Age of Mike is 56 and Sam is 17 years according to given equation.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
Let the age of mike be x and age of sam be y .
According to question :
Mike's age is 5 more than 3 times Sam's age , which means
x = 3y+5 -------(1)
The sum of their ages is 73.
x +y = 73 -------(2)
using eqn 1 in 2,
3y +5 +y = 73
4y = 68
y = 17
x = 3*17 +5
x = 56
hence , age of mike is 56 and sam is 17 years.
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Write a cosine function that has a midline of 3, an amplitude of 5 and a period of 2.
Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
What is a Cosine Function?A crucial periodic function in trigonometry is the cosine function.
Utilizing the unit circle will make understanding the cosine function the simplest.
Draw a unit circle on the coordinate plane, center the angle at the origin, and label one side as the positive x-axis for the supplied angle measure.
The point where the other side of the angle intersects the circle has an x-coordinate of cos(), and a y-coordinate of sin().
According to our answer-
B = 2pi/T, where T is the period and T = 1/f is the frequency; T is the period
Determines horizontal phase shift by using
C =determines vertical shift.
When solving the given issue, D = midline = 5
A = amplitude = 2.
B = 2pi/T = 2pi/(2/3) = 3pi since frequency = 3/2 means that the period is T = 2/3, which is the reciprocal of the frequency.
C = 0.
The result of adding everything up is A = 2, B = 3pi, C = 0, and D = 5.
so,
A*cos(B(x-C)) + D = y
y = 2*cos(3pi(x-0)), plus 5.
y = cos(3pi*x) * 2 * + 5
Hence, Y = 2*cos(3pi*x) + 5 is the cosine function with a midline of 5, an amplitude of 2, and a frequency of 3/2.
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Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).
and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).
The glide reflection that maps ABC to A'B'C' is given as follows:
Reflection over the line y = x - 9.Translation right 8 units.What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.
The midpoint of segment A'B' is given as follows:
x = (4 + 6)/2 = 5.y = (-2 - 6)/2 = -4.The slope of this segment is given as follows:
m = (-6 - (-2))/(6 - 4) = -1.
Then the slope of the reflection line is of:
m = 1.
(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).
Then:
y = x + b.
When x = 5, y = -4, then the intercept b is calculated as follows:
-4 = 5 + b
b = -9.
Thus the reflection line is of:
y = x - 9.
Then the translation is given subtracting the coordinates of one of the vertices, as follows:
4 - (-4) = 4 + 4 = 8 units right.-2 - (-2) = -2 + 2 = 0 units vertically.More can be learned about glide reflections at https://brainly.com/question/5612016
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Need help asap.
Calculate the residuals for the scatterplot.
The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
How to determine the residuals?The regression equation is given as:
y = 0.138x + 1.166
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 20 + 1.166 = 3.93
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 16.7 + 1.166 = 3.47
y = 0.138 * 15.5 + 1.166 = 3.31
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 3.7 - 3.65 = 0.05
Residual = 3.69 - 4.19 = -0.5
Residual = 3.8 - 3.65= 0.15
Residual = 4 - 3.93 = 0.07
Residual = 4 - 3.65= 0.35
Residual = 1.11 - 1.26 = -0.15
Residual = 3.69 - 4.19 = -0.5
Residual = 1.11 - 1.26 = -0.15
Residual = 3.5 - 3.47 = 0.03
Residual = 3.92 - 3.31 = 0.61
Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
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Answer:
The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
How to determine the residuals?
The regression equation is given as:
y = 0.138x + 1.166
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 20 + 1.166 = 3.93
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 16.7 + 1.166 = 3.47
y = 0.138 * 15.5 + 1.166 = 3.31
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 3.7 - 3.65 = 0.05
Residual = 3.69 - 4.19 = -0.5
Residual = 3.8 - 3.65= 0.15
Residual = 4 - 3.93 = 0.07
Residual = 4 - 3.65= 0.35
Residual = 1.11 - 1.26 = -0.15
Residual = 3.69 - 4.19 = -0.5
Residual = 1.11 - 1.26 = -0.15
Residual = 3.5 - 3.47 = 0.03
Residual = 3.92 - 3.31 = 0.61
Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
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Step-by-step explanation:
A college student is deciding how many hours to work at a part time job(x) and how many hours to work at an internship (y). The job pays $24 and hour, and the internship pays $12 an hour. The student needs to work less than 15 hours a week but needs to earn at least $240 a week to pay expenses. Write 2 systems of inequalities to represent all the combinations of number of hours the student can work at the job and internship
Answer:
x + y < 152x + y ≥ 20-------------------------------
Total hours worked is x + y.
Earning from the part time job is 24x, from the internship is 12y.
Inequality for the number of hours:
x + y < 15Inequality for the earning:
24x + 12y ≥ 240This can be simplified by dividing all terms by 12:
2x + y ≥ 20Answer:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
Step-by-step explanation:
Part-time job
Let x be the number of hours worked.$24 = pay per hour.Internship
Let y be the number of hours worked.$12 = pay per hour.The student needs to work less than 15 hours a week:
[tex]\implies x+y < 15[/tex]
The student needs to earn at least $240 a week:
[tex]\implies 24x+12y \geq 240[/tex]
Therefore, the system of inequalities is:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
The second inequality can be simplified by dividing each term by 12:
[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]
[tex]\implies 2x+y \geq 20[/tex]
Therefore, a second system of inequalities is:
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
To solve the system of equalities, graph both inequalities and shade the overlapping region.
Any (x, y) point in the overlapping region is a solution to the system of inequalities.
What is the slope of y = − 5 + 4x
90°
bº
aº
110°
what is the value of a+b?
The value of a+b is 67.5+52.2=120.1 degree.
Which is the value of B?
The middle number, the one immediately following the x, is the b-value. A and C are also numerals, much as the letter B. These can all have any number. They all work together to show you how the quadratic function will be graphed. If you haven't used your y = mx + b equation in a while, dust it off and use the three values you were given for x, y, and m to solve for the b-value, which is the value of the y-intercept. The equation is then solved for the last variable: b, the y-value intercept's.
[tex]\begin{aligned}& 360-90=270 \\& 270-2=135 \\& 180-135=45 \\& \frac{45}{2}=22.5 \\& 90-22.5=67.5 \\& b=67.5^{\circ}\end{aligned}[/tex]
90 *67.8+a 110 =360
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Look at the triangles shown below.
5
Which statement is TRUE?
Answer: B
Step-by-step explanation:
vertical angles are =
Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
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Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Proof of ray BC is the angle bisector of angle ABA' is given.
What are angle bisectors?Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.
A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.
Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.
Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.
Therefore, <A'B'C' = <ABC
by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.
Therefore, the ray BC is the angle, bisector of angle ABA'.
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What is the experimental probability that the coin will land on heads?
Step-by-step explanation: Without more information, it is impossible to determine the experimental probability that a coin will land on heads. The experimental probability of an event is determined by performing experiments and observing the results. For example, if we were to flip a coin 10 times and it landed on heads 6 times, we could say that the experimental probability of the coin landing on heads is 6/10, or 0.6. However, without knowing the results of any experiments, it is impossible to determine the experimental probability of the coin landing on heads.
Answer: We should ASSUME 1/2 or 50%
Step-by-step explanation: Since we don't know the exact number of times the person flipped the coin, we must infer you mean he/she flips the coin once. So, If a coin has 2 sides and the probability is 100% total, we can write an expression to help us solve:
P(Probability)= 100/2
P= 50% or 1/2
How I got 50% or 1/2 is I took the whole probability (100%) and divided it by 2. (2 sides on a coin)
I hope this helped (at least)
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.
What is a sphere?
The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.
Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.
The radius of a sphere is the half of its diameter.
The radius of the bottom ball is 3/2 feet =1.5 feet
The radius of the middle ball is 2/2 feet = 1 feet.
The radius of the top ball is 1/2 feet = 0.5 feet.
The volume of a sphere is 4/3 × ∏r³.
The volume of bottom ball is 4/3 × ∏ × (1.5)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (1)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (0.5)³ cubic foot.
The total amount of snow is
4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³
= 4/3 × ∏ [1.5³ +1³ + 0.5³ ]
= 4/3 × ∏× 4.5
= 18.84
≈ 19 cubic foot
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Solve a triangle proof
the triangle of the given figures are congruent and ∠1 = ∠2.
What is congruent by SAS?
The side-Angle-Side congruence rule is referred to as ASA. Two triangles are said to be congruent according to this rule if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. See if the two triangles given, ABC and XYZ, are congruent according to the ASA rule by looking at the image provided below. According to the ASA congruence rule, two triangles are said to be congruent if two of their respective sides and angles are equal to those of two other triangles and their respective sides and angles, respectively.
In the triangle ΔABD and ΔAED
Here AD is a common side
AB = AE
BC = EC
So both triangles are congruent.
So we can have ∠1 = ∠2
Hence, the triangle of the given figures are congruent and ∠1 = ∠2.
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What is the order of this matrix?
Answer: C
Step-by-step explanation:
It should be 5 x 3, considering that rows come before the columns.
pls help due tommaorw
(i also have other unanswered questions posted)
a number increased by 4 is 12
Answer: x=8
Step-by-step explanation:
This would be your equation:
x+4=12
Solve.
x=12-4
x=8
100 POINTS IF YOU CAN ANSWER THIS
Which of the following number of selected people having received a ticket would constitute an unusual event?
A. 4
B. 5
C. 1
D. 2
Answer: B
Step-by-step explanation:
Answer: The answer is D. 2 | 0.25
Step-by-step explanation:
I don't really have a good explanation, but I hope it helps!
What is the equation of a line, in slope-intercept form, which passes through (4, -1) and has a slope of 1/3
Answer:
The answer is y = 0.333x + -2.332
Step-by-step explanation:
All you have to do is put above values in equation, which should get you to:
-1 = 0.333 (4) + b
-1 = 1.332 + b
-2.332 = b
b = -2.332
y = 0.333x + -2.332
x = [?]
4x-2 3x + 14
PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!!!
Answer:
x=-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
which analysis technique simulates a model's outcome many times to provide a statistical distribution of the calculated results?
The answer is that the Monte Carlo analysis simulates a model’s outcome many times to provide a statistical distribution of the calculated results.
Now, what is Monte Carlo analysis technique?
Monte Carlo Analysis is a risk management technique used to conduct a quantitative analysis of risks.
This mathematical technique is used to analyze the impact of risks on your project — in other words, if this risk occurs, how will it affect the schedule or the cost of the project?
So, Monte Carlo Analysis gives you a range of possible outcomes and probabilities to allow you to consider the likelihood of different scenarios.
For example, let’s say you don’t know how long your project will take. You have a rough estimate of the duration of each project task. Using this, you develop a best-case scenario (optimistic) and worst-case scenario (pessimistic) duration for each task.
You can then use Monte Carlo to analyze all the potential combinations and give you probabilities of when the project will complete.
Other major benefits of this technique is -
1. It Provides early indication of how likely you are to meet project targets.
2. Can be used to create a more real budget and schedule.
3. Predicts the likelihood of schedule .
4. Gives quantitative measure of risks to assess impacts
5. Provides objective data for decision making.
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the economic policy institute periodically issues reports on worker's wags. the institute reported that mean wags for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2020. assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. (12 points) what is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.97? what is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean $27.83? in which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? why? what is the probability that a sample of 120 female graduates will provide a sample mean more than $0.60 below the population mean, 27.83?
The probability that a sample of 120 female graduates will = 0.8905
what is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
= |y -µ| ≥ 0.60
z = y -µ /σ√n
= 0.60/4.10√120
= 0.60/0.3742770
=1.60
Pr ( y -µy) ≤ 0.60 = P |z|≤1.60
=P ( -1.60≤ Z≤ -1.60)
=P (Z ≤ 1.60) -P ( Z≤ -1.60)
= 0.9452 - 0.0547 using z table
= 0.8905
Female graduates
mean = 27.83
sd = 4.10
sample = 120
µx = 27.83
σx = σ/√n
= 4.10/√120
a) P (X bar > 27.83)
= P (X bar -µx)/ σx > 27.83-27.83/4.10/√120
= P ( z > -1.60)
= 0.9452
For men
Mean=µ=37.39
Sd=σ=4.60 ,n=50
Probability that sample mean within $1.00 of the population mean
u-1=37.39-1=36.39
u+1=37.39+1=38.39
P = (36.39 <X bar < 38.39)
= P [tex]\frac{36.39-37.39 }{4.60/\sqrt{60} } < \frac{X bar - µ}{σ/\sqrt{n} } < \frac{39.39-37.39}{4.60/\sqrt{60} }[/tex]
= P ( -1.6839 < Z <1.6839
= P ( -1.68 < Z <1.68)
= P (Z < 1.68) - P(Z < -1.68)
= 0.9535- 0.0465
= 0.9070
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Which system of inequalities is shown?
The equations of inequalities are y < 4 and y > x.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.
One graph line is parallel to x-axis and it intersect y axis at (0,4).
The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a
The equation of the line parallel to x-axis is y = 4.
The equation of line that passes through origin is y = mx
The line passes through the point (1,1).
Putting x = 1 and y = 1 in y = mx:
1 = m
Therefore the equations of lines are y = x and y = 4
The inequality will be y < x or y > x for the line y = x.
The inequality will be y < 4 or y > 4 for the line y = 4.
(-2,0) is a point on the shaded area.
Putting x = -2 and y = 0 in y > x
0 > -2 true.
The inequality is y > x
Putting x = -2 and y = 0 in y < 4
0 < 4 true.
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Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it she paused it for 16 minutes what time did the movie end?
Answer:
The movie ended at 7:39 a.m.
