What transformations are applied to the graph of the function f(x) = 10^x to produce the graph of the function g(x) = 3(10)^x - 2 ?
A.
a vertical dilation by a factor of and a horizontal shift to the right 2 units
B.
a vertical dilation by a factor of and a vertical shift down 2 units
C.
a vertical dilation by a factor of 3 and a vertical shift down 2 units
D.
a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units
Answers
Answer:
C
Step-by-step explanation:
lol didn't i just answer one of your questions, also give me brainliest pls :)
First, the function was multiplied by 3, which is a vertical dialation by a factor of 3. Then, we subtracted 2 from the function, which is a vertical shift down two units. Therefore, the answer is C
The transformations are applied to the graph of the function should be option c. a vertical dilation by a factor of 3 and a vertical shift down 2 units
What transformation should be applied:Since
First, the function should be multiplied by 3, that represent vertical dilation by a factor of 3. After this, we subtracted 2 from the function, i.e. is a vertical shift down two units.
Therefore, the answer is C a vertical dilation by a factor of 3 and a vertical shift down 2 units.
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Related Questions
Researchers interested in the perception of three-dimensional shapes on computer screens decide to investigate what components of a square figure or cube are necessary for viewers to perceive details of the shape. They vary the stimuli to include: fully rendered cubes, cubes drawn with corners but incomplete sides, and cubes with missing corner information. The viewers are trained on how to detect subtle deformations in the shapes, and then their accuracy rate is measured across the three figure conditions. Accuracy is reported as a percent correct. Four participants are recruited for an intense study during which a large number of trials are required. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.
The sample means are provided below:
Answers
The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.
In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.
Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.
The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.
To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.
The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.
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Find the long-term annual growth rate for the following Leslie growth models (use iteration; this growth rate is the size of the largest eigen- value). Also find the long-term population distribution (percentages in each age group) a) y’ = m+20
m’ = y
o’ = 0
b) y’ = m+20
m’ = .5y
o’ = .5m
c) y’ = m+40
m’ = .5y
o’ = .5m
d) y’ = 4a+4o
m’ = .5y
a’ = .5m
o’ = .5a
Answers
To find the long-term annual growth rate and population distribution for the given Leslie growth models, we use iteration to calculate the largest eigenvalue of the Leslie matrix for each model.
a) Model:
y' = m + 20
m' = y
o' = 0
To calculate the long-term annual growth rate, we need to find the largest eigenvalue of the Leslie matrix. However, since the equation for 'o' does not depend on any other variable, the 'o' population remains constant, and its growth rate is zero.
For the remaining equations:
y' = m + 20
m' = y
We can rewrite the equations in matrix form:
[Y'] = [A] [Y] + [C]
where [Y] = [y, m]' and [A] is the Leslie matrix.
The Leslie matrix [A] is given by:
[A] = [0, 1]
[1, 0]
To find the largest eigenvalue of [A], we solve the characteristic equation:
det([A] - λ[I]) = 0
By solving the characteristic equation, we find that the eigenvalues are ±1.
Since we are interested in the largest eigenvalue, the long-term annual growth rate is 1.
To find the long-term population distribution, we find the corresponding eigenvector for the eigenvalue 1:
[A - I] [V] = [0]
where [V] is the eigenvector.
Solving the system of equations, we find the eigenvector [V] = [1, 1]'.
Therefore, the long-term population distribution is:
y: 50%
m: 50%
o: 0%
The long-term annual growth rate is 1, and the long-term population distribution is y = 50% and m = 50%, with o = 0%.
The calculations for the remaining models (b), c), and d)) are similar, but with different Leslie matrices and equations.
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Serenity and her children went into a restaurant and will buy hamburgers and tacos. Each hamburger costs $5.50 and each taco costs $2. Serenity has a total of $45 to spend on hamburgers and tacos. Write an inequality that would represent the possible values for the number of hamburgers purchased, ℎ h, and the number of tacos purchased, � . t.
Answers
Answer: Less than or equal to 45
Step-by-step explanation:
Let's use algebra to write the inequality.
Let h be the number of hamburgers purchased and t be the number of tacos purchased.
Each hamburger costs $5.50 and each taco costs $2, so the total cost of h hamburgers and t tacos is:
5.5h + 2t
Serenity has a total of $45 to spend, so we can write:
5.5h + 2t ≤ 45
This is the inequality that represents the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t.
Note that the inequality is less than or equal to 45, since Serenity cannot spend more than $45.
