The end behaviour of the function [tex]y = -x^{2} + 4[/tex] is
f(x) → −∞, as x → −∞
f(x) → −∞, as x → +∞
The degree of the function is even, and the leading coefficient is negative.
End behaviour of a function:
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behaviour is determined by a polynomial function's degree and leading coefficient.
For very big or very small values, the leading coefficient is more important than the other function coefficients. Therefore, it is sufficient to forecast the function's final behaviour based on the sign of the leading coefficient.
To predict the end-behaviour of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.
To know more about End behaviour of a function:
https://brainly.com/question/14625447
#SPJ1
his question is about filling in the blanks in the derivation of the first and second barycentric interpolation formulas. recall that the j-th lagrange polynomial is defined as
A variation on Lagrange polynomial interpolation is called barycentric interpolation. Second, just use Newton interpolation formula to assess p(x) for each x.
Why is the Lagrange interpolation theorem important?The Lagrange interpolation theorem can be used to create a polynomial that traverses a specified set of points and takes particular values at random locations. This theorem provides the approximate formula for the nth degree polynomials to the function f if a variable f (x) is available at discrete places xi, I = 0, 1, 2,... (x).
What is the LaGrange theorem's conclusion?The Lagrange theorem extrapolates well-known mathematical principles like the statement that a line is uniquely specified by two points, the knowledge that the quadratic function polynomial is completely determined by three points, and so forth.
To know more about Lagrange visit:
https://brainly.com/question/4609414
#SPJ4
Find the equation of the exponential function represented by the table below:
The equation of the exponential function represented by the table will be:
[tex]f(x) = 2(4)^{x}[/tex]
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
We know the equation of exponential function such as
[tex]f(x) = ab^{x}[/tex]
Put x=0, and y=2 in the function
[tex]2 = ab^{0} \\2 = a[/tex]
Also x=1, and y=8 in the function
[tex]8 = 2b^{1} \\b = 4[/tex]
Thus,
[tex]f(x) = ab^{x} \\f(x) = 2(4)^{x}[/tex]
Therefore, the equation of the exponential function represented by the table will be:
[tex]f(x) = 2(4)^{x}[/tex]
To know more about exponential function
https://brainly.com/question/19582051
#SPJ4
True or false equation 2/3 - 1/6=1/3
Answer:
False
Step-by-step explanation:
2/3 - 1/6 = 3/6
Assuming that the annual rate of inflation averages 4% over the next 10 years, the approximate costs С of goods or services during any year in that decade will be modeled by C(t) = P(1.04)’. where t is the time in years and P is the present cost. The price of an oil change for your car is presently $23.95. Estimate the price 10 years from now.
By using the provided formula of inflation, the answer is $35.35.
What do you mean by inflation?The rate at which consumer prices for a variety of products and services are increasing is known as inflation.
What are the ways for measuring inflation?The common ways followed are:
The Consumer Price Index (CPI)CPI, less food and energy.Personal Consumption Expenditures (PCE)Personal Consumption Expenditures excluding food and energy or “Core PCE”[tex]C(t) = P(1.04)^{t}[/tex]
P= $23.95
t=10
The estimated price is [tex]23.95*(1.04)^{10}[/tex]
=$35.35
To learn more about inflation rate visit:
https://brainly.com/question/29308595
#SPJ4
Jacket and Jill are planning to meet at the top of the hill. Jack is 2 miles away and Jill is 3 miles away. Jill walks 1.5 miles per hour faster than Jack. It takes them the same amount of time to get there. What are their rates and how long will it take?
Answer:
Jacks Rate: 3 miles per hour
Jills Rate: 4.5 miles per hour
Time: 40 minutes or 2/3 of an hour
Step-by-step explanation:
Setting up the Algebraic Expressions:This problem in it self isn't necessarily too complex, but a crucial part of it is taking the context given and somehow making that into a algebraic expression which we can then use to solve the equation.
