Determine if the two triangles in the following diagram are congruent. If so, select the correct way they can be proven congruent.
SSS - Side, Side, Side
SAS - Side, Angles, Side
ASA - Angle, Side, Angle
AAS - Angle, Angle, Side
HL - Hypotenuse, Leg
Answers
The two triangles in the following diagram are congruent. The proofs are mentioned below.
SSS (Side-Side-Side)
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
SAS (Side-Angle-Side)
If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.
ASA (Angle-Side- Angle)
If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.
AAS (Angle-Angle-Side) [Application of ASA]
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
AAS congruence can be proved in easy steps.
RHS (Right angle- Hypotenuse-Side)
If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.
Hence, the two triangles in the following diagram are congruent.
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Related Questions
a crime reporter was told that on average, 3000 burglaries per month occurred in his city. the reporter examined past data, which were used to computed a 95% confidence interval for the number of burgalries per month. the confidence interval was from 2176 to 2784. at the 5% level of significance, do these data tend to support the alternative hypothesis, $h 1 \ne 3000$? calculate z test score
Answers
We need to calculate the z-test score. It is a statistical test for inference that tests the null hypothesis that the mean of a sample from a normal population equals a specified value, and it is a test of statistical significance. Z-score: Z = (x - μ) / (σ / √n)μ = 3000, x = (2176 + 2784) / 2 = 2480, σ is the standard error of the mean, and n is the number of data points.
Z = (2480 - 3000) / (3000 / √n). The standard error of the mean (SEM) is calculated as follows: SEM = σ / √nσ = (2784 - 2176) / (2 × 1.96) = 303.64. Therefore, SEM = σ / √n=303.64 / √n(303.64 / √n) = (3000 - 2176) / 1.96n = 141.56n = 142Z = (2480 - 3000) / (303.64 / √142)Z = -12.95.
Since Z is less than -1.96, the test is significant at the 5% level of significance. Therefore, we can refuse the null hypothesis, and the alternative hypothesis is accepted. Therefore, the data support the alternate hypothesis that the number of burglaries per month is not equal to 3000.
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Kevin bought snacks for his team's practice. He bought a bag of popcorn for $1.60 and a 8-pack of juice bottles. The total cost before tax was $16.80. How much was each bottle of juice?
Answers
Answer:
$1.90
Step-by-step explanation:
16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.
1) Set up and equation equated to 15.20.
8x = 15.20
x = 15.20/8
x = 1.90
Therefore, each bottle of juice costs $1.90.
Determine how many meters Penelope jogs in three laps
Answers
Penelope jogs a distance of 2898 meters in three laps around the rectangular playground.
To solve this problem, we need to first find the perimeter of the rectangle. For a rectangle with a length of L and a width of W, the perimeter P can be found using the following formula:
P = 2L + 2W
In this case, the length of the playground is 320 m and the width is 163 m. So, the perimeter of the playground is:
P = 2(320 m) + 2(163 m)
P = 966 m
This means that if Penelope jogs around the entire playground once, she will run a distance of 966 meters.
Since Penelope jogs three laps around the playground, we need to multiply the perimeter by 3 to find out how far she runs in total. So, the distance that Penelope jogs in three laps is:
Distance = 3 x P
Distance = 3 x 966 m
Distance = 2898 m
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Complete Question:
Every day, Penelope jogs three laps around the playground to keep in shape. The playground is rectangular with a width of 163 m and a length of 320 m.
Determine how many meters Penelope jogs in three laps.
What is 5 1/2 x 5 = ?
Answers
Answer:27.5
Step-by-step explanation:
i did this with a calculator, but the answer is
27.5
What is the area of this figure?
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
wios,wal
Which picture should be next in the sequence?
Answers
The next picture in the sequence of pictures is a picture that has 16 cells
Identifying the next picture in the sequenceA pattern is a recurring design, shape, or arrangement that has a regular or logical repetition.
