Identify the elements of the range of the function shown in the graph.
Responses
6
3
1
5
2
-6
The range of the relation on the graph is:
R: {1, 2, 6}
How to identify the range on the graph?For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).
Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:
(3, 6), (5, 2) and (6, 1)
The range is the set of the second values of each of these pairs, so the range in this case is:
R: {1, 2, 6}
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What is the degree of the polynomial 2x² 5x²³ 7?
In this case, the highest power on any variable is 23. As a result, the degree of polynomial is 23.
What is degree of the polynomial?The degree of a polynomial in mathematics is the highest of the degrees of the polynomial's monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer. The degree of a polynomial is the greatest or maximum power of a variable in a polynomial equation. A degree represents the polynomial with the greatest exponential power. Finding the degree of a polynomial. 2 x 2 + 2 x - 364 = 0. The maximum degree of the polynomial in the preceding equation.
Here,
Given : 2x^2 + 5x^23 + 7
Degree of polynomial = Highest power of a variable.
Here, 23 is the highest power on any variable. So, degree of polynomial is 23.
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FOR SOME WHO CAN ANSWER THESE 4 QUESTIONS!!!
The number and percentages of the parameters in the question are;
652 people make more than $60,000About 19.9% of all police officers make less than $40,000What is a percentage?A percentage is a representation of a part of a whole as a fraction with a hundred (100) as the denominator.
T
From the attached table in the question, we get;
The number of people that make more than $60,000 = 388 + 198 + 66 = 652
The number of people in the survey including the teachers, police officers and firefighters, that make more than $60,000 are 652 peopleThe number of police officers in the survey = 224 + 703 + 198 = 1125
The number of police officers that make less than $40,000 = 224
The percentage of police officers that make less than $40,000 is therefore;
(224 ÷ 1125) × 100 ≈ 19.9%The percentage of all police officers that make less than $40,000 is about 19.9%Other information obtainable from the table are as follows;
The number of police officers that make more than $40,000 = 703 + 198 = 901
The percentage of all police officers that make more than $40,000 is therefore;
(901 ÷ 1125) × 100 ≈ 80.09%
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Rebecca
pays $3.50 per gallon for 12 gallons of gas.
How much did Rebecca pay in all for the gas?
Answer:
3.50 × 12 = 42
Therefore, she spent 42 dollars.
Suppose a ball was dropped from a TV tower 2120 feet high. The time it takes an object to free-fall from the top of this tower to the ground can be represented by the equation s = -16t^2 + 2120, where s is the distance from the ground in feet and t is the time in seconds. Approximately how long will it take the object to reach the ground?
Applying the equation of free fall the time it will take for the ball dropped from a TV tower 2120 feet high to reach the ground is 11.51 seconds
When will the ball reach the groundThe equation relating time and distance travelled which is s = -16t² + 2120, as used in the problem is a quadratic equation
The equation is already modelled for the height of the tower which is 2120 feet high. because of this calculating the time the ball will reach the ground is done when the s = 0
Time when the ball will reach the ground
s = -16t² + 2120
0 = -16t² + 2120
16t² = 2120
divide both sides by 16
t² = 132.5
t = √132.5
t = 11.51 seconds
The time is 11.51 seconds
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Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
10. The table below shows the changes in value for a share of stock that
started at $37.69 on Monday.
Changes in the Value
of Stock by Day
C. $37.79
D. $39.71
Day of
the Week
Tuesday
Wednesday
Thursday
Friday
Changes in
Stock Value
$ 0.69
-$ 0.82
$ 0.37
-$ 0.14
What is the value of the stock at the end of the day on Friday?
A $35.67
B. $37.71
On solving the provided question we can say that the equation will be -
37.79x + 39.71y = 0.69 = 75.4 +75.4 = 150.8
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 equivalence 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 explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the equation will be -
37.79x + 39.71y = 0.69
x = 2
y = 2
75.4 +75.4 = 150.8
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Are complex numbers greater than real numbers?
