To rotate a triangle 180° about the origin counterclockwise, we can take each vertex of the triangle and reflect it across the origin. This will produce a new set of coordinates for each vertex that is the same distance from the origin as the original, but on the opposite side of the origin.
For example, the vertex F has coordinates (6, 3). If we reflect this point across the origin, we get the new point (-6, -3). Similarly, the vertex G has coordinates (3, 4), which become (-3, -4) when reflected across the origin, and the vertex H has coordinates (1, 7), which become (-1, -7) when reflected across the origin.
Therefore, the coordinates of each vertex of the triangle after rotating it 180° about the origin counterclockwise are as follows:
F: (-6, -3)G: (-3, -4)H: (-1, -7)Note: When rotating a point about the origin, the direction of rotation (clockwise or counterclockwise) is important. If we had rotated the triangle 180° about the origin clockwise instead of counterclockwise, the new coordinates of each vertex would have been the same as the original, since the triangle would be reflected across the origin and end up in the same position as it started.
Please give me brainliest for more high quality answers! - longstretch
What is the square root of 81b^2?
Answer:
Step-by-step explanation:
9 bytes2
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games
The inference from given boxplot is : The visiting team had more variability in the number of shots taken.
In this question we have been given two boxplots.
For the boxplots that the coach made,
for the home team:
Whiskers range is:16 to 32
So, the minimum value = 16
the maximum value = 32
the box ranges from 20 to 23. A line divides the box at 22.
so, the first quartile = 20
the third quartile = 23
the Median = 22
interquartile range(IQR) = 23 - 20
= 3
And for the visiting team
Whiskers range :14 to 32
This means, the minimum value is 14 and the maximum value = 32
As the box ranges from 16 to 24 and a line divides the box at 18,
the first quartile is 16, the third quartile = 24 and the median = 18
So, the interquartile range (IQR) = 24 - 16
= 8
From above data analysis the inference is that the visiting team had more variability in their shots, because their distribution has a higher interquartile range (8 > 3)
Learn more about the boxplot here:
https://brainly.com/question/12992903
#SPJ4
Given question is incomplete.
The complete question is:
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.
Number of Shots Taken by Home Team Players
A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.
Number of Shots Taken by Visiting Team Players
Which describes an inference that the coach might make after comparing the medians of the two data sets?
The points (-7, 3) and (9, r) lie on a line with slope 1/4
Find the missing coordinate r.
Answer:
Use the formula y-3= 1/4(x--7) ---> y-3= 1/4(x+7)
4.75 is the y intercept
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
To find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
The cost of 4 small greeting cards is 4 * $1.80 = 4 * 1.8 = $7.20.
The cost of 3 large greeting cards is 3 * $3.85 = 3 * 3.85 = 11.55.
The total cost of 4 small greeting cards and 3 large greeting cards is $7.20 + $11.55 = 7.2 + 11.55 = 18.75.
To find the cost of x small greeting cards and y large greeting cards, you can use the following equation:
cost = x * $1.80 + y * $3.85
Substituting the values of x and y into this equation will give you the total cost of the greeting cards.
Hence, to find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.
To learn more about the system of linear equations visit,
https://brainly.com/question/2226590
#SPJ1
According to a survey conducted by Independent Sector, the percent of their income that Americans give to charities is related to their household income. For families with an annual income of $100000 or less, the percent approximately given by P(x)=0.0014[tex]x^2[/tex] - 0.1529x + 5.855, 5≤x≤100 where P is the percent of annual income given and x is the annual income in thousands of dollars. According to this model , what income level corresponds to the minimum percent of charity contributions,to the nearest whole number?
According to given model income level corresponds to the minimum percent of charity contributions is 5%.
The given function is P(x)=0.0014x² - 0.1529x + 5.855, 5≤x≤10.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Check the critical points and end points to test for any absolute extrema over the given interval.
Absolute Maximum: (5,5.1255)
Absolute Minimum: (10,4.466)
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (54.60714285,1.68028392)
Focus: (54.60714285,180.2517125)
Axis of Symmetry: x=54.60714285
Directrix: y=−176.89114464
Now, P(5)=0.0014(5)² - 0.1529(5)+5.855
= 5.1255
≈5%
Therefore, according to given model income level corresponds to the minimum percent of charity contributions is 5%.
To learn more about the function visit:
https://brainly.com/question/28303908.
#SPJ1
Please help I’ll give brainliest what is the slope of the line
-1/2
1/2
-2
2
Answer:
2
Step-by-step explanation:
Pick 2 coordinates on the line and do the formula for slope.
ex: (2,4) and 3,6)
4-6/2-3 = -2/-1 = 2
Match the linear equation to the correct graph.
