The twelve thrones of Olympus are occupied by the major gods and goddesses in Greek mythology, including Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and Dionysus. However, there are two gods who are not given a place on the throne - Hades and Hestia.
Hades, the god of the underworld, is not included in the twelve thrones because he rules over the dead in the underworld. As a result, he does not need a place on Olympus. Hestia, the goddess of the hearth, voluntarily gave up her seat to Dionysus, as she preferred to live a peaceful and uneventful life on earth. She is regarded as one of the "lesser" gods but still holds great importance in Greek mythology, as she is responsible for the protection of the home and family.
Overall, while the 14 gods and goddesses play important roles in Greek mythology, only twelve are given seats on Olympus. Hades and Hestia have their own roles to play and, for different reasons, do not have a place on the thrones.
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what is the slope-intercept form of the equation y ≥ -1/3x+1
Answer:
Step-by-step explanation:
Nothing can further be done to this equation so it would stay the same!
500 to the square root of 5?
If events A and B are independent, what must be done to find the probability of event A AND B?
A. Multiply the probability of A and the probability of B.
B. Divide the probability of A and the probability of B.
C. Subtract the probability of A and the probability of B.
D. Add the probabilities of A and the probability of B.
The correct answer is A. When events A and B are independent, it means that the occurrence of one event does not affect the probability of the other event occurring.
In other words, the probability of A occurring does not depend on whether B occurs or not, and vice versa.
To find the probability of both A and B occurring, we need to use the multiplication rule of probability. The multiplication rule states that the probability of two independent events occurring together is equal to the product of their individual probabilities. That is, P(A and B) = P(A) × P(B).
For example, if the probability of event A occurring is 0.3 and the probability of event B occurring is 0.4, then the probability of both events occurring together is:
P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12
Therefore, to find the probability of event A AND B when events A and B are independent, we simply multiply the probability of A by the probability of B.
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The value of c in the perfect square trinomial x^2 + 10x + c can be determined by examining the entries in the 6-column table.
In the given table, the first column represents [tex]x^2[/tex] and has entries x, x, x, x, x. The second column represents x and has missing entries, which we need to determine. The third, fourth, fifth, and sixth columns also have missing entries.
To find the value of c in the perfect square trinomial [tex]x^2[/tex] + 10x + c, we need to complete the table and observe the entries in the second column. Since the first column represents [tex]x^2[/tex], we can see that each entry is [tex]x^2[/tex]. Thus, the missing entries in the second column are x, x, x, x, x, respectively.
The perfect square trinomial [tex]x^2[/tex] + 10x + c can be factored as [tex](x + 5)^2[/tex], which expands to [tex]x^2[/tex] + 10x + 25. Comparing this with the given expression, we can conclude that c = 25.
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Help me solve this please
The segment lengths on the similar triangles are given as follows:
SU = 7.YZ = 3.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The proportional relationship for the side lengths in this triangle is given as follows:
SU/5.25 = 4/3 = 5/YZ
Hence the length SU is obtained as follows:
SU/5.25 = 4/3
SU = 5.25 x 4/3
SU = 7.
The length YZ is obtained as follows:
5/3 = 5/YZ
YZ = 5 x 3/5
YZ = 3.
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Solve for j.
-41j+ 14j-28j - 10 = 45
Answer:
j = -1
Step-by-step explanation:
add the 10 to right side
-41j + 14 j - 28j = 55
-41j+ 14j -28j = -55j
-55j = 55
j = -1
Please help with this math equation.
The roots of the function f ( x ) are x = 1 and x = 3
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x⁴ - 13x³ + 38x² - 23x - 3
On simplifying , we get
The possible factors of the constant term (-3) are ±1 and ±3, while the possible factors of the leading coefficient (1) are ±1.