From the figure, we can see that teh pattern is
Picture = 2^n
Where n is the position
For the next picture, we have
n = 4
This means that
Picture = 2^4
So, we have
Picture = 16
Hence, the next picture would have 16 cells
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Compare the variations.
The mean absolute deviation of the number of wins is 1 of 2.
greater/leaser
for the Bears than for the Saints. This means the data values for the, 2 of 2.
saints/bears
are closer to the mean.
Answers
Therefore , the solution of the given problem of mean comes out to be one team's data values are closer to the median mean than that of the other.
Define mean.The result from a set, also known as the arithmetic mean, is the sum of all values split by all of the values. It is frequently referred to as "mean" and is thought to be among the most commonly employed primary trend average. To obtain this answer, multiply the total number of numbers in the collection by the total number of values present.
Here,
The closer the data values are to the mean, the less variable they are, and the smaller the MAD.
A higher MAD shows that the data values are more variable and dispersed from the mean.
In this instance, the Bears' MAD of the amount of victories is 1, while the Saints' MAD is unspecified.
We cannot compare the distinctions of the two teams based solely on MAD since the Saints' MAD is not stated.
Since we cannot tell which team has a larger or smaller MAD, we cannot draw the conclusion that one team's data values are closer to the median mean than that of the other.
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PACKAGING A video game system is packaged in a box that is in the shape of a cube. The length of the packaging box is 4x^2 y^5 . What is the volume of the packaging box in terms of x and y?
Answers
Answer: 64x^6y^15
Step-by-step explanation:
If the packaging box is in the shape of a cube, then all its sides are equal in length. Let's call the length of each side "s".
We know that the length of the packaging box is 4x^2 y^5, so:
s = 4x^2 y^5
To find the volume of the packaging box, we need to calculate s^3 (since the box is a cube).
s^3 = (4x^2 y^5)^3
s^3 = 4^3 (x^2)^3 (y^5)^3
s^3 = 64x^6 y^15
Therefore, the volume of the packaging box in terms of x and y is 64x^6 y^15.
Make a graph of kinetic energy versus mass for the bikers. Label each biker on your
graph. (4 points)
Answers
See Below
HAVE A NICE DAY !
SOLVE WITH EXPLANATION GIVING BRAINLIEST IF YOU SOLVE IT CORRECTLY WITH EXPLANATION IF YOU DONT YOU GET REPORTED :/
Answers
Answer:
6.
[tex]2x - 1 = x + 3[/tex]
[tex]x = 4[/tex]
[tex] y = 4 + 3 = 7[/tex]
So the solution is (4, 7).
7. Substituting 4x into the second equation:
[tex]4x + x = 5[/tex]
[tex]5x = 5[/tex]
[tex]x = 1[/tex]
[tex]y = 4(1) = 4[/tex]
So the solution is (1, 4).
The ordered pairs (−4, 7) and (2, −2) are points on a graph of a linear equation. Which other points are also on the same line?
Select ALL that apply.
(−2, −6)
(−2, −5)
(4, −6)
(4, −5)
(0, −5)
(0, 1)
Answers
We can find the equation of the line passing through the given two points (-4, 7) and (2, -2) using the slope-intercept form of a linear equation:
slope (m) = (change in y) / (change in x) = [tex](-2 - 7) / (2 - (-4)) = -9/6 = -3/2[/tex]
Using point-slope form with the first given point (-4, 7), we get:
[tex]y - 7 = (-3/2)(x - (-4))\\y - 7 = (-3/2)x - 6\\y = (-3/2)x + 1[/tex]
Now we can plug in the x-coordinates of the other points given and check if they satisfy the equation.
[tex](−2, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(-2) + 1\\-6 = 3 + 1\\-6 ≠ 4 (not on the line)[/tex]
[tex](−2, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(-2) + 1\\-5 = 3 + 1\\-5 ≠ 4 (not on the line)(4, −6):\\y = (-3/2)x + 1\\-6 = (-3/2)(4) + 1\\-6 = -6 + 1\\-6 ≠ -5 (not on the line)(4, −5):\\y = (-3/2)x + 1\\-5 = (-3/2)(4) + 1\\-5 = -6 + 1\\-5 = -5 (on the line)[/tex]
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how to do this.............
