Which triangle congruence postulate would be used to prove the following triangles congruent?
1. SSS
2. HL
3. AAS
4. SAS
Answers
According to the SSS Postulate, two triangles are congruent if three of one triangle's sides are congruent with three of another triangle's sides.
Explain about the Congruence postulate?
A postulate is an assertion that is not backed by any evidence. Axiom is another name for a postulate. For instance, you would believe Pam if she said that all of her siblings were at least five feet one tall since you are aware of her height and that of all of her siblings, who are all taller than her.
When two figures or objects in geometry have the same shapes, sizes, or are mirror images of one another, they are said to be congruent.
Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
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Related Questions
utomobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. (Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system?Formulas for 13.17 What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customer receiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?
Answers
Answer:
The answers to the questions are well numbered below.
Step-by-step explanation:
We have arrival rate
λ = 7 in every 10 minutes = 0.7
Service time u = 7 minutes
1. Average time a car is in system
W = 1/u - λ
= 1/7-0.7
= 0.1587
= 0.16 to 2 decimal places
2. Average number of cars in system
= λ/u-λ
= 0.7/7-0.7
= 0.1111
= 0.11 to 2 decimal places
3. Average time that cars spend to receive service
= λ/u(u-λ)
= 0.7/7(7-0.7)
= 0.01587
= 0.016 to 2 decimal places
4. Average number of cars in line behind customer receiving service
= λ²/u(u-λ)
= 0.7²/7(7-0.7)
= 0.49/44.1
= 0.011 to 2 decimal places
5. Probability no cats at window
1-λ/u
= 1-0.7/7
= 0.9 = 9%
6. Percentage of time postal clerk is busy
= λ/u = 0.7/7 = 0.1 = 10%
7. Probability of exactly 2 cars
= λ²e^-λ/2!
= 0.7²e^-0.7/2!
= 0.1217
= 12.17%
9(a^2 b^2-ab) -6(ab+9ab^2) + (b^2-ab+a^2b^2)
Answers
Answer:
The correct answer is 10a^2 b^2-54ab^2-16ab+b^2.
Step-by-step explanation:
I hope this helps! All you needed to do was distribute and then combine like terms.
A number pattern starts with 10 and follows the rule "multiply by 3." What is true
about all of the numbers in this pattern?
Answers
Ciana earns an hourly wage of $30 at her job. In order to purchase her sneakers she will have to take time off work, so each hour away from her job
costs her $30 in lost Income. Assume that ciana travel time is the same each way (to and from the store) and that it will take her 30 minutes once
she reaches a store to complete her shopping. Assume throughout the question that ciara incurs no additional costs other than the sneakers, such as
gas.
complete the following table by computing the opportunity cost of ciana’s time and the total cost of shopping at each location
Answers
Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.
How to determine the opportunity cost?Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:
Total economic cost:
Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144
Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131
Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135
Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).
Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.
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The line represented by y = 3x − 2 and a line perpendicular to it intersect at R(3, 7). What is the equation of the perpendicular line? y = − negative start fraction one over three end fractionx + 4 y = − negative start fraction one over three end fractionx + 8 y = start fraction one over three end fractionx + 6 y = −3x + 7
Answers
Answer:
y= -1/3(x) + 8
Step-by-step explanation:
slope of the 1st line = 3
slope of the line perpendicular to the first is its opposite reciprocal, so
slope of the 2nd line = -1/3
now we have a point and the slope of the perpendicular line, so we use the point slope formula to get:
y-7=-1/3(x-3)
y= -1/3(x) + 1 + 7
y= -1/3(x) + 8
Which of the following statements is not true?
Choose the incorrect statement below.
The three-part inequality - 1 <-3x ≤ 1 is equivalent to -5x<
15x2
<3 is equivalent to -6≤5-x<6.
The three-part inequality - 3s-
OD. The three-part inequality -7≤11-x<7 is equivalent to 4 < x≤ 18.
OA.
OB.
C.
The three-part inequality -5s-10x<5 is equivalent to
5-x
...
Answers
The incorrect statement is:
B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.
In the given statement, there is an error in the inequality. The correct statement should be:
The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.
When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:
- 5x < 15x^2 and 15x^2 < 3
Simplifying the first inequality:
- 5x < 15x^2
Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:
- 5 < 15x
Simplifying the second inequality:
15x^2 < 3
Dividing by 15, we get:
x^2 < 1/5
Taking the square root (assuming x ≥ 0), we have two cases:
x < 1/√5 and -x < 1/√5
Combining these inequalities, we get:
- 5 < 15x and x < 1/√5 and -x < 1/√5
Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.
