The measure of ∠JKM is 145°.
What is exterior angle theorem?The measure of an exterior angle of a triangle is bigger than either of the measures of the distant interior angles, according to the external angle theorem, Proposition 1.16 in Euclid's Elements.
Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry. Three of a triangle's corners are its vertices.
Two angles are produced by a triangle's sides (line segments) meeting at its apex (four angles if you consider the sides of the triangle to be lines instead of line segments). An interior angle of the triangle is the only one of these angles that has the third side of the triangle inside of it.
Here it is given that, ∠JLK= 70°
∠LJK = x°
(2x-5)°= 70°+x°
now applying exterior angle theorem,
x=75°
substitute 75 for x in 2x-5 to find m∠JKM.
=2x-5
=2×75-5
=145°
Hence, The measure of ∠JKM is 145°
To learn more about angle theorem refer to:
https://brainly.com/question/27962469
#SPJ1
please help!!! 5x – 2(2x – 1) = 6 show your work!!!
Answer:
Can I get brainliest please?
Step-by-step explanation:
Ok so, Let's solve your equation step-by-step.
5x−2(2x−1)=6
Step 1: Simplify both sides of the equation.
5x−2(2x−1)=6
5x+(−2)(2x)+(−2)(−1)=6(Distribute)
5x+−4x+2=6
(5x+−4x)+(2)=6(Combine Like Terms)
x+2=6
x+2=6
Step 2: Subtract 2 from both sides.
x+2−2=6−2
x=4
So, your answer would be:
x=4
Answer:
x=4
Step-by-step explanation:
5x-2(2x-1)=6
multiply 2 to the parathesis
5x-4x+2=6
collect like terms
x+2=6
subtract both sides by 2
x=4
What is 57.000 divided by 67,398?
57.000/67,398 = 0.00084572242
hope this helps!!
What is online calculator of variable cost ?
Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.
A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:
Raw materialsPackagingLabourTransportation fee, commissionUtility billsVariable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.
The following calculation is the break-even point:
Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)
Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.
Learn more about Variable cost:
https://brainly.com/question/13896920
#SPJ4
Find the point on the line 3x + y = 8 that is closest to the point (-3,2)
Answer: To find the point on the line 3x + y = 8 that is closest to the point (-3,2), we need to minimize the distance between the line and the point.
Let (x, y) be the point on the line that is closest to (-3, 2). Then the vector from the point (-3, 2) to (x, y) is orthogonal (perpendicular) to the line. The direction vector of the line is <3, 1>, so the direction vector of the orthogonal vector is <-1/3, 1>.
Now we can write an equation for the line passing through (-3, 2) with the direction vector <-1/3, 1>:
(x - (-3))/(-1/3) = (y - 2)/1
Simplifying, we get:
3x + y = 11
This is the line passing through (-3, 2) that is orthogonal to the original line 3x + y = 8.
To find the intersection of these two lines, we can solve the system of equations:
3x + y = 8
3x + y = 11
Subtracting the first equation from the second, we get:
0 = 3
This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.
However, we can still find the closest point to (-3, 2) on the line 3x + y = 8. This point will be the intersection of the line passing through (-3, 2) with the direction vector <-1/3, 1> and the line 3x + y = 8.
The equation of the line passing through (-3, 2) with the direction vector <-1/3, 1> is:
(x - (-3))/(-1/3) = (y - 2)/1
Simplifying, we get:
3x + y = 11
To find the intersection point with the line 3x + y = 8, we can solve the system of equations:
3x + y = 8
3x + y = 11
Subtracting the first equation from the second, we get:
0 = 3
This is a contradiction, which means the two lines do not intersect. Therefore, the point on the line 3x + y = 8 that is closest to (-3, 2) does not exist.
Step-by-step explanation:
What is a possible solution to x ≥ −2?
Answer:
5
Step-by-step explanation:
What is the equation of the line that passes through the point (-5,4)(−5,4) and has a slope of 3/5?