Answers
Answer:
The one selected is correct
Step-by-step explanation:
Use the drop-down menus to complete the sentence. the transformation is because the preserved.
Answers
A transformation is said to be not rigid because the segments is preserved.
A transformation is a function that maps one set of points to another set of points. There are different types of transformations, including translation, rotation, reflection, dilation, and combinations of these. Each type of transformation preserves certain properties of the shape or object.
The properties that are preserved during a transformation depend on the type of transformation
Similarly, a rotation is a transformation that rotates a shape or an object around a fixed point. During a rotation, the distance between any two points on the shape or object is preserved, but the direction may change. A reflection is a transformation that flips a shape or an object across a line. During a reflection, the distance between any two points on the shape or object is preserved, but the orientation may change.
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1. nonrigid
2. segment lengths are not
pleaseeee help!!!!!!!!!
Answers
The phrase that reflects the amount of recordings, in thousands, owned by the collector 4 years later if it continues to expand at this rate is: [tex]O 12 • (1.02)^48[/tex] Thus, option C is correct.
What number of records will increase by a factor?o calculate the number of records that will increase by a factor, you first need to know the initial number of records. Let's call this number "N".
To increase the number of records by a factor of "F", you can simply multiply the initial number of records by the factor:
New number of records = N x F
For example, if you have 100 records and you want to increase the number of records by a factor of 3, the new number of records would be:
New number of records [tex]= 100 x 3 = 300[/tex]
So, the new number of records would be 300.
The growth rate is 2% per month, which means that the number of records will increase by a factor of 1.02 each month. After 4 years (48 months), the number of records owned by the collector can be calculated using the formula:
[tex]12,000 x (1.02)^48[/tex]
Simplifying this expression, we get:
[tex]12,00x0 1.02^48[/tex]
Therefore, the expression that represents the number of records, in thousands, owned by the collector 4 years later if it continues to grow at this rate is: O 12 • (1.02)^48
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A population of a town increases by 7% every year. If its population today is 40,000, what is its population in 3 years?
Answers
A = 40,000(1 + 0.07)^3
A = 40,000(1.07)^3
A = 47,676.08
Therefore, the population of the town in 3 years will be approximately 47,676.
a computer table is given a discount of 20% the original price of the computer id php 850. What is the discounted price
Answers
To hire an accountant to prepare taxes costs a flat fee and an additional hourty rate. The amount the accountant costs can be modeled by the function A(X) = 140 +
25x, where x represents the number of hours the accountant works to prepare the taxes and 140 represents the flat fee. What is the value of A(215) and its
interpretation?
a A(215) = 3; If the accountant takes 215 hours to prepare the taxes, the cost wil be $2.
b A(215) = 3; If the account takes 3 hours to prepare the taxes, the cost wil be $215.
c A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost wil be $5,515.
d A(215) = 5515; If the accountant takes 5,515 hours to prepare the taxes, the cost will be $215.
Answers
Answer: The given function is:
A(x) = 140 + 25x
We need to find the value of A(215), which means we need to substitute x = 215 in the function and simplify:
A(215) = 140 + 25(215)
A(215) = 140 + 5375
A(215) = 5515
Therefore, the correct answer is (c) A(215) = 5515. The interpretation of this result is that if the accountant works for 215 hours to prepare the taxes, the cost will be $5,515, which includes the flat fee of $140 and an additional hourly rate of $25 for each hour worked.
