What is the measure of <KJL?
130°
180°
50°
25°
Answer:
The measure of KJL is 25 degrees
Alt. interior angles
Step-by-step explanation:
11+5(−3+1)−2=−(4−8)−5
Answer:
True
Step-by-step explanation:
Solve what's in parentheses: -3 + 1 = -2, 4 - 8 = -2Plug -2 and -2 in: 11 + 5(-2) - 2 = -(-2) - 5Simplify: 11 + 5(-2) - 2 = 2 - 55 × -2 = -10Plug -10 in: 11 + -10 - 2 = 2 - 52 - 5 = -3Plug -3 in: 11 + -10 - 2 = -311 + -10 = 1Plug 1 in: 1 - 2 = -31 - 2 = -3, so we know it's correctI hope this helps!
When you started working at your job, you earned $7.25 an hour. Now, you earn $15.65. What is the Percent of Change From when you started at your job to now? (Round to the nearest TENTH)
Answer:
I don't know
Step-by-step explanation:
Answer:
115.8%
Step-by-step explanation:
\(\frac{7.25}{15.65} =\frac{100}{y}\)
7.25 × y = 15.65 × 100
7.25y = 1565
7.25y ÷ 7.25 = 1565 ÷ 7.25
\(y=215\frac{25}{29}\)
As a decimal this is 215.862068966
Rounded to the nearest tenth this is 215.8
215.8% - 100%
115.8%
Use a quadratic equation to find two real numbers with a sum of -15 and a product of -54
The two real numbers with a sum of -15 and a product of -54 are -18 and 3.
What is defined as the quadratic equation?A quadratic equation, or simply quadratics, is a polynomial equation with the highest degree of two. It is written as follows:ax² + bx + c = 0in which x is the unknown element and the constant terms are a, b, and cVariable x's power always is non-negative integers. As a result, this same equation is a polynomial with the highest power as 2Let α and β be the two roots of the quadratic equation.
Then,
sum of roots; α + β = -15
Product of roots: α β = -54
The quadratic equation in the form of roots are -
x² - (α + β)x + αβ = 0
x² - (-15)x - 54 = 0
x² + 15x - 54 = 0
Factorize the above quadratic equation.
x² + 18- 3x - 54 = 0
(x + 18)(x - 3) = 0
x = -18 and x = 3
Thus, the two real numbers with a sum of -15 and a product of -54 are -18 and 3.
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Margaret is going on vacation to Alaska. She has 13 sweaters and needs to choose to take with her on vacation. How many ways can she choose the 6 sweaters to take?
A.) 1,716
B.) 1,235,520
C.) 78
D.) 575
Answer:
The answer is A
Step-by-step explanation: I just took the quiz.
Describe the shape of the distribution.
A. It is symmetric.
B. It is uniform.
C. It is bimodal.
D. It is skewed.
anybody know the answer to this?
Help ASAP!!!
Solve the equation by completing the square. Show your reasoning. (Step by step)
a^2+14a=51
NO LINKS!!!!! ANSWER IN HERE!!!!!
PLZZZZ HURRY ILL GIVE BRAINLEST POINTS PLZZZZ I NEED A 100% ON THIS TEST
determine the equation of the line given by the graph y=2/3x-1 y=3/2x-1 y=-2/3x-1 y=-3/2x-1
Answer:
y=2/3-1
Step-by-step explanation:
Two coordinate points are (-3,-3) and (3,1). If you use Y2-Y1/X2-X1, you will find the slope. Then use y=mx+b to find the equation.