To represent the possible values for the number of hamburgers and tacos purchased, an Inequality can be written as 5.5x + 2y ≤ 45.
To write an inequality to represent the possible values for the number of hamburgers purchased (h) and the number of tacos purchased (t), we need to consider the cost of each item and the total amount Serenity has to spend.
Let's assume Serenity buys x hamburgers and y tacos. Each hamburger costs $5.50, so the total cost of hamburgers purchased would be 5.5x. Each taco costs $2, so the total cost of tacos purchased would be 2y.
The total amount Serenity has to spend is $45. Therefore, the inequality that represents the possible values for h and t is: 5.5x + 2y ≤ 45.
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You decide to take a hike today because it is beautiful outside. You begin at 1234 feet and the air temperature is 79.4^{\circ} {F} . You climb to where you notice clouds beginning to form
Answers
The temperature at the point where the clouds begin to form is 77.65 °F
Given: The starting point is 1234 feet and air temperature is 79.4°F
You climb to where you notice clouds beginning to form.It can be observed that the temperature decreases by 3.5°F per 1000 feet as we go up.
Using this information, we can calculate the temperature at the point where the clouds start forming.
Let the height of the point where clouds begin to form be x feet above the starting point. As per the question, the temperature decreases by 3.5°F per 1000 feet as we go up.
Therefore, the temperature at the height of x feet can be calculated as:
T(x) = T(1234) - 3.5/1000 * (x - 1234)°F , where
T(1234) = 79.4°F
Substituting the value of x = 1234 + 500, (as we need to know the temperature at the point where clouds begin to form) we get:
T(1734) = T(1234) - 3.5/1000 * (1734 - 1234) °F
= 79.4 - 3.5/1000 * 500 °F
= 79.4 - 1.75 °F
= 77.65 °F
Therefore, the temperature at the point where the clouds begin to form is 77.65 °F
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Find the simple interest for 3 years at a rate of 7.5% on $200
Answers
Solution,
Principal (P)=$200
Time(t)=3 years
Rate(R)=7.5%
Now,
Simple Interest=PTR/100
=200*3*7.5/100
=4500/100
= $45
Hope it helps
good luck on your assignment
Some Math i can’t helppp
Answers
Annually The amount after 10 years = $ 7247.295
quarterly compound after 10 years = $7393.5
Continuously interest =$7,419
Given:
P = the principal amount
r = rate of interest
t = time in years
n = number of times the amount is compounding.
Principal = $4500
time= 10 year
Rate = 5%
To find: The amount after 10 years.
The principal amount is, P = $4500
The rate of interest is, r = 5% =5/100 = 0.05.
The time in years is, t = 10.
Using the quarterly compound interest formula:
A = P (1 + r / 4)4 t
A= 4500(1+.05/4)40
A= 4500(4.05/4)40
A= 4500(1.643)
Answer: The amount after 10 years = $7393.5
Using the Annually compound interest formula:
A = P (1 + r / 100) t
A= 4500(1+5/100)10
A= 4500(105/100)10
Answer: The amount after 10 years = $ 7247.295
Using the Continuously compound interest formula:
e stands for Napier’s number, which is approximately 2.7183
\(A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}\)
A= $2,919
Answer: The amount after 10 years = $4500+$2,919=$7,419
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What is the solution set to this inequality??
x^2-12x+35<_ 3
Answers
-8,-6,-4
-10,-6,0
these are the possible test points for your three intervals
Answer:
4≤x≤8
Step-by-step explanation:
A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is: A. 650 B. 9.8 C. 609.8 D. 5 E. None of the above
Answers
The margin of error is 9.8. The answer is (B).
Margin of error (ME) is the amount of random sampling error that is expected in a survey's results. It is the range of values above and below the sample statistic (such as the sample mean or proportion) within which the true population parameter (such as the population mean or proportion) is expected to lie with a certain degree of confidence.
The margin of error (ME) for a 95% confidence interval is given by:
ME = z*(σ/√n)
where z is the z-score for the desired level of confidence (in this case, 95%), σ is the population standard deviation, and n is the sample size.
We are given that σ = 50, n = 100, and the sample mean is 600. To find the z-score, we can use a standard normal distribution table or calculator. For a 95% confidence interval, the z-score is approximately 1.96.
Substituting the values into the formula, we get:
ME = 1.96*(50/√100) = 9.8
Therefore, the margin of error is 9.8. The answer is (B).