Assigning Unknowns and Variables:So let's first assign two unknowns to the rates at which Jack and Jill walk. Since both of there names start with J, I'll use a subscript to differentiate between the two.
[tex]\text{let }J_a=\text{Jack's walking rate}\\\text{let }J_i = \text{Jill's walking rate}[/tex]
Notice that both have a J, but there is a little letter to the right and below, which is a subscript. This way we can easily tell which person we are referring to while not having to write out their entire name as a variable.
Now let's assign two variables. First let's assign distance: [tex]D=\text{distance from top of hill}[/tex]
and let's also assign time to a variable: [tex]t = \text{time in hours}[/tex]
Deriving Equations:Now let's start making some equations! If jack is two miles away from the top of the hill, in general, the distance from the hill can be calculated using the following equation: [tex]D=2-t*j_a[/tex]
Essentially, Jack starts off with a distance of two miles away, and after one hour, Jack will walk [tex]j_a[/tex] miles, this is his rate, what Jake travels in one hour. After another hour passes, he will do the same thing, but twice. So this is why we're multiplying by time. Since for each hour that passes, he will walk a further: [tex]j_a[/tex] miles, meaning he will be that much closer, so we subtract it from 2, the initial distance.
The same logic can be applied to Jill, except with an initial distance of 3 miles and using the unknown: [tex]j_i[/tex] which is Jill's rate. So we get the following equation: [tex]D=3-t*j_i[/tex]
If we're looking for when they reach the top of the hill, that means that the distance from the hill is zero. So let's set both equations to zero.
[tex]0=3-t*j_i\\0=2-t*j_a[/tex]
From here let's solve for time for both equations. So let's start with the first equation.
[tex]0=3-t*j_i[/tex]
From here let's subtract 3 from both sides to get rid of the 3 on the right side.
[tex]0-3=(3-3)-t*j_i\implies-3=-t*j_i[/tex]
from here let's divide both sides by Jill's rate.
[tex]\frac{-3}{j_i} = \frac{-t*j_i}{j_i} \implies \frac{-3}{j_i}=-t[/tex]
From here let's divide both sides by -1 to get t isolated.
[tex]\frac{\frac{-3}{j_i}}{-1} = \frac{-t}{-1} \implies \frac{3}{j_i}=t[/tex]
We can essentially apply the same steps to the equation we derived from Jack's rate.
[tex]0=2-t*j_a\\\\(0-2)=(2-2)-t*j_a \implies -2 = -t*j_a\\\\ \frac{-2}{j_a} = \frac{-t}{j_a} \implies \frac{-2}{j_a} = -t\\\\\frac{\frac{-2}{j_a}}{-1} = \frac{-t}{-1} \implies \frac{2}{j_a} = t[/tex]
Now we have the equations:
[tex]\frac{2}{j_a} = t\\\\\frac{3}{j_i} = t[/tex]
and this represents the time needed to reach the top of the hill (since we set both equations equal to zero)
Substituting and Solving:From here we need to look once more at the question, specifically where it says: "It takes them the same amount of time to get there". So we set the equations equal to each other.
[tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex]
Now we use our last piece of needed context: "Jill walks 1.5 miles per hour faster than Jack". We can set up one more equation: [tex]J_i = J_a+1.5[/tex].
This is super useful to have, since we can now make a substitution give this equation, converting our two-variable equation into a one-variable equation, allowing us to solve for one numerical value.
We have: [tex]\frac{2}{j_a} = \frac{3}{j_i}[/tex] and we know that: [tex]J_i = J_a+1.5[/tex], so let's simply plug in [tex]J_a+1.5[/tex] for [tex]j_i[/tex].
This gives us the equation:
[tex]\frac{2}{J_a}= \frac{3}{J_a + 1.5}[/tex].
Cross Multiply:
[tex]2(J_a+1.5) = 3(J_a) \implies 2J_a + 3 = 3J_a[/tex].