Now, we can test these factors by substituting them into the function and checking if the result is zero:
f(1) = (1)⁴ - 13(1)³ + 38(1)² - 23(1) - 3 = 1 - 13 + 38 - 23 - 3 = 0
f(-1) = (-1)⁴ - 13(-1)³ + 38(-1)² - 23(-1) - 3 = 1 + 13 + 38 + 23 - 3 = 72
f(3) = (3)⁴ - 13(3)³ + 38(3)² - 23(3) - 3 = 81 - 351 + 342 - 69 - 3 = 0
f(-3) = (-3)⁴ - 13(-3)³ + 38(-3)² - 23(-3) - 3 = 81 + 351 + 342 + 69 - 3 = 840
From the above calculations, we can see that f(1) = f(3) = 0. This means that x = 1 and x = 3 are roots of the polynomial function
Hence , the function is solved and x = 1 and x = 3
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someone help please and asap
Answer:
8.66 m
Step-by-step explanation:
using Sin, Cos, Tan
sin 60° = AB/AC
sin 60° = AB/ 10
AB = sin 60° × 10
AB = 8.660254038
Therefore AB = 8.66 m
numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are group of answer choices parameters. probabilistic input. controllable input. events.
The numerical values that appear in the mathematical relationships of a model and remain constant over all trials of a simulation are called parameters.
Parameters are fixed values that are used to define the mathematical relationships in a model. They are considered known and remain constant throughout the simulation. Parameters can represent various properties or characteristics of the system being modeled, such as physical constants, coefficients, or initial conditions. They provide a way to define the behavior and constraints of the model. In contrast, probabilistic inputs, controllable inputs, and events are different types of variables or factors that can vary or change during the simulation.
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Let x and y be rational and irrational numbers, respectively. Is x+y necessarily an irrational number? Give an example in support of your answer.
Answer:
Step-by-step explanation:
yes it will be always irrational
EG :
1) 2 , root(3) , 2 + root(3)
2) 4 , root(8) = 2root(2) , 4 + 2root(3)
etc
If y is a real number greater than 1, which of the following must be true for the value of y-2?
The value of y-2 is less than 0.
The value of y is between 0 and 1.
The value of y-2 is 1.
The value of y-2 is greater than 1.
Answer:
The answer would be
y-2 greater than one
Step-by-step explanation:
y>1
y=2,3,4,5.....
y-2=0,1,2,3...
There are 90 girls and 60 boys is the sixth grade at a middle school. Of these students, 9 girls and 3 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed?
Group of answer choices
Remember that percentage is just a glorified division problem with the number of things that we want the percentage of on the top and the total on the bottom.
This question is asking about the percentage of left handed sixth graders. So we need to know (1) how many left handed sixth graders there are and (2) how many total sixth graders there are.
The problem states that there are 9 girls and 3 boys that are left handed. To get the total, we add.
9 girls + 3 boys = 12 students that are left handed.
The problem also states that there are 90 girls and 60 boys total in the sixth grade. To get this total, we also add.
90 girls + 60 boys = 150 students
Now, we can calculate the percentage.
We take the 12 lefties and divide that by the 150 total sixth graders. When we get a decimal, we multiply by 100 to get the percentage.
So
[tex]\sf \dfrac{12}{150} = 0.08[/tex]
[tex]\sf 0.08 \times 100 = \boxed{\bold{8\%}}[/tex]
Hence, the percentage of the sixth graders at this middle school write left-handed is 8%.
the variance and standard deviation are the most widely used measures of central location.
T/F
False , the variance and standard deviation are not measures of central location
Given data ,
The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset
Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset
The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.
In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.
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please help me ill give brainliest
The surface area of the triangular prism is 684.15 m².
How to find the surface area of a triangular prism?The prism above is a triangular base prism. The surface area of the triangular base prims can be found as follows:
surface area of the prism = (a + b + c)l + bh
where
a = a, b and c are the side of the trianglel = height of the prismb = base of the triangleh = height of the triangleTherefore,
surface area of the prism = (9 + 13 + 15.81)15 + 13 × 9
surface area of the prism = (37.81)15 + 117
surface area of the prism =567.15 + 117
surface area of the prism = 684.15 m²
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11% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 people are 65 or older. The probability that at least 3 are 65 or older is
The probability that at least 3 out of 25 people selected at random are 65 or older can be found using binomial probability.
The answer to the problem is 0.583, or 58.3% rounded to one decimal place. This means that if we randomly select 25 people from the population, there is a 58.3% chance that at least 3 of them will be 65 or older.