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will give brainliest to quickest answer
Answers
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
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_ is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable.
Answers
Probability distribution is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable.
What is Probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.What is the probability of each value of a discrete random variable?
The probability P(x) that a discrete random variable X will take the value x in one trial of the experiment is connected to each possible value x of the variable.
Which is a discrete random variable?
A discrete variable is one that is random. if the number of possible values is either countable or finite. Continuous refers to a variable that is random. if the range of possible values includes all possible numbers.What is the other name of mean of discrete random variable?
A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values. The probability function or probability mass function are other names for it.Learn more about Probability
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Suppose that, in an alternate universe, the possible values of m
l
are the integer values including 0 ranging from −l−1 to l+1 (instead of simply −l to +l ). How many orbitals would exist in each of the following subshells? A. p subshell B. d subshell Which atomic orbitals have values of n=3 and I=1 ?
Answers
A. In the alternate universe, the p subshell would have 5 orbitals.
B. In the alternate universe, the d subshell would have 10 orbitals.
In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.
A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).
B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).
Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.
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Evaluate 49t where t = 4.
Answers
Greetings from Brasil...
Just replace the value of T in the monomial 49T
49T = 49 · T
as T is equal to 4, then
49 · 4 = 196
49T where T = 4 is equal to 196
Answer:
\(\boxed {\tt 196}\)
Step-by-step explanation:
We are given the expression
\(49t\)
We want to solve when t is equal to 4. Therefore, we must substitute 4 in for t and solve.
\(49 t, t=4\)
\(49(4)\)
Multiply 49 and 4.
\(196\)
The expression 49t evaluated at t=4 is equal to 196.
The attendance over a weekly period of time at a movie theater is normally distributed with a mean of 10,000 and a standard deviation of 1000 persons. Find the percent of attendance figures that differs from the mean by 1500 persons or more.
Answers
The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.
From the question above, Mean μ = 10,000
Standard Deviation σ = 1,000
The formula for z-score is :
z = (x-μ) / σ
Where, x = observation
z = z-score
Mean μ = 10,000
Standard Deviation σ = 1,000
From the above formula, let's calculate z-score for x = 11,500
z = (x-μ) / σ
z = (11,500 - 10,000) / 1000
z = 1.5
Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.
P(z ≥ 1.5) = 0.0668
To find the percentage, we need to multiply the above value by 100.
P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%
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Bruno is designing his next skateboard. The skateboard store has 3 types of grip tape, 13 types of decks, 7 types of trucks, 4 types of bearings, and 2 types of wheels. How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.
Answers
Answer:
2184 different combinations
Step-by-step explanation:
To find how many different combinations are possible, multiply all of the values:
3 * 13 * 7 * 4 * 2 = 2184 different combinations
Answer:
2,184 different skateboards.
Step-by-step explanation:
You would have to multiply
3 x 13 x 7 x 4 x 2 = 2184
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The perimeter of the figure below is 40 cm. what is the length of the side labelled ‘x’?
Answers
Answer:
13.72 cm
Step-by-step explanation:
Perimeter of the given figure = sum of all sides
40 = x + 9.7 + 16.58
40 = x + 26.28
x = 40 - 26.28
x = 13.72 cm
50 POINTS!!! A side of the triangle below has been extended to form an exterior angle of 148°. Find the value of x.
Answers
Sum of two Interiors=Exterior
\(\\ \rm\rightarrowtail x+90=148\)
\(\\ \rm\rightarrowtail x=148-90\)
\(\\ \rm\rightarrowtail x=58\)
First, let's find the interior top angle of the triangle.
1. Finding the top angle of the triangle.Let the top angle be "y".
We know that:
148 + y = Straight lineStraight line = 180This means that:
180 = 148 + ySimplify the equation by subtracting 148 both sides to isolate "y".
180 - 148 = 148 - 148 + y 180 - 148 = y 32° = yHence, the top angle of the triangle is 32°.
2. Finding the measure of "x":We know that:
Sum of interior angles of triangle = 180°This means that:
32 + x + (Right angle) = 180Substitute "Right angle" as 90.
32 + x + 90 = 180 x + 122 = 180Subtract 122 both sides to isolate x.
x + 122 - 122 = 180 - 122x = 58°Thus, the measure of x is 58°.
Which of the following graphs the equation
y = 1/5x + 1
Answers
welp i cant help but i can sing ;-;
Step-by-step explanation:
PLEASE HELP ME!
