A function is a set of ordered pairs (x,y) where for each x value there is only one corresponding y value, and the relation between x and y is such that for any x value there is a unique y value.
One way to determine if a set of ordered pairs is a function is to use the vertical line test. This test involves drawing a vertical line on the coordinate plane and seeing if it intersects the graph of the ordered pairs at more than one point. If a vertical line intersects the graph of the ordered pairs at more than one point, then the set of ordered pairs is not a function. If a vertical line intersects the graph of the ordered pairs at only one point, then the set of ordered pairs is a function.
Another way to determine if a set of ordered pairs is a function is to use the rule of correspondence. If every first element of the ordered pair corresponds to one and only one second element, then the set of ordered pairs is a function, otherwise is not.
Additionally, you can also use algebraic methods like the definition of a function, where a function is a relation from a set A to a set B, such that for each element in A there is exactly one element in B.
For example, the set of ordered pairs {(1,2), (2,4), (3,6)} is a function because for each x-value (1,2,3) there is only one corresponding y-value (2,4,6) and this is unique.
In contrast, the set of ordered pairs {(1,2), (2,4), (3,6), (1,3)} is not a function because for x = 1 there are two different y values, 2 and 3.
It's important to remember that it's not enough to just check a few ordered pairs, you need to check all of them.
A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches.
The best estimate for the perimeter of the triangle will be 23.7 inches.
In Δ ABC ∠B =90° , ∠C = 30° , ∠A = 60° and hypotenuse AC = 10 inches
It has been described in the attachment.
Now, we shall calculate side AB and BC by using Trigonometric Ratios.
Sin 30° = AB / AC
or, AB = 10 × Sin 30° = 10 × 0.5 = 5 inches
And, Cos 30° = CB / AC
or,CB = 10 × Cos 30° = 10 × 0.866 = 8.66 inches
Now, we calculate the perimeter of the given triangle
The perimeter of the triangle is = AB + BC + CA
= (5.0 + 8.66 + 10.0 ) inches
= 23.66 inches ≈ 23.7 inches
Hence, the best estimate for the perimeter of the triangle will be 23.7 inches.
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The complete question is:
A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.
A system of equations is given.
Equation 1: 4x − 6y = 10
Equation 2: 9x + 2y = 7
Explain how to eliminate x in the system of equations.
Step-by-step explanation:
multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.
in our case the least common multiple of 4 and 9 is 36.
so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract
36x - 54y = 90
- 36x + 8y = 28
-------------------------
0 -62y = 62
so, x is "eliminated", and we can solve for y : y = -1.
and then we can use one of the original equations to solve for x.
e.g.
9x + 2×-1 = 7
9x - 2 = 7
9x = 9
x = 1
Answer:
First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, we have to multiply Equation 1 by 9 and Equation 2 by -4.
9(4x - 6y = 10) is equivilant to 36x - 54y = 90
-4(9x + 2y = 7) is equivilant to -36x - 8y = -28
Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:
-62y = 62 we have successfully eliminated x!
The last step will be to divide both sides by -62
-62y/-62 = 62/-62
y = -1
A lot measures 63.41 feet. What is the measurement in feet’s inches and fractions of an inch? Answe to the nearest 1/16
The measurement 63.42 feet after conversion is 760.92 inches.
What is conversion of measurement?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. If a conversion is required, the right conversion factor to an equivalent value must be applied. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
Here the given measurement is ,
=> 63.41 feet
To convert feet into inches we need to multiply by 12. Then
=> 63.41 × 12 = 760.92 inches.
Hence the given measurement into inches 760.92 inches.
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In DABC AB=17cm, AD=15cm, BC=13cm and BD is perpendicular to AC. Calculate the length of BD
The length of BD is approximately 22.67cm.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental result in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). It is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that it is knowledge that was already known to the ancient Babylonians and Indians.