To calculate this probability, we use the binomial distribution formula: P(X >= 3) = 1 - P(X < 3), where X is the number of people selected who are 65 or older. Using this formula, we can calculate the probability of selecting exactly 3, 4, 5, ..., 25 people who are 65 or older and sum them up. Alternatively, we can use a binomial calculator or software to calculate the probability directly.
The binomial probability formula is P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the sample size (25), k is the number of successes (i.e., people who are 65 or older), p is the probability of success (0.11), and C(n, k) is the binomial coefficient (i.e., the number of ways to select k items out of n). We need to sum up the probabilities for k = 3, 4, 5, ..., 25 to get the probability of at least 3 successes. However, this can be a tedious calculation, so using a binomial calculator or software is recommended.
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make a mapping diagram for the relation (-2 -6) (0 3) (1 -5) (5 0)
Mapping refers to the process of associating or pairing elements from one set to another set.
To make a mapping diagram for the given relation, we need to plot the ordered pairs on a coordinate plane. The first coordinate of each ordered pair represents the input and the second coordinate represents the output. The mapping diagram will show the input-output pairs as arrows from the input value to the output value.
The mapping diagram for the relation (-2, -6), (0, 3), (1, -5), and (5, 0) is:
-2 ---> -6
|
|
v
0 ---> 3
|
|
v
1 ---> -5
|
|
v
5 ---> 0
In the above diagram, each arrow represents an input-output pair, starting from the input value on the left and ending at the output value on the right.
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please help me!!!
Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB?
y – 4 = 3x
y – 2 = 3(x – 6)
y + 4 = x
y + 6 = x - 2
Step-by-step explanation:
Therefore, the equation that represents line AB is y + 4 = x, which is the fourth option: y + 4 = x - 2.
What multiplies to 200 and adds to 45
Answer:
To find two numbers that multiply to 200 and add to 45, we can use a trial and error method or we can use algebraic equations. Here's how to do it using the algebraic method:
Let x and y be the two numbers we're looking for. Then we have:
xy = 200 (equation 1)
x + y = 45 (equation 2)
We can solve for one of the variables in terms of the other in equation 2:
y = 45 - x
Substitute this expression for y into equation 1:
x(45 - x) = 200
Simplify and solve for x:
45x - x^2 = 200
x^2 - 45x + 200 = 0
This is a quadratic equation that we can solve using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -45, and c = 200. Substituting these values, we get:
x = (45 ± sqrt(45^2 - 4(1)(200))) / 2(1)
x = (45 ± sqrt(2025 - 800)) / 2
x = (45 ± sqrt(1225)) / 2
x = (45 ± 35) / 2
We get two possible values of x:
x = 10 or x = 35
Substitute these values of x into equation 2 to get the corresponding values of y:
y = 45 - x
If x = 10, then y = 45 - 10 = 35
If x = 35, then y = 45 - 35 = 10
Therefore, the two numbers that multiply to 200 and add to 45 are 10 and 35.
Step-by-step explanation:
Out of 144 passengers travelling in a double- decker bus, 5/12
of the passengers are sitting on the lower
deck and the rest of the passengers are on the upper deck. If 1
4
of the passengers are standing on the
upper deck, then how many passengers are sitting there?
Answer:
70
Step-by-step explanation:
5/12 X 144 = 720/12 = 60 passengers are sitting on lower.
rest of passengers = 144 - 60 = 84 are on upper.
14 on upper are standing on upper, then 84 - 14 = 70 are sitting there (on upper).
HELP ASAP Which points are on the graph of the function rule ƒ(x) = 10 – 4x?
a. (18, –2), (10, 0), (2, 2)
b. ( –18, 2), ( –10, 0), ( –2, –2)
c.(–2, 18), (0, 10), (2, 2)
d. (2, –18), (0, –10), ( –2, –2)
If f(x) = 10 - 4x...
f(18) = 10 - 4(18) = 10 - 72 = -62 ≠ -2
This rules out answer a, since (18,-62) would be a point, not (18,-2).
f(-18) = 10 - 4(-18) = 10 + 72 = 82 ≠ -2
This rules out answer b, since (-18,82) would be a point, not (-18,2).
f(-2) = 10 - 4(-2) = 10 + 8 = 18
Answer c seems to be ok so far, since (-2,18) is a point in answer c.
f(2) = 10 - 4(2) = 10 - 8 = 2 ≠ =18
This rules out answer d, since (2,2) would be a point, not (2,-18).
