Answers
The value of angle BCD is determined as 108⁰.
option B is the correct answer.
What is the value of angle BCD?The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc AB = m∠ACB
m∠ACB = 72⁰
The value of angle BCD is calculated as follows;
angle BCD = 180 - 72⁰ (sum of angles in a circle)
angle BCD = 108⁰
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Related Questions
2. Consider this dilation.
Pre-image
9 cm
B
Image
3 cm B
(a) Find the scale factor. Show your work. (5 points)
(2- a.) Scale factor= Image length
Pre-image length
Answers
Explanation:
The scale factor is the ratio of the image length to the pre-image length.
Scale factor = Image length / Pre-image length
In this case, the image length is 3 cm and the pre-image length is 9 cm.
Scale factor = 3 cm / 9 cm = 1/3
Direction: Read each item carefully. Encircle the best answer from the given
choices.
1. What is A U B; if A = {<, +, =, x) and B = {=, +, /, >}
A. {<, +, =, X}
C. {<, +, =, x, /, >}
B. (=, +, /, >}
D. {<, +, =, x, =, +, /, >}
2. What is An M; if A = {1, 2, 4) and M = {2, 3, 5}?
A. {1}
C. (3)
B. (2)
D. (4)
3. What is Bn C; if B = {C, O, U, G, H) and C = {F, E, V, E, R)
C. (F, E, V, E, R}
A. {}
B. (C,O,U,G,H}
D. (C, O, U, G, H, F, E, V, E, R}
4. What is M - J; if M = {soap, alcohol, sanitizer, mask) and J = {alcohol,
sanitizer, mask, gloves}?
A. {alcohol)
C. {mask}
B. (gloves)
D. (soap}
5. What is complement of set A if U = {Frontliners, sacrifice, their, lives, to,
combat, coronavirus) and B = {Frontliners, sacrifice, their, lives)
A. (Frontliners)
C. (to, combat, coronavirus}
Answers
1) The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) The value of A ∩ M is,
A ∩ B = {2}
3) The value of B ∩ C is,
B ∩ C = { }
4) The value of M - J is,
M - J = {soap}
5) The complement of set A is,
A' = (to, combat, coronavirus}
Now, WE can simplify as;
1) We have;
A = {<, +, =, x) and B = {=, +, /, >}
Hence, We get;
The value of A ∪ B is,
A ∪ B = {<, +, =, /, >, x }
2) Given that,
A = {1, 2, 4) and M = {2, 3, 5}
Hence, The value of A ∩ M is,
A ∩ B = {2}
3) Given that;
B = {C, O, U, G, H) and C = {F, E, V, E, R)
Hence, The value of B ∩ C is,
B ∩ C = { }
4) Given that;
M = {soap, alcohol, sanitizer, mask) and J = {alcohol, sanitizer, mask, gloves}
Hence, The value of M - J is,
M - J = {soap}
5) Given that;
U = {Frontliners, sacrifice, their, lives, to, combat, coronavirus) and A = {Frontliners, sacrifice, their, lives)
Hence The complement of set A is,
A' = U - A
A' = (to, combat, coronavirus}
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which of the following exponential regression equations best fits the data shown below?
Answers
The exponential regression equation that best fits the data is y = 2^x.
To determine which exponential regression equation best fits the given data points (2, 4), (3, 8), (4, 16), and (5, 32), let's analyze the options for regression equations:
Option 1: y = 2^x
Option 2: y = 3^x
Option 3: y = 4^x
Option 4: y = 5^x
To find the best fit, we need to compare the predicted y-values from each equation with the actual y-values of the given data points.
The equation that produces the least amount of error or the closest predicted y-values to the actual ones will be the best fit.
Let's calculate the predicted y-values for each option using the given x-values:
Option 1: [tex]y = 2^2, 2^3, 2^4, 2^5 = 4, 8, 16, 32[/tex]
Option 2:[tex]y = 3^2, 3^3, 3^4, 3^5 = 9, 27, 81, 243[/tex]
Option 3:[tex]y = 4^2, 4^3, 4^4, 4^5 = 16, 64, 256, 1024[/tex]
Option 4:[tex]y = 5^2, 5^3, 5^4, 5^5 = 25, 125, 625, 3125[/tex]
By comparing the predicted y-values with the actual y-values of the data points, we can determine which option provides the closest fit.
Based on the given data points, we can observe that the predicted y-values from Option [tex]1 (y = 2^x)[/tex] match the actual y-values most closely.
The predicted values for Option 1 are 4, 8, 16, and 32, which exactly match the given data points.
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The complete question may be like: Consider the following data points: (2, 4), (3, 8), (4, 16), (5, 32). We need to determine which exponential regression equation best fits this data. Please provide the options for the regression equations so that I can assist you in finding the best fit.
What is the value of x
Enter your answer in the box
Answers
Answer:
x = 8 units
Step-by-step explanation:
Because this is a right triangle, we can find x using the Pythagorean theorem, which is given by:
a^2 + b^2 = c^2, where
a and b are the shorter sides called legs,and c is the longest side called the hypotenuse (always opposite the right angle).In the triangle, the 6 unit side and the x unit sides are the legs while the 10 unit side is the hypotenuse.
Thus, we can solve for x by plugging in 6 for a and 10 for c in the theorem and solving for a (aka x, simply a in the theorem):
a^2 + 6^2 = 10^2
a^2 + 36 = 100
a^2 = 64
a = 8
x = 8
Thus, x is 8 units.
Use the function f(x) to answer the questions:
f(x) = 2x2 − 5x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answers
The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.
Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x^2 - 5x + 3 = 0
To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.
2x^2 - 3x - 2x + 3 = 0
x(2x - 3) - 1(2x - 3) = 0
(2x - 3)(x - 1) = 0
Setting each factor equal to zero, we get:
2x - 3 = 0 --> x = 3/2
x - 1 = 0 --> x = 1
Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.
Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.
To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.
x = -(-5) / (2*2) = 5/4
Substituting this value of x back into the equation, we can find the y-coordinate:
f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8
Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.
Part C: To graph f(x), we can use the information obtained in Part A and Part B.
- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.
- The vertex is at (5/4, 3/8). This is the minimum point of the graph.
We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.
Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.
By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).
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write an explicit formula for an the nth term of the sequence 40, 33, 26
Answers
Answer:
[tex]a_{n}[/tex] = - 7n + 47
Step-by-step explanation:
there is a common difference between consecutive terms , that is
33 - 40 = 26 - 33 = - 7
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 40 and d = - 7 , then
[tex]a_{n}[/tex] = 40 - 7(n - 1) = 40 - 7n + 7 = - 7n + 47
Use the space below to show your work.
45 points PLEASE HELP
Answers
The total number of each type of ball:
Football: Given as 8
Basketball: 18
Baseball: 40
Softball: 15
For basketball:
2 + 2(8) = 18
First, we evaluate the expression inside the parentheses: 2(8) = 16
Then, we add 2 to the result: 16 + 2 = 18
So, the total number of basketballs is 18.
For baseball:
5(8) = 40
We simply multiply 5 by 8 to get the total number of baseballs, which is 40.
For softball:
6 + 1/2(18) = 24
First, we evaluate the expression inside the parentheses: 1/2(18) = 9
Then, we add 6 to the result: 9 + 6 = 15
So, the total number of softballs is 15.
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1-56.
The owner of Universal Widgets has two teams of employees and
wants to know which team is working the "best." The assistant
manager gathered data for the number of widgets made per team
member on various days. He presented the data to the owner as
two boxplots, shown at right. The owner is confused.
a. Help the owner decide which team is working the "best"
by comparing center, shape, spread, and outliers.
b. Which team had a smaller standard deviation? Explain.
200
150
100
30
Team I
Answers
Center: We can compare the medians of the two boxplots to get an idea of the center. From the boxplots, we see that the median of Team I is around 110 widgets per team member, while the median of Team II is around 90 widgets per team member. This suggests that Team I is working better in terms of productivity.
Shape: We can compare the shapes of the two boxplots to see if there are any differences in the distributions. From the boxplots, we see that both teams have roughly symmetric distributions, with no significant skewness.
Spread: We can compare the interquartile ranges (IQRs) of the two boxplots to get an idea of the spread. From the boxplots, we see that the IQR of Team I is around 30 widgets per team member, while the IQR of Team II is around 40 widgets per team member. This suggests that Team I has a smaller spread and is more consistent in their productivity.
Outliers: We can compare the number of outliers in the two boxplots to see if there are any extreme values. From the boxplots, we see that both teams have a similar number of outliers, with a few points outside the whiskers.
Based on these comparisons, we can conclude that Team I is working better than Team II in terms ofproductivity. Team I has a higher median, a smaller spread, and a similar number of outliers compared to Team II.
b. To determine which team had a smaller standard deviation, we need to calculate the standard deviation for each team. However, the boxplot only gives us information about the quartiles, the median, and the outliers, and not the individual data points. Therefore, we cannot directly calculate the standard deviation from the boxplot.
However, we can make an inference based on the spread of the boxplots. We saw in part (a) that the IQR of Team I is smaller than the IQR of Team II. Since the IQR is a measure of spread that includes the middle 50% of the data, we can infer that the standard deviation of Team I is likely smaller than the standard deviation of Team II. This is because a smaller IQR suggests that the data is more tightly clustered around the median, which would result in a smaller standard deviation.
Therefore, based on the boxplots, we can infer that Team I had a smaller standard deviation than Team II.
helpppppppppppppppppoooo
Answers
The probability that a given student said math was their favorite subject was 3.44
The mathematical notion of probability measures the possibility of an event happening. A number between 0 and 1 is used to indicate it, with 0 denoting impossibility (the event won't happen) and 1 denoting certainty (the event will unquestionably happen). In probability theory, the probability of an event is determined based on a set of assumptions or information available. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Here, the total outcome is 299 and favorable outcome is 87.
Hence, the probability is 299/87 = 3.44
Therefore, probability that a given student said math was their favorite subject was 3.44.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The calculated measure of the angle 1 is 43 degrees
How to determine the measure of the angle 1From the question, we have the following parameters that can be used in our computation:
The circle
Also, we have
The line AB tangent to the circle
This means that
Angle 1 = 1/2 * the arc subtended by the line
So, we have
Angle 1 = 1/2 * 86
Evaluate
Angle 1 = 43
Hence, the measure of the angle 1 is 43 degrees
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The average fourth grader is about three times as tall as the average newborn baby. If babies are on average 45cm 7mm when they are born, What is the height of the average fourth grader?
Answers
The height of the average fourth grader is 137cm 1mm. This height can be determined by multiplying 3 by the average height of a newborn baby.
Given information,
The average height of babies = 45 cm 7mm
45 cm 7 mm is equivalent to 45.7 cm (since there are 10 millimeters in a centimeter).
Let the height of a fourth grader be x.
According to the question,
The height of a fourth grader (x) = 3 × the average height of a newborn baby
The height of a fourth grader (x) = 3 × 45.7
The height of a fourth grader (x)= 137.1 = 137cm 1mm
Therefore, the height of a fourth grader is 137cm 1mm.
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Pedro observed what customers ordered at his ice cream shop and found the following probabilities:
�
(
vanilla
)
=
0.3
�
(
sundae
)
=
0.2
�
(
vanilla and sundae
)
=
0.15
P(vanilla)=0.3
P(sundae)=0.2
P(vanilla and sundae)=0.15
Find the probability that a customer ordered vanilla ice cream given they ordered a sundae.
Answers
The probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
To find the probability that a customer ordered vanilla ice cream given they ordered a sundae, we can use the concept of conditional probability.
The conditional probability of an event A given event B is denoted as P(A|B) and is calculated as the probability of both events A and B occurring divided by the probability of event B.
In this case, we want to find P(vanilla|sundae), which represents the probability of a customer ordering vanilla ice cream given that they ordered a sundae.
Using the given probabilities:
P(vanilla) = 0.3
P(sundae) = 0.2
P(vanilla and sundae) = 0.15
The probability of a customer ordering a sundae is the denominator for the conditional probability. Therefore, P(sundae) will be the denominator.
P(vanilla|sundae) = P(vanilla and sundae) / P(sundae)
Substituting the given values:
P(vanilla|sundae) = 0.15 / 0.2
Now we can simplify:
P(vanilla|sundae) = 0.15 / 0.2
= 0.75
Therefore, the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75, or 75%.
In conclusion, based on the given probabilities, there is a 75% chance that a customer who ordered a sundae also ordered vanilla ice cream.
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Using a calculator or statistical software, find the linear regression line for the data in the table below.
Using the regression with the values rounded to the nearest hundredth, find the value of y at x=7. Round your answer to the nearest hundredth if necessary.
x y
0 2.83
1 3.33
2 6.99
3 8.01
4 7.62
5 7.66
Answers
Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.
To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.
Using the provided data, the linear regression line equation is:
[tex]\[ y = 1.3642x + 3.2324 \][/tex]
To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:
[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]
Simplifying the equation, we get:
[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]
In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.
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find the surface area
Answers
400Answer:
Step-by-step explanation:
May I please get a little help with this question? Thank you so much.
Answers
The y-intercept of the function is (0, c)
The coefficients b determine the horizontal shift of the parabola compared to the parent function
If a is negative, the parabola opens downward
The y-intercept of the function is (0, c).
This means that when x = 0, the y-value is equal to c.
The constant term c represents the y-coordinate of the point where the parabola intersects the y-axis.
The coefficient b determines the horizontal shift of the parabola compared to the parent function.
The value of b affects the position of the vertex and determines if the parabola is shifted to the left or right.
A positive value of b shifts the parabola to the left, while a negative value of b shifts it to the right.
If a is negative, the parabola opens downward.
The coefficient a determines the shape of the parabola.
If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward. The sign of a determines the direction in which the parabola faces.
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Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answers
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
625 x 33/75 = 275
100 Points! Geometry question. Photo attached. Determine whether each pair or figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning. Please show as much work as possible. Thank you!
Answers
The figures are similar because the ratio of segment BC to segment EF is equal to the of segment AB to segment DE.
The scale factor is equal to 3/2.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following:
Scale factor = BC/EF = AB/DE
Scale factor = 9/6 = 6/4
Scale factor = 3/2 = 3/2 (similar)
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The equation of the circle is (x - 2)² + (y - 3)² = 36
Determining the equation of the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (2, 3)
Radius, r = 6 units
The equation of the circle is represented as
(x - a)² + (y - b)² = r²
So, we have
(x - 2)² + (y - 3)² = 6²
Evaluate
(x - 2)² + (y - 3)² = 36
Hence, the equation is (x - 2)² + (y - 3)² = 36
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please answer asap!!!!!!!!
Answers
hope this helps :)
Which statement correctly explains the association of the scatter plot? Since the Y values increase as the X values increase the Scatter plot shows a positive association. Sense to Weibo use decrease as the X values increase the scatter plot shows a positive association.
Answers
The correct statement regarding the association in the scatter plot is given as follows:
Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.
How to classify the association between variables?There can either be a positive association between variables or a negative association between variables, as follows:
Positive association happens when both variables have the same behavior, that is, as one increases the other increases, and as one decreases the other also decreases.Negative association happens when the variables have opposite behavior, as one variable is increasing the other is decreasing, or as one variable is decreasing, the other is increasing.In this problem, we have a decreasing scatter plot, hence there is a negative association between the variables.
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Which of the following is the result of expanding ____
A.8.5
b.15.5
C.32
D.60
Answers
The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.
Which is the value of the summatory?Here we have the summatory:
[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]
So we just need to add the 5 terms (between n = 1 and n = 5)
So we will get the sum:
S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]
S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]
S = [0.5 + 1 + 2 + 4 +8]
S = 15.5
So the correct option is the second one.
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HELPP PLEASEE I REALLY NEEED THIS 7 cm
What is the volume of the figure?
3 cm
5 cm
Answers
7 x 5 x 3
= 105cm^3
Answer:
Volume = 105 cm³
Step-by-step explanation:
Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)
Volume = 7 × 5 × 3
Volume = 35 × 3
Volume = 105 cm³
23 POINTS PLS HELPPP!!!
Use the Law of Sines to find the length of side b in ABC. Round to the nearest tenth. Show your work.
Consider
ABC.
B
28°
112°
37
Answers
Angle C of the triangle measures 40°.
Side AC = 18.84
Side AB= 25.79
Given triangle,
∠A = 112°
∠B = 28°
BC = 37
Now,
Sum of all the interior angles of triangle is 180.
So,
∠A + ∠B +∠C = 180°
112° + 28° + ∠C = 180°
∠C = 40°
Now,
According to sine rule,
Ratio of side length to the sine of the opposite angle is equal.
Thus,
a/SinA = b/SinB = c/SinC
Let,
BC = a
AC = b
AB = c
So,
a/Sin112 = b/Sin28 = c/Sin40
37/0.921 = b/0.469 = C/0.642
Solving,
AB = c = 25.79
AC = b = 18.84
Thus with the properties of triangle side length and angles can be calculated.
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subtract 8.263 from 13.48.
Answers
Answer:
13.48 - 8.263 = 5.217
Answer:5.217
Step-by-step explanation: caculate it
Write the quadratic equation in standard form that corresponds to the graph shown below.
Answers
The quadratic equation shown in the graph is:
y = x² + 2x - 8
How to write the quadratic equation?Here we want to find the graph of the given quadratic equation, where we only know the zeros of it.
Remember that if a quadratic equation has the zeros:
x = a
x = b
Then we can write it as:
y = (x - a)*(x - b)
Here the zeros are:
x = -4
x = 2
Then we can write:
y = (x + 4)*(x - 2)
Expanding that we will get the standard form:
y = x² + 4x - 2x - 8
y = x² + 2x - 8
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Pls help me in math!!!!!!!!!!
Answers
In the given triangle value of b is,
⇒ b = 16
We have to given that,
A triangle with three angles (b + 20), (b + 32) and 6b.
Now, WE know that;
Sum of all interior angles of triangle is 180 degree.
Hence., We can formulate;
⇒ (b + 20) + (b + 32) + 6b = 180
Solve for b,
⇒ 8b + 52 = 180
⇒ 8b = 180 - 52
⇒ 8b = 128
⇒ b = 128/8
⇒ b = 16
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The area of the parallelogram of triangle would be listed below as follows:
19A.) = 336mm²
19B.) = 416in²
How to calculate the area of the parallel of triangle?To calculate the area of the parallelogram of triangle, the formula for the area of the parallelogram should be used and it is given as follows:
Area of parallelogram = base×height
For A.)
Base = 18+10 = 28mm
height = 12mm
Area = 28×12 = 336mm²
For B.)
Base = 26in
Height = 16(using the sine rule)
Area = 26×16 = 416in²
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6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answers
Answer:
65/100 that is the answer to this question
HELP PLEASEE PLEASE I NEED TO PASS THIS LESSON
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The function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
The given table is
Days After Number of
Release Date Games sold
0 1024
1 512
2 256
3 128
Here, the common ratio = 512/1024
= 1/2
The formula to find nth term of the geometric sequence is aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.
Here, [tex]G(t)= 1024(0.5)^{t-1[/tex]
Therefore, the function [tex]G(t)= 1024(0.5)^{t-1[/tex] models the number of computer games sold where t is the number of days since the release date and G(t) is the number of computer games sold.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
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Answer: Area = = 38.5 - Perimeter - 29.6819.
Step-by-step explanation:
To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.
Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the lengths of LM, MN, and NL:
LM = √((-2 - 5)^2 + (-4 - 5)^2)
= √((-7)^2 + (-9)^2)
= √(49 + 81)
= √130
MN = √((5 - (-2))^2 + (-6 - (-4))^2)
= √((7)^2 + (-2)^2)
= √(49 + 4)
= √53
NL = √((5 - 5)^2 + (-6 - 5)^2)
= √((0)^2 + (-11)^2)
= √(0 + 121)
= √121
= 11
The perimeter of the triangle is the sum of these three sides:
Perimeter = LM + MN + NL
= √130 + √53 + 11 = 29.6819
Area:
To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:
Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|
= 0.5 * |5(2) + (-2)(-11) + 5(9)|
= 0.5 * |10 + 22 + 45|
= 0.5 * |77|
= 38.5
Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.