Answer: y = 3/5x + 7
Explanation:What we know:
The final equation will be in the form y=mx+bThe slope (m) is 3/5The slope must go through the point (-5,4)How to solve:
By substituting the point the slope passes through into slope-intercept form, we can calculate the y-intercept (b.) From here, we can use our slope and y-intercept values to set up the final equation.
Process:
Finding the y-intercept
Set up equation y = mx + b
Substitute 4 = 3/5(-5) + b
Simplify 4 = -3 + b
Simplify +3 +3
Solve 7 = b
Creating final equation
Set up equation y = mx + b
Substitute y = (3/5)x + 7
Answer: y = 3/5x + 7Check:
If you graph this equation (a good tool to use is desmos graphing calculator,) then this equation creates a line that has a slope of 3/5 and passes through the point (-5,4)
Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 13π 15 cos − π 5 − sin 13π 15 sin − π 5 Find its exact value.
As per the addition formula, the value of the trigonometric function is -0.809.
In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.
Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5) by using the addition and subtraction formula.
Here we have the following trigonometric function:
=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)
Now, we have to use the trigonometric addition formula,
=> Cos (A+B) = Cos A Cos B - Sin A Sin B
To solve the given function,
Here let us rewrite the given function based on the addition formula, then we get,
=> Cos ( 13π/15 + (-π/5) )
=> Cos( 12π/5)
=> Cos(144°)
=> -0.809
To know more about function here.
https://brainly.com/question/10354322
#SPJ4
Caleb wants to make sure that there is not too much pressure on his watering hose for his garden. The nozzle pressure
(in pounds per square inch) of a hose with diameter
(in inches) and water-flow rate
(in gallons per minute) is given by the equation
.
Find the nozzle pressure in Caleb's hose which has a water-flow rate of
gallons per minute and a diameter of
inches. (Hint: Round to the nearest hundredth)
The nozzle pressure in Caleb's hose which has a water-flow rate of
275 gallons per minute and a diameter of 2.5 inches is: 2.15 pounds per square inch
How to simplify equations through subject of formula?Simplifying expressions means rewriting the identical algebraic expression with no like terms and in a compact manner. To simplify expressions, we combine all the like terms and solve all the given brackets, if any, then in the simplified expression, we will be only left with unlike terms that cannot be reduced further.
The given rate of flow of water 'r'=275 gallons per minute
The diameter of the nozzle 'd'=2.5 inches
The given equation is: r = 30d²√P
Rearranging the equation to find the nozzle pressure 'P':
√P = r/30d²
P = (r/30d²)²
Plugging in 275 for r gives:
P = (275/30(2.5)²)²
P = 2.15 pounds per square inch
Read more about subject of formula at: https://brainly.com/question/657646
#SPJ1
If f(x) = x/3 and g(x)=1/x find f(x)-g(x)
A.
x-1/3-x
C. 1/3
B. x²-3/3x
D. 3-x²/3x
Please select the best answer from the choices provided
Answer:
x^2-3/3x
Step-by-step explanation:
x/3-1/x=x*x-1*3/3*x
=x^2-3/3x
which ordered pairs in the form (x, y) are solutions to the equation 4x−5y=24
Answer:
\(\(\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{1000000pt}}\)
which of the following is described below: there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
The description you provided corresponds to an independent variable in an experiment.
How are independent variables used in an experiment?In scientific experiments, researchers manipulate certain factors or conditions to observe their effect on the outcome, which is known as the dependent variable.
The independent variable is the specific factor that is deliberately changed or controlled by the experimenter. It is called "independent" because its value is not influenced by other variables in the experiment.
Thus, the description you provided corresponds to an independent variable in an experiment.
Read more about independent variable here:
https://brainly.com/question/82796
#SPJ4
The Complete Question
which of the following is described below:
independent variable
dependent variable
controlled experiment
uncontrolled experiment
there is only one of these in an experiment. they are the cause of some change in the experiment. they are the only thing different between two trials or groups in an experiment.