More detailed:
1+3/3+3 ** It is + because when there are minus signs it turns to a plus
4/6 Then simplify it
2/3
Now that the slope is found, we need to use y=mx+b
(I used the point (3,1)) 1=2/3(3)+b
1=2+b
-1=b
I hope this is helpful gl on the test! :)
A graphing calculator is recommended. Find the maximum and minimum values of the function. (Round your answers to two decimal places.) y = sin x + sin 2x maximum value minimum value
The maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
To find the maximum and minimum values of the function y = sin x + sin 2x, we can first take its derivative with respect to x:
y' = cos x + 2 cos 2x
Then, we can set y' equal to zero and solve for x:
cos x + 2 cos 2x = 0
We can use a graphing calculator to find the solutions to this equation, which are approximately x = 0.285 and x = 2.857. We can then evaluate the original function at these values to find the maximum and minimum values:
y(0.285) ≈ 1.724
y(2.857) ≈ -1.724
Therefore, the maximum value of the function is approximately 1.724 and the minimum value is approximately -1.724.
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I am a factor of 40
When you pair me with 15 we have an LCM of 15
I am not one
The number that is a factor of 40 and when you pair it with 15 you have an LCM of 15 is; 5
What is the LCM of the numbers?LCM in mathematics simply means Least Common Multiple which is defined as the least common multiple of two numbers is the very lowest possible number that is divisible by both numbers.
Now, we are told that it is a factor of 40. Let us first list the factors of 40.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Now, since you will pair it with 15, the number also has to be a factor of 15 because only a number that is a factor of 15 can have 15 as a multiple.
Factors of 15 are; 1, 3, 5, 15
Now, the only number that is common to both 40 and 15 are 1 and 5. However we are told that it is not 1. Thus, the number is 5.
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Which of these settings does not allow use of a matched pairs t procedure? (a) You interview both spouses in 400 married couples and ask each about the average number of minutes each day they spend using social media. (b) You interview a sample of 225 unmarried male students and another sample of 225 unmarried female students and ask each about the average number of minutes each day they spend using social media. (c) You interview 100 female students in their freshman year and again in their senior year and ask each about the average number of minutes each day she spends using social media. 20.26. Becaucoth
Setting (a) does not allow the use of a matched pairs t procedure. As both spouses in 400 married couples are being interviewed and asked about their social media use.
A matched pairs t procedure is used when the samples being compared are related or matched in some way. This means that the same individuals are being measured or that the individuals in one sample are paired with corresponding individuals in the other sample.
The matched pairs t procedure is a statistical test used to compare the means of two related samples. This means that the samples being compared are related or matched in some way. The purpose of using a matched pairs t procedure is to control for individual differences between the samples and to increase the power of the statistical test.
Setting (a) does not allow the use of a matched pairs t procedure because the spouses in 400 married couples are not related or matched in any way. Each spouse is being measured independently, and there is no corresponding spouse in the other sample. Therefore, a different statistical test, such as a two-sample t-test or ANOVA, would need to be used to compare the means of the two groups.
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I need help please answer quick!
Answer:
3in. is the answer
doooo itttt fassstttt
mark it as brInlist
Help now. a storage tank in the shape of a cuboid of base 2.5 m by 2 m can hold up to 7500 litres of water. Calculate the height of the tank.
Answer:
Height of the tank is 1.5m
Step-by-step explanation:
Given
Shape: Cuboid
Base Dimension = 2.5m by 2m
Volume = 7500 litres
Required
Determine the height of the tank
First, the area of the base has to be calculated;
\(Area = 2.5m * 2m\)
\(Area = 5.0m^2\)
Next is to calculate the height using volume formula;
\(Volume = Area * Height\)
Recall that Volume = 7500L [Convert to m³]
\(1 L = 0.001m^3\)
So;
\(7500L = 7500 * 0.001m^3\)
\(7500L = 7.5m^3\)
Hence;
\(Volume = 7.5m^3\)
Substitute 7.5m³ for Volume and 5.0m² for Area in the following formula
\(Volume = Area * Height\)
\(7.5m\³ = 5.0m\² * Height\)
Divide both sides by 5.0m²
\(\frac{7.5m\³}{5.0m\²} = \frac{5.0m\² * Height}{5.0m\²}\)
\(\frac{7.5m\³}{5.0m\²} = Height\)
\(1.5m = Height\)
\(Height = 1.5m\)
Hence, the height of the tank is 1.5m
The relationship between the amount of time a basketball player spent practicing the day before a game and the number of points he scored in the game is graphed on the scatter plot shown.
Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
See image down below-
As a result, we may draw the conclusion that there is a connection between the amount of time spent training and the total number of points scored during a game.
what is plotting data?The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.
The right response is: There is a significant linear correlation between the quantity of points scored in a game and the amount of time a basketball player spends practising, according to the scatter plot.
A positive linear relationship between practise time and game point totals is shown in the scatter plot. This implies that as practise time grows, so do the amount of points scored during a game. Furthermore, the points are closely packed together along a straight line with an upward slope, suggesting that the link is strong
As a result, we may draw the conclusion that there is a connection between the amount of time spent training and the total number of points scored during a game. This makes reasonable because training helps athletes develop their
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Pls help as fast as possible
Answer:
452.389342 cubic inches
Step-by-step explanation:
The volume of a sphere is calculated using the formula V = 4/3 pi r^3
to determine the radius, you can notice that 4 spheres take up 24 in in length. This means that the radius of 1 sphere is 24/4/2 = 3 inches.
from there we plug and play: V = 4/3 * pi * 3^3 = 113.097336 cubic inches.
Note that this is only the volume of 1 sphere, so we multiply by 4
and we get 452.389342 cubic inches
Answer:
452.4
Step-by-step explanation:
Radius of each sphere: 24/4/2=3
Formula for volume: (4pir^3)/3
Formula for 4 spheres: 4 times (4pir^3)/3
Substitute 3 for r
is 4393 is divisible by which number
Answer:
4393 is divisible by 1 ,23 and 191
Answer:
the answer is 23
Step-by-step explanation:
1/5 of a wall every 1/4 hour what fraction represents the section of a wall jeb can paint in one hour
Answer:
4/5 of the wall
Step-by-step explanation:
In 1/4 of an hour, 1/5 of the wall is painted. That means that
in 4/4 of an hour (which is an hour), 4/5 of the wall is painted.
4/5 is your answer
Un grupo de amigos cenan en un restaurante y deciden repartir el valor de la cuenta
en partes iguales. Si cada uno contribuye con Q125.00 faltan Q50.00 para pagar la
cuenta, pero si cada uno contribuye con Q150.00, entonces sobran Q75.00. ¿Cuál es
el valor de la cuenta?
Based on the equation, the total value of the bill is Q75.00.
How to explain the valueTotal contribution - Total bill = Shortage
125 * Number of people - X = 50
Total contribution - Total bill = Surplus
150 * Number of people - X = 75
We now have a system of two equations with two variables. Let's solve it to find the value of the total bill (X).
Equation 1: 125 * Number of people - X = 50
Equation 2: 150 * Number of people - X = 75
We can rearrange Equation 1 to solve for X:
X = 125 * Number of people - 50
Substituting this expression for X into Equation 2, we get:
150 * Number of people - (125 * Number of people - 50) = 75
Simplifying the equation:
150 * Number of people - 125 * Number of people + 50 = 75
25 * Number of people + 50 = 75
25 * Number of people = 25
Number of people = 1
Substituting the value of the number of people into Equation 1 to find X:
X = 125 * 1 - 50
X = 125 - 50
X = 75
Therefore, the total value of the bill is Q75.00.
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A group of friends have dinner at a restaurant and decide to share the value of the bill in equal parts. If each one contributes Q125.00, Q50.00 is missing to pay the account, but if each one contributes Q150.00, then Q75.00 is left over. Which account value?
Which list shows the following numbers in order from greatest to least: -5, 12, 2, -4, 0
12, 2, 0, -4, -5
12, -5, -4, 2, 0
-5, -4, 0, 2, 12
12, 2, -4, 0, -5
Find the equation of a line that passes through the points (3,2) and (5,6).
Leave your answer in the form y=mx+c
Answer:
Step-by-step explanation:This particular answer works out to be undefined because it is a straight line and there is no slope and no equation for it. I will show you how to work it out though so you will know how to do it with other problems. We will still be using the y = mx + b formula. First step is to find m. In order to find the slope we would use the equation:
m = (y2 - y1) / (x2 - x1) Note: The number behind the letter designates which x or y value you will use of the 2 (x, y) plots
m = (-5 - 2) / (3 - 3)
m = -7 / 0 Note: A number divided by 0 is undefined which means your slope is undefined
Since your slope is undefined your equation would be x = 3 because your x values are both 3.
