To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.
For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).
This will move the triangle 5/2 units to the left along the x-axis.
It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.
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Given f(x) = − x² - 4x – 12, find f(-7)
Answer:
f(-7) = -33
Step-by-step explanation:
f(x) = − x² - 4x – 12
f(-7) = ?
We put -7 in for x and solve
f(-7) = -(-7)^2 -4(-7) - 12
f(-7) = -(49) + 28 - 12
f(-7) = -49 + 28 - 12
f(-7) = -33
A car moving at a constant speed passed a timing device at t=0. After 9 seconds the car has traveled 1,053ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Answer:
d = 117t
Step-by-step explanation:
The equation is
y = mx + b
Here m is the function's slope, and b is the y-intercept.
We know
As the car moves at a constant speed passes a timing device at t=0.
After 9 seconds, the car traveled 1053ft.
We have to find the slope
Slope = rise/run or (y2 - y1) / (x2 - x1)
We have the slope is
m = 1053/ 9 = 117
So, the equationn is d = 117t
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Given P(A) = 0.32, P(B) = 0.2 and P(AU B) = 0.366, find the value of
P(An B), rounding to the nearest thousandth, if necessary.
By using formula, P(A n B) = 0.346. Rounded to the nearest thousandth, P(A n B) = 0.346
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between 0 and 1, the closer the probability is to 1, the more likely the event is to occur. The probability of an event is usually represented by the letter P, followed by the event in parentheses.
What is rounding off?Rounding off is a mathematical operation that is used to reduce the number of digits in a number while maintaining its value within a certain degree of accuracy. When we round off a number, we look at the digit that is immediately to the right of the last digit that we want to keep. If the number is less than 5, we keep the last digit as it is, but if the number is greater than or equal to 5, we add 1 to the last digit.
We can use the formula of conditional probability to find the value of P(A n B).
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
So we can substitute this in the first equation:
P(A n B) = P(A U B) - P(A) - P(B) + P(An B)
P(An B) = P(A U B) - P(A) - P(B) + P(An B)
Now we can substitute the given values:
P(An B) = 0.366 - 0.32 - 0.2 + P(An B)
P(An B) = 0.346 + P(An B)
To find P(An B) we can subtract 0.346 from both sides of the equation:
P(An B) = P(An B) - 0.346
P(An B) = P(An B) - 0.346
So, P(An B) = 0.346
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20. Below are massesof students taken in a medical centre. 37 60 35 38 59 34 56 42 55 48 39 33 36 35 43 52 39 64 41 35 20 31 29 45 32 54 66 44 47 45 27 24 48 28 55 (a) Starting with the class 20-29 and class size of 10, make a frequency distribution table for the data. (2 marks)
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Class} & \text{Frequency}\\\cline{1-2}20-29 & 5\\\cline{1-2}30-39 & 12\\\cline{1-2}40-49 & 9\\\cline{1-2}50-59 & 6\\\cline{1-2}60-69 & 3\\\cline{1-2}\end{array}[/tex]
=====================================================
Explanation:
The given data set is
{37, 60, 35, 38, 59, 34, 56, 42, 55, 48, 39, 33, 36, 35, 43, 52, 39, 64, 41, 35, 20, 31, 29, 45, 32, 54, 66, 44, 47, 45, 27, 24, 48, 28, 55}
It sorts to
{20, 24, 27, 28, 29, 31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39, 41, 42, 43, 44, 45, 45, 47, 48, 48, 52, 54, 55, 55, 56, 59, 60, 64, 66}
The five values 20,24,27,28,29 are between 20 and 29. This means the first class or bin will have a frequency of 5.
The next interval spans from 30 to 39. There are 12 items in this interval, and those 12 items are this subset {31, 32, 33, 34, 35, 35, 35, 36, 37, 38, 39, 39}. This means we have a frequency of 12 for the interval from 30 to 39.
Keep this process going until you get to the end of the data set.
What is meant by halting problem?
Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.