Suppose the following sequence of matrix operations was used to translate AABC.
The horizontal and vertical translations applied to ΔABC:
A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
What is matrix ?It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.
Given that,
\(\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right]\) = ?
After using matrix operation it can be further solved as,
\(\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right]\)
Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.
To know more about matrix check:
https://brainly.com/question/29132693
#SPJ1
(Will give brainliest)
A candy company claims that their bags of jellybeans have a mean weight of 9.45 oz. 125 randomly chosen bags of jellybeans were sampled, and it was discovered that their mean weight was 9.68 oz, with a standard deviation of 1.23 oz. Test this hypothesis using a 99% confidence level.
A- Reject the null hypothesis. There is not enough evidence to oppose the company's claim.
B- Reject the null hypothesis. There is enough evidence to oppose the company's claim.
C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
D- Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.
Answer: C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
Note: I'm not sure this is correct o_O
I used a graphing calculator and calculated the t-interval of the jellybean sample using a 99% confidence level:
tInterval 9.68,1.23,125,0.99
It resulted in 9.68 ± 0.287805.
Therefore, we're 99% confident that the weight number of jellybeans would lie between 9.3922 oz and 9.9678 oz.
A weight of 9.45 oz lies within this range, therefore, it is possible that the candy company's claim is true.
Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Mean weight was 9.68 oz
standard deviation of 1.23 oz
n=125
µₙ=9.68
σₙ=1.23/√125
=0.11
Confidence level 99%
z=2.58
-z<x-µₙ/σₙ<z
9.68-2.58(0.11)<x<9.68+2.58(0.11)
9.3962<x<9.9638
9.45 is between this range
Fail to reject the null hypothesis. There is not enough evidence to oppose the companys claim.
Hence, Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.
To learn more on Statistics click:
https://brainly.com/question/29093686
#SPJ2
What did the Romans do to help protect most cities from attack?
They built them on hills.
They surrounded them with canals.
They bordered them with farmland.
They constructed walls around them.
Answer:
A
Step-by-step explanation:
Answer:A They built them on hills.
Step-by-step explanation:
They built them on hills bc they elwanted to keep them safe and B C and D would not provide the proper protection.
Test the series for convergence or divergence.
∑n=1[infinity] n!/ 5⋅11⋅17⋯(6n−1).∑n=1[infinity]n!5⋅11⋅17⋯(6n−1).
Which test is the best test to use for this series?
Select Divergence Test Geometric Test p-Series Test Integral Test Comparison Test Alternating Series Test Ratio Test Root Test .
Let's try Ratio Test:
Compute limn→[infinity]∣∣∣an+1an∣∣∣=limn→[infinity]|an+1an|= . (Note: Use INF for an infinite limit, DNE if the limit does not exist.)
Since the limit is Select > greater than or equal to = less than or equal to < not equal to , the Ratio Test tells us Select that the series converges absolutely that the series converges conditionally that the series diverges nothing .
Answer: The test tells us that the series diverges.
The series ∑n=1[infinity] n!/5⋅11⋅17⋯(6n−1) diverges according to the Ratio Test.
Let's try the Ratio Test:
To test the series for convergence or divergence, the best test to use for this series is the Ratio Test.
Compute lim(n→infinity)|a(n+1)/a(n)| = lim(n→infinity)|((n+1)!5⋅11⋅17⋯(6(n+1)−1))/(n!5⋅11⋅17⋯(6n−1))|.
By simplifying, we get lim(n→infinity)|((n+1)(6n+5))/(6n+5)| = lim(n→infinity)|(n+1)| = infinity (INF).