The set of real numbers is a subset of the set of complex numbers because any real number, a, can be written as a + 0i
Is complex number greater than real number?A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1. Every complex number is a real number, but not every real number is a complex number. Z C Z in mathbb C ZC stands for the set of all complex numbers. Real numbers are all decimal fractional, negative, and positive integers. Complex numbers, on the other hand, can be expressed as the product or difference of two real numbers and an imaginary number, such as 4 - 2i or 6 + 6i.To learn more about complex number refer to:
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In your school, a skating competition was organized and you were asked to find the best skater out of 5 participants of class 7 students.
Contestant A covered a distance 1100m within 40 minutes.
Contestant B covered a distance 1800m within 1 hour and 10 minutes.
Contestant C covered a distance 1000m within 60 minutes.
Contestant D covered a distance 900m within half an hour.
Contestant E covered a distance 1500m within 55 minutes.
Best saker out of 5 participants is Contestant D because his speed of skating is the highest. He has a speed 30 m/min.
what is skating?Skating is a kind of sports as well as exercise. It is such a sport in where a participant needs to move on skates.
Who is the best skater out of 5 participants?
Best skater is determined by the performance of each participant.
The performance can be detected by observing the speed of skater.
speed = distance travelled by skater / time
we notice from the above question that contestant A covered a distance 1100m within 40 minutes.
so, speed of A = 1100 m/ 40 min = 27.5 m/min
Contestant B covered a distance 1800m within 1 hour and 10 minutes.
speed of B contestant = 1800m/ 70 min= 25.71 m/min
Contestant C covered a distance 1000m within 60 minutes.
speed of contestant C = 1000m/ 60 min = 16.67 m/min
Contestant D covered a distance 900m within half an hour.
speed of D = 900m /30 min = 30 m/min
Contestant E covered a distance 1500m within 55 minutes.
speed of contestant E = 1500m/ 55 min = 27.27 m/min
from the above discussion, we find that contestant D has the highest speed among all other skaters.
speed of contestant D = 30 m/min
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Which set of ordered pairs (x,y)(x,y) could represent a linear function?
\mathbf{A}=
A=
\,\,\left\{(0, 3),\,\,(3, 0),\,\,(6, -3),\,\,(9, -6)\right\}
{(0,3),(3,0),(6,−3),(9,−6)}
\mathbf{B}=
B=
\,\,\left\{(-1, 9),\,\,(2, 7),\,\,(4, 5),\,\,(7, 3)\right\}
{(−1,9),(2,7),(4,5),(7,3)}
\mathbf{C}=
C=
\,\,\left\{(-6, 4),\,\,(-3, 3),\,\,(1, 2),\,\,(7, 0)\right\}
{(−6,4),(−3,3),(1,2),(7,0)}
\mathbf{D}=
D=
\,\,\left\{(-3, -2),\,\,(0, -1),\,\,(2, 0),\,\,(8, 3)\right\}
{(−3,−2),(0,−1),(2,0),(8,3)}
The set of ordered pairs (x, y) that could represent a linear function include the following:
A. A = {(0, 3), (3, 0), (6, -3), (9, -6)}
C. C = {(−6,4),(−3,3),(1,2),(7,0)}.
How to determine the ordered pairs that represent a linear function?In order to determine the ordered pairs that could represent a linear function, we would have to determine the slope of each ordered pair. In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;
Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (0 - 3)/(3 - 0) = (-6 + 3)/(9 - 6)
Slope = -1 = -1 (it represents a linear function).
For ordered pair B, we have:
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (7 - 9)/(2 + 1) = (3 - 5)/(7 - 4)
Slope = -2 ≠ -1 (it does not represents a linear function).
For ordered pair C, we have:
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (3 - 4)/(-3 + 6) = (0 - 2)/(7 - 1)
Slope = -1/3 = -1/6 (it represents a linear function).
For ordered pair C, we have:
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (-1 + 2)/(0 + 3) = (3 - 0)/(8 - 2)
Slope = 1/3 ≠ 1/2 (it does not represents a linear function).
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I need help pleaseee with work
Isosceles, equilateral, scalene, obtuse, acute, and right triangles are the six different forms of triangles. Shapes with three sides are called triangles. The various triangle varieties go under various names.