The theorem can be written mathematically as:
c^2 = a^2 + b^2
This is a classic problem in trigonometry known as the Pythagorean theorem in a right triangle. Since BD is perpendicular to AC, we can use the Pythagorean theorem to find the length of BD, which states that in a right triangle, the square of the length of the hypotenuse (BD in this case) is equal to the sum of the squares of the other two sides (AB and AD).
So, BD^2 = AB^2 + AD^2
We are given that AB = 17cm and AD = 15cm, so we can substitute those values into the equation and solve for BD:
BD^2 = (17cm)^2 + (15cm)^2 = 289 + 225 = 514
To find the length of BD, we take the square root of both sides:
BD = √514cm
BD ≈ 22.67cm
Hence, the length of BD is approximately 22.67cm.
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Use transformations to solve the inequality. Write down all the steps
Answer:
u ≤ 15
Step-by-step explanation:
=> u/3 ≤ 5
Multiplying both sides by 3
=> 3×u/3 ≤ 5 ×3
=> u ≤ 15
7. Find FH
F
37-
H 13
G
FH = _
Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.
Describe the triangle.Given its three sides and three vertices, a triangles is a polygon. A fundamental geometric shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric shapes. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.
Here,
The given number indicates that FG is 8 & GH is 14.
FG + GH = FH thanks to the segment addition postulate.
In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.
This results in FH = 8 + 14 => FH = 22.
Therefore, is 22 miles away.
Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.
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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"
Adam earn 13.72 each hour that he works.He works 9 hours each week.How much does Adam earn each week.
Answer:
He makes $123.48 a week
Please explain how to work out angle BAC
The angle measure BAC is the sum of angles BAD and CAD.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Given a triangle ABC.
A line is drawn inside the triangle from vertex A to the opposite side BC.
Given that AD = BD = CD.
That is the line AD bisects the line BC.
So here we have two smaller triangles ABD and ACD.
Two corresponding sides of both the triangles are equal.
Then the third side is also equal.
AB = AC
And we get angle A is bisected.
By the angle bisector theorem,
Measure of angle BAC = Measure of angle BAD + Measure of angle CAD
Hence, Measure of angle BAC = Measure of angle BAD + Measure of angle CAD
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The graph shows a linear function. Which equation is best represented by this graph?
Answer:
C
Step-by-step explanation:
The graph passes through [tex](-2,-5)[/tex] but not [tex](2,5)[/tex].
Eliminate B and D.The line is steep, and has a slope of more than 1.
Eliminate A.Aiden run at a contant peed of 3. 5 meter per econd for 1/2 hour. Then, he walk at a rate of 1. 6 meter per econd for 1/2 hour. How far did Aiden run and walk in 60 minute?
Aiden run and walk in 60 minute, then the distance = 9180 meters
Given that,
Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.
Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.
(1) 3. 5 meter per second for 1/2 hour.
We can,
1 hour = 3600 seconds
Then,
[tex]\frac{1}{2}[/tex] hour = 1800 seconds
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
So,
We can write,
Distance = speed * time
3.5 * 1800 = 6300 meters (Equation-1)
(2) 1. 6 meter per second for 1/2 hour.
We can,
1 hour = 3600 seconds
Then,
[tex]\frac{1}{2}[/tex] hour = 1800 seconds
So,
We can write,
Distance = speed * time
1.6 * 1800 = 2880 meters (Equation-2)
Then,
We can add the equation - 1 and 2,
= 6300 meters + 2880 meters
= 9180 meters
Therefore,
Aiden run and walk in 60 minute, then the distance = 9180 meters
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1.5x+3=-39
Solve for x
Show work
Answer: x=-28
Step-by-step explanation:
Answer: -28
Step-by-step explanation:
1.5x+3=-39
-3 -3
1.5x=-42
__ __
1.5 1.5
x = -28
lines mean divide
Boden's account has a principal of $400 and a simple interest rate of 4.4%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Assuming Boden does not add or take out any money, he would have $470.4 in the account after 4 years.
How to calculate simple interest?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P represents the principal or starting amount.R represents the interest rate.A represents the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 400 × 4.4/100 × 4
S.I = 400 × 0.044 × 4
S.I = $70.4.