The only answer that wasn't ruled out by check the first point in each answer is answer C.
The question in the pic below..please help will give brainlist who gets it right..
All the given options represents a logarithmic shape for the graph.
Given data ,
a) Milk production by the cows as their feed is increased
b) Grade improvement by their hours of study.
c) Plant growth by a number of daylight hours.
d) Monthly sales for a bakery over a year.
e) Housing prices in a neighbourhood.
The term "logarithmic shape of a graph" refers to a graph that follows a logarithmic relationship. In a logarithmic graph, the relationship between the variables is expressed using logarithmic functions.
A logarithmic function is the inverse of an exponential function. It represents the relationship between the logarithm of a number and its base. In a logarithmic graph, the x-axis represents the input values, and the y-axis represents the corresponding logarithmic values.
Hence , he shape of a logarithmic graph depends on the base of the logarithmic function.
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Dwayne has collected data on the number of occupants of cars travelling on the road past his house for the past week. Based on this data, he has constructed a probability model for the number of occupants of a randomly-selected car on his street. Which of the following could be his model?
Chart..
Prob.
0.5
0.25
0.15
0.06
0.04
Based on the given chart, Dwayne has constructed a probability model for the number of occupants of a randomly-selected car on his street. The chart shows the probabilities of different numbers of occupants in a car. These probabilities add up to 1, as the number of occupants in a car can only be one of the given possibilities.
The chart shows that the most likely number of occupants in a car is 1, with a probability of 0.5. This means that half of the cars on the street have only one person in them. The second most likely possibility is 2 occupants in a car, with a probability of 0.25. This means that one-quarter of the cars have two people in them. The probabilities for 3, 4, and 5 occupants are progressively lower, with probabilities of 0.15, 0.06, and 0.04, respectively.
Therefore, Dwayne's model is a discrete probability distribution, where the possible outcomes are the number of occupants in a car, and the probabilities of each outcome are given by the chart. This model is based on the data that Dwayne collected on the number of occupants of cars travelling on the road past his house for the past week. The model can be used to predict the likelihood of different numbers of occupants in a car on Dwayne's street.
Dwayne's probability model for the number of occupants in a randomly-selected car on his street can be represented by the given chart. The chart shows the probabilities for different numbers of occupants:
1. Probability of 1 occupant: 0.5 (50%)
2. Probability of 2 occupants: 0.25 (25%)
3. Probability of 3 occupants: 0.15 (15%)
4. Probability of 4 occupants: 0.06 (6%)
5. Probability of 5 occupants: 0.04 (4%)
To confirm that this is a valid probability model, we need to ensure that the sum of all probabilities is equal to 1:
0.5 + 0.25 + 0.15 + 0.06 + 0.04 = 1
Since the sum is 1, the chart represents a valid probability model for the number of occupants in a car on Dwayne's street. This model can be used to make predictions about the number of occupants in future cars passing by Dwayne's house, based on the data he collected during the past week.
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Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double the height. . . . Question content area top right
Part 1
6 in. 5 in. (This figure is not to scale. )
Question content area bottom
Part 1
The volume of the cylinder is enter your response here in. 3. (Type an exact answer in terms of π. )
The volume of the cylinder with the same radius and double the height is 300π cubic inches.
Given that the cylinder has a radius of 5 inches and a height of 6 inches, we can find its volume as:
V = π(5 in)²(6 in)
V = 150π cubic inches
Therefore, the volume of the cylinder is 150π cubic inches.
If we double the height of the cylinder, the new height becomes 2(6 in) = 12 in.
The radius remains the same at 5 inches.