What do you meant by triangle ?Having three sides, three angles, and three vertices, a triangle is triangular. Every triangle's internal angles add up to 180 degrees. We refer to this as the triangle's angle sum attribute. Any two triangle sides can be added up to make any two sides longer than the third side.
Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle A B C" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each determine a distinct triangle and plane. 12 times the base plus the height, Triangle's side lengths added together to form the perimeter. 3, vertices total. 3 edges total Inside angle: 60 degrees (for equilateral) 180 degrees is the sum of interior angles. Consists of convex, cyclic, equilateral, isogonal, and isotoxal properties.
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16x^2+8x+1-9y^2. Factorize the following completely
The factorization of the given expression is 16x² + 8x + 1- 9y² = (4x +3y +1)(4x -3y +1).
What is the meaning of Factorize?
Factorization or factoring is defined in mathematics as the breaking or breakdown of one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together provide the original number or matrix, etc.
Given expression is 16x² + 8x + 1- 9y²
Now make two groups of the expression:
(16x² + 8x + 1)- (9y²)
= (16x² + 8x + 1)- (3y)²
Now applying Algerical identity (a + b)² = a² + 2ab + b².
= ((4x)² + 2×4x×1 + 1²)- (3y)²
= (4x + 1)² - (3y)²
Now applying Algerical identity (a² - b²) = (a+ b)(a - b)
= (4x + 1 + 3y)(4x + 1 - 3y)
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There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.
A. Express y in terms of x
B. Make a table to show the relationship between y and x. Use values of x=10,20,30,40, and 50 in your table
A. Using the given information, y expressed in terms of x is y = x + 50
B. The table that shows the relationship between y and x is
x y
10 60
20 70
30 80
40 90
50 100
Expressing y in terms of xFrom the question, we are to express y in terms of x
From the given information,
There are x sparrows in a tree and 50 sparrows on the ground beneath the tree
If y represent the total number of sparrows in the tree and on the ground,
Then,
We can write that
y = x + 50
B.
We are to make a table to show the relationship between y and x
Using the equation above
y = x + 50
When x = 10
y = 10 + 50
y = 60
When x = 20
y = 20 + 50
y = 70
When x = 30
y = 30 + 50
y = 80
When x = 40
y = 40 + 50
y = 90
When x = 50
y = 50 + 50
y = 100
Thus,
The table is:
x y
10 60
20 70
30 80
40 90
50 100
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What stage is 2cm dilated?
Two centimeters of dilation is considered early labor. At this stage, the cervix is considered "soft" or "favorable" for labor to begin. The cervix has become thinner and softer, allowing the baby to move into the birth canal.
However, the cervix is still long and closed, and the baby is not yet ready to come out. During this stage, contractions may become more frequent and intense, but they are usually not regular and will often stop and start. Women in early labor may feel cramping, backache, and increased pressure in the pelvis and vagina as the cervix begins to open. If a woman is not having regular contractions, she may be instructed to rest until labor progresses to the active phase.
Women in early labor may also begin to experience increased vaginal discharge, the "bloody show," as the cervix further softens and thins. At this stage, it is common for the amniotic sac to begin to bulge out of the cervix. This is a sign that the cervix is continuing to dilate, and it may rupture when contractions become more powerful.
At two centimeters of dilation, labor is just beginning, but the cervix is showing signs that it is opening and preparing for delivery. Women should be aware of the signs of early labor and discuss any changes they experience with their healthcare provider.
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What are the 5 types of problem-solving?
Define the problem , Gather information, Generate possible solutions, Evaluate ideas and then choose one, Evaluate are the 5 types of problem-solving.
What are fundamental techniques for fixing issues?
Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.
Different problem-solving techniques include elucidating, ideating, developing, and implementing.
What advantages does problem-solving have?
Making decisions is necessary to solve issues. People who are "happier, more confident, and more autonomous" are typically those who have good problem-solving abilities.
Children develop resilience when they take on challenges individually or in groups. They pick up the ability to approach problems from a different angle.
