Answers
What is four fifths divided by two thirds?
Answers
Answer:6/5 or 1.2
Step-by-step explanation:
4/5 divided by 2/3
=4/5 *3/2
=12/10
=6/5
=1.2
1. Jon waits on tables and is paid $6.75an hour. In a 40-hour period, he earned $310.50 in tips. What were his total earnings?
Answers
Answer:
$617.25
Step-by-step explanation:
$617.25 Because, $310.50(tips) + $306.75(hourly wage)=$617.25
Answer:$580.50
Step-by-step explanation:
:)
PLEASE TELL ME WHAT TO WRITE HEREee :’)
Answers
The inequality is 12b > 180 and the number of books, b, she must sell in order to meet her goal must be more than 15 (b > 15)
How to write and solve an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given that:
Erin sells books for $12 each.
She wants to make more than $180 in book sales.
The number of books, b
Erin sells books for $12 each: 12 × b = 12b
More than $180 in book sales: > $180 (i.e greater than $180)
Thus, the inequality is:
12b > 180
Solve for b:
12b > 180
Divide both sides by 12
b > 180/12
b > 15
Therefore, the inequality is 12b > 180 and the number of books, b, she must sell in order to meet her goal is b > 15 (greater than 15)
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TRUE OR FALSE to calculate the average of the numeric values in a list, the first step is to get the total of values in the list.
Answers
The given statement 'to calculate the average of the numeric values in a list the first step is to get the sum of all the given values ' is a true.
Average of the numeric values in a list,
First step is to get the sum of values in the list.
It is not the total number of values.
Once we have the sum, we can divide it by the number of values to get the average.
Here is an example,
Suppose we have a list of numeric values are as follow,
[2, 4, 6, 8, 10].
To calculate the average of these values, we first find their sum,
2 + 4 + 6 + 8 + 10 = 30
Next,
divide the sum by the number of values in the list
Number of values = 5
30 / 5 = 6
This implies,
The average of the values in the list is 6.
Therefore, to get the average first step is to get the total of all values is true statement.
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Change 48.2% to it’s fractional equivalent. Please show work
Answers
As asked in the question, 48.2% is equivalent to the fraction 241/500.
To convert a percentage to a fractional equivalent, we divide the percentage by 100 and simplify the resulting fraction.
So, to convert 48.2% to a fraction, we divide 48.2 by 100:
48.2/100 = 0.482
This gives us the decimal equivalent of 48.2%.
To convert the decimal to a fraction, we write it over 1 and simplify it:
0.482/1 = 482/1000
We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
482/1000 = (241/500)
Therefore, 48.2% is equivalent to the fraction 241/500.
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Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
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Anyone I need this please
Answers
Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
Answers
The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.
40/(-10) 40/10 40/40 40/(-40)Please refer to the attached picture.
We have a rectangular shape as shown in the picture.
Total number of square units = 40
Each row has 10 units cube.
Each cube = 40/10
Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
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