Now let's assume your second (x, y) plot was actually (-3, -5).
m = (-5 - 2) / (-3 - 3)
m = -7 / - 6 Note: A negative divided by a negative is a positive. The negatives cancel each other out.
m = 7/6
Okay now back to our slope-intercept formula.
y = 7/6x + b
Now in order to figure out what b is, we will again take the plot point and plug the values into the equation. You can use either point because either way the answer will come out the same. In this case we will use (3, 2).
2 = 7/6(3) + b
2 = 21/6 + b Note: The easiest way to do the next part is to make the 2 into a fraction over 6
12/6 - 21/6 = b
-9/6 = b or -3/2
So now all we have to do is plug this value into our equation.
y = 7/6x - 3/2
Lin runs 6 laps around a track in 9 minutes ( use ratio table)A. How many minutes per lap is that?B. How many laps per minute is that?C. If Lin runs 21 laps at the same rate, how long does it take her?
Given
Lin runs 6 laps around a track in 9 minutes
Part A
How many minutes per lap is that?
\(\begin{gathered} 6\text{laps =9minutes} \\ 1\text{ lap =}\frac{9}{6}\text{minutes} \\ 1\text{lap}=\frac{3}{2}\text{minutes} \\ 1lap=1\min utes\text{ 30seconds} \end{gathered}\)The final answer
1.5minutes per lap
Part B
How many laps per minute is that?
\(\begin{gathered} 6\text{laps =9minutes} \\ \frac{6}{9}\text{laps =1minute} \\ \frac{2}{3}\text{laps}=1\text{minute} \\ 0.66666666667lap=1\min ute \end{gathered}\)The final answer
0.66666666667lap per minute
Part c
If Lin runs 21 laps at the same rate, how long does it take her?
\(\begin{gathered} 6\text{laps =9minutes} \\ 21\text{laps =y minutes} \\ \frac{6}{21}=\frac{9}{y|} \\ \text{cross multiply} \\ 6y=189 \\ \text{divide both sides by 6} \\ \frac{6y}{6}=\frac{189}{6} \\ y=31.5\text{ minutes} \end{gathered}\)The final answer
Lin runs 21 laps for 31.5 minutes
Wally and drake both wanted to see the moons of jupiter. they each wanted to buy a telescope that sold for $62.48. together they had a total of $95. how much more money did they have left to save?
The amount of money Wally and Drake have left to save is equal to $29.96 if each one of them wanted to buy a telescope.
The amount of money left to be saved can be calculated by using an algebraic expression.
First, we determine the cost of two telescopes if each one of them wanted to buy a telescope to see the moons of Jupiter.
As the cost of one telescope is $62.48, the cost of two telescopes will be;
62.48 + 62.48 = 124.96
An algebraic expression can be given as;
95 + x = 124.96
where x is the money left to be saved.
Solving for x;
x = 124.96 - 95
x = 29.96
Hence, $29.96 is the amount left to be saved for each one of them to buy a microscope.
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A boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water. From point
�
A, the boat’s crew measures the angle of elevation to the beacon, 13
∘
∘
, before they draw closer. They measure the angle of elevation a second time from point
�
B at some later time to be 20
∘
∘
. Find the distance from point
�
A to point
�
B. Round your answer to the nearest foot if necessary.
If boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water, the distance from point A to point B is approximately 226.6 feet.
