Find the coordinates of the centroid of ️RST with vertices R(-5,-9), S(6,-3), T(-1,6)
The coordinates of the centroid of the triangle RST is (0, -2)
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The coordinates of the vertices of the triangle RST:
R(-5,-9), S(6,-3), T(-1,6)
The coordinates (x, y) of the centroid of a triangle.
x = (a + c + e) / 3
y = (b + d + f) / 3
Where (a, b), (c, d), and (e, f) are the coordinates of the vertices of a triangle.
Now,
(a, b) = (-5, -9)
(c, d) = (6, -3)
(e, f) = (-1, 6)
The coordinates (x, y) of the centroid of a triangle is (0, -2).
x = (-5 + 6 - 1) / 3
x = 0
y = (-9 - 3 + 6) / 3
y = -6/3
y = -2
Thus,
The coordinates of the centroid are (0, -2).
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For any real number a, \(\sqrt{a^{2} }\)=
Step-by-step explanation:
for any real number a, the definition is:
\( \sqrt{ {a}^{2} } = |a| \)
Select all sets in which the number - 15 is an element.
A. natural numbers
B. real numbers
C. irrational numbers
D. rational numbers
E. whole numbers
F. integers
-15 is an element of-
B. real numbers
D. rational numbers
F. integers
What is a number?A number is a mathematical object used to count, measure, and label. The original examples are natural number 1,2,3,4 and so forth.
Given number is 15.
A. natural numbers
The natural numbers are the set of all the whole numbers excluding zero. They are positive whole number.
Here, -15 is a negative number,
Hence, -15 is an not element of natural number.
B. real numbers
Real numbers are those numbers that has no imaginary part. It also include both rational and irrational number.
Since -15 has no imaginary part
Hence, -15 is an element of real number.
C. irrational numbers
An irrational number is real number that cannot be expressed as a ratio of two integers.
Here -15 can be expressed as ratio of two integers,
Hence,-15 is not an element of irrational number.
D. rational numbers
A rational number is real number that can be expressed as a ratio of two integers.
Here -15 can be expressed as ratio of two integers,
Hence, -15 is an element of rational number.
E. whole numbers
Whole numbers are positive numbers, including zero, without any decimal or fractional parts. Negative numbers are not considered "whole numbers."
Since,Negative numbers are not considered whole numbers
Hence, -15 is not an element of whole number.
F. integers
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043
Hence, -15 is an element of integers.
Hence, we conclude that,
-15 is an element of-
B. real numbers
D. rational numbers
F. integers
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-x+3y=11 pls sove by elimation and step by step
Answer:
Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.
Step-by-step explanation:
The given equation is:
-x + 3y = 11
To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.
Let's suppose we have another equation with x, for example:
2x + 5y = 7
We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:
-2x + 6y = 22 (multiply the first equation by -2)
2x + 5y = 7 (the second equation)
Now we can add the two equations to eliminate x:
-2x + 2x + 6y + 5y = 22 + 7
Simplifying the equation, we get:
11y = 29
Dividing both sides by 11, we get:
y = 29/11
Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
-x + 3y = 11
Substituting y = 29/11, we get:
-x + 3(29/11) = 11
Simplifying the equation, we get:
-x + 87/11 = 11
Subtracting 87/11 from both sides, we get:
-x = 11 - 87/11
Multiplying both sides by -1, we get:
x = 87/11 - 11
Simplifying the equation, we get:
x = (87 - 121)/11
x = -34/11
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
show all steps
On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).
The sample has 100 bottles in total.
As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:
P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles
P(properly positioned and Plastic #4) = 15 / 100
P(properly positioned and Plastic #4) = 0.15 or 15%
Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
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Find the circumference of the object.
2 meters
Answer:
circumference =2×3.14
circumference =6.28 m
Solve for x.
A)-6
B)-9
C)-15
D)-18
A question asks: How many hours per week do you watch television? The respondent can answer in minutes and/or hours. What would be the best numerical summary of data from 300 participants? A. Mean, standard deviation, and range B. Median, IQR, and range C. Number and percent of total for each response option D. A or B depending on the distribution of the sample E. B and C
Answer: D. A or B depending on the distribution of the sample
Step-by-step explanation:
Given: A question ask about how many hours per week do you watch television?
Total participants = 300
Since all participants are different , so have their own answer to this question in numerical terms.