Answer: y= -1x + 2
Step-by-step explanation:
The linear equation is y= mx + b
Y-intercept here is at (0,2), so b is 2
Let pick point (0,2) (2,0)
The slope is rise/run, and we see that the graph is going down by 2 and goes over by 2, so it is -2/2 = -1
So the equation is y=1x +2
If you can, please give me a Brainliest, I only need 1 more to become an Ace, thank you!
A student incorrectly says the solution to the equation +2/3y-1/7y =357 is y = 289. What error did the student make?
A: The student subtracted 1/7 from -2/3
B: The student multiplied 357 by 17/21
C: The student multiplied 357 by 21/17
D: The student added −2/3 to -1/7
a. Find SL
Explain your reasoning.
b. Explain how the captain can use a similar process to find the distance between the boat and the shoreline.
Answer:
SL = 2.1 miles
Step-by-step explanation:
Given ∆LRS with RS extended to point T, and angles R = 35° and exterior angle LST = 70°, you want the measure of SL. You want to apply the process to finding distance to shore.
a. Isosceles triangleThe exterior angle LST is the sum of interior angles SRL and SLR. In equation form, this is ...
∠LST = ∠SRL +∠SLR
70° = 35° +∠SLR
∠SLR = 35°
The angles at either end of segment LR are both 35°, so the triangle is isosceles. That means sides SR and SL are congruent:
SL = SR = 2.1 miles
b. Distance to shoreThe distance from the boat to the lighthouse has been found using an isosceles triangle. A similar method can be used to find the distance to shore. It requires the captain to be able to identify a point on shore, and measure the distance traveled parallel to the shore.
By using a 45° angle to start, and a 90° angle at the second measurement, the distance traveled between angle measurements will be exactly the (closest) distance to shore from the point of the second measurement.
Other angle measures can be used with trigonometric methods.
I ordered some books online for myself and friends.
Each book costs $13 and the store charges a one-time shipping fee of $ 20
Write an expression for the cost of buying nn books.
The expression for the cost of buying n book will be 20 + 13n.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
In this case, the person some books online for myself and friends and each book costs $13 and the store charges a one-time shipping fee of $20.
The expression for the cost of buying n books is:
= 20 + (13 × n)
= 20 + 13n
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
On a cale drawing of a hore, the cale i 1 in: 10 ft. If the real hore i 25 ft tall, how tall i the hore on the cale drawing?
If the scale of drawing is 1 inches : 10 feet and the real horse height is 25 feet, then the height of the horse in drawing is 2.5 inches
The scale of drawing the horse = 1 inch : 10 feet
Therefore in scale
The height of the horse in drawing = 1 inch
The height of the horse = 10 feet
The original height of the horse = 25 feet
The height in the picture = x inches
To find the height the horse in the picture, we have to use proportion
1 inch : 10 feet = x inches : 25 feet
1 / 10 = x / 25
1 × 25 = 10x
10x = 25
x = 25/10
x = 2.5 inches
Therefore, the height of the horse in drawing is 2.5 inches
Learn more about scale here
brainly.com/question/28651690
#SPJ4
Write an explicit formula for each sequence and find the 7th term for each
1. -4, 12, -36
2. 12, 3, 3/4
Answer:
a[n] = -4·(-3)^(n-1); -2916a[n] = 12·(1/4)^(n -1); 3/1024Step-by-step explanation:
You want the explicit formula for each of the geometric sequences, and the 7th term.
-4, 12, -36 12, 3, 3/4Explicit formulaThe explicit formula for a geometric sequence with first term a[1] and common ratio r is ...
a[n] = a[1]·r^(n-1)
1. a[1] = -4, r = -3The explicit formula is ...
a[n] = -4·(-3)^(n-1)
The 7th term is ...
a[7] = -4·(-3)^(7-1) = -2916
2. a[1] = 12, r = 1/4The explicit formula is ...
a[n] = 12·(1/4)^(n -1)
The 7th term is ...
a[7] = 12·(1/4)^(7-1) = 3/1024
Find the surface area of a square pyramid with a side length of 5cm and slant height of 6cm.
Answer:
85 cm^2
Step-by-step explanation:
The surface area of a square pyramid is given by the formula:
Surface area = base area + 4 * (base edge length * slant height) / 2
In this case, the base area is 25 cm^2, because the side length of the base is 5 cm. The base edge length is also 5 cm, because it is a square pyramid. Plugging these values into the formula above, we get:
Surface area = 25 cm^2 + 4 * (5 cm * 6 cm) / 2
= 25 cm^2 + 60 cm^2
= 85 cm^2
So the surface area of the square pyramid is 85 cm^2.
evaluate the expression 3^3
Answer:
27
Step-by-step explanation:
3*3*3 equals 27. I hope this helps.
Answer: The solution to this problem is 27.