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Hi, what would not be a linear equation? I know a linear equation is y=mx + b, which m represents slop and b is the y-intercept. For example, it be it costs five dollars per hour to rent a movie and a two-dollar fee when purchasing the movie, This as a linear equation would be y= 5x + 2. But can a linear equation be y= 3/x + b or y= x (square root sign on it) + b?
A linear equation can either be y = 5x + 2 or y = 3/x + b.
But the equation y= x² + b would not be a linear equation.
What is a linear equation?An equation is said to be a linear equation if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
The general equation of a linear equation is given below:
y = mx + b
where;y is the dependent variablem is the slope or gradientx is the independent variableb is the intercept of the line on the y-axis.Hence, the equation y = x (square root sign on it) + b would not be a linear equation because the power of the variable x is greater than 1.
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Someone PLEASE PLEASE PLEEEEASE HELP
Graph the linear relationship
15 points
The graph of the linear relationship is represented by the equation y = 3x - 5
What is an equation?An equation is an expression relating two or more numbers and variables.
The standard form of a linear equation is:
Ax + By = C
where A, B and C are constants
The slope - intercept form of a linear equation is:
y = mx + b
Where m is the rate of change(slope) and b is the y intercept.
The graph of the linear relationship was plotted using the points from the table. The graph is attached
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Help pls I am struggling with this
Slope = 1/4. Now let's put it into point slope form to find out the y-intercept. Then convert it into y=mx+ b form, the standard slope intercept form
How to calculate the linear equation?
Step1:
(-4,-2) and (4,0)
y=1/4x-1
Let's find the slope first, with the two given ordered pairs.
Slope = 1/4.
Now let's put it into point slope form to find out the y-intercept.
Then convert it into y=mx+ b form, the standard slope intercept form.
y + 2 = 1/4(x+4)
Then we convert it into y=mx+ b form (our final answer);
y=1/4x-1
Step 2:
(0,1)and(5,3)
y=2/5x+1
the equation of a line in slope-intercept form is.
y=mmx+ b
where m is the slope and b the y-intercept
to calculate the slope use the gradient formula
m=y2-y1/x2-x1
(x1,y1)=(0,1) and (x2,y2)=(5,3)
m=3-1/5-0=2/5
using m=2/5 and b=1
y=2/5x+1
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Draw a net for a cube with a edge length x centimeters? What is the surface area of this cube? What is the volume of this cube?
The net of the cube is attached to this answer, and;
a. The surface area of the cube = 6X^2 squared centimeters
b. The volume of the cube = x^3 cubic centimeters
What is a net of a given shape?The net of a shape or figure is the shape gotten when it is opened through its edges and spread out on a flat surface. If this shape is folded with respect to its edges, the original shape would be reproduced.
The net of the given cube is attached to this answer.
a. To determine surface area of the cube, we have;
surface area of a cube = 6*length*length
= 6l^2
Given that the length of the sides of the cube is x centimeters,
area of the cube = l^2
= x^2
surface area of the cube = 6x^2
b. The volume of a cube = length^3
= l^3 ;l
The volume of the cube = x^3
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Your younger brother is getting stickers from a vending machine at the local supermarket. A proportion of stickers have the phrase "Girls
Rule!" If there are 12 stickers with this message in a sample of 36 stickers, what is the 95% confidence interval for this proportion? (1 point)
O a (0.1764, 0.4836)
Ob(0.1793, 0.4873)
Oc (0.1676, 0.4724)
Od (0.1799, 0.4881)
The formulae that specify how much 8% solution in equation and how much 24% solution were utilized are x+ y=200 and x+3y=450.
What is an equation ?A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.
The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: x +y=200
Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:
[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]
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On solving the provided question, we can say that For the specified percentage, the 95% confidence interval is (0.864, 0.3580).
A confidence interval is defined.A confidence interval in statistics expresses the probability that a population parameter would fall between a set of values for a specific percentage of the time. Analysts commonly utilize 95% or 99% confidence intervals for their predictions.
If total samples = E = 36, then
8 results were obtained.