We use proportion or percentage to summarize data if data is categorical, but here data is numerical (continuous).
here , we can use either mean or median ( if it has outliers).
For this we need to check the distribution of the data, if it is normal then Mean, standard deviation, and range would be a better option (as mean is the best measure of tendency)otherwise Median, IQR, and range would be a better option .
hence, the correct option is D. A or B depending on the distribution of the sample
2. Trapezoid WXYZ is located at W(2.1) X[3.
5) Y(6.5) and Z[7. 1). After being translated 6
Units down, what are the new coordinates
of Point Y?
Point Y is (6, -1)
Subtract 6 from the y coordinate in point y since it is translated down. keep the x coordinate since it is only being translated up and down, or by the y axis
Jamal hiked on two trails. The first trail was 8 1/3 miles long, and the second trail was 1 3/5 time as long as the first trail. How many miles did Jamal hike ? Enter as a mixed number in simplest form
Answer:9 14/15
Step-by-step explanation:
hope that helped
Given f(x) = 3x-2 and g(x)=-1/2x3, find the following problems
1. F(5).
2. G(8)
3.f(-8)
4.G(-10)
Answer:
f(5)=13 g(8)=12 f(-8)= -26 g(-10)=-15
Step-by-step explanation:
1) 5*3=15
15-2=13
2) 8*.5*3=12
3) -8*3=-24
-24-2= -26
4) -10*.5*3= -15
Side XY of triangle XYZ is extended to point W, creating a linear pair with <WYZ and <XYZ. What is the value of x?
Answer:
80
Step-by-step explanation:
I just did this and its right!
Answer:
80
Step-by-step explanation:
step-by-step explanation is xy xyz wyz xyz 80
3
4
A pitcher contains 1 quarts of milk. How
many cups of milk are in the pitcher?
Answer: 4
Step-by-step explanation:
there are 4 cups in 1 quart!
Find the work done by a force that is given by the vector (2,6) in moving an object in a straight line from point
R(-3, 2) to point S(9,7). Assume that the units in the coordinate plane are meters.
Answer:
B. 54 Joules
Step-by-step explanation:
Answer: B. 54 Joules
Step-by-step explanation:
Work = Force * displacement
W = F * d
To find the product of two vectors: F * d = F1 * d1 + F2 * d2
Force: (2, 6) <--- (to clarify above formula, F1 = 2, F2 = 6)
displacement: R(-3, 2) to S(9, 7)
Let's convert the displacement vector to component form:
(9 - (-3), 7 - 2) ---> (12, 5)
Now let's use the formula shown above to solve the problem:
F * d = F1 * d1 + F2 * d2
F * d = (2 * 12) + (6 * 5)
F * d = 24 + 30
F * d = 54
Work is expressed in Joules. So, the work done is 54 JOULES.
I hope that makes sense! Leave a comment or send a message if you have a question.
How many times did the team score less than 60 points?
Stem
4
5
6
7
Leaf
2,5,9
3,4,6,8,8,9
0,2,3,4,4,6,8
0,0,1,2
100 POINTS WILL GIVE BRAINLIEST If businesses lower prices, consumers want more. What is it called when businesses have negative products to provide to demanding consumers?
A. supply surplus
B. consumer surplus
C. producer surplus
D. profit surplus
Answer:consumer surplus
Step-by-step explanation:
Answer:
Its B consumer
Step-by-step explanation:
The one-to-one functions g and h are defined as follows.g(x) = 4x - 3h={(-6, 3), (-4, 7), (3, -8), (6, 4)Find the following
It is given that
\(g(x)=4x-3\)Now to find the inverse of g
Let
\(\begin{gathered} y=4x-3 \\ 4x=y+3 \\ x=\frac{y+3}{4} \end{gathered}\)So
\(g^{-1}(x)=\frac{x+3}{4}\)Now we know that
\((g^{-1}.g)(x)=\text{ x}\)So
\((g^{-1}.g)(2)=2\)And since
\(h(-6)=3\)So
\(h^{-1}(3)=-6\)Find the sum. Write your answer in simplest form. 1 1/2 + 2 3/10
Answer:
\( = 3 \frac{4}{5} \\ \)
Step-by-step explanation:
\( 1\frac{1}{2} + 2 \frac{3}{10} \\ \frac{3}{2} + \frac{23}{10} \\ \frac{15 + 23}{10} \\ = \frac{38}{10} \\ = 3 \frac{8}{10 } \\ = 3 \frac{4}{5} \)
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4,6,9,...
