The correct function that expresses the town's population after n decades is: p(n) = 8000 × 2ⁿ. So the initial population of the town is 8,000, which is consistent with the problem statement.
What is function?A function is a mathematical concept that describes the relationship between a set of inputs, called the domain, and a set of outputs, called the range.
A function assigns a unique output to each input, meaning that for a given input, there is only one possible output.
Starting with a population of 8,000, the population doubles every decade, which means it multiplies by 2.
After n decades, the population will have doubled n times, so we can express the population as 8,000 multiplied by 2 raised to the power of n:
p(n) = 8000 × 2ⁿ
This function gives us the population of the town after n decades, where n is a non-negative integer. If we substitute n=0 into the function, we get:
p(0) = 8000 × 2⁰ = 8000
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Is it possible to become smart without going to school?
Answer: it depends; if exam day, no
Step-by-step explanation:
I please need help matching the angles. I cannot seem to get it right.
The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description are;
Alternate Interior Angles; 2. ∠4 and ∠8
Consecutive Exterior Angles; 5. ∠1 and ∠6
Alternate Exterior Angles; 3. ∠1 and ∠5
Transversal; line l
Consecutive Interior Angles; 4. ∠3 and ∠4
Corresponding Angles; 1. ∠1 and ∠7
What is a transversal line?A transversal is a line that intersects two or more other lines.
The description of the relationship between the angles in the question are;
Alternate Interior Angles
Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.
Consecutive Exterior Angles
Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal
Alternate Exterior Angles
Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.
Consecutive Interior Angles
Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.
Corresponding Angles
Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.
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Can someone help me, please
Step by step please
The number of bacteria in a culture is given by the function
n(t)=90e^0.15t
(a) What is the relative rate of growth of this bacterium population?
Your answer is ---------percent
(b) What is the initial population of the culture (at t=0)?
Your answer is---------
(c) How many bacteria will the culture contain at time t=5?
Your answer is----------
(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.
(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:
relative rate of growth = (dn/dt) / n(t)
= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])
= 0.15
Therefore, the relative rate of growth is 15%.
(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):
n(0) = 90[tex]e^0.15[/tex]*0
= 90
Therefore, the initial population of the culture is 90.
(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):
n(5) = 90[tex]e^0.15[/tex]*5
= 385.97 (rounded to two decimal places)
Therefore, the culture will contain approximately 385.97 bacteria at time t=5.
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
The constant of proportionality for vanilla to chocolate ice cream is 2/3.
Constant of Proportionality for Vanilla to Chocolate Ice CreamThe constant of proportionality represents the fixed relationship between two quantities in a proportional relationship.
In this case, we are given that there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream.
To find the constant of proportionality in terms of vanilla to chocolate, we need to express this relationship as a fraction with the same units.
We can start by setting up the ratio of vanilla to chocolate ice cream, which would be 2:3.
This can then be expressed as
2/3
Therefore, the constant of proportionality for vanilla to chocolate ice cream is 2/3.
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which of the following values are needed to determine the area of the trapezoid? choose all that apply
A. 5 mm
B. 6 mm
C. 8 mm
D. 10 mm
if the mean of a symmetric distribution is 130 which of these values could be the median of the distribution
in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.
In probability and statistics, the mean and median are two measures of central tendency that are commonly used to describe a data set. The mean, also known as the arithmetic mean or average, is calculated by summing up all the values in the data set and dividing by the total number of values. The median, on the other hand, is the middle value of a data set when the values are arranged in order from lowest to highest.
For a symmetric distribution, the mean and median are the same, because the data values on one side of the mean balance out the values on the other side. In other words, if the distribution is symmetric, then the data values are evenly distributed around the mean.
In this case, if the mean of a symmetric distribution is 130, then the median must also be 130. This is because the median is the middle value of the data set, and in a symmetric distribution, the middle value is the same as the mean.
To illustrate this, consider a simple example of a symmetric distribution with the following values: 125, 130, 135, 140. The mean of this distribution is (125 + 130 + 135 + 140) / 4 = 132.5. However, the median is the middle value of the data set, which is 130. Since the distribution is symmetric, the middle value is the same as the mean.