To find the distance from point A to point B, we can use the tangent function. Let x be the distance between point A and the lighthouse, and let y be the distance between point B and the lighthouse. We can then set up two equations based on the angles of elevation:
tan(13°) = 142/x
tan(20°) = 142/y
Solving for x and y, we get:
x = 142/tan(13°) ≈ 627.8 feet
y = 142/tan(20°) ≈ 401.2 feet
The distance between point A and point B is the difference between x and y:
x - y ≈ 226.6 feet
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Complete question is:
A boat is heading towards a lighthouse, whose beacon-light is 142 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 13 degree, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 20 degrees . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
develop a class shapes 2d to represent all 2d geometric shapes excluding line. class should represent the name of the object (a string) the color of the objects (color) and methods that all subclasses should implement (abstract methods) including:
This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.
This is the program in C++ demonstrating the above classes.
#include<iostream>
using namespace std;
class shapes
{
public:
string name;
string color;
virtual void getAttributes()=0;
};
class Circle: public shapes
{
public:
float radius;
Circle(string n,string c, float r)
{
name=n;
color=c;
radius=r;
}
float getPerimeter()
{
return(2*(3.142)*radius);
}
float getArea()
{
return((3.142)*(radius*radius));
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Square:public shapes
{
public:
float side;
Square(string n,string c, float s)
{
name=n;
color=c;
side=s;
}
float getPerimeter()
{
return(4*side);
}
float getArea()
{
return(side*side);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Triangle:public shapes
{
public:
float base;
float height;
float side1;
float side2;
float side3;
Triangle(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter side1\n";
cin>>side1;
cout<<"Enter side2\n";
cin>>side2;
cout<<"Enter side3\n";
cin>>side3;
return(side1+side2+side3);
}
float getArea()
{
cout<<"Enter base\n";
cin>>base;
cout<<"Enter height\n";
cin>>height;
return((0.5)*base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rectangle:public shapes
{
public:
float length;
float breadth;
Rectangle(string n,string c, float l,float b)
{
name=n;
color=c;
length=l;
breadth=b;
}
float getPerimeter()
{
return(2*(length+breadth));
}
float getArea()
{
return(length*breadth);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rhombus:public shapes
{
public:
float diagonal1;
float diagonal2;
float side;
Rhombus(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter Side\n";
cin>>side;
return(4*side);
}
float getArea()
{
cout<<"Enter diagonal 1\n";
cin>>diagonal1;
cout<<"Enter diagonal 2\n";
cin>>diagonal2;
return((0.5)*diagonal1*diagonal2);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Parallelogram:public shapes
{
public:
float base;
float height;
Parallelogram(string n,string c, float b,float h)
{
name=n;
color=c;
base=b;
height=h;
}
float getPerimeter()
{
return(2*(base+height));
}
float getArea()
{
return(base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
int main()
{
int choice;
while(1)
{
cout<<"\n\nEnter your choice :";
cout<<"\n1 for Circle\n";
cout<<"2 for Square\n";
cout<<"3 for Triangle\n";
cout<<"4 for Rectangle\n";
cout<<"5 for Rhombus\n";
cout<<"6 for Parallelogram\n";
cin>>choice;
system("cls");
switch(choice)
{
case 1:
{
float r;
cout<<"Enter radius\n";
cin>>r;
Circle c("Circle","Yellow",r);
c.getAttributes();
cout<<"Perimeter : "<<c.getPerimeter()<<endl;
cout<<"Area : "<<c.getArea()<<endl;
}break;
case 2:
{
float side;
cout<<"Enter side\n";
cin>>side;
Square s("Square","Red",side);
s.getAttributes();
cout<<"Perimeter : "<<s.getPerimeter()<<endl;
cout<<"Area : "<<s.getArea()<<endl;
}break;
case 3:
{
Triangle t("Triangle","Green");
t.getAttributes();
cout<<"Perimeter : "<<t.getPerimeter()<<endl;
cout<<"Area : "<<t.getArea()<<endl;
}break;
case 4:
{
float l,b;
cout<<"Enter Length and breadth\n";
cin>>l>>b;
Rectangle r("Rectangle","Blue",l,b);
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 5:
{
Rhombus r("Rhombus","Purple");
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 6:
{
float b,h;
cout<<"Enter base\n";
cin>>b;
cout<<"Enter height\n";
cin>>h;
Parallelogram p("Parallelogram","Pink",b,h);
p.getAttributes();
cout<<"Perimeter : "<<p.getPerimeter()<<endl;
cout<<"Area : "<<p.getArea()<<endl;
}break;
}
}
}
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a line slope is 1 , and its y - intercept is 8. What is its equation in slope - intercept form ?