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someoneeeee helppppop asappp 1st and second option positive or negative
Answers
Use a geometric tool to draw a circle. Draw and measure a radius and a diameter of the circle .
Answers
Answer:
Attached is an example of a circle with a radius of 5 and a diameter of 10.
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days.
(1) Using the 68-95-99.7% rule, between what two lengths do the most typical 68% of all pregnancies fall 95%, 99.7%?
(2) What percent of all pregnancies last less than 250 days?
(a) What percentage of pregnancies last between 241 and 286 days?
(b) What percentage of pregnancies last more than 286 days?
(c) What percentage of pregnancies last more than 333 days?
(3) What length cuts off the shortest 2.5% of pregnancies?
(4) Find the quartiles for pregnancy length.
(5) Between what two lengths are the most typical 72% of all pregnancies?
Answers
Answer:
1) The most typical 68% of pregnancies last between 250 and 282 days, the most typical 95% between 234 and 298 days, and the most typical 99.7% between 218 and 314 days.
2) 15.87% of all pregnancies last less than 250 days
2a) 83.5% of pregnancies last between 241 and 286 days
2b) 10.56% of pregnancies last more than 286 days.
2c) 0% of pregnancies last more than 333 days
3) A pregnancy length of 234.6 days cuts off the shortest 2.5% of pregnancies.
4) The first quartile of pregnancy lengths is of 255.2, and the third quartile is of 276.8 days.
5) The most typical 72% of all pregnancies last between 248.72 and 283.28 days.
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 266 days and a standard deviation of 16 days.
This means that \(\mu = 266, \sigma = 16\)
(1) Using the 68-95-99.7% rule, between what two lengths do the most typical 68% of all pregnancies fall 95%, 99.7%?
68%: within 1 standard deviation of the mean, so 266 - 16 = 250 days to 266 + 16 = 282 days.
95%: within 2 standard deviations of the mean, so 266 - 32 = 234 days to 266 + 32 = 298 days.
99.7%: within 3 standard deviations of the mean, so 266 - 48 = 218 days to 266 + 48 = 314 days.
The most typical 68% of pregnancies last between 250 and 282 days, the most typical 95% between 234 and 298 days, and the most typical 99.7% between 218 and 314 days.
(2) What percent of all pregnancies last less than 250 days?
The proportion is the p-value of Z when X = 250. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{250 - 266}{16}\)
\(Z = -1\)
\(Z = -1\) has a p-value of 0.1587.
0.1587*100% = 15.87%.
15.87% of all pregnancies last less than 250 days.
(a) What percentage of pregnancies last between 241 and 286 days?
The proportion is the p-value of Z when X = 286 subtracted by the p-value of Z when X = 241. So
X = 286
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{286 - 266}{16}\)
\(Z = 1.25\)
\(Z = 1.25\) has a p-value of 0.8944.
X = 241
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{241 - 266}{16}\)
\(Z = -1.56\)
\(Z = -1.56\) has a p-value of 0.0594.
0.8944 - 0.0594 = 0.835*100% = 83.5%
83.5% of pregnancies last between 241 and 286 days.
(b) What percentage of pregnancies last more than 286 days?
1 - 0.8944 = 0.1056*100% = 10.56%.
10.56% of pregnancies last more than 286 days.
(c) What percentage of pregnancies last more than 333 days?
The proportion is 1 subtracted by the p-value of Z = 333. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{333 - 266}{16}\)
\(Z = 4.19\)
\(Z = 4.19\) has a p-value of 1
1 - 1 = 0% of pregnancies last more than 333 days.
(3) What length cuts off the shortest 2.5% of pregnancies?
This is the 2.5th percentile, which is X when Z = -1.96.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.96 = \frac{X - 266}{16}\)
\(X - 266 = -1.96*16\)
\(X = 234.6\)
A pregnancy length of 234.6 days cuts off the shortest 2.5% of pregnancies.
(4) Find the quartiles for pregnancy length.
First quartile the 25th percentile, which is X when Z = -0.675.
\(Z = \frac{X - \mu}{\sigma}\)
\(-0.675 = \frac{X - 266}{16}\)
\(X - 266 = -0.675*16\)
\(X = 255.2\)
Third quartile is the 75th percentile, so X when Z = 0.675.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.675 = \frac{X - 266}{16}\)
\(X - 266 = 0.675*16\)
\(X = 276.8\)
The first quartile of pregnancy lengths is of 255.2, and the third quartile is of 276.8 days.
(5) Between what two lengths are the most typical 72% of all pregnancies?
Between the 50 - (72/2) = 14th percentile and the 50 + (72/2) = 86th percentile.