Therefore, in a symmetric distribution, the value that could be the median of the distribution must be equal to the mean.
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Complete question:- If the mean of a symmetrical distribution is 130, which of these values could be the median of the distribution?
Use graphical methods to solve this linear programming problem.
Maximize z = 3x + 4y
subject to 2x - 3y ≤ 12
x + y ≥ 3
3x + 4y ≥ 24
x ≥ 0
y ≥ 0
What is the maximum value of z? Select the correct choice below, and if necessary, fill in the answer box to complete your choice.
A. The maximum value is ___ (Simplify answer)
B. There is no maximum.
At what point(s) does the maximum value of z occur? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The maximum value of z occurs only at the point(s) ___
(Type an ordered pair. Use a comma to separate answers as needed.)
B. The maximum value of z occurs at the points ___ and at all points on the line segment connecting them. (Type an ordered pair. Use a comma to separate answers as needed.)
C. There is no maximum value of z.
Answer:
B. There is no maximum value.
C. There is no maximum value of z.
Step-by-step explanation:
To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:
2x - 3y ≤ 12x + y ≥ 33x + 4y ≥ 24x ≥ 0y ≥ 0We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.
Rearrange the first three inequalities to isolate y:
[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex] [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]
Graph the inequalities.
If the inequality sign is ≥, draw a solid line and shade above the line.If the inequality sign is ≤, draw a solid line and shade below the line.The feasible region is the region that is shaded by all of the inequalities.
Please see the attached graph.
A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.
If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.
Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.
10. Point A is located at (4, 3). Point A is reflected
across the line y = -2, then rotated 90 degrees
clockwise about the origin. What is the final
location of A after both transformations?
If Point A is located at (4, 3). Point A is reflected. the final location of A after both transformations is (-4, -7).
What is the final location of A after both transformations?To reflect point A across the line y = -2, we need to find the point that is the same distance from the line but on the other side. The line y = -2 is a horizontal line that is 5 units above the point A (since the y-coordinate of A is 3). Therefore, the reflected point will be 5 units below the line, which gives us:
A' = (4, -7)
To rotate point A' 90 degrees clockwise about the origin, we can use the following rotation matrix:
| 0 1 |
| -1 0 |
Multiplying this matrix by the coordinates of A', we get:
| 0 1 | | 4 | | -7 |
| -1 0 | * | -7 | = | -4 |
So the final location of A after both transformations is (-4, -7).
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Pls help meee!!
Anybody!!!
Answer:
85 degrees.
Step-by-step explanation:
These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.
The average overseas trip cost 2708 per visitor. If we assume a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000? If we elect a random sample of 30 overseas trips and find the mean of the sample, what is the probability that the mean is greater than 3000
Randomly selected trip: 24.5% chance > $3000. Sample mean of 30 trips: very small chance > $3000.
Utilizing z-score recipe:
z = (x - μ)/σ
where x is the worth we're keen on, μ is the mean, and σ is the standard deviation.For the primary inquiry:
z = (3000 - 2708)/405 = 0.69
Utilizing a standard typical circulation table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 0.69 is around 0.245. Consequently, the likelihood that the expense for a haphazardly chosen trip is more than 3000 is around 0.245 or 24.5%.
For the subsequent inquiry:
The example size (n) = 30, and the standard deviation (σ) = 405/sqrt(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
Utilizing a standard typical dissemination table or number cruncher, we can track down that the likelihood of getting a z-score more prominent than 3.94 is tiny, near 0. Consequently, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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The probability that the mean is greater than 3000 is 24.5%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that, the average overseas trip cost 2708 per visitor, assuming a normal distribution with a standard deviation of 405 what is the probability that the cost for a randomly selected trip is more than 3000
z-score:
z = (x - μ)/σ
where μ is the mean, and σ is the standard deviation.
So,
z = (3000 - 2708)/405 = 0.69
Z-score 0.69 = 0.245.
Thus, the likelihood that the expense of the chosen trip is more than 3000 is around 0.245 or 24.5%.
The sample size (n) = 30, and the standard deviation (σ) = 405/√(30) = 74.02 (approx.)
z = (3000 - 2708)/74.02 = 3.94
z-score 3.94 = 0.
Thus, the likelihood that the mean expense of an example of 30 abroad excursions is more noteworthy than 3000 is tiny.
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Each side of a regular hexagon measures 20 inches. What is the exact area of the hexagon?
Answer:
1039.23 square inches
Step-by-step explanation:
a = 20 inches
[tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]
[tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]
Can someone help me please?
Answer: yes, no, yes, no
Step-by-step explanation:
PLEAS HELP!
Which best describes why it is helpful to know the slant height of a pyramid to find its surface area?
Responses
1)Knowing the slant height helps because it represents the height of the triangle that makes up the base. So, the slant height helps you to find the area of the base.
2)Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face.
3)Knowing the slant height helps because it represents the height of the triangle that makes up two of the lateral faces. So, the slant height helps you to find the area of those two lateral faces.
4)Knowing the slant height helps because it represents the height of the triangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face.
Therefore, knowing the slant height is important in calculating the lateral area of the pyramid, which is one component of the total surface area.
by the question.
Option 2 is the correct response. Knowing the slant height is helpful because it represents the height of the rectangle that makes up each lateral face of the pyramid. The lateral faces are made up of triangles and rectangles, and the slant height is used to find the height of these rectangles.
Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face. The formula for the lateral area of a pyramid involves the slant height, the perimeter of the base, and the apothem (the distance from the center of the base to the midpoint of a side). Once you know the lateral area, you can add it to the area of the base to find the total surface area of the pyramid.
The slant height of a pyramid is the height of each triangular lateral face, which is an essential component in calculating the lateral surface area of a pyramid. Knowing the slant height is used in the formula for finding the lateral area of a pyramid, which is the sum of the areas of all the triangular lateral faces. Additionally, the base area of the pyramid is also needed to find the total surface area of the pyramid. So, knowing the slant h
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Review the graph of a piecewise function.
The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
What is a piecewise function ?
A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.
The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.
On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.
On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.
At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.
The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.
Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.
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Use the standard normal table to find the z-score that corresponds to the cumulative area 0.3897. If the area is not in the table, use the entry closest to the are
between two entries, use the z-score halfway between the corresponding z-scores.
Click to view page 1 of the standard normal table) Click to view page 2 of the standard normal table.
Z= (Type an integer or decimal rounded to two decimal places as needed.)
The z-score that corresponds to a cumulative area of 0.3897 is 0.25.
What is the z-score:A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.
It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.
Here we have
The cumulative area is 0.3897
Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:
1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.
2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.
3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.
Therefore,
The z-score that corresponds to a cumulative area of 0.3897 is 0.25.
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if y varies jointly with the square of x and inversely as z, what is the change in y when both x and z are tripled
Step-by-step explanation:
y = x^2 / z now triple x and z
y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z <==== this is 3 times the original
y is tripled
During the candy sale, nick sold 100 bars,Olivia sold 94,Brandon sold 53, and Grace sold 75. (Rank from greatest to least
The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.
So in this, we have to rank the person who got most of the candy bars first and that is Nick.
After Nick Olivia has 94 candy bars so she is second in order.
Then on the third Grace had 75 candy bars.
And at the least Brandon is there with 53 candy bars.
Nick sold 100 candy bars
Olivia sold 94 candy bars
Grace sold 75 candy bars
Brandon sold 53 candy bars
Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.
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Let's say you took a sample of 445 voice-activated smart TVs. The mean rate at which these TVs need to be serviced or replaced is every 3.5 years, with a standard deviation of 0.8 years. Given a confidence level of 95%, what is the maximum error of estimate?
The maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth.
What is Standard Deviatiοn?The standard deviatiοn is a measure οf the amοunt οf variatiοn οr dispersiοn οf a set οf vaIues frοm their mean οr average. It is caIcuIated as the square rοοt οf the variance.
Tο find the maximum errοr οf estimate, we need tο use the fοrmuIa:
Maximum errοr οf estimate = z * (standard deviatiοn / √(sampIe size))
where z is the z-scοre assοciated with the given cοnfidence IeveI, standard deviatiοn is the pοpuIatiοn standard deviatiοn (0.8 years), and sampIe size is the number οf TVs sampIed (445).
At a cοnfidence IeveI οf 95%, the z-scοre is 1.96.
Substituting the vaIues in the fοrmuIa, we get:
Maximum errοr οf estimate = 1.96 * (0.8 / √(445))
= 0.092 years (rοunded tο 3 decimaI pIaces)
Therefοre, the maximum errοr οf estimate is 0.092 years οr apprοximateIy 1 mοnth. This means that we can be 95% cοnfident that the true mean rate at which the TVs need tο be serviced οr repIaced is within 1 mοnth οf the sampIe mean οf 3.5 years.
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If the diameter of a circle is
30
30 centimeters, what is the radius of the circle?
Answer:
15 centimeters
Step-by-step explanation:
radius is half of the circles diameter
i have an upcoming exam
I need help with inequalities
can someone give me problems then put the answers below?
Thanks
Please at least 5
Reward- Brainliest and 25 Tokens
Problems:
Solve for x: 2x - 5 > 9x + 2
Solve for x: 3x + 2 < 7x - 5
Solve for x: 4x + 3 < 2x - 1
Solve for x: -2x - 4 > -8x + 3
Solve for x: 5x + 1 < 2x + 7
Answers:
x < -0.7
x > 1.75
x < -1
x < 0.875
x < 1.2
Answer:
Example 1
Solve 3x − 5 ≤ 3 − x.
Solution
We start by adding both sides of the inequality by 5
3x – 5 + 5 ≤ 3 + 5 − x
3x ≤ 8 – x
Then add both sides by x.
3x + x ≤ 8 – x + x
4x ≤ 8
Finally, divide both sides of the inequality by 4 to get;
x ≤ 2
Example 2
Calculate the range of values of y, which satisfies the inequality: y − 4 < 2y + 5.
Solution
Add both sides of the inequality by 4.
y – 4 + 4 < 2y + 5 + 4
y < 2y + 9
Subtract both sides by 2y.
y – 2y < 2y – 2y + 9
Y < 9 Multiply both sides of the inequality by −1 and change the inequality symbol’s direction. y > − 9
Solving linear inequalities with subtraction
Let’s see a few examples below to understand this concept.
Example 3
Solve x + 8 > 5.
Solution
Isolate the variable x by subtracting 8 from both sides of the inequality.
x + 8 – 8 > 5 – 8 => x > −3
Therefore, x > −3.
Example 4
Solve 5x + 10 > 3x + 24.
Solution
Subtract 10 from both sides of the inequality.
5x + 10 – 10 > 3x + 24 – 10
5x > 3x + 14.
Now we subtract both sides of the inequality by 3x.
5x – 3x > 3x – 3x + 14
2x > 14
x > 7
Solving linear inequalities with multiplication
Let’s see a few examples below to understand this concept.
Example 5
Solve x/4 > 5
Solution:
Multiply both sides of an inequality by the denominator of the fraction
4(x/4) > 5 x 4
x > 20
Step-by-step explanation:
Hope this helps :3
20 points! please help please give the right answer
Answer:
260
Step-by-step explanation:
First you find the area of the triangle
1/2×base×height
1/2×20×10
=100
Then you find the area of the rectangle
A=l×b
=20×8
=160
Then you add the area of the triangle with the area of the rectangle
160+100=260
what are the different types of graphs; i know there’s constant speed, things like that. looking for a quick answer!!
A graph is made up of vertices, or points, and edges, or lines connecting those vertices.
Explain about the graphs and its types?Graphs come in a wide variety of forms in discrete mathematics.
These are a few of them:
A graph with no edges connecting all of its vertices is referred to as a null graph, sometimes known as an empty graph.A graph that has assigned weights, essentially numerical values, to each of its edges is referred to as a weighted graph.A disconnected graph is one in which not every vertex is always connected by the path of the edges.Simple graph: Any undirected graph where there is just one edge, or an edge from one vertex to itself, among each pair of vertices and there are no loops.Know more about the graph
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The correct question is-
what are the different types of graph.