The volume of the new cylinder can be found using the same formula:
V = πr²h
V = π(5 in)²(12 in)
V = 300π cubic inches
Therefore, the volume of the cylinder with the same radius and double the height is 300π cubic inches.
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The base of a right triangular prism is right angle triangle if the height of the prism is 12 cm and the longer side of the base is 5 cm while the shortest side is 3 cm then find A)The lateral surface area B)The total surface area
Answer:
A) 144 cm²;B) 156 cm².-------------------------------
The base is a right triangle with shortest side of 3 cm and hypotenuse of 5 cm.
Then, according to Pythagorean Theorem, its longer leg is:
[tex]\sqrt{5^2-3^2} =\sqrt{25-9} =\sqrt{16}=4 \cm[/tex] Part AFind the lateral surface area:
LSR = Ph = (3 + 4 + 5)*12 = 12*12 = 144 cm²Part BFind the area of two triangle bases:
A = 2*(1/2)bh = 3*4 = 12 cm²Find the total surface area by adding up base area and lateral surface area:
TSA = 12 + 144 = 156 cm²The percentage of alcohol in the cough syrup was measured in 101 randomly selected samples. The sample standard deviation is s = 0.15 Construct a 90% two-sided confidence interval for o Round your answers to three decimal places (e.g. 98.765)
We can be 90% confident that the population standard deviation of alcohol in cough syrup falls between 0.017 and 0.027. Rounded to three decimal places, the confidence interval is [0.017, 0.027].
To construct a 90% two-sided confidence interval for the population standard deviation of alcohol in cough syrup, we can use the formula:
CI = [(n-1)s^2 / χ^2(α/2, n-1), (n-1)s^2 / χ^2(1-α/2, n-1)]
Where CI is the confidence interval, n is the sample size (101 in this case), s is the sample standard deviation (0.15), χ^2 is the chi-squared distribution, and α is the significance level (0.1 for a 90% confidence interval).
Using a chi-squared distribution table or calculator, we can find that χ^2(0.05, 100) = 124.34 and χ^2(0.95, 100) = 77.93.
Plugging in the values, we get:
CI = [(100)(0.15^2) / 124.34, (100)(0.15^2) / 77.93]
CI = [0.017, 0.027]
Therefore, we can be 90% confident that the population standard deviation of alcohol in cough syrup falls between 0.017 and 0.027. Rounded to three decimal places, the confidence interval is [0.017, 0.027].
The percentage of alcohol in the cough syrup was measured in 101 randomly selected samples with a sample standard deviation of s = 0.15. To construct a 90% two-sided confidence interval for the population standard deviation (σ), you will need to use the chi-square distribution.
However, the given information is not sufficient to construct the confidence interval, as the sample mean (x) is not provided. If the sample mean were given, you could use the formula for the confidence interval with the chi-square distribution and round your answers to three decimal places.
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if two nonzero vectors point in the same direction, their dot product must be zero. T/F
False. If two nonzero vectors point in the same direction, their dot product will not be zero.
The dot product of two vectors is a mathematical operation that measures the degree of similarity or alignment between the vectors. It is calculated by multiplying the corresponding components of the vectors and summing the results.
When two vectors point in the same direction, their dot product will be positive, indicating that they are aligned or have a certain degree of similarity. The dot product will be equal to the product of the magnitudes of the vectors multiplied by the cosine of the angle between them.
If two nonzero vectors are parallel and point in the same direction, the angle between them is 0 degrees, and the cosine of 0 degrees is 1. Therefore, the dot product of two nonzero vectors pointing in the same direction will be equal to the product of their magnitudes.
In other words, if the vectors are represented as A and B, and they point in the same direction, the dot product (A · B) will be equal to ||A|| * ||B||, where ||A|| and ||B|| represent the magnitudes of the vectors A and B, respectively.
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PLEASE HELP!!!! WILL MARK BRAINLYIST!!!!
What do you know about the trigonometric ratios for similar triangles?
Trigonometric ratios for similar triangles are mathematically established relationships used to solve for missing sides or angles as the ratio of corresponding sides are the same for all similar triangles.
TRIGONOMETRIC RATIOS
Trigonometric ratios for similar triangles include the sine , cosine and tangent relationships.