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer:
1 : 2
or
1/2
Step-by-step explanation:
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
6 : 12
semplify
1 : 2
in fraction
1/2
eternity greatful if you help me
Answer:
1) Associative
2) Distributive
3) Distributive
4) Associative
Erica read 4 pages on Wednesday, 20 pages on Thursday, 100 pages on Friday, and 500 pages on Saturday. What kind of sequence is this?
Answer:
Geometric sequence
Step-by-step explanation:
A geometric sequaence is when the term is multiplied or divided to get to the next term.
each term is being multiplied by 5
Ms caraballo visits the zoo and sees a total of 40 animals all of them lions tigers or bears she sees four more lions than tigers and three fewer bears than tigers
Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.
What is the system of linear equations?
A system of linear equations is a collection of two or more linear equations, and a solution to a system of linear equations consists of values of each of the unknown variables in the system that satisfies all of its equations or makes them true.
Let L be the number of lions, T be the number of tigers, and B be the number of bears. We can set up the following system of equations to represent the given information:
L + T + B = 40
L = T + 4
B = T - 3
We can solve this system of equations using substitution. Starting with the second equation, we can solve for T:
T = L - 4
Substituting this expression for T into the third equation, we get:
B = L - 4 - 3
B = L - 7
Substituting this expression for B into the first equation, we get:
L + L - 4 + L - 7 = 40
3L - 11 = 40
3L = 51
L = 17
Now that we know the number of lions, we can substitute this value back into the equation T = L - 4 to find the number of tigers:
T = 17 - 4
T = 13
Finally, we can substitute these values for L and T into the equation B = L - 7 to find the number of bears:
B = 17 - 7
B = 10
Hence, Ms. Caraballo saw 17 lions, 13 tigers, and 10 bears at the zoo.
To learn more about the system of linear equations, visit:
https://brainly.com/question/13729904
#SPJ1
An amusement park says "You must be 40 inches tall to ride" What percentage of this height is:
a. 34 inches?
b. 54 inches?
Answer:85%, 135%
Step-by-step explanation:
2/40 is 5%. There is 17 2's in 34 so the percentage is 17x5=85.
There is 27 2's in 54 so the percentage is 27x5=135.
What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
In determining a mean, the 90% C.I. is more accurate than the 95% C.I.
What is confidence interval mean ?A confidence interval is the mean of your estimate plus or minus the range of that estimate's variability.
You can reasonably anticipate that if you repeat the test, your estimate will fall within these values. In statistics , confidence is another name for probability
What does "confidence interval" actually mean?A statistician who declares that they have a 95% confidence level has basically seen one possible interval out of many possible ones, and 19 out of 20 of those intervals include the correct value of the parameter.
In determining a mean, the 90% C.I. is more accurate than the 95% C.I.
To know more about confidence intervals.
https://brainly.com/question/24131141
#SPJ4
A model car is 12 inches long. Using a scale of 3 inches : 4 feet ,how long is the actual car
Length of the car is 12 inches equal to 192 feet.
What is unit of length?Using measuring instruments like a ruler, measuring tape, etc., one can measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A feet scale can be used to gauge the height of each student in a class.
The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.
Given ,
3 inches : 4 feet
3 inches : 4*12
3 inches :48
1 inches : 16 feet
Length of the car is 12 inches = 12 * 16
Length of the car is 12 inches = 192 feet
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, a rectangle's length and width are its dimensions.
To learn more about unit of length refer to:
https://brainly.com/question/27351903
#SPJ1
What are the domain restrictions of the expression g^2−2g−24/g^3−4g^2−12g?
Select each correct answer.
Responses
g≠6
g ≠ -6
g≠−4
g≠0
g≠−2
g≠2
When working with rational functions, your main concern to not divide by 0. Dividing by 0 can't be done.
So, you need to look at the denominator of your fraction and figure out what values of g will make that denominator become 0.
Option #1 is to plug in each option from your list to see which ones make the denominator equal 0. If that g-value makes the denominator equal zero, then it has be excluded.
Option #2 is to set the denominator equal to 0 and solve that equation:
g^3 - 4g^2 - 12g = 0
To solve this, you could do it by factoring.
g^3 - 4g^2 - 12g = 0
g ( g^2 - 4g -12) = 0
g ( g - 6 ) ( g + 2) = 0
This splits into:
g = 0, g = 6, g = -2
So those are the three values of g that you cannot use.
g ≠ 0; g ≠ 6, g ≠ –2
Kevin and Randy Muise have a jar containing 62 coins, all of which are either quarters or nickels. The total value of the coins in the jar is
$7.90. How many of each type of coin do they have?