14th percentile:
X when Z = -1.08.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.08 = \frac{X - 266}{16}\)
\(X - 266 = -1.08*16\)
\(X = 248.72\)
86th percentile:
X when Z = 1.08.
\(Z = \frac{X - \mu}{\sigma}\)
\(1.08 = \frac{X - 266}{16}\)
\(X - 266 = 1.08*16\)
\(X = 283.28\)
The most typical 72% of all pregnancies last between 248.72 and 283.28 days.
what sum of money must be invested the interest of 4% to given on interest Rs900 in 5 yearr
Answers
Answer:
5
Step-by-step explanation:
trust
Help what is eqation for this.
Answers
Answer:
y=-x+10
Step-by-step explanation:
The formula is y=mx+b, where m is the slope and b is the y-intercept. To solve plugin the values for the corresponding variables. It has a slope of -1 and a y-intercept of 10.
Oh there is a free grid sheet that you can put there
Step-by-step explanation:
Search it up and the website will appear where it will give you pretty much all of the information about it
You pick a marble, roll a die, and pick a card. How many outcomes are possible?
Answers
The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
How to determine How many outcomes are possibleTo determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.
1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.
2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.
3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.
To find the total number of possible outcomes, we multiply the number of outcomes for each event together:
Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)
Total number of outcomes = n × 6 × 52
Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.
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What is the y-intercept of this graph?
Answers
Answer:
The Y-intercept is 0.
Step-by-step explanation:
The coordinates of midpoint M and endpoint C or a segment are M(-2,-7) and C(12,-9). Find the coordinates of the other endpoint15 )
Answers
we have that the midpoint is (-2,-7)
and the endpoint is (12,-9)
We remember the midpoint formula:
\(M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)Where (x1,y1) are the coordinates of one endpoint and
(x2,y2) are the coordinates for the other endpoint.
Here, we are trying to find (x2,y2) given that
(x1, y1) ---> (12, -9)
\(\begin{gathered} x_1=12 \\ y_1=-9 \end{gathered}\)And since we also know the midpoint M(-2, -7), making a comparison with this and the midpoint formula, we get two equations, the first one is:
\(\frac{x_1+x_2}{2}=-2\)substituting x1 and solving for x2:
\(\frac{12+x_2}{2}=-2\)\(\begin{gathered} 12+x_2=4 \\ x_2=4-12 \\ x_2=-8 \end{gathered}\)And now, with the second equation which is:
\(\frac{y_1+y_2}{2}=-7\)we substitute y1 and solve for y2:
\(\frac{-9+y_2}{2}=-7_{}\)solving for y2:
\(\begin{gathered} -9+y_2=-14_{} \\ y_2=-14+9 \\ y_2=-5 \end{gathered}\)This the other endpoint (x2,y2) is at (-8,-5)
Use the law of sines to complete an expression that represents the angle measure x. Geometry
Answers
Answer:
a = 14.9
b = 75
c = 22.5
Step-by-step explanation:
The equation given is just the law of sines converted into terms of x.
help....................
Answers
The unit of the rate of change is (b) dollars per month
How to determine the unit of the rate of changeFrom the question, we have the following parameters that can be used in our computation:
The table of values
Where we have
y = total amount in dollars
x = number of months
The rate of change is calculated as
Rate = y/x
substitute the known values in the above equation, so, we have the following representation
Rate = total amount in dollars/number of months
So, we have
Unit = dollars per month
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Simplify the expression and choose the appropriate result.
3(2 + 3g)
Answers
6+3x3g
= 6+9g
Describe the graph of y = 3 x squared and compare it with the graph of y = x squared
Answers
Answer:
\(y=3x^{2}\) has a higher vertical scaling compared to \(y=x^{2}\)
Step-by-step explanation:
Graph it! (:
Answer:
Both graphs are parabolas and they both open upward and pass through 0, 0. The first graph is more narrow than the second graph.
Step-by-step explanation:
This was the possible answer provided :)
Suppose that in a certain sinkhole the ground dropped 69.6 ft in 24 hr. Find the unit rate representing the change in altitude per hour ..the unit rate representing the change in altitude is how many feet per hour
Answers
Answer:
2.9 per hour
Step-by-step explanation:
Divide 69.9 by 24
If you spin the spinner 72 times, what is the best prediction possible for the number of times it will land on yellow?
Answers
the best prediction possible for the number of times the spinner will land on yellow if it is spun 72 times is 12. This means that out of 72 spins,
how to solve probability
If the spinner has 12 equal parts and 2 of them are yellow, then the probability of the spinner landing on yellow is 2/12, or 1/6. This means that out of every 6 spins, we can expect the spinner to land on yellow once.