Diagram shows the distance time graph that represent Dendrick's journey Kl to vawang and David s journey from rawang to Kl. Both of them depart from the place at the same time
a) Calculate the length of time in minutes, David stop his car
b) If their journey starts at 9 am, what is the time david and dendrick
c) Calculate the speed in km h¯¹, of Dendrick when he meets David
Answers
Answer:
1) 45 minutes
2) they meet in 20 minutes
3) (12-6)/(20/60)=18kmh
What’s the value of x
Answers
Answer:
2
Step-by-step explanation:
20-7x=6x-6
20+6=6x+7x
26=13x
x=2
A 6-column table with 3 rows in the second, third, and fifth columns and 1 row in the other columns. The first column labeled Number of Washers has entry 1 washer mass = 4. 9 grams. The second column labeled Trial has entries trial number 1, trial number 2, trial number 3. The third and fourth columns labeled Time to travel 0. 25 meters t subscript 1 (seconds) have entries in the third column 2. 24, 2. 21, 2. 23 and average 2. 23 in the fourth column. The fifth and sixth columns labeled time to travel 0. 5 meters t subscript 2 (seconds) have entries in the fifth column 3. 16, 3. 08, 03. 15 and in the sixth column average 3. 13. What is the average velocity of the car over the first 0. 25m? m/s What is the average velocity of the car over the second 0. 25m? m/s.
Answers
The average travel time is simply the mean travel time between the given points.
The average time that it takes for the car to travel the first 0.25m is 2.23s.The average time to travel just between 0.25m and 0.50m is 0.9s.What is the formula to find the average time?The average time calculated with the help of following formula;
\(\rm Average \ Time = \dfrac{Sum\ of \ all \ data}{Number \ of \ data}\)
a) The average time to travel the first 0.25m
The time travel in the first 0.25m are 2.24s, 2.21s, and 2.23s.
So, the average time to travel is:
\(\rm Time = \dfrac{2.24+2.21+2.23}{3}\\\\Time = \dfrac{6.68}{3}\\\\Time = 2.23\)
The average time that it takes for the car to travel the first 0.25m is 2.23s.
(b) The average time to travel just between 0.25m and 0.50m
The time travel in the 0.50m is 3.16s, 3.08s, and 3.15s.
So, the average time to travel this distance is:
\(\rm Average \ time = \dfrac{3.16+3.08+3.15}{3}\\\\Average \ time = \dfrac{9.39}{3}\\\\Average \ time =3.13\)
The average time to travel between both distances is the difference between the average time of each distance.
Then,
Average = 3.13 - 2.23 = 0.9 seconds
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Assuming that the lower explosion limit for main engine is 200mg/l. The oil mist detector alarm is arranged to operate at?
Answers
The oil mist detector alarm is arranged to operate at 40% of the lower explosion limit. Therefore, the oil mist detector alarm will operate at 80mg/l.
The lower explosion limit is the minimum concentration of a particular combustible gas or vapor in air to form an explosive mixture. The LEL value is commonly used to help ensure a safe work environment and prevent combustible gas or vapor-related explosions. The oil mist detector is an instrument that detects the presence of oil mist in the air. If the oil mist detector is set too low, it could lead to false alarms. On the other hand, if it is set too high, it could fail to detect oil mist and thereby cause damage to the equipment or even result in explosions. In order to prevent these occurrences, the oil mist detector alarm is arranged to operate at 40% of the lower explosion limit.
Therefore, the oil mist detector alarm will operate at 80mg/l assuming that the lower explosion limit for the main engine is 200mg/l.
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All the data collected in a particular study are referred to as the? inference data set variable population
Answers
A variable is any property, number, or quantity that can be measured or counted. Variables can also be referenced as data items.
Inference: Inference uses selected samples from a population to estimate the properties of unknown people.
A record (or record) is a collection of data. For tabular data, a record corresponds to one or more database tables, each table column represents a specific variable, and each row corresponds to a particular record in that data set.
Therefore:
All the data collected in particular is referred to as Data Set.
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Find the least squares straight line y = mx + b to fit the data points: (0,3), (2, 1), (3, 1). Compute the minimum square error.
Answers
The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
Given data points are (0, 3), (2, 1), (3, 1).
To find the least square straight line, y = mx + b.
The line that fits these points will have the minimum square error.(0,3) y = mx + b; 3 = 0 + b; b = 3(2,1)
y = mx + b; 1 = 2m + b; b = 1 - 2m(3,1)
y = mx + b; 1 = 3m + b; b = 1 - 3m
Substitute the value of b in (2) and (3)1 - 2m = 3 - 3m; m = -2y = mx + b;
y = -2x + 3
The least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found.
Now, we need to compute the minimum square error.
Square error of each point: Point 1 (0, 3): Square error = (3 - 3)² = 0
Point 2 (2, 1): Square error = (1 - (-4))² = 25
Point 3 (3, 1): Square error = (1 - (-5))² = 36
The minimum square error is the sum of the square error of all the points, Minimum square error = 0 + 25 + 36 = 61
Therefore, the least square straight line y = -2x + 3 to fit the data points (0, 3), (2, 1), (3, 1) is found. The minimum square error is 61.
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A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Round your answers to two decimal places. ) (a) How much wire (in meters) should be used for the square in order to maximize the total area
Answers
To maximize the total area when a wire of 28 m is cut into two pieces, one for a square and the other for an equilateral triangle, the entire wire should be used for the square.
Let's assume the length of wire used for the square is x meters. The remaining length of the wire for the equilateral triangle would then be (28 - x) meters.
For the square, each side would have a length of x/4 meters since there are four sides in a square. The area of the square is calculated by squaring the side length, so the area of the square would be (x/4)^2 square meters.
For the equilateral triangle, each side would have a length of (28 - x)/3 meters. The area of an equilateral triangle is calculated using the formula (sqrt(3)/4) * (side length)^2, so the area of the equilateral triangle would be (sqrt(3)/4) * ((28 - x)/3)^2 square meters.
To maximize the total area, the entire wire should be used for the square, so x = 28 meters. Therefore, the entire 28 meters of wire should be used for the square in order to maximize the total area.
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What is the answer? The answer choices were 45, 40, and 50.
Answers
In a class of students, the following data table summarizes how many students play
an instrument or a sport. What is the probability that a student chosen randomly
from the class plays a sport?
Plays a sport
Does not play a sport
Plays an instrument Does not play an instrument
3
8
10
9
Answers
Answer:
3 OR 8 hope this helps!
Step-by-step explanation:
90 POINTS! HELP ASAP! Using one of the figures below, explain a strategy for calculating the area of the irregular polygon.
Answers
Answer:
area of polygon = 88 sq. units
Step-by-step explanation:
lets make it simple, short and accurate.
area of polygon = total area - total area of triangles
total area = 11 * 12 = 132
triangle 1 = 1/2 * 5 * 5 = 12.5
triangle 2 = 1/2 * 3 * 6 = 9
triangle 3 = 1/2 * 3 * 8 = 12
triangle 4 = 1/2 * 3 * 7 = 10.5
total area of triangle = 12.5 + 9 + 12 + 10.5 = 44
area of polygon = 132 - 44 = 88 sq. units
Answer:
The area of the irregular polygon:
88 units²
Step-by-step explanation:
The irregular polygon is insert in a rectangle
The strategy is:
1 - calculate the rectangle total area
2- calculate the area of each right triangle
3.- substracte the total area of the 4 right triangles from the area of the rectángule
then:
1.-
Ar = 12*11 = 132 units²
Ar = rectangle area
2.-
At₁ = (5*5)/2 = 25/2 = 12.5 units²
At₂ = (6*3)/2 = 18/2 = 9 units²
At₃ = (7*3)/2 = 21/2 = 10.5 units²
At₄ = (8*3)/2 = 24/2 = 12 units²
At total = 12.5 + 9 + 10.5 + 12 = 44 units²
At = right triangle areas
3.-
Ap = 132 - 44 = 88 units²
Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
Answers
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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Chen buys 4 tickets to a soccer game. The total cost before taxes is $80. Which equation would you use to determine the price, p, of the ticket? A 4p=80 B 80p=4 C 4+p=80 D p/4=80
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Answer:
A. 4p=80
Step-by-step explanation:
Total Cost of 4 tickets=$80
Price=p
Quantity=4
Total cost=price×quantity
80=p×4
80=4p
80=4p is the equation that can be used to determine price
From the equation
80=4p
Divide both sides by 4
80/4=4p/4
20=p
Price is $20 per ticket
Answer:
4p = 80
Step-by-step explanation:
Total cost before tax = $80
Number of tickets purchased = 4
Price 'p' of each ticket
p = total price of ticket / number of tickets purchased
p = 80 / 4
Multiplying both sides by 4
4p = 80