Chance = p = 8/36 = 0.2222
Z value at 95% confidence level = 1.96
p = [tex]0.2222 + 1.96 ( \sqrt{ 0.2222() 1 - 0.2222) / 36 } ) = 0.3580[/tex]
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I need this now please
Ms.N has tutoring every 3weeks and cooking class every 2weeks when is the first time she will have tutoring and cooking class at the same time
The first time that she will have tutoring and cooking class at the same time is given as follows:
6 weeks.
How to obtain the period?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for each event in this problem are given as follows:
Tutoring: 3 weeks.Cooking class: 2 weeks.The least common factor of 3 and 2 is given as follows:
3 x 2 = 6.
(prime numbers, hence we just multiply them to obtain the least common factor).
The least common factor of six means that the period is of six weeks.
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The side lengths of a triangle are 15 units, 47 units and $\dfrac{x}{2}$ units. How many integer values of $x$ are possible
There can be an infinite number of integer values of x possible.
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side for it to be a valid triangle. So, for a triangle with side lengths 15, 47 and [tex]$\dfrac{x}{2}$[/tex] the condition for the triangle to be valid is:
15 + 47 >[tex]$\dfrac{x}{2}$[/tex]
30 > [tex]$\dfrac{x}{2}$[/tex]
2\times30 > x
x > 60
Since xmust be an integer, the possible values of x are any integer greater than 60. Thus, there can be an infinite number of integer values of x possible.
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Does it make sense to draw a kin through the points explain. ?
help asap will give briniest.
3 seconds.
Step-by-step explanation:1. Identify the given values.The problem states that the ball was kicked from a height of 12 ft, this would be the initial height of the ball. Hence:
h₀= 12 ft
Also, initial velocity is 44ft/s. Hence:
v₀= 44ft/s
2. Substitute the variables by the given values in the formula.[tex]h(x)=-16x^{2} +v_{0} x+h_{0} \\ \\h(x)=-16x^{2} +(44ft/s) x+(12ft)[/tex]
3. Rewrite as a common mathematical equation.[tex]h(x)=-16x^{2} +44 x+12[/tex]
4. Solve for time (x).Since the height when the ball hits the ground is 0, we need to substitute the height value (h(x)) by 0, and then solve the equation for "x".
Using the quadratic formula (check the attached image) we can get the value of time.
Taking the coefficients:
A= -16
B= 44
C= 12
[tex]x_{1} =\frac{-(44)+\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)}= -0.25s\\ \\x_{2} =\frac{-(44)-\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)} =3s[/tex]
Since "x" is being used to represent time, and time is a variable that can only be positive, we're only taking the positive value.
Hence, we can conclude that after 3 seconds after being kicked, the ball wil hit the ground.
Which measure of center should Raul use to calculate his overall performance if he hits a line drive to the outfield on each pitch?
Because the ten distances are not evenly distributed, Raul's overall performance should be determined by the median. Although nine distances are clustered together, the homerun is an outlier in the data set. The median is the best measure of centre for a data set with outliers.
What is median?The median is defined as the middle value in a given set of numbers or data. In mathematics, there are three different measures for determining the average value of a given set of numbers.
They are as follows: mean, median, and mode. These three measures are referred to as central tendency measures. Mean calculates the average value of the given data. A median defines the data's middle value.
The median is defined as the middle value of a sorted list of numbers in mathematics. By ordering the numbers, the middle number is discovered. The numbers are sorted ascending. After the numbers are ordered, the middle number is referred to as the data set's median.
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Full question:
Of the 10 swings, Raul hit 1ball over the outfield fence for a home run, but the other 9 hits were ground balls that stayed in the infield. Which measure of center will best summarize Raul’s overall performance? Why?
Which of the following best describes the solutions to the equation below?
3x+8=2(x+4)
A: x=1
B: x=0
C: inf solution
D: No Solution
Answer:
B
Step-by-step explanation:
3x + 8 = 2(x + 4) ← distribute parenthesis
3x + 8 = 2x + 8 ( subtract 2x from both sides )
x + 8 = 8 ( subtract 8 from both sides )
x = 0
B is the correct answer
Step-by-step explanation:
B is the correct answer
someone please help :D
The correct option is A) √0.036 as it is the only irrational number.