Subtract [tex]2J_a[/tex]:
[tex]3=J_a[/tex].
We can solve for Jills value, since Jill's value is just 1.5 miles per hour more than this, so [tex]J_i = 3+1.5=4.5[/tex]
Now let's take Jacks value and substitute it into his time equation
[tex]t = \frac{2}{3}[/tex]
we can keep this in hours, or we can convert this into minutes. We can convert this in to minutes by multiplying the amount of minutes in an hour by 2/3, so: [tex]60 * \frac{2}{3} = \frac{120}{3} = 40\text{ minutes}[/tex]
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2122 pounds. When carrying 35 gallons of fuel, it weighs 2296 pounds. How much does the airplane weigh if it is carrying 45 gallons of fuel?
The weight of 45 gallons of fuel is 2412 pounds.
What is weight ?
The force exerted on an object by gravity is known as the weight of the object in science and engineering. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
Weight is a gauge of how strongly gravity is pulling something down. It relies on the mass of the item and the acceleration brought on by gravity, which on Earth is 9.8 m/s2. F = m 9.8 m/s2 is the formula for computing weight, where m is the object's mass in kilograms and N is the object's weight in Newtons (N).
The weight of one gallon is
w = (2296 - 2122) / (35 - 20)
= 174 / 17
= 11.6 pounds
Now, to answer the question, we need to add the weight of (45-35) = 10 gallons of fuel to the weight of the plane
carrying 35 gallons of fuel, 2296 pounds.
So, the answer is 2296 + 10*11.6
= 2412 pounds.
To learn more about weight from the given link
https://brainly.com/question/25973294
#SPJ1
Castel bought 5 writing utensils for a total of $8. Pens cost $1 and pencils cost $2. How many of each writing utensil did he buy?
Answer: 8 = 1x + 2y
Step-by-step explanation:
this could be multiple answers, is this a multiple-choice question? follow that equation to find the answer that fits.
I got the equation by these steps:
total money spent is $8, so you start with 8 =
you don't know the specific number of pens so make that x. the cost of pens is $1, so the total cost will be $1 times however many pencils are bought, ie 1x.
repeat that for pencils, replacing $1 with $2, and making pencils mean y. you get 2y.
now to find your answer, insert numbers into x and y until they equal 8.
possible answers:
x=4, y=1
x=2, y=2
x=0, y=4
(18 - 4) to the power of 2
Answer:
196
Step-by-step explanation:
(18-4)^2
14^2 or 14x14
14x14=196
You want to format a 64GB USB disk to use it in Windows. Which file system should you use? FAT FAT32 ONTFS
Answer: FAT32
you're welcome :D
Answer:
use fat32
FAT32 is regarded as the default file system for external drives, especially the removable USB flash drives and SD memory cards. It's the most compatible file system that can be used on major devices and operating systems like Windows and macOS. So, the advantage of using FAT32 is portability.
However, FAT32 has some disadvantages, or let's say limitations as well. First and foremost, if you use a single file over 4GB in size, you'll need to convert FAT32 to NTFS or exFAT; What's more, due to the manufacturers' specifications, FAT32 can only be used to format drives between 2GB and 32GB, and that's why native tools on Windows have that limit, too. When you try to format a USB drive over 32GB in Windows Explorer, there is no "FAT32" option at all.
Simplify the expression.
8x-4y-8
-2xy5
Write your answer without negative exponents.
On solving the problem of expression we can say that , the answer is 5x + 9.A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
What is an Expression in Math?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6. Complex riddles are solved using mathematical expressions.
[tex]3x + 2 - 3x + 7 + 5x = 5x + 9[/tex]
Group the like terms
[tex]3x - 3x + 5x + 2 + 7[/tex]
now adding similar elements: 3x - 3x + 5x = 5x
[tex]5x + 2 + 7[/tex]
and add the numbers: 2+7=9
To know more about expression visit:
https://brainly.com/question/14083225
#SPJ1
What is the range of h?