Since the limit is greater than 1 (INF > 1), the Ratio Test tells us that the series diverges.
https://brainly.com/question/31959374
#SPJ11
please help second question
Answer:
I have not J.H.S 3 , because the questions look like some J.H.S 3 ,so please I am very sorry that I can't help u in this questions . Thanks
the bloch sphere geometric representation of a quantum state is parameterized by two angles and such that . what are the values of the angles and for the state
The range of values for θ and φ is such that they must not repeat in order to cover the entire sphere θ∈[0,π) and φ∈[0,2π).
The Bloch sphere representation, which bears Felix Bloch's name, is the outcome of the foregoing. This illustration is a unit 2-sphere with two mutually placed spheres at the north and south poles. In contrast, quantum bits cover the entire sphere, whereas these are the only conceivable states for the classical bit representation.
(Disclaimer: One could counter that since the classical bit is represented by voltages, the classical bit representation also contains the axis linking the two poles. As a result, the Bloch sphere illustrates that there is substantially more information involved in quantum bits. When the qubit is measured, one of the two poles is what remains. Exactly which pole is determined by the direction the arrow in the Bloch representation points.
To learn more about bloch sphere: https://brainly.com/question/24214824
#SPJ4
Is (2, 8) a solution to the equation y = 6x?
Is (2, 8) a solution to the equation y = 6x?
Answer:
No.
Step-by-step explanation:
Substitute 2 for x and 8 for y in y=6x
8 = 6(2) -> 8 = 12
This is false, so (2,8) is not a solution for y=6x
Evaluate f(-3), show all work:
F(x) = 2/3x + 8
Answer:
f(-3) = 6
Step-by-step explanation:
\(f(-3)=\frac{2}{3} (-3)+8=\frac{2(-3)}{3} +8=-\frac{6}{3}+8= -2+8=6\)
Hope this helps.
Answer:
f(x) = 6
Step-by-step explanation:
f(-3) means replace the x in f(x) with a -3, and replace every x in the equation with -3.
f(-3) = (2/3)x + 8
= (2/3) (-3) + 8
= (2 X -3)/3 + 8
= -6/3 + 8
= - 2 + 8
= 6
In a certain arithmetic sequence, consecutive terms have a positive common difference. The first 4 terms of the sequence have a sum of 80. Which of the following values CANNOT be thefirst term of the arithmetic sequence?
a - 10
b - 12
c - 16
d - 18
e - 20
Answer:
E:20
Step-by-step explanation:
I had the same question and it correct answer was E.
The first term of the arithmetic sequence will be 20. Then the correct option is E.
What is an arithmetic sequence?Arithmetic succession or arithmetic sequential is a numerical series in which the difference between subsequent terms is uniform.
In a specific number juggling grouping, successive terms have a positive normal distinction. The initial 4 terms of the grouping have an amount of 80.
Let the four terms be a - 3d, a - d, a + d, and a + 3d. Then the sum of the four-term is given as,
a - 3d + a - d + a + d + a + 3d = 80
Simplify the equation, then we have
a - 3d + a - d + a + d + a + 3d = 80
4a = 80
a = 80 / 4
a = 20
The first term of the arithmetic sequence will be 20. Then the correct option is E.
More about the arithmetic sequence link is given below.
https://brainly.com/question/15412619
#SPJ2
Find the value of x. Then find the angle measures of the polygons
Answer:
x = 43
Step-by-step explanation:
The sum of angles in a triangle is equal to 180.
x + 2x + x + 8 = 180 add like terms
4x + 8 = 180 subtract 8 from both sides
4x = 172 divide both sides by 4
x = 43
To find the measure of each angle, replace x with 43
Grapes cost $1.87 per pound. How much would it cost for 4.25 pounds of grapes?
Answer:
7.95$
Step-by-step explanation:
1.87 $ per 1 lb
1.87 * 4.25 = 7.95$
Answer:
$7.95 for 4.25 lbs. of grapes
Step-by-step explanation:
so your going to multiply $1.87 by 4.25 to get the total amount of money needing to be paid in or der to buy the 4.25 lbs. of grapes:
$1.87 * 4.25 = 7.9475
now turning it into money by rounding to the hundredths place:
7.9475 = $7.95
So you would have to pay $7.95 for 4.25 lbs. of grapes but logically you would bring 8 dollars to buy it, but down to the cents it would be $7.95.
solve and show working:- log(x^2 + 7) base 4 = 2
The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
It is known that \(log_{a}b\) = c can be written as \(a^{c}\) = b.