Answer:
I tjink so , I am not sure
Step-by-step explanation:
y=mx+c
this is a formula ......above one
y=8x+1
andreas höring and thomas peternell. algebraic integrability of foliations with numerically trivial canonical bundle
Andreas Höring and Thomas Peternell have made significant contributions to the study of algebraic integrability of foliations with numerically trivial canonical bundle.
Andreas Höring and Thomas Peternell are mathematicians who have made significant contributions to the study of algebraic integrability of foliations with numerically trivial canonical bundle.
Algebraic integrability refers to the property of a foliation (a geometric structure defined on a manifold) to have certain algebraic properties. In particular, it relates to the existence of rational functions that preserve the foliation structure.
A foliation is said to have a numerically trivial canonical bundle if the line bundle associated with the canonical divisor of the foliation has degree zero on every curve. The canonical bundle is a fundamental object in algebraic geometry that captures the intrinsic geometry of a variety.
Höring and Peternell have studied the algebraic integrability of foliations with numerically trivial canonical bundle from various perspectives. They have investigated the existence and properties of meromorphic first integrals, which are rational functions that preserve the foliation. These integrals play a crucial role in understanding the dynamics of the foliation.
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Complete question:
Aandreas höring and thomas peternell. algebraic integrability of foliations with numerically trivial canonical bundle. prove that the the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle.
Which of the following r-values represents the strongest correlation?
A. 0.55
B. 0.65
C. 0.35
D. 0.45
Answer:
0.65
Step-by-step explanation:
The r-value option (B) 0.65 represents the strongest correlation.
What is the correlation coefficient?The correlation coefficient is a quantitative method of calculating correlation. It is a statistical concept, which helps in establishing a relation between predicted and actual values obtained in a statistical experiment.
For the given situation,
We need to determine the r-value that represents the strongest correlation.
The relationship between two variables is generally considered strong when their r value is larger than 0.7.
Among the options, 0.65 is near to 0.7, so it has strongest correlation.
Hence we can conclude that the r-value option (B) 0.65 represents the strongest correlation.
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Why is it helpful to rewrite inequalities
with the variable on the left side of the
inequality sign?
Answer:
that puts the solution in the form ...
variable is ...
Step-by-step explanation:
It isn't always.
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Often, we like to have a solution be in the form ...
variable is ...
So, for an inequality, that puts the variable on the left:
x > 3
y < 27
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Personally, I like to see the answer in a form that has the variable and its values in the same relation as on a number line. This means, my preferred inequality symbols are < or ≤, since those have the smaller numbers on the left. I would write the first example above as ...
3 < x
showing that the shaded portion of the number line (representing possible values of the variable) is to the right of the open circle at 3. For me, it is more mental effort to translate x > 3 to the same image.
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The forms we choose to use are all about making communication as easy as possible.
On a coordinate plane, triangle x y z has points (negative 5, 3), (negative 2, 3), (negative 2, 1). triangle x prime y prime z prime has points (5, negative 1), (5, negative 4), (3, negative 4). complete the sequence of transformations that produces △x'y'z' from △xyz. a clockwise rotation ° about the origin followed by a translation units to the right and 6 units down produces δx'y'z' from δxyz.
180° rotation rule (x, y) → (–x, –y)..
Triangle XYZ is rotated to create the image triangle X'Y'Z'. On a coordinate plane, 2 triangles are shown.
The first triangle has points X (-5, 3), Y (-2, 3), Z (2, 1).
The second triangle has points X prime (5, - 1), Y prime (5, - 4), Z prime
(3, - 4).
Here the sign of both coordinates has been changed but the magnitude remains same.
So, the rule is (x, y) → (–x, –y) which is for 180° rotation.
Hence, the 180° rotation rule (x, y) → (–x, –y).
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