To find the best prediction for the number of times the spinner will land on yellow if it is spun 72 times, we can use the idea of expected value. The expected value of an event is the average value we would expect to see if the event were repeated many times.
In this case, the expected value of the number of times the spinner will land on yellow in 72 spins is simply the probability of landing on yellow multiplied by the number of spins:
Expected value = Probability of yellow x Number of spins
Expected value = (1/6) x 72
Expected value = 12
Therefore, the best prediction possible for the number of times the spinner will land on yellow if it is spun 72 times is 12. This means that out of 72 spins, we can expect the spinner to land on yellow approximately 12 times on average. However, it's important to remember that this is just a prediction based on probability, and the actual number of yellow spins may vary.
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the question is in the image below
Answers
Factor out the coefficient of the variable 2/3j - 2/9
Answers
answer: hey lol*sharts loudly*
Step-by-step explanation:
you just need to use the bathroom next time;))))
A bucket contains 72 red, 48 blue, 48 green, and 48 yellow crayons. The art teacher also has 120 pieces of drawing paper. What is the largest number of identical kits the art teacher can make with all of the crayons and all of the paper?
Answers
The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.
To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.
The GCD represents the largest number that can divide all the quantities without leaving a remainder.
The GCD of the quantities of crayons can be found by considering the prime factorization:
72 = 2³ × 3²
48 = 2⁴ × 3
48 = 2⁴ × 3
48 = 2⁴ × 3
The GCD of the crayons is 2³ × 3 , which is 24.
Now, we need to find the GCD of the quantity of drawing paper:
120 = 2³ × 3 × 5
The GCD of the drawing paper is also 2³ × 3 , which is 24.
Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.
Each kit would contain an equal distribution of crayons and drawing paper.
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translated 1 unit right and five units down
Answers
Answer:
y'=|x-5|-1
Step-by-step explanation:
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The probability that event A occurs is 12%. The probability that event B occurs is 15%. The probability that both events occur is 3%. What are the conditional probabilities of the two events? Are A and B independent events? Drag an answer into each empty box to complete the equations and sentence correctly.
Answers
The conditional probabilities of the two events are P(A|B) = 0.2 and P(B|A) = 0.25
The events are not independent
How to determine the conditional probabilities of the two events?From the question, we have the following parameters that can be used in our computation:
P(A) = 12%
P(B) = 15%
P(A and B) = 3%
The conditional probability of the event A given B is calculated as
P(A|B) = P(A and B)/P(B)
Substitute the known values in the above equation, so, we have the following representation
P(A|B) = 3%/15%
Evaluate
P(A|B) = 0.2
The conditional probability of the event B given A is calculated as
P(B|A) = P(A and B)/P(A)
Substitute the known values in the above equation, so, we have the following representation
P(B|A) = 3%/12%
Evaluate
P(B|A) = 0.25
Are A and B independent events?For the events to be independent, then we must have
P(A) * P(B) = P(A and B)
So, we have
12% * 15% = 3%
Evaluate
1.8% = 3%
This is false
Hence, they are not independent
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solve the equation x/5+x/4=1
Answers
Answer:
exact form: x=20/9
decimal Form: x=2.222...
Step-by-step explanation:
Why do you think
being able to solve
a literal equation
for a variable
would be useful in
certain situations
Answers
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
Find the area of the hexagon
Answers
Area of Hexagon having six sides = \(\frac{3\sqrt{3}s^{2} }{2}\)
How to find the area of Hexagon ?Hexagons are polygons with six sides and six angles.
Six equilateral triangles make up a regular hexagon, which has six equal sides and six angles. Whether you're dealing with an irregular hexagon or a standard hexagon, there are numerous approaches to figure out the area of a hexagon.
The area of hexagon formula can be calculated in a number of different ways. The various techniques primarily depend on the hexagon's spitting motion.
It can be split into two triangles and one rectangle, or six equilateral triangles. We shall examine numerous approaches to calculating the hexagon's surface area in this post.
According to the given information
Area of Hexagon having six sides = \(\frac{3\sqrt{3}s^{2} }{2}\)
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If a fair, -sided die is rolled twice, what is the probability It will land on 1 and then 6?
Answers
Answer:
The probability that the die will land on 1 and then 6 is 2.77%.
Step-by-step explanation:
Given that a fair sided die is rolled twice, to determine what is the probability It will land on 1 and then 6 the following calculation must be performed:
1/6 x 1/6 = X
0.166666 x 0.166666 = X
0.0277777 = X
0.0277777 x 100 = 2.77
Therefore, the probability that the die will land on 1 and then 6 is 2.77%.
Answer:
2.78%
Step-by-step explanation:
got it right on test