Express the trig ratios as fractions in simplest terms.
cOS K =
sin L=
cos K and sin L
Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.
Trigonometric Ratios of Particular Angles: What Are They?It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.
The Pythagorean formula can be applied to the illustration to determine the length of the third side:
c²= a²+ b²
c²= 8² + √(17)²
c²= 64 + 17
c² = 81
c = 9
We can now calculate the trigonometry ratios of angles K and L:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:
cos(K) = adjacent/hypotenuse = √(17)/9
sin(L) = opposite/hypotenuse = 8/9
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Please help asap, will give brainliest if correct. What is the constant of proportionality of this table?
Show your work.
The constant of proportionality of this table is: k = 1/7.
Explain about the constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional.Proportional relationships appear as straight lines that go through the origin on a graph. The slope of a graph is equal to the constant of proportionality in the equation, and it refers to how steep a line is relative to other lines.When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.
Thus, using the x and its respective y values.
As the values are in direct proportion.
The constant of proportionality is:
k = 1/7
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What is the measure of ∠m
Answer:
26° 180 -81 - 73 = 26
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
triangle= 180
81 + 73 = 154
180 - 154= 26
Im stuck on these questions I need help
Answer:
Step-by-step explanation:
modal weight: the weight that appear most often
4.5 kg appears 3 times
6-sided polygon: even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720
therefore, angle f = 720 - 576 = 144 (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)
modal score: read this right off the graph. The score with the highest frequency is the modal score: 14 (meaning, 9 contestants got this score)
log x / 3 + log y / 3 + logz / 3
how do you condense
Using the product rule of logarithms, we can condense the expression as follows:
log(x/3 * y/3 * z/3)
= log((xyz) / 27)
So, the condensed form of the given expression is log((xyz) / 27).
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
Step-by-step explanation:
Let x be the measure of the first angle.
According to the problem, we know that:
The sum of the angles of the triangle is 180: x + y + z = 180
The sum of the second and third angles is five times the measure of the first angle: y + z = 5x
The third angle is 16 more than the second: z = y + 16
We can substitute the third equation into the second equation to get:
y + (y + 16) = 5x
Simplifying this equation, we get:
2y + 16 = 5x
We can rearrange this equation to get:
y = (5/2)x - 8
Now we can substitute this equation and the equation z = y + 16 into the first equation to get:
x + (5/2)x - 8 + (5/2)x + 8 = 180
Simplifying this equation, we get:
6x = 360
Dividing both sides by 6, we get:
x = 60
Now we can use this value of x to find y and z:
y = (5/2)x - 8 = (5/2)(60) - 8 = 58
z = y + 16 = 58 + 16 = 74
Therefore, the measures of the three angles are x = 60, y = 58, and z = 74.
Determine if the information given represents a liner,exponetial, or quadratic function and explain why.
Answer:
linear
Step-by-step explanation:
this is a linear function!
linear functions follow y = mx+b, where m is the slope and b is the y-intercept
let's write our y = mx+b equation
for each value that x increases, y increases by DOUBLE that amount. slope is y/x, so since y increases by 2 and x increases by 1, the slope is 2/1 which is 2.
the y-intercept is where the line passes the x axis, or when x is 0. in this table, it gives you your y-intercept, which is -6
your equation is y=2x+(-6); which simplified to y=2x-6
if you plug in the y and x values, you'll get the same thing. i hope this helped!
Find the average rate of change of g(x) = 3x² + 3 on the interval [ - 9, 4].
Answer:
-15
Step-by-step explanation:
You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].
Average rate of changeThe average rate of change is defined as ...
AROC(g) = (g(b) -g(a))/(b -a)
We can evaluate this directly, or we can simplify it a bit first.
AROC = ((3b² +3) -(3a² +3))/(b -a)
= (3b² -3a²)/(b -a)
= 3(b -a)(b +a)/(b -a)
= 3(b +a)
Interval [-9, 4]The AROC on the interval [a, b] = [-9, 4] is then ...
AROC = 3(4 +(-9)) = 3(-5)
AROC = -15
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Additional comment
In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.