Step-by-step explanation:
The value of A(215) and its interpretation are captured thus:
A(215) = 5515; If the accountant takes 215 hours to prepare the taxes, the cost will be $5,515
What does the function represents?The function given as A(x) = 140 + 25x, represents the total cost of using the services of the accountants for tax computation and preparation, bearing in mind that the 140 means $140 which is the fixed charged irrespective of the number of hours it takes to prepare the tax returns whereas the 25x means that $25 is charged as variable fee for every hour the accountant works on the tax computation
A(x) = 140 + 25x
In this case, A(215) means that 215 hours were made use of by the accountants, hence, to determine the total fees, we simply substitute for x
A(215) = 140+(25*215)
A(215) = 140+5375
A(215)=$5,515
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mike and alain play a game in which each player is equally likely to win. the first player to win three games becomes the champion, and no further games are played. if mike has won the first game, what is the probability that mike becomes the champion?
Answers
The probability that Mike becomes the champion given that he has won the first game is 7/12.
To find the probability that Alain wins the championship given that Mike won the first game, we can repeat the same reasoning as before, but with Alain as the starting player.
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game)
This leads to:
P(Alain wins championship | Alain won first game) = 5/8
Therefore, we can conclude that:
P(Mike wins championship | Mike won first game) = 1 - P(Alain wins championship | Mike won first game) = 1 - 5/8 = 3/8 + 1/8 = 4/8 = 1/2
Thus, The probability that Mike becomes the champion given that he has won the first game is 7/12.
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Triangle WXY, with a vertex X at (3, 0), is rotated clockwise 270° about the origin.
Which of the following rotations is equivalent 270° clockwise rotation about the origin?
clockwise 270°
counterclockwise 90°
counterclockwise 360°
clockwise 90°
Answers
Answer: A rotation of 270° clockwise is equivalent to a rotation of 90° counterclockwise, because a full rotation is 360° and 270° clockwise is the same as 90° counterclockwise in terms of direction.
Therefore, the answer is: counterclockwise 90°.
Step-by-step explanation:
7 2/9 - 5 5/7 = ?
rlly stuck on this math assignment currently
Answers
Answer:
95/63 or 1 32/63
Step-by-step explanation:
turn the fraction into a mixed number/improper fraction
65/9-40/7
find a common denominator which in this case is 63
so, the first fraction you will multiply the numerator and denominator by 7 to get
455/63
then the second fraction multiply the numerator and the denominator by 9
360/63
then you would subtract the two numerators KEEP THE DENOMINATOR THE SAME
455/63-360/63=95/63
Please help! Im a struggling depressed student that needs to desperately catch up.
Answers
Answer:
25%
Step-by-step explanation:
30/120 = 1/4
1/4 = 25%
Tristan was out at a restaurant for dinner when the bill came. His dinner came to $22. He wanted to leave a 16% tip. How much do was his meal plus the tip, before tax, in dollars and cents
Answers
Answer: 25 dollars and 52 cents
Step-by-step explanation:
Bill = $22
Tip = 16/100 X 22 = $3.52
Total = 22 + 3.52 = $25.52
Answer:
$25.52
Step-by-step explanation:
16% × 22= $3.52
3.52 + 22= $25.52
What percent of 15 is 5?
Answers
Answer: 33.33%
Step-by-step explanation:
5/15 divided
Winston is baking a pie. The diameter of the pie is 12 inches. What is the area of the pie? Use 3. 14 for pi and round your answer to the nearest tenth
Answers
If the diameter of the pie is 12 inches, then the area of pie is 113.04 in² and 113 in² after rounding to the nearest tenth.
The formula for the area of a circle is: A = π × r²
where A is the area, pi is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given the diameter of the pie, which is 12 inches. To find the radius, we need to divide the diameter by 2:
r = 12 / 2
= 6 inches
Now we can use the formula for the area of a circle to find the area of the pie:
A = π × r²
A = 3.14 × 6²
A = 113.04 square inches
Rounding to the nearest tenth gives:
A ≈ 113.0 square inches
Therefore, the area of the pie is approximately 113.0 square inches.
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3x (x-4) (3x + 5) = 0
Answers
Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.
what is equation ?An equation in mathematics is a claim that two expressions are equivalent. An equals sign (=) separates the left and right sides of an equation, which usually has two sides. Variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots may be used in the formulas on either side of the equals sign. Finding the number of the variable or variables that make an equation true is the goal of an equation.
given
The zero product property, which asserts that at least one of the factors must be zero if the product of two or more factors equals zero, can be used to solve the equation 3x(x-4)(3x+5) = 0.