Describe a tractable problem.an algorithm that takes a polynomial amount of time to solve a tractable issue. The upper bound is described by a polynomial. Any issue that cannot be addressed in a polynomial period of time is considered to be intractable. The lowest limit is exponential.
Here,
The halting problem claims that no computer can be created that can anticipated.
the likelihood that any other program will halt after a certain number of steps, making it an unsolved algorithmic challenge.
Software development is directly affected in practice by the stopping problem's insoluble nature.
Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.
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Pls help me with math
Answer:1
Step-by-step explanation:;
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information.
If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?
2a+b=15.7 is the formula used to get the base's length and b has a value of 3.
What is an isosceles triangle?Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and Skelos are the source of the name (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.
An isosceles triangle has 2 equal sides that are longer than the length of the base
perimiter=15.7
equation is 2a+b=15.7
so if the longer side is 6.3
we know that identical sides are bigger so 6.3 is one of the identical sides
2a means the 2 identical sides
2(6.3) + b = 15.7
12.6 + b = 15.7
subtract 12.6 from both sides
b = 3.1
therefore, The equation used to find the length of the base is 2a+b=15.7
and the value of b is 3.1
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Answer:
12.6 + b = 15.7
Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true? A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. C. $a-b$ is a multiple of $6$. D. $a-b$ is a multiple of $2$. List the choices in your answer separated by commas. For example, if you think they are all true, then answer "A,B,C,D".
The statements that are true, based on the multiples of 3 and 6 are:
A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. How do multiples relate ?When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.
This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.
It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.
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All the backpacks at sports galore are on sale at 30% off the marked price. Tracy bought a backpack that was marked $60. What was the sale price?
Answer:
Step-by-step explanation:
we know the 30% off the marked price.
so the sale price is 60-60*30%=42
Answer:$42.00
Step-by-step explanation:
What is a shape called with 1000000000 sides?
Answer:
Regular megagon
Step-by-step explanation:
Regular megagon is a shape called with 1000000000 sides.
Can someone tell me how to do this?
solve 4x + 3 = 11
x = ?
Answer:
x = 2
Step-by-step explanation:
4x + 3 = 11
(4x + 3) - 3 = 11 - 3
4x = 8
4x/4 = 8/4
x = 2
As you can see, to isolate x, we must do the opposite operations to both sides.
Luke just accepted a job at a new company where he will make an annual salary of $58000. Luke was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Luke make as a salary after 9 years working for the company? What would be his salary after tt years?
Answer:
1. $76,000
2. $58,000 + $2,000 * t
Step-by-step explanation:
2. Now, you might be questioning why we are going with the second question first, but this will be useful as it sets up our equation to make the first question easier. So, we will start with Luke's base salary of $58,000. Then, we will add $2,000 for every year he works at the company. If he works for t years and gains $2,000 on his salary per year, our equation will look like this:
$58,000 + $2,000 * t
That is the equation.
1. Now, using our previous equation, $58,000 + $2,000 * t, we will substitute 9 in for t. We get:
$58,000 + $2,000 * 9
Then, we simplify, giving us:
$58,000 + $18,000 = $76,000
(a) Write an inequality for which 3, -4, 0, and 2,300 are solutions
(b) How many total solutions are there to your inequality?
(hurry)
The inequality be -4 ≤ x ≤ 2,300
If x is a real number, we have infinite solutions.
If x is an integer number, we have 2,305 solutions.
What is meant by inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.
The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.
Let the given data be 3, -4, 0, and 2,300 are solutions.
If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}
Let the inequality be -4 ≤ x ≤ 2,300
The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.
Here x exists a real number, then we contain infinite solutions.
If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)
the number zero (1)
We would have: 4 + 2,300 + 1 = 2,305 integer solutions.
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The inequality be -4 ≤ x ≤ 2,300
If x is a real number, we have infinite solutions.
If x is an integer number, we have 2,305 solutions.
What is meant by inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers.
The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus.
Let the given data be 3, -4, 0, and 2,300 are solutions.
If we order these numbers from smallest to largest, we get: {-4, 0, 3, 2,300}
Let the inequality be -4 ≤ x ≤ 2,300
The four values in the set {-4, 0, 3, 2,300} exists solutions for our inequality.
Here x exists a real number, then we contain infinite solutions.
If x exists an integer, then the total number of solutions will be equivalent to the number of negative solutions (4) and number of positive solutions (2,300)
the number zero (1)
We would have: 4 + 2,300 + 1 = 2,305 integer solutions.
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How to do proofs with perpendicular lines theorem?
Answer:
"If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular."
Step-by-step explanation:
how do simplify -5x+5x or is it already simplified?
Answer:
zero is the simplified answer
Step-by-step explanation:
it's just as adding -5 to 5 which are additive inverse to each other so they cancel each other out ,, so -5 + 5 = 0
same for -5x +5X =0
What is an angle with 3 acute angles?
Three straight sides and three angles make up the shape of a triangle. The angles of a triangle can either be acute, right, or obtuse. An angle with three acute angles is a triangle where all three angles measure less than 90 degrees.
A triangle is a three-sided shape with three angles. The sum of the internal angles of a triangle is always 180 degrees. An angle is the amount of turn or change in direction between two lines. There are three types of angles, acute, right and obtuse. An acute angle is an angle which measures less than 90 degrees. A right angle is an angle which measures exactly 90 degrees, and an obtuse angle is an angle which measures more than 90 degrees. Therefore, an angle with three acute angles is a triangle where all three angles measure less than 90 degrees. A triangle with three acute angles is also known as an acute triangle. All three angles must add up to 180 degrees, so the measure of each angle must be less than 60 degrees.
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Is 16x2 40x 25 a perfect square trinomial?
No, 16x2 40x 25 is not a perfect square trinomial.
What is perfect squares?Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.
A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.
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Question
Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.
Let c represent the number of additional customers Joshua must have to meet his goal.
Drag and drop the answer into the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Joshua needs to have more than Response area additional customers to meet his goal.
Joshua will need 7 additional customers.
How to determine the number of customers he needs?
The parameters that will help us to determine the number of customers is give as follows:
Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.
Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:
= (20 - 6) / 2
This is given as 14 / 2
The the number of customers needed = 7
In conclusion He will need 7 additional customers.
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28.2, 27.22, 27.62 , 27.54 , 27.5 in Greatest to Least
Answer:
28.2, 27.63, 27.54, 27.5, 27.22
Answer: 28.2, 27.62,27.5,27.22
Step-by-step explanation:
The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.
I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)
+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78
This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
What is volume?Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.
The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
= 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.
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Hello can someone help me with this please
Answer:
Below
Step-by-step explanation:
x - 6 = 12 add 6 to both sides of the equation
x - 6 + 6 = 12 + 6 simplify
x = 18
3x-1 = 11 add 1 to both sides of the equation
3x -1 + 1 = 11 + 1
3x = 12 now divide both sides by 3
3x/3 = 12 / 3 simplify
x = 4
The nine points of this grid are equally spaced horizontally and vertically. The distance between two neighboring points is 1 unit. What is the area, in square units, of the region where the two triangles overlap
The area, in square units, of the region where the two triangles overlap is found as 1 square units.
What is described as the coordinates?A point's position with regard to a specific reference frame is indicated by its coordinates, which can be either linear or angular values. X and Y are frequently used to denote a point's coordinates in a two-dimensional plane.We can determine the equation for each line with in diagram using its coordinates.
We can determine the coordinates for each point. (1/4,3/4) is one of the intersections.
d² = 2² + 2² = 8
A₁ = (1/3d + 1/6d )/2 * 1/4d
A₁ = 1/4d * 1/4d
A₁ = 1/ 16 d²
Now,
A = 2A₁
A = 2.(1/16)d²
A = 1/8d²
A = 1/8 *8
A = 1
Thus, the area, in square units, of the region where the two triangles overlap is found as 1 square units.