What is an irrational numberIrrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, like p/q where p and q are integers.
Considering option A) √0.036, there is no number among integers and fractions that equals
√0.036
option B) is a terminating decimal and can be expressed as a fraction.
option C) will result to the whole number 1 just like the option D) 10 which is also a whole number.
In conclusion, only option A) √0.036 is an irrational number as it cannot be expressed as the quotient of two integers.
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Given that the triangles are
similar. Use the Pythagorean
Theorem to help you on these.
Solving for the missing values.
a² + b² = c²
X =
y=_
X =
y =
and
6
y
3
3
4
The value of x is x = 5, and the value of y is y = 6.
What is Pythagorean theorem?
The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
We have to find the values of x and y.
First to find the value of x.
Since, by Pythagorean theorem,
3^2 + 4^2 = x^2
9 + 16 = x^2
25 = x^2
5 = x
x = 5
Now to find the value of y.
Again by using the Pythagorean theorem,
[tex](3 + 5)^2 + 6^2 = (y+4)^2\\64 + 36 = y^2 + 8y + 16\\100 = y^2 + 8y + 16\\y^2 + 8y - 84 = 0\\y^2 + 14y - 6y - 84 = 0\\y(y+14) - 6(y + 14) = 0\\(y -6)(y+14)=0[/tex]
(y - 6) = 0, (y + 14) = 0
y = 6, y = -14
Length is not negative.
⇒ y = 6
Hence, the value of x is x = 5, and the value of y is y = 6.
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The points L ( 1 , 8 ) (1,8), M ( 0 , 0 ) , and N ( − 8 , 1 ) (−8,1) form a triangle. Plot the points then click the "Graph Triangle" button. Click on the graph to plot a point. Click a point to delete it. L M N Find the desired slopes and lengths, then fill in the words that characterize the triangle. slope of LM = slope of MN = slope of NL = length of LM = length of MN = length of NL =
For a triangle with vertices L (1 , 8),, M (0 , 0) , and N (-8 , 1) the plot is plotted and the slope and lengths are
slope of LM = 8
slope of MN = 8
slope of NL = 7/9
length of LM = √65
length of MN = √65
length of NL = √130
How to find the slope and length of the lineThe slope, m of the lines is calculated the formula
m = (y₀ - y₁) / (x₀ - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
Slope of LM L (1 , 8), M (0 , 0)
m = (8 - 0) / (1 - 0)
m = (8) / (1)
m = 8
Slope of LM L (1 , 8), M (0 , 0)
m = (8 - 0) / (1 - 0)
m = (8) / (1)
m = 8
Slope of NL, N (-8 , 1), L (1 , 8)
m = (1 - 8) / (-8 - 1)
m = (-7) / (-9)
m = 7/9
The length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
For LM L (1 , 8), M (0 , 0)
d = √{(1 - 0)² + (8 - 0)²}
d =√{1 + 64}
d = √65
For MN M (0, 0) N (-8 , 1)
d = √{(0 + 8)² + (0 - 1)²}
d =√{64 + 1}
d = √65
For NL N (-8 , 1), L (1 , 8)
d = √{(-8 - 1)² + (1 - 8)²}
d =√{81 + 49}
d = √130
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Which of the following is not a pythagorean triplet a) 3,4,5 b) 6,8,10c) 5,12,13d) 2,3,4
D) 2, 3, 4 is not a pythagorean triplet.
Pythagoras theorem is in the form of;
a²+b²=c²
Applying this formula to the given options we get'
a) 3, 4, 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25 = 5^2
b) 6, 8, 10 is not a Pythagorean triplet because 6^2 + 8^2 = 36 + 64 = 100 = 10^2
c) 5, 12, 13 is a Pythagorean triplet because 5^2 + 12^2 = 25 + 144 = 169 = 13^2
d) 2, 3, 4 is not a Pythagorean triplet because 2^2 + 3^2 = 4 + 9 = 13 ≠ 4^2
In other words the pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is the sum of the squares of the other 2 sides.
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