Given that, log(x^2 + 7) base 4 = 2
Therefore, x² + 7 = 4²
x² + 7 = 16
x² = 16 - 7 = 9
x² = 9
x = ±3
Hence "The value of x for the given logarithm equation log(x^2 + 7) base 4 = 2 is x = ± 3".
For more about logarithms
https://brainly.com/question/20785664
#SPJ1
I have no clue how to do this
Answer:
$4
Step-by-step explanation:
We are told that Roxanne:
Has a checking account onlyUses online bankingUses the bank ATM once a monthUses a nonbank ATM twice a monthWe need to work out how much it costs for Roxanne to bank with each bank each month, then compare the total costs to see how much Roxanee could save if she switch from East Median to Jasmine bank.
Cost of monthly banking at East Medina Bank:
Checking account services = $6
Online banking = $5 (remember, she doesn't have a linked savings a/c)
ATM (1 use) = $1
nonbank ATM (2 uses) = $6
Total = $18
Cost of monthly banking at Jasmine Bank:
Checking account services = $10
Online banking = $4
ATM (1 use) = $0
nonbank ATM (2 uses) = $0
Total = $14
To calculate the money Roxanne could save by switching to Jasmine Bank, simply find the difference between the monthly costs:
Savings = $18 - $14 = $4
PLEASE SOLVE USING DETERMINANT
One large jar and two small jars together can hold 8 ounces of jam. One large jar minus one small jar can hold 2 ounces of jam.
A matrix with 2 rows and 2 columns, where row 1 is 1 and 2 and row 2 is 1 and negative 1, is multiplied by matrix with 2 rows and 1 column, where row 1 is l and row 2 is s, equals a matrix with 2 rows and 1 column, where row 1 is 8 and row 2 is 2.
Use matrices to solve the equation and determine how many ounces of jam are in each type of jar. Show or explain all necessary steps.
PLEASE SOLVE USING DETERMINANT
The number of ounces of jam that all of the jar can hold is about 4 large jars and 2 small jars.
What is Matrix equation ?A matrix represents a mathematical entity or characteristic through a table or array of expressions, numbers, or symbols arranged in rows and columns.
So, from the given matrix in the question, one has to compare the equations, So we have:
l + 2s = 8 ...........(i)
l - s = 2 .............(ii)
Then do subtract the second equation from the first, to remove l
3s = 6
s = 2
So also substitute 2 for s in l - s = 2
l - 2 = 2
Then sum up the 2 to both sides
l = 4
Therefore, the number of ounces of jam that each jar can hold is about 4 large jars and 2 small jars.
Learn more about matrix from:
https://brainly.com/question/27922899
#SPJ1
URGENT: find the volume of the shapes
Answer:
First one should be 309 second one should be 624 I may be wrong though since I haven't done volume in years
Step-by-step explanation:
:)
Answer:
A is 381 for the whole thing
B is 792 i think i am not one hundred percent sure on this one but it should be right
Step-by-step explanation:
(d) what proportion of strength observations in this sample exceed 10 mpa? (round your answer to two decimal places.)
By applying the probability concept, it can be concluded that the proportion of strength observations in this sample exceeding 10 MPa is 0.15.
Probability is a value used to measure the degree of occurrence of a random event.
P(A) = f / N where:
f = frequency of event A
N = number of possible outcomes / sample space
There are 27 strength data for beams (in MPa), which are our sample space:
5.7 7.2 7.3 6.2 8.1 6.8 7.0 7.6 6.8
6.5 7.0 6.3 7.9 9.0 8.2 8.7 7.8 9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.5 11.8 10.6
We want to determine the proportion of strength observations in this sample exceeds 10 MPa.
