The equation for the segment AB is;
[tex]2x^2-x-42[/tex]The equation for the segment BC is ;
[tex]x^2+11x+21[/tex]If segment AC has midpoint at B , this means ;
AC = AB + BC
To get AC we add the equation for AB and BC
Performing addition as;
[tex]2x^2-x-42+x^2+11x+21[/tex]Collect like terms as;
[tex]2x^2+x^2+11x-x-42+21=AC[/tex][tex]3x^2+10x-21=AC[/tex]Answer
[tex]AC=3x^2+10x-21[/tex]
what is the surface are of this cone rounded to the nearest tenth of a square foot?
ANSWER
[tex]282.7ft^2[/tex]EXPLANATION
Recall, the formula for calculating the surface area of a cone is;
[tex]A=\pi r^2+\pi r\sqrt{r^2+h^2}[/tex]Given;
[tex]\begin{gathered} radius(r)=5 \\ height(h)=12 \end{gathered}[/tex]Substitute the values into the formula;
[tex]\begin{gathered} A=\pi 5^2+\pi 5\sqrt{5^2+12^2} \\ =\pi5^2+\pi5\sqrt{25+144} \\ =25\pi+5\pi\times13 \\ =25\pi+65\pi \\ =90\pi \\ =90\times3.14 \\ =282.74 \\ \cong282.7 \end{gathered}[/tex]Solve the following simultaneous equation using the inverse matrix method
3x + 4y = 18
4x - y = 5
The values of x and y obtained by inverse matrix method are 2 and 3 respectively
What is an inverse matrix?An inverse of a matrix, A, is a matrix [tex] A^{-1}[/tex], that multiplies matrix A to give an identity matrix.
The inverse matrix method involves defining and making use of a coefficient matrix, A, a variable matrix, X, and a constant matrix, B, which are obtained from the system of equations as follows;
A·X = B
The system of equations is presented as follows;
3·x + 4·y = 18
4·x - y = 5
From the above system of equations, we have:
[tex]The \ coefficient \ matrix, \ A = \begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex]
[tex]The \ variable \ matrix, \ X = \begin{bmatrix} x \\ y \end{bmatrix}[/tex]
[tex]The \ constant \ matrix, \ B = \begin{bmatrix} 18 \\ 5 \end{bmatrix}[/tex]
From the equation, A·X = B, we have;
[tex]\therefore X = \dfrac{B}{A} = A^{-1} \times B[/tex]
Where: A⁻¹ is the inverse matrix of A, which is found as follows;
[tex]If\ A = \begin{bmatrix} a&b \\ c&d \end{bmatrix}[/tex]
[tex]Then, \ A^{-1} = \dfrac{1}{a\cdot d-b\cdot c} \cdot \begin{bmatrix} d& -b \\ -c& a \end{bmatrix}[/tex]
Which gives the value of A⁻¹ obtained from the coefficient matrix, A = [tex]\begin{bmatrix} 3&4 \\ 4& -1 \end{bmatrix}[/tex] as follows;
[tex]A^{-1} = \begin{bmatrix} 3 & 4 \\ 4 & - 1 \end{bmatrix}^{ - 1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix}[/tex]
[tex]A^{-1} = \dfrac{1}{(3 \times - 1) - (4 \times 4)} \times \begin{bmatrix} - 1 & - 4 \\ - 4 & 3 \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} & \dfrac{ - 4}{ - 19} \\\\ \dfrac{ - 4}{ - 19} & \dfrac{3}{ - 19} \end{bmatrix}[/tex]
The variable matrix, [tex]X = A^{-1} \times B[/tex], which gives the value of the variables in the solution is therefore;
[tex]X = \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} \dfrac{ - 1}{ - 19} &\dfrac{ - 4}{ - 19} \\ \\\dfrac{ - 4}{ - 19} &\dfrac{3}{ - 19} \end{bmatrix} \times \begin{bmatrix} 18 \\ 5 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
[tex]\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}[/tex]
Therefore;
x = 2 and y = 3
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The flow of water from a faucet can fill a 4-gallon container in 28 seconds Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction. The faucet fills the container at rate of——gallon per second
The flow of water can fill a 4-gallon container in 28 seconds.
Given:
Number of gallons = 4
Time = 28 seconds
Hence, the ratio of gallons to seconds will be 4 : 28
[tex]\begin{gathered} As\text{ a rate in gallons per second = }\frac{\text{number of gallons}}{time\text{ taken}} \\ As\text{ a rate in gallons per second = }\frac{4}{28}=\frac{1}{7} \\ As\text{ a reduced fraction, the rate in gallons per second is }\frac{1}{7}\text{gallons per second} \end{gathered}[/tex]Therefore, the faucet fills the container at the rate of 1/7 gallon per second
calculate the slope of a line passing through the given points (5,-2) and (5,-3)
Given the points (5,-2) and (5,-3), we can find the slope of the line that passes through them with the following formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-3-(-2)}{5-5}=\frac{-1}{0} \end{gathered}[/tex]since we have that the slope is not defined, the line that passes through the points (5,-2) and (5,-3) is the vertical line x=5
An employee makes $10.59 per hour but is getting a 4% increase. What is his new wage per hour to the nearest cent?
In order to calculate the new wage per hour, we just need to multiply the old value of $10.59 by 1.04, that is, an increase of 4%, so we have:
[tex]10.59\cdot1.04