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Answer:
1 square unit
Step-by-step explanation:
Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
Answer:
Alex deleted 37.5 selfies
Step-by-step explanation:
Let X be the number of selfies that Vic deleted.
Alex deleted 3X selfies.
After deleting selfies, Alex has 90-3X selfies left.
Vic has 75-X selfies left.
Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2
Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2
Combining like terms, we get: 2X = 15
Dividing both sides by 2, we get: X = 7.5
Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.
Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.
The number of selfies deleted by Alex is 51.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.
Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,
Therefore,
Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2
180 - 6x = 75 - x
5x = 105
x = 17
3x = 51
Hence, the number of selfies deleted by Alex is 51.
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The minimum value of G in G ( x ) = 3 tan x is
The function G(x) = 3 tan(x) does not have a minimum value.
What are the relative extremas of a function?The relative extremas of a function are the values of x for which the derivative of the function assumes a value of zero.
The extremas are classified as local minimum or local maximum, as follows:
Local minimum: the function changes from decreasing to increasing.Local maximum: the function changes from increasing to decreasing.The tangent function does not have a local minimum, as it is increasing over it's entire domain.
The function G(x) = 3 tan(x) is a vertical stretch by a factor of 3 of the tangent function, which changes only the range, thus the function continues without a local minimum.
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On a certain hot summer day, 481 people used the public swimming pool. The daily prices are $1. 25 for children and $2. 25 for adults. Receipts for admission totaled $865. 25. How many children and how many adults swam at the public pool that day?
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.
given
The number of children =X=217
The number of adults=264
Let say the number of children are denoted by X
Then the number of adults are (481-X)
Price for children =1.25X
Price for adults=2.25(481-X)
Price for children +Price for adults=865.25
1.25X+2.25(481-X)=865.25
Solving for X:
1.25X+1082.25-2.25X=865.25
-X=865.25-1082.25
-X=-217
X=217
The number of children =X=217
The number of adults=(481-X)
The number of adults=(481-217)
The number of adults=264
There were 481 people that utilized the public swimming pool that day, including 217 children and 264 adults.
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Find 1)
4 integral 0 f(x) dx
if f(x) = 2 for x < 2
= x for x ? 2
Answer:
X = 1 and below
Step-by-step explanation:
since X is less than 2.
the value of X will be 1 and below.
Complete the table using the relationship between A and B
Answer:
Step-by-step explanation:
1) 6.2
2)12.4
3) 18.6
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Step-by-step explanation:
continuation of the previous answer:
now, for the final step angie should use the change of base formula in order to make the logarithmic expression simpler to analyze.
[tex]x = \frac{ log(6) }{ log(23) } [/tex]
after applying this formula Angie has successfully solved her exponential equation.
Answer:
Angie should use the change of base formula to make this equation faster. Which would be x= log(6)/log(23). Then, after using this formula and just plugging it into your calculator, Angie should have successfully answered her question.
Step-by-step explanation:
I took the exam
An experiment was conducted to evaluate the success of an Ebola virus vaccine. The subjects were unaware of the treatment they were given. What is this type of blinding used to prevent? Grounds for malpractice suits Subjects assigned randomly to treatments A possible source of bias Injury to the subjects The placebo effect
This type of blinding is used to prevent a potential source of bias in the experiment. By keeping the subjects unaware of the treatment they are receiving, the researchers can eliminate the possibility of any psychological effects influencing the outcome of the study. This is particularly important in cases where a treatment is being evaluated for subjective outcomes such as pain, anxiety, or depression, as the subjects' expectations and beliefs can influence their perception of the treatment's effectiveness. By keeping the subjects blinded to their treatment, researchers can ensure that the results of the study are as unbiased as possible.
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What is the Value of P? 9=p÷9
Answer:
p = 81
Step-by-step explanation:
9 = [tex]\frac{p}{9}[/tex] Multiply both sides by 9
9(9) = [tex]\frac{p}{9}[/tex][tex](\frac{9}{1})[/tex] another name for 9 is [tex]\frac{9}{1}[/tex]
81 = p