Answer: 38 nickels, 24 quarters
Step-by-step explanation:
x=number of quarters
y=number of nickels
x + y = 62
$0.25x + $0.05y = $7.90
solve for x in terms of y, then substitute into the 2nd equation:
x = 62-y
.25(62-y) + .05y = 7.90
15.5 - .25y + .05y = 7.90
15.5 - .20y = 7.90
-.20y = -7.6
y = -7.6/-.20
y = 38
now solve for x:
x + 38 = 62
x = 62-38 = 24
x = 24
what is the answer for 3y2 + 4y2 =
Answer:
y^2(3+4)
7y^2
BTW isn't it too much to ask for high school level question?
choose each digit of a 5 digit number at random from digits 1, . . . , 9. compute the probability that no digit appears more than twice.
The probability that no digit appears more than twice is 0.648.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
We will choose each digit of 5-digit numbers at random from digits 0,1,2,..,9.
We have to compute the probability that no digit appears more than twice.
So, we have to form a five-digit number say "abcde".
Now, for 'a' we have 10 choices.
For 'b' we have again 10 choices because a digit can appear at most two.
For 'c' we have 9 choices because the digit in 'a' can not be chosen as a digit can appear at most two.
For 'd' we have again 9 choices by a similar argument.
Finally, for 'e' we have 8 choices because the digit chosen previously can not be repeated more than twice.
The total number of such 5-digit numbers is = 10*10*9*9*8 = 64800.
Now, a total number of 5-digit numbers = 10*10*10*10*10 = 100000.
Hence, the probability that no digit appears more than twice is given by,
= 64800/ 100000
= 0.648
Hence, the probability that no digit appears more than twice is 0.648.
To learn more about the probability from the given link
https://brainly.com/question/24756209
#SPJ1
Michelle is playing a board game. At the end of the first round, she has
-2.3 points. During the second round, she gains 4.5 points. During the third round, she loses 6.7 points. What is Michelle's point value after the third round?
Show your work.
After Solving the provided question, the Michelle's point value after the third round is -4.5 by the third round
What are mathematical operations?A value is computed using operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or numbers, the math operator's symbol has predetermined rules.
What is the Order of Operations?Mathematical operations like addition (+), subtraction (-), multiplication (*), and division (**) take precedence over one another. Neither of the two operators can be used to solve an equation by itself. The brackets in any equation, whether arithmetic or algebraic, must be evaluated first, according to the order of operations principles, which we must abide by. The second place is where the order will be determined. After evaluating addition and subtraction, we'll analyze multiplication and division.
[tex]she starts off with a negative 2.3 of you add positive 4.5 = > (-2.3) + 4.5 = 2.2[/tex]
but after that, she lost another 6.7 points, leaving her with a negative score of 4.5.
[tex]= > 2.2 - 6.7 = ( -4.5 )[/tex]
To know more about Mathematical operation visit:
https://brainly.com/question/20628271
#SPJ1
William buys a T.V that is on sale for 40% off the original price. The original price is $140 more than the sale price.
What is the original price of the T.V?
30 POINTS ANSWER ASAP!!!!
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 4 comma 4, 4 comma 4, and 4 comma negative 2
10 units
24 units
36 units
64 units
Answer: 24 units.
Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.
The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - (-4))^2 + (4 - 4)^2)
= sqrt(8^2 + 0)
= sqrt(64)
= 8
The length of the side between the second and third vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 4)^2 + (-2 - 4)^2)
= sqrt(0 + (-6)^2)
= sqrt(36)
= 6
The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
= sqrt(8^2 + 6^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.
Therefore, the perimeter of the right triangle is 24 units.
The population of Browne County is represented by the function f(x)=87,000(0.9)x, where x is the number of years since 2010. The population of Orange County was 102,000 in 2010 and has decreased exponentially at a rate of 16% each year. How do the populations of these counties compare in 2015? In 2015, the population of Browne County was approximately and the population of Orange County was approximately. In 2015, which County was more populous?
Browne County shows a population bigger than Orange County in 2015.
How to compare two populations that change exponentially in time
Herein we find the case of two cities in the United States that changes exponentially in time, the population of Browne County decrease in time, while the population of Orange County decreases at a lower rate in time in time. Exponential model is introduced below:
p'(n) = p · (1 + r / 100)ⁿ
Where:
p - Initial population.p'(n) - Final population.r - Growth rate, in percentage.n - Period, in years.Now we proceed to build the equation that explain the growth of the two cities:
Browne County (p = 87,000, r = - 10)
p'(n) = 87,000 · 0.9ⁿ
Orange County (p = 102,000, r = 16)
p'(n) = 102,000 · 0.84ⁿ
Now we evaluate the two functions at n = 5:
Browne County
p'(5) = 87,000 · 0.9⁵
p'(5) = 51,372
Orange County
p'(5) = 102,000 · 0.84⁵
p'(5) = 42,657
Browne County has more population than Orange County.
To learn more on exponential equations: https://brainly.com/question/29506679
#SPJ1
Jane received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.68 per pound. After buying the coffee, she had $37.92 left on
her card. How many pounds of coffee did she buy?