The sine is the ratio of opposite and hypotenuse side of a triangle
The cosine is the ratio of the adjacent and hypotenuse side of the triangle
The tangent is the ratio of the opposite and adjacent sides of the triangle.
Hence , the sine , cosine and tangent relationships are essential trigonometric ratios of similar triangles .
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I’m stuck on this question. Can anybody help? Please include the steps
The volume of the composite Figure is 1168.08 m³.
What is volume:Volume is the space occupied by a solid shape.
To calculate the volume of the composite shape, we use the formula below
Formula:
Volume of the composite shape = Volume of the cone+ Volume of the CylinderV = (πr²h/3)+(πr²H)................................... Equation 1From the question,
Given:
r = Radius of the base of the cone and the base of the cylinderh = Height of the coneH = Height of the cylinderπ = Constant PieFrom the question,
Given:
r = 6 mh = 7 mH = 8 mπ = 3.14Substitute these values into equation 1
V = (6²×7×3.14/3)+(6²×3.14×8)V = 263.76+904.32V = 1168.08 m³Learn more about volume here: https://brainly.com/question/28795033
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AEFG is dilated from the origin at a scale factor of 2 to create AEF'G'
Select the option that completes the statement:
The triangles' corresponding sides are
congruent; similar; proportional
congruent; proportional; similar
proportional; congruent; similar
Oproportional; similar; congruent
and their corresponding angles are
therefore, the triangles are
The triangles' corresponding sides' are proportional and their corresponding angles are congruent therefore, the triangles are sim
The correct option is C). proportional; congruent; similar
When the triangle is dilated from the origin at a scale factor of 2 to create Triangle then, the image of the triangle and the original triangle are similar to each other
However for similar triangles, corresponding angles are equal or congruent, and corresponding sides are in ratio or scaled
For example : A triangle ABC is dilated by a factor of 3 and centered at (-5,-4)
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PLEASE HELP I AM GROUNDED AND DONT UNDERSTAND
Answer: 35
Step-by-step explanation: interior angles add up to 180
because the outside angle is 125, we can subtract 125 from 180 because a straight line is also 180 degrees, which gives us 55
so for the interior angles, we now have 55 and 90 (because the top angle is a perfect right angle)
so 180-55-90= 35
Answer:
x=35 degrees
Step-by-step explanation:
The 125 degree angle and the angle right next to it (inside the triangle) add up to 180.
180-125 = 55 degrees.
All 3 inside (interior) angles of a triangle = 180.
So we know that top angle = 90 degrees. (That little square means that it's a 90 degree right triangle.)
And that bottom right angle is 55 degrees.
So we just need to find x.
180 = x+ 55 + 90
180 = x + 145
180-145 = x
35 = x
So x = 35 degrees.
Check that everything adds up: 35+90+55 = 180
I'm sorry you are grounded :(
Janine is six years younger than Paul. Paul is three times the age of their son Brett. Brett is
five years older than his sister Amanda. The sum of all their ages is 125 years. How old is
each person?
Let x be Amanda's age. Then Brett's age is x + 5. Paul's age is 3(x + 5), and Janine's age is 3(x + 5) - 6. The sum of all their ages is 125 years. On solving we get, Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old.
We can use algebra to solve the problem. Let x be Amanda's age. Then Brett's age is x + 5. Paul's age is 3(x + 5), and Janine's age is 3(x + 5) - 6, as given in the problem.
The sum of all their ages is 125 years. Using this information, we can set up the following equation:
x + (x + 5) + 3(x + 5) + (3(x + 5) - 6) = 125
Simplifying and solving for x, we get:
8x + 22 = 125
8x = 103
x = 12.875
Since x represents Amanda's age, which must be a whole number, we can conclude that there is an error in the problem statement.
Assuming that Amanda's age is actually a whole number, we can solve for all their ages. We find that Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old. We can check that the sum of their ages is indeed 125 years:
21 + 26 + 78 + 72 = 125
Therefore, Amanda is 21 years old, Brett is 26 years old, Paul is 78 years old, and Janine is 72 years old.
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