We then solve for x by setting each component equal to zero:
3x = 0, 3x + 4, or 3x + 5 = 0.
When we factor x into each solution, we obtain:
3x = 0 --> x = 0
x-4 = 0 —> x = 4
Therefore, x = 0, x = 4, and x = -5/3 are the answers to the equation 3x(x-4)(3x+5) = 0.
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question 1(multiple choice worth 3 points) (05.05 lc) according to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise. the numbers for each year are, roughly, 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3. what is the mean of these statistics? 24 2.18 24.18 2
Answers
The mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18. (option 2).
To find the mean of a set of numbers, we add up all the numbers in the set and then divide by the total number of items in the set. In this case, we have the following numbers: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, and we want to find the mean.
To do so, we first add up all the numbers:
2 + 1 + 2 + 2 + 1 + 2 + 2 + 3 + 3 + 3 = 21
Then we divide by the total number of items in the set, which is 10:
21 / 10 = 2.1
Therefore, the mean of the unintentional drug overdose deaths per 100,000 population from 1986-1996 is 2.18.
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1. What is the diameter of the circle above?
2.
What is the radius of the circle above?
Answers
Answer:
diameter = 34 radius = 17
Step-by-step explanation:
Look at the line in the middle of the circle that is the diameter, diameter is a straight line passing from side to side through the center of a circle.
radius is the distance from the center of the circle to any point on its circumference.
Can someone please
Help me on this? I’ll give 20 points for this
Answers
Answer:
a) 6x10^-6 b) 0.000006 c) I would not be concerned
Step-by-step explanation:
a)
50% is just half and more just means added onto.
Half of 4x10^-6 is 2x10^-6
If you add that onto the original value, you will have:
6x10^-6 (standard form)
b)
0.000006 (ordinary number)
c)
I would not be concerned about the increase in probability of a side effect while using the new medicine. The probability to begin with is extremely low, almost insignificant. While the 50% increase may sound intimidating, it is just a 50% increase on a number that is already very very small. Honestly, it makes almost no difference.
a 17 ft ladder is leaning against a wall. if the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 2ft/s, how fast will the top of the ladder be coming down the wall when the top is 8 ft above the ground
Answers
The top of the ladder is coming down the wall at a rate of 15.39 ft/s
Let's assume that the ladder makes a right angle with the wall and the ground. Let's call the distance between the bottom of the ladder and the wall "x" and the height of the ladder at a given time t "y". We want to find the rate of change of "y" with respect to time "t", or dy/dt, when y = 8 ft.
We can use the Pythagorean theorem to relate "x" and "y":
x^2 + y^2 = 17^2
Taking the derivative of both sides with respect to time "t", we get
2x(dx/dt) + 2y(dy/dt) = 0
We want to find dy/dt when y = 8 ft and dx/dt = 2 ft/s. We can solve for dy/dt
2x(dx/dt) + 2y(dy/dt) = 0
2y(dy/dt) = -2x(dx/dt)
dy/dt = -x/y(dx/dt)
Substituting x = sqrt(17^2 - y^2) and dx/dt = 2 ft/s, we get:
dy/dt = -(17^2 - y^2)/y
When y = 8 ft, we get
dy/dt = -(17^2 - 8^2)/8 = -15.39 ft/s
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how do you do this? I need helppppp
Answers
The constant of proportionality of the graph is k = 3/2.
How to get the constant of proportionality?A general proportional relation between two variables y and x can be written as:
y = k*x
Were k is the constant of proportionality.
To find the value of k, we need to identify a point of the form (x, y) on the given graph, and then replace the values in the equation above, for example, we can use the point (4, 6), replacing that we will get:
6 = k*4
6/4 = k
3/2 = k
That is the constant of proportionality.
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