Next, we would calculate the future value as follows;
S.I = A - P
Future value, A = S.I + P
Future value, A = $70.4 + $400
Future value, A = $470.4.
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The table gives the annual global plastic production over time, in years, since 1960.
Fit an exponential model to this data.
The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____
correlation between the model and the data, this prediction (4) _____.
Answer options:
1-
increased by 4.9 metric tons
decreased by 4.9 metric tons
increased by 4.9%
decreased by 4.9%
2-
40
60
70
3-
moderate
strong
weak
4-
is unreliable
can be accepted with confidence
The exponential model indicates that plastic production has increased by 4.9% per year.
Fit an exponential model to this data
The exponential model indicates that plastic production has increased by 4.9% per year.The model predicts that plastic production 15 years after 1960 was closest to 70 million metric tons.Because the correlation coefficient indicates strong correlation between the model and the data,this prediction can be accepted with confidence.The exponential model is a powerful tool for predicting future trends in plastic production, and it indicates that plastic production has been increasing at an annual rate of 4.9%.This is an important insight, as it can help us to anticipate the future of the industry.With this information, we can estimate that plastic production 15 years after 1960 was likely to be around 70 million metric tons.The strength of this prediction is supported by the correlation coefficient, which suggests a strong correlation between the model and the data.This suggests that the model is a good predictor of future plastic production, and that the prediction of 70 million metric tons is reliable.To learn more about the annual global plastic production over time refer to:
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the time required to complete a job varies inversely as the number o people working. it took 4 hours for 7 electricians to wire a building. how long would it have taken 3 electricians to have done the job
The time taken by 3 electricians to complete the work is 9 1/3 hours.
Inverse proportionality:When one quantity's value rises relative to another's decrease or vice versa, it is said that the two are inversely proportionate.
It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between time and speed is inverse.
If x and y are inversely proportionate to each other
=> x ∝ 1/y
=> xy = k [ where 'k' is proportionality constant ]
Here we have
The time required to complete a job varies inversely to the number of people working. It took 4 hours for 7 electricians to wire a building.
Let x be the time and y be the number of people
Given that the time required to complete a job varies inversely to the number of people working.
=> xy = k ---- (1) [ Since they are inversely proportional to each other ]
Given that it took 4 hours for 7 electricians to wire a building.
=> 4(7) = k
=> k = 28
Substitute k = 28 given number of electricians y = 3 in equation (1)
=> x (3) = 28
=> x = 28/3 = 9 1/3hrs
Therefore,
The time taken by 3 electricians to complete the work is 9 1/3 hours.
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(4x - 8) - (3x + 10)
[tex](4x - 8) - (3x + 10)[/tex]
Distribute negative sign:
[tex]4x-8+-1(3x)+(-1)(10)[/tex]
[tex]4x-8-3x-10[/tex]
Combine Like Terms:
[tex](4x-3x)+(-8-10)[/tex]
[tex]=\fbox{x - 18}[/tex]
Answer:
[tex]x - 18[/tex]
[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]
Linear equation with colors lines black orange green and blue
The graph of Linear equation with colors lines black, orange, green and blue is shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that;
Linear equation with colors lines black orange green and blue.
Now, We know that;
The graph of linear equation is always a straight line.
Hence, The graph of Linear equation with colors lines black orange green and blue is shown in figure with straight line.
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Solve the equation below for x.
Answer:
x=-9ln(1/2)/[ln(4)-ln(1/2)]
Step-by-step explanation:
4^{x}=(1/2)^{x-9}
ln(4^{x})=ln((1/2)^{x-9})
xln(4)=(x-9)ln(1/2)
xln(4)=xln(1/2)-9ln(1/2)
xln(4)-xln(1/2)=-9ln(1/2)
x[ln(4)-ln(1/2)]=-9ln(1/2)
x=-9ln(1/2)/[ln(4)-ln(1/2)]
In two or more complete sentences, compare the number of -intercepts in the graph of f(x) =x^2 to the number of x-
intercepts in the graph of g(x) = x^2 +2. Be sure to include the transformations that occurred between the parent function
f(x) and its image g(x).
The number of y-intercepts for g(x) is larger than that for f. (x). The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).
what is coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
The graph of f(x) is moved two units to the right and three units downward to get the graph of g. (x).
The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).
Given that a>0, f(x) and g(x) are ascending parabola.
Since the origin is f(x vertex, )'s f(x) has just one y-intercept, or (0,0).
Given that g(x) is an upward parabola with a vertex at (2,-3), g(x) has two y-intercepts.
Because of this, the number of y-intercepts for g(x) is larger than that for f. (x).
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PLS HELP i rlly need to get this done
Answer:
1. yes
2. no
3. no
4. yes
Step-by-step explanation:
i need help with this please hurry!!!
So on solving the provided question, we can say that fraction we have are [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex] = 14/6
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here the fraction we have are
[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]
12/3 + 12/4 + 15/2
14/6
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What is a pixel Mcq?
The fundamental color-programming unit on a computer screen or in a digital image is the pixel, a word that was created from the phrase "picture element." Consider it more as a conceptual than a physical unit. In a digital display, pixels are the smallest unit.
What is pixel made of?The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.
For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.
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Pls help me with this
The percent of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
f(x) = 500 (0.67)ˣ
Part A :
x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500
x = 1 ⇒ f(x) = 500 (0.67)¹ = 335
x = 2 ⇒ f(x) = 500 (0.67)² = 224.45
x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815
Part B :
Here 0.67 is the decay rate.
That is the rate of decay of the bug is 0.67.
67% of the bugs are decaying with each day.
Part C :
Percent of bugs remaining each day = 100% - 67% = 33%
Part D:
f(x) < 40
500 (0.67)ˣ < 40
(0.67)ˣ < 40 / 500
(0.67)ˣ < 0.08
Taking logarithms on both sides,
㏒ (0.67)ˣ < ㏒ 0.08
x ㏒ (0.67) < ㏒ 0.08
x (-0.1739) < (-1.0969)
Dividing doth sides by (-0.1739), the sign of inequality changes because of dividing by a negative number.
x > 6.3
Hence the percentage of the bugs eaten and remained are calculated.
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What is the length of ? Two perpendicular lines R S and P Q within a circle intersect at the point P. The lengths of the line segments are labeled as follows. R T equals x, T S equals x, P T equals 4, and T Q equals 16. Figure not drawn to scale A. 8 B. 10 C. 16 D. 20
Answer:
16
Step-by-step explanation:
option c 16 is the answer
Please Help!
Reduce The following -
4:8
3:9
10:2
3:18
Answer:
4:8=1:2
3:9=1:3
10:2=5
3:18 is the same thing as 3:18
d) Consider your answer in part (e). What is the probability that P-P is greater
than the value found in part (a)? Show your work.
The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.
What is probability?Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is mainly the study of events subject to probability.