Find the 8th term.
Find the 8th term.
Answer:
4, 6, 9, 12, 15, 18, 21, 24.
Step-by-step explanation:
The 8th term is 24.
just +2 (add 2) every time.
are they inverse ? please hurry
Answer:
no
Step-by-step explanation:
Simplify 2x^2-7x-4/x^2
Answer:
Option 1
Step-by-step explanation:
\(\frac{2x^2 - 7x-4}{x^2 - 5x+4}=\frac{(x-4)(2x+1)}{(x-4)(x-1)}=\frac{2x+1}{x-1}\)
Solve 2(x+5)=18+xanswer?!
Answer:
x=4
Step-by-step explanation:
1. Divide both sides of the equation by 2
x+5=9
2. Move the constant to the right -hand side and change its sign
x=9-5
3. Subtract the numbers
x=4
-1000 2/3 is not real fraction. True or false
True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.
In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.
To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.
It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.
In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.
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Write the expression for the following statement without
any spaces:
the sum of 64y and 3, cubed can be expressed as
The expression of the statement that is given above can be written as follows: 262144y³ + 27.
How to determine a way to express the given statement?To determine how to express the given statement the following should be carried out.
When a number is said to be cubed, it means that the number should be times by itself three consecutive times.
That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,
= 64×64×64(y)³ + 3×3×3
= 262144y³ + 27.
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Need help on this!!! Pls help!!!
a) The mean of the data-set is of 2.
b) The range of the data-set is of 4 units, which is of around 4.3 MADs.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.
The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:
Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)
Mean = 2.
The range is the difference between the largest observation and the smallest, hence:
4 - 0 = 4.
4/0.93 = 4.3 MADs.
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PLEASE HELP!!!!!!
will mark as brainliest!!!!!
Answer:
Far left one, A
Step-by-step explanation:
Answer:
As 4 of the 22 males questioned liked talking on the phone, the odds are 4/22
Step-by-step explanation:
Match each function with the correct translation of the parent function f(x) = x.
160=1x1-4
f(x) = (x+4)
fx)=p+4
0
00
vertical translation down 4 units
horizontal translation right 4 units
horizontal translation left 4 units
vertical translation up 4 units
It is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in
the graph intersecting the x- or y-axis at a different point.
Function is an operation that takes an input, performs some processing on it, and returns a result. It is a set of instructions that performs a specific task. Functions are typically used to perform repetitive tasks, like finding the sum of two numbers, adding two strings together, or finding the maximum of a list of numbers. Functions are essential to programming and can be used to make code more organized, reusable, and efficient.
The function f(x) = x is the parent function for linear equations. This equation is generally used to graph a line with a slope of 1 and a y-intercept of (0, 0). In order to translate this parent function, different transformations are applied to it.
A vertical translation down 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function down 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, -4).
A horizontal translation right 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function right 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (4, 0).
A horizontal translation left 4 units would be represented by the equation f(x) = x - 4. This transformation would shift the graph of the parent function left 4 units on the x-axis. This would result in the graph intersecting the x-axis at the point (-4, 0).
Finally, a vertical translation up 4 units would be represented by the equation f(x) = x + 4. This transformation would shift the graph of the parent function up 4 units on the y-axis. This would result in the graph intersecting the y-axis at the point (0, 4).
In conclusion, it is possible to translate the parent function f(x) = x using various transformations including vertical and horizontal translations. Each transformation will result in the graph intersecting the x- or y-axis at a different point.
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I will mark you brainiest!
What is the length of EF?
A) 2.4
B) 3.8
C) 0.5
D) 1.2
Answer: 2.4
Step-by-step explanation: Given the angles below, the length of EF will be 2.4
Answer:
B) 3.8.
EF = 3.8
Use the law of sines to find the unknown length EF
need help plz can someone please help
Answer:
D
Step-by-step explanation:
Answer:
d. 40
Step-by-step explanation:
Mia has a collection of vintage action figures that is worth $190. If the collection appreciates at a rate of 6% per year, which equation represents the value of the collection after 5 years?
The equation that represents the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
Explanation:
To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).
Therefore, the equation for the value of the collection after 5 years is:
Value of collection after 5 years = 190 x (1 + 0.06)^5
This can also be written as:
Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)
Therefore, the value of the collection after 5 years is $246.90.
Answer: 254.26
Step-by-step explanation: