Given the coordinates, determine whether PQR & XYZ are congruentP(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)PQ=XY=QR=YZ=PR=XZ= Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.

The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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Answer:

x = 17

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

x + 17 + 4x - 34 + 6x + 10 = 180  Combine like terms

11x -7 = 180  Add 7 to both sides

11x - 7 + 7 = 180 + 7

11x = 187  Divide both sides by 11

\(\frac{11x}{11}\) = \(\frac{187}{11}\)

x = 17

Answer:

the answer is x=17 because the triangle is isosceles

The mean body mass of the Adelie species is  3706.164 g.

Original chunk of code:

penguins %>%

drop_na() %>%

group_by(species) %>%

The code chunk summarize(mean(body_mass_g)) lets you find the mean value for the variable body_mass_g. The correct code is

penguins %>% drop_na() %>% summarize (mean(body_mass_g)).

The summarize () function displays summary statistics. We can use the summarize() function in combination with other functions - such as mean(), max(), min() - to calculate specific statistics. In this case, you use mean() to calculate the mean value for body mass.

Hence, The mean body mass for the Adelie species is 3706.164 g.

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Answer:

A. 366-249=125

B. 13386-9608=4788

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

10 bucks

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

10%=0.1

100*0.1=10

$10

The expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

From the question, we have the following polynomial that can be used in our computation:

P(x) = 2x² (x + 3) − (7x − 10)

Q(x) = 8(x − 1) (x² + x + 1) − 3x² + 4

R(x) = (2x + 1)² - (2x² + 7)

S(x) = 2(5x³+6) + x(x - 11)

Add the expressions P(x) and Q(x)

So, we have

P(x)  + Q(x) = 2x² (x + 3) − (7x − 10) + 8(x − 1) (x² + x + 1) − 3x² + 4

Evaluate

P(x)  + Q(x) = 10x³ + 3x² - 7x + 6

Add the expressions R(x) and S(x)

So, we have

R(x) + S(x) = (2x + 1)² - (2x² + 7) + 2(5x³+6) + x(x - 11)

R(x) + S(x) = 10x³ + 3x² - 7x + 6

So, we have

P(x) + Q(x)} − {R(x) + S(x)} = 10x³ + 3x² - 7x + 6 - (10x³ + 3x² - 7x + 6)

Evaluate

P(x) + Q(x)} − {R(x) + S(x)} = 0

Hence, the expression {P(x) + Q(x)} − {R(x) + S(x)} is a zero polynomial.

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Answer:

z=5

Step-by-step explanation:

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

In this Venn  diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.

Let's use T to represent the set of people who like tea, M to represent the set of people who like milk, and U to represent the universal set of all 180 people. We know that:

|T| = 95 (the number of people who like tea)

|M| = 80 (the number of people who like milk)

|T ∪ M| = 180 - |T ∩ M| = 180 - 35 = 145 (the number of people who like either tea or milk)

To find the number of people who like both tea and milk, we can use the formula:

|T ∩ M| = |T| + |M| - |T ∪ M|

Substituting in the values we know, we get:

|T ∩ M| = 95 + 80 - 145 = 30

Therefore, 30 people like both tea and milk.

To represent this information in a Venn diagram, we can draw two overlapping circles to represent the sets T and M. The circle for T should contain 95 elements, and the circle for M should contain 80 elements. The overlap region between the circles should contain 30 elements. The region outside of both circles should contain 35 elements, since 35 people do not like either tea or milk. The Venn diagram would look like this:

         _______________

        /               \

       /                 \

      /         T         \

      \                   /

       \_________________/

              |

              |     30

              |

       ______/ \______

      /               \

     /                 \

    /         M         \

    \                   /

     \_________________/

In this diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.

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Answer:

\((m-n)^{2}-9r\)

Step-by-step explanation:

m²-2mn+n²-9r​

\((m-n)^{2}-9r\)

Answer:

(x, -y)

Step-by-step explanation:

When you reflect across the x-axis, the point moves vertically up or down to the other side of the x-axis. The x-coordinate of the point remains the same. The y-coordinate of the point becomes the opposite of the original value.

x remains x. y becomes -y.

Answer: (x, -y)

Airplane 1 had the fastest rate of descent during its landing.

To compare the rates of descent of the two airplanes, we need to convert both rates to a common unit of measurement. Let's convert both rates to feet per minute (ft/min) to make the comparison easier.

Airplane 1 had a rate of descent of -130 ft/s, which is equivalent to:

-130 ft/s × 60 s/min = -7800 ft/min

Airplane 2 had a rate of descent of -97/8 ft/s, which is equivalent to:

(-97/8) ft/s × 60 s/min = -729.375 ft/min

Comparing these two rates, we can see that Airplane 1 had the faster rate of descent during its landing:

-7800 ft/min (Airplane 1) > -729.375 ft/min (Airplane 2)

Therefore, Airplane 1 had the fastest rate of descent during its landing.

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Answer:

table 2

Step-by-step explanation:

see attached

Answer:

table no. 2

Step-by-step explanation:

Answer: 3/9 should be the answer :)

Step-by-step explanation:

Answer:

a) The percentage that the student does not read any paper is  10%  

b) The percentage that the student reads the local paper is 40%

c) the percentage that the student reads exactly two papers is 23%

d) the percentage that the student reads at least two papers is 25%

Step-by-step explanation:

Given the data in the question;

as illustrated in the Venn diagram below,

a)The student does not read any paper;

The percentage that the student does not read any paper will be;

100% - 90% = 10%

Therefore, The percentage that the student does not read any paper is  10%  

b) The percentage that the student reads the local paper;

from the Venn diagram below;

⇒ ( 20 + 15 + 3 + 2 )%    

= 40%

Therefore, The percentage that the student reads the local paper is 40%

c) The percentage that the student reads exactly two papers

⇒ ( 15 + 5 + 3 )%

= 23%

Therefore, the percentage that the student reads exactly two papers is 23%

d) The percentage that the student reads at least two papers;

⇒( 15 + 5 + 3 + 2 )%      

= 25%

Therefore, the percentage that the student reads at least two papers is 25%

The inequality will be 5(w+16)≥19.

What are inequality?
A disparity in size, quantity, quality, social standing, or another aspect is what is meant by the term "inequality." When you have ten of something and someone else has none, that is an instance of inequality. noun. 5. When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other.

The expression a ≠ b implies that a and b are not equal.

If a< b, then a must be less than b.

If a > b, then an is bigger than b. (these are called strict inequality)

The phrase "a ≤b" denotes that an is less than or equal to b.

a ≥ b means that an is greater than or equal to b.

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Answer:

y=-1

x=-3

Step-by-step explanation:

Answer:

Front, 60, back 60, right, 30, left, 30. And the triangle's surface area is 15 + 15 = 30, And 20 / 2 = 10. SO the surface area is 190 cm^2

Step-by-step explanation:

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Therefore , the solution of the given problem of probability comes out to be AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

(a) The voting box contains a total of seven slips, four of which are for candidate A and three for candidate B. Thus, there are 35 events that can occur from 7 choose 4 (or 7 choose 3) options.

Each vote can be represented by a letter, with A standing for a vote for candidate A and B for candidate B, so that all outcomes can be listed. These are the potential results:

AAAA

AAAB

AABA

ABAA

BAAA

AABB

ABAB

BABA

BBAA

ABBB

BABB

BBAB

BBBA

(b)

For instance, the following results could occur if the slips were removed in the following order:

A (1 vote for contender A) (1 vote for candidate A)

AA (2 ballots for candidate A) (2 votes for candidate A)

AAB (2 ballots for candidate A, 1 vote for candidate B) (2 votes for candidate A, 1 vote for candidate B)

AAAB (3 ballots for candidate A, 1 vote for candidate B) (3 votes for candidate A, 1 vote for candidate B)

AAAAB (4 ballots for candidate A, 1 vote for candidate B) (4 votes for candidate A, 1 vote for candidate B)

AAAABB (4 ballots for candidate A, 2 votes for candidate B) (4 votes for candidate A, 2 votes for candidate B)

AAAABBB (4 ballots for candidate A, 3 votes for candidate B) (4 votes for candidate A, 3 votes for candidate B)

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Answer:

So you can cancel out the 16. See, the -16 is negative, and if we add +16 to it, then it cancels out and is 0. That way, you have x=1.

Step-by-step explanation:

-16x+x=-15

+16x      +16

   0+x=1

       x=1

The linear function graphed is defined as follows:

y = 3x/2 - 3.

(third option).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = -3.

When x increases by 2, y increases by 3, hence the slope m is given as follows:

m = 3/2.

Then the function is defined as follows:

y = 3x/2 - 3.

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Answer:

the first blank is corresponding and the second blank is 105.

Step-by-step explanation:

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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