In Population D:
Population Proportion :Turtles have shell length greater than 2 feet = 0.3
Random Sample = 40
Turtles have shell length greater than 2 feet in random sample = 15
In Population E:
Population Proportion :Turtles have shell length greater than 2 feet = 0.2
Random Sample = 60
Turtles have shell length greater than 2 feet in random sample = 11
Let [tex]\hat{p}_D[/tex] represents sample proportion for D
Let [tex]\hat{p}_E[/tex] represents sample proportion for E
[tex]$ \text{SampleProportion} =\frac{\text { Count of Success }}{\text { Size of the population }}$[/tex]
[tex]$$\begin{aligned}\hat{p}_D & =\frac{\text { Turtles have a shell length greater than } 2 \text { feet in random sample }}{\text { Random Sample }} \\& =\frac{15}{40} \\& =0.375\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\hat{p}_E & =\frac{\text { Turtles have a shell length greater than 2 feet in random sample }}{\text { Random Sample }} \\& =\frac{11}{60} \\& =0.183\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\text { Difference in sample proportion } & =\hat{p}_D-\hat{p}_E \\& =0.375-0.183 \\& =0.1917\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\hat{\boldsymbol{p}} & =\frac{X_1+X_2}{N_1+N_2} \\& =\frac{15+11}{40+60} \\& =0.26\end{aligned}$$[/tex]
[tex]$$\begin{aligned}Z & =\frac{\left(\hat{p}_D-\hat{p}_E\right)-\left(p_D-p_E\right)}{\sqrt{\hat{p}(1-\hat{p}) \times\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} \\& =\frac{(0.375-0.183)-(0.3-0.2)}{\sqrt{0.26 \times 0.74 \times\left(\frac{1}{40}+\frac{1}{40}\right)}} \\& =\frac{0.0917}{\sqrt{0.1924 \times 0.04166}} \\& =0.0087\end{aligned}$$$$[/tex]
[tex]\begin{aligned}P\left(\hat{p}_D-\hat{p}_E\right. & > 0.1917) \\& =P(Z > 0.0087) \\& =1-P(Z \leq 0.0087) \\& =0.4681\end{aligned}$$[/tex]
Therefore, The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.
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Evaluate each expression if a=2.5 and b=-8
-|b=2a|
3|b+6|-|a|
Answer: First=Undefined (if you had a typo, please respond and I will edit)
Second=3.5
Step-by-step explanation:
-|b=2a|
-|-8=2(2.5)|
-8=5
Undefined
3|b+6|-|a|
3|-8+6|-|2.5|
3|-2|-2.5
3*2-2.5
6-2.5
3.5
I need help, answer quick and pls explain
The LCM of the numbers 1 - x² and (x - 1)³ is (1 - x²)(x - 1)
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The least common multiple (LCM) of a set of numbers is the smallest number that can be divisible by the set of numbers
Given the numbers:
1 - x² and (x - 1)³
(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)
(x - 1)³ = (x - 1)(x - 1)(x - 1)
The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)
The LCM is (1 - x²)(x - 1)
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Which of the ratios below is equivalent to 1:3? Select all that apply.
A) 4:12
B) 6:18
C) 6:2
D) 8:24
E) 5:8
Answer:
A, B,D
Step-by-step explanation:
Find the value of x.
Answer:
x=15
Step-by-step explanation:
[tex]\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15[/tex]
Answer:
x = 15.
Step-by-step explanation:
By the External angle of a triangle theorem:-
The external angle = the sum of the 2 opposite internal angles.
So:
10x - 23 = 7x - 26 + 5x - 27
10x - 7x - 5x = -27 - 26 + 23
-2x = -30
x = 15.
A(-2, 5), and B(2, 3), find the coordinate so that p is 4/5 of the way from A to B
The coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].
What is simplest form?When the numerator and denominator have no common factors other than one, the fraction is in its simplest form. Use division to find the simplest form of a fraction.
Given set of points
A(-2, 5)
B(2, 3)
ratio 3:5 or r = 3/5
We will use the following formula to find the coordinate
[tex]$x=\frac{x_1+r x _2}{1+r}[/tex]
[tex]$y=\frac{y _1+r y _2}{1+r}$[/tex]
Substitute the values in the formula
[tex]$ x=\frac{-2+(3 / 5) 2}{1+3 / 5}[/tex] [tex]$y=\frac{5+(3 / 5) 3}{1+(3 / 5)}[/tex]
[tex]$x=\frac{-2+6 / 5}{5+3 / 5}[/tex] [tex]$ y=\frac{59 / 5}{5+8 / 5}$[/tex]
[tex]$x=\frac{-10+6 / 5}{8 / 5}[/tex] [tex]$ y=\frac{25+9 / 5}{8 / 5}$[/tex]
[tex]$x=\frac{-4}{8}[/tex] [tex]$y=\frac{17}{4}$[/tex]
x = -1/2 y = 3[tex]\frac{1}{4}[/tex]
Thus, the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in simplest form is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].
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Full question:
Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3: 5. Write the answer in lowest simplified fraction if necessary.