Step-by-step explanation:
She started at 6:30. 53 minutes added to that would be 7:23. Another 16 minutes added to that would be 7:39.
The movie will end at 20:39.
What is time conversion?Conversion Time means a time which falls after the Calculation Time and is the time at which the admission of the Ordinary Shares arising on Conversion to the Official List becomes effective.
Given that, Josephine started to watch a movie the movie starts at 18:30 the movie was 1 hour and 53 minutes long but part way through it, she paused it for 16 minutes
The total time taken = 1 hour + 53 minutes + 16 minutes = 1 hours + 69 minutes
= 1 hour + 60 minutes + 9 minutes
= 1 hours + 1 hours + 9 minutes
= 2 hours + 9 minutes
Therefore, total time she took for movie is 2 hr 9 min
Since, the movie started at 18:30,
Therefore, 18:30 + 2 hour 9 minute
= 20 hours + 39 minutes
Hence, The movie will end at 20:39
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Determine which of the lines, if any, are parallel or perpendicular. Explain.
Line A: 4x-3y=2
Line B: y=4/3x+2
Line C: 4y+3x=4
Answer:
Line A parallel
Line B perpendicular
Line C parallel
40 PTS
TWO PART QUESTION NEED! :)))
You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
Part a. The future value in 4 years.
Part b. The interest gained in 4 years.
The future value of investment is $560.30, and interest gained in 4 years is 136.8%
What is compound interest?The interest regarding loan or investment that increases exponentially with respect to time is called compound interest.
Why is compound interest used?We use compound interest so as to enhance our investment in a large scale.
Given, Amount invested, P= $500
compound interest rate, r= 2.85%
number of time period, t = 4 years
number of times interest applied per time period, n =12 (as interest compound monthly)
Final amount, A
we used compound interest formula, A= P(1+r/n)∧nt
A= 500(1+0.0285/12) ∧12×4
Final amount, A= $560.30
The future value = $560.30
Interested gained in 4 years with compound monthly =2.85x12x4 =136.8%
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is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero?
True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.
When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.
While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.
When there is no association in a correlational analysis, what happens?
The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.
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Lian gives his friend Patti a lottery ticket for her birthday. The ticket cost Lian $2, and the back of
the ticket says, "The overall odds of winning a prize with this ticket are 1: 50, and the expected
return for this ticket is $0.89."
Lian says, "If 1,000 people each bought one of these tickets, they'd have spent $2,000 in total
and get back about $890"
Patti says, "The probability that one of these tickets wins a prize is 0.89, on average."
Answer: Lian is correct.
Step-by-step explanation:
He is correct because he is one person and ticket cost him 2 dollars.
So by doing simple multiplication we multiply both variables by 1,000 to get 1,000 people spend 2,000 dollars.
Answer:
Lian is correct
Step-by-step explanation:
Khan Academy
Point C is 3/4 of the way from point A(−4, −2) to point B(8, 6). What are the coordinates of C?
The coordinates of C are (8/7, 10/7) if point A is (-4, -2) and point B is
(8, 6)
What is section formula?The section formula aids in finding a point's coordinates so that the line connecting two points can be divided in a ratio. This involves both internal and external activities. P (x, y) = (c, m, plus a, plus n, plus d, plus b, plus n). The Section formula is used to determine the ratio by which a line segment is divided by a point either internally or externally in coordinate geometry. It is used to identify a triangle's centroid, incenter, and excenter. Physics uses this technique to determine equilibrium points, the centers of mass of systems, and other things.
A(-4, -2), B(8, 6)
m:n=3:4
((3(8)+4(-4))/(3+4) , ((3(6)+4(-2))/(3+4))
=((24-16)/7, (18-8)/7)
=(8/7, 10/7)
Therefore, the coordinates of C are (8/7, 10/7)
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Can someone pls help me with this
The Rule is [tex]2^x[/tex].
The type of function is exponential.
Formula is [tex]y=2^x[/tex].
What does exponential function mean?
A mathematical function of the following format is an exponential function:
[tex]f(x)=a^x[/tex], where a is a constant which is also called the base of the function and x is a variable.
The information we can get from the given table is
when x=-2, y= 1/4=[tex]2^{-2}[/tex]
when x=-1, y=1/2=[tex]2^{-1}[/tex]
when x=-0, y=1=[tex]2^0[/tex]
when x=1, y=2=[tex]2^1[/tex]
when x=2, y=4=[tex]2^2[/tex]
when x=3, y=8=[tex]2^3[/tex]
By observing all the points, we know that [tex]y=2^x[/tex].
Therefore the rule for the table is [tex]f(x)=2^x[/tex].
The Formula for the given table is [tex]y=2^x[/tex].
The type of function is exponential.
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