Since there are only 4 samples that exceed 10 MPa, thus the proportion of these 4 samples can be calculated as follows:
P (x>10) = f / N
= 3 / 27
= 0.148
≈ 0.15
Thus the proportion of strength observations in this sample exceeding 10 MPa is 0.15.
To learn more about probability, click here: brainly.com/question/13604758
#SPJ4
suppose we have dollars and each day we buy either milk (2$), juice (2$), coffee ($3) or cookies ($1) let be the number of ways of spending all the money. the recurrence relation for is:
The recurrence relation N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1) represents the number of ways to spend all the money when we have a certain amount of dollars and four options for spending it: milk, juice, coffee, and cookies.
Let's denote the number of ways of spending all the money as N(n), where n represents the amount of money we have. Our goal is to find the recurrence relation for N(n).
To start, let's consider the base cases. When n = 0, it means we have no money left. In this case, there is only one way to spend the money, and that is by not buying anything. Therefore, N(0) = 1.
Now, let's consider the cases when n > 0. We have four options for spending the money: milk, juice, coffee, and cookies. Let's analyze each option separately.
If we decide to buy milk, it costs $2. After buying milk, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).
Therefore, the number of ways of spending all the money when buying milk is equal to N(n - 2).
If we decide to buy juice, it also costs $2. After buying juice, we are left with n - 2 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 2).
Therefore, the number of ways of spending all the money when buying juice is equal to N(n - 2).
If we decide to buy coffee, it costs $3. After buying coffee, we are left with n - 3 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 3). Therefore, the number of ways of spending all the money when buying coffee is equal to N(n - 3).
If we decide to buy cookies, it costs $1. After buying cookies, we are left with n - 1 dollars. We need to find the number of ways to spend the remaining money, which is N(n - 1). Therefore, the number of ways of spending all the money when buying cookies is equal to N(n - 1).
Now, let's consider the total number of ways to spend all the money when considering all the options. Since each option is independent, we can add up the number of ways for each option. Therefore, the recurrence relation for N(n) can be expressed as:
N(n) = N(n - 2) + N(n - 2) + N(n - 3) + N(n - 1)
This recurrence relation allows us to compute the number of ways of spending all the money for any given amount of money. By using dynamic programming techniques, we can start with the base case N(0) = 1 and compute the values of N(n) iteratively until we reach the desired amount of money.
To know more about recurrence relation here
https://brainly.com/question/30895268
#SPJ4
can you help me please?
Step-by-step explanation:
option d is correct
as,
corresponding angles are = 1 & 5 , 2 & 6 , 3 & 7 and 4 & 8
alternate interior angle are 3 & 6 and 4 & 5
alternate Exterior angles are 2 & 7 and 1 & 8
hope this answer helps you dear...may u have a great day ahead..take care!
Find an equation of the line that satisfies the given conditions.
Through (-1, -2) and (4, 3)
The final equation is y =x-1.
To find the line that satisfies the given, we will use the two-point form
\(y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )\)
Before we use this, however, we need to assign to the points given the variables they represent:
(-1, -2) and (4, 3)
\(x_{1} = -1\)
\(x_{2} = 4\)
\(y_{1} = -2\)
\(y_{2} = 3\)
Now, we will substitute these values
\(y - y_{1} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } (x - x_{1} )\)
⇒ \(y - (-2) = \frac{3 - (-2) }{4-(-1) } (x -(-1) )\)
⇒ \(y +2 = \frac{3 +2 }{4 +1 } (x +1 )\)
⇒ \(y +2 = \frac{5 }{5 } (x +1 )\)
⇒ \(y +2 = x +1\)
⇒ \(y = x -1\)
Thus, the final equation is y =x-1.
Read more about equations:
https://brainly.com/question/22688504
#SPJ4