A)All real numbers greater than or equal to -7
B)All real numbers greater than or equal to -3
C)All real numbers greater than or equal to 41
D)All real numbers
The range of h of the given function table is; A)All real numbers greater than or equal to -7
What is the range of the function?The range of a function is defined as the set of all possible output values for which the function is valid.
From the given function table, we can see the following coordinates;
(-3, 18)
(-1, 8)
(2, -7)
(3, -12)
(4, 17)
(6, -27)
Now, from the above coordinates, we can see that the maximum value of h(x) is 17 while the minimum value is -27.
Looking at the options, the only one that fits the available range of the function is option A.
Read more about range of function at; https://brainly.com/question/2264373
#SPJ1
HELP ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ITS DUE IN 15 MINS
Answer:
[tex]2 x 3^{2} x 7[/tex]
Step-by-step explanation:
The answer is 2 × 3 × 3 × 7 which is 2 x 3^2 x 7
Help please what is this answer
Answer: there is nothing
Step-by-step explanation: there is nothing to see so if there is no photo nobody can help you. Sorry
Given quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Find the area in square units.
The area of the quadrilateral is equal to √901 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the quadrilateral in a two-dimensional plane is called the area of the quadrilateral.
Given that quadrilateral ABCD with A(-4,-2), B(-3,2), C(2,4) and D(4,-3). Calculate the sides of the quadrilateral by the distance formula,
AB = √[(2+2)² + (-3+4)²]
AB = √(16+1)
AB = √17
CD = √[(4-2)² + ( 4 + 3)²]
CD = √ (4+49)
CD = √53
The area will be calculated as,
Area = AB x CD
Area = √17 x √53
Area = √901 Square units
To know more about an area follow
https://brainly.com/question/12441195
#SPJ1
Farmer and Taylor formed a partnership with capital contributions of $255,000 and $305,000, respectively. Their partnership agreement calls for Farmer to receive a $81,000 per year salary allowance. The remaining income or loss is to be divided equally. If the net income for the current year is $201,000, then Farmer and Taylor's respective shares of income are:
Which quotient is positive? A. -24 ÷6 B. 42-7 C. -35-5 D. 28 ÷ -4
Technically none of them because "quotient" means the answer to a division problem. But the only positive answer is B
A dog is running
around a circular track of radius 14
meters at a constant speed of 9 meters
per second. His owner is standing at a
distance 48 meters from the center of
the track.
-How fast is the angle theta changing?
- How fast is the distance between the dog and his owner changing when the dog
is at the northernmost point of the track?
The angle θ is changing is 36.9 degrees per second.
The distance between the dog and its owner when the dog is 46 meters at the northernmost point of the track.
As per the question, the circumference of the circular track is
⇒ 2 × 3.14 × 14 = 87.92 meters.
Since the dog is running at a constant speed of 9 meters per second, it will take the dog 87.92 / 9 = 9.77 seconds to complete one lap of the track.
The angle θ is defined as the angle between the position of the dog and the position of the owner, measured from the center of the track.
Since the track is circular, the angle theta will change at a constant rate of 360 degrees per lap. Since it takes the dog 9.77 seconds to complete one lap, the rate at which the angle θ is changing is 360 / 9.77 = 36.9 degrees per second.
To answer the second question, we must first calculate the distance between the dog and its owner when the dog is at the northernmost point of the track.
The owner is standing a distance of 48 meters from the center of the track, and the radius of the track is 14 meters, the distance between the dog and its owner is given by the Pythagorean theorem: d = √(48² - 14²) = 46 meters.
Learn more about the circumference of the circle here:
brainly.com/question/19794723
#SPJ1
I NEED THIS FAST THIS IS TIMED PLEASE
The equations representing the situations are P + S = 384 and 2.5P + 1.25S = 696.25. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cost of pizza is $2.5 and the soda is $1.25 and the total cost is $696.25. The total number of the Pizza and the Soda is 384.
The equations can be written as,
P +S = 384
2.5P + 1.25S = 696.25
To know more about an expression follow
https://brainly.com/question/18453221
#SPJ1
Your neighbor is digging a hole in his back yard for an in-ground swimming pool. The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep. If his pickup truck can haul one cubic meter, how many trips will it take him to haul all of the dirt away?
(please show work)
There are 896 trips will it take him to haul all of the dirt away.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.
Now,
Since, The rectangular hole is 8 feet wide, 16 feet long, and 7 feet deep.
And, His pickup truck can haul one cubic meter.
Hence, Number of trips will it take him to haul all of the dirt away will be;
⇒ 16 × 7 × 8 / 1
⇒ 896
Thus, Number of trips = 896
Learn more about the multiplication visit:
https://brainly.com/question/28768606
#SPJ1
How many three-digit natural numbers have digits that sum to 13 and leave a remainder of 1 when divided by 4?
On the coordinate plane below, draw a line through C point ths is parallel to AB.
Based on your drawing write equation of line that passes through point C and is parallel to AN. Your equation should be in the form y = mx + b. Desribe how you determined the equation.
Answer:
y = 2/3x -7
see the attachment for a graph
Step-by-step explanation:
You want the equation and graph of a line through point C(6, -3) parallel to the line shown through points A(-3, 3) and B(3, 7).
SlopeYou can count the grid squares to see that the slope of line AB is 2 units up for each 3 units to the right. The line through C will have the same slope:
m = rise/run = 2/3
Y-interceptThe line drawn with that slope through point C will cross the y-axis at y = -7. This value is the "b" in the slope-intercept equation for the line:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 2/3x -7
Graph
A graph of the line is shown in the attachment.
Determine probability of selecting at least 1 marble that is not red
The probability of selecting at least one marble that is not red is given as follows:
1.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Considering a success as selecting non-red marbles, the values of these parameters are given as follows:
N = 4, n = 2, k = 3.
The probability of at least one not red is given as follows:
P(X > 0) = 1 - P(X = 0).
In which:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,4,3,2) = \frac{C_{3,0}C_{1,2}}{C_{4,2}} = 0[/tex]
Hence the probability is of:
P(X > 0) = 1 - P(X = 0) = 1 - 0 = 100%.
Missing InformationThe problem is given by the image shown at the end of the answer.
More can be learned about the hypergeometric distribution at
https://brainly.com/question/14741653
#SPJ1
The Banana Apple company sells its Golden, Macintosh, and Red Ida apples in mixes Box A costs 3€, Box B 3€ and Box C 4€. Box A contains 4 Golden, 2 Macintosh and 4 Red Ida; Box B contains 6 Golde, 2 Macintosh, and 2 Red Ida; and Box C contains no Golden, 6 Macintosh and 4 Red Ida apples. At the end of the season, the company has altogether 2800 Golden, 2200 Macintosh, and 2300 Red Ida apples left. Determine the number of each kind of boxes that the company should make to maximize their profit.
Answer:
To maximize profit, the Banana Apple company should determine the number of each kind of apple box that they should make. To do this, they need to know the number of each type of apple that they have, as well as the price of each box.
Based on the information provided, the company has 2800 Golden apples, 2200 Macintosh apples, and 2300 Red Ida apples. This means that they can make 700 Box A's (2800 / 4 = 700), 1100 Box B's (2200 / 2 = 1100), and 575 Box C's (2300 / 4 = 575).
The price of each box is also given: Box A costs 3€, Box B costs 3€, and Box C costs 4€. This means that if the company makes 700 Box A's, they will earn 2100€ (700 x 3 = 2100€), if they make 1100 Box B's, they will earn 3300€ (1100 x 3 = 3300€), and if they make 575 Box C's, they will earn 2300€ (575 x 4 = 2300€).
To maximize profit, the company should make as many of the most profitable box as possible. In this case, the most profitable box is Box B, which earns 3€ per box. The company should make 1100 Box B's, which will earn them a total of 3300€.
Answer:
To solve this problem, we need to determine how many boxes of each type the company should make to maximize their profit. We can set up a system of equations to represent the number of apples in each box and the total number of apples the company has.
Let's call the number of boxes of type A x, the number of boxes of type B y, and the number of boxes of type C z. We can represent the number of apples in each box using the following equations:
x + y + z = 2800
4x + 6y + 0z = 2200
2x + 2y + 6z = 2300
To maximize the profit, the company should make as many boxes as possible while still having enough apples to fill all the boxes. We can solve this system of equations using substitution to find the values of x, y, and z that maximize the profit.
First, we can solve the first equation for z in terms of x and y:
z = 2800 - x - y
Next, we can substitute this expression for z into the second and third equations to eliminate z:
4x + 6y + 0(2800 - x - y) = 2200
4x + 6y = 2200
2x + 2y + 6(2800 - x - y) = 2300
2x + 2y + 17600 - 6x - 6y = 2300
2x + 2y = -15300
We can then solve this system of equations using substitution. From the second equation, we have:
4x + 6y = 2200
2x + 2y = -15300
We can solve the second equation for y in terms of x:
y = -15300/2 - x/2
We can substitute this expression for y into the first equation to solve for x:
4x + 6(-15300/2 - x/2) = 2200
4x - 45300 - 3x = 2200
x = (2200 + 45300) / (4 - 3)
x = 13600/1
x = 13600
We can then use this value of x to find the value of y:
y = -15300/2 - 13600/2
y = -13650
Finally, we can use these values of x and y to find the value of z:
z = 2800 - 13600 - (-13650)
z = 1650
Therefore, the company should make 13600 boxes of type A, -13650 boxes of type B, and 1650 boxes of type C to maximize their profit.
Step-by-step explanation:
Help pls I don’t understand
The missing length and the missing angle are approximately 40.447 and 20.034°.
How to determine the length of missing side and the measure of the missing angle
In this question we have a geometric system formed by a equilateral triangle divided into two triangles by a line segment. The missing sides and angles can be found by means of algebra properties, Euclidean geometry and trigonometry.
First, obtain the missing side by taking approach of properties for equilateral triangles:
y = 46 - 16
y = 30
Second, find the length of line segment by law of cosine:
l = √(46² + 16² - 2 · 46 · 16 · cos 60°)
l ≈ 40.447
The missing length is approximately 40.447.
Third, the measure of the missing angle by law of sine:
16 / sin x = 40.447 / sin 60°
sin x = (16 / 40.447) · sin 60°
sin x = 0.343
x ≈ 20.034°
The missing angle is approximately 20.034°.
To learn more on law of sine and law of cosine: https://brainly.com/question/17289163
#SPJ1
One less than five times a number is fewer than twenty-four. 24
Answer: 4 x 4 = 16
Step-by-step explanation: If you want a number one less that 5, subtract 1 from 5, then find a number that you can multiply by the answer to 1-5 to get less than 24. In this case, we used 4, to get 16. 16<24.
Which of the following properties could be used to rewrite the expression (1/3+2/7) + 3/4 as 3/4 + (2/7 + 1/3)
Answer: Commutative Property
find the slope of the line that passes through T(-2,11) U(3,11)
Answer:
Step-by-step explanation:
use equation [tex]\frac{y2-y1}{x2-x1}[/tex] to calculate the slope, in this case the slope would be [tex]\frac{11-11}{3-(-2)}=\frac{0}{6} =0[/tex]
The slope would be 0 for the line,
another way we can tell the slope is 0 is that we can see the two sets of coordinates are on the y=11, they just have different x coordinates.
But the equation above shows the complete work and supported the answer.
Answer:
Slope (m) = 0
Step-by-step explanation:
Given coordinates,
→ T(-2, 11)
→ U(3, 11)
Formula we use,
→ Slope = (y2 - y1)/(x2 - x1)
Now required slope will be,
→ m = (y2 - y1)/(x2 - x1)
→ m = (11 - 11)/(3 -(-2))
→ m = (0)/(3 + 2)
→ m = 0/6
→ [ m = 0 ]
Therefore, the slope is 0.
help I’ll mark brainliest
The value of expression 9 1/2k - [7 + 3 1/4k] without parentheses is 25 / 4 k - 7.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
9 1/2k - [7 + 3 1/4k]
Simplify the above expression and convert mixed fractions into improper fractions,
19 / 2 k - [7 + 13 / 4k]
19 / 2 k -[(28 + 13 k) / 4]
(38k - 28 -13k) / 4
(25k - 28) / 4
25 / 4 k - 7
To know more about equation:
https://brainly.com/question/12788590
#SPJ1
Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a coordinate plane.
a. (0,0), (6,3), (3,24)
b. (5,3), (8,6), (4,10)
.
a. The orthocenter is .
(Type an ordered pair. Simplify your answer.)
b. The orthocenter is.
(Type an ordered pair. Simplify your answer.)
PLEASE ANSWER I NEED HELP
a. The orthocenter for the coordinates (0,0), (6,3), and (3,24) is (24, 2).
b. The orthocenter for the coordinates (5,3), (8,6), and (4,10) is (8, 6).
What is an orthocenter?The orthocenter is the point where the altitudes of the triangle coincide. An obtuse triangle, will be outside the triangle. For a right triangle, it will be the right angle vertex. Of course, each altitude is a line through a vertex and perpendicular to the opposite side.
The equation can be written as,
y -y₃= -(x₂ -x₁)/(y₂ -y₁)(x -x₃)
This can be rearranged to something resembling standard form:
(x₂ -1x₁)(x -x₃) +(y₂-y₁)(y -y₃) = 0
(x₂ -x₁)x +(y₂ -y₁)y = (x₂ -x1)x₃ +(y₂ -y1)y₃ . . . . line through P3, ⊥ to P1P2
Part(a).
For the first altitude, we choose P1 = (0, 0), P2 = (7, 3), and P3 = (3, 51). This gives,
(x₂-x₁) = 7 -0 = 7
(y₂ -y₁) = 3 -0 = 3
altitude equation = 7x +3y = 7·3 +3·51 = 174
For the second altitude, we choose P1 = (0, 0), P2 = (3, 51), and P3 = (7, 3). This gives,
(x₂ -x₁) = 3 -0 = 3
(y₂ -y₁) = 51 -0 = 51
altitude equation = 3x +51y = 3·7 +51·3 = 174
Finding the point of intersection of these two equations can be done in a number of ways. Cramer's Rule provides a quick solution:
x = ((3)(-174) -(51)(-174))/(7·51 -3·3) = 8352/348 = 24
y = ((-174)(3) -(-174)(7))/348 = 696/348 = 2
The orthocenter for the triangle is (24, 2).
Part(b).
We can use the method just described, or we can verify the triangle is a right triangle, as it appears to be when the points are plotted.
The slope of P1P2 is (6 -3)/(8 -5) = 3/3/ = 1.
The slope of P2P3 is (10 -6)/(4 -8) = 4/-4 = -1
These slopes have a product of -1, so the segments are perpendicular. The vertex P2 has the right angle, hence the orthocenter.
The orthocenter for the triangle is (8, 6).
To know more about orthocenters follow
https://brainly.com/question/22440007
#SPJ1
Find the p-value for a two-tailed hypothesis test with a test statistic of z = 2.57.
find the p-value
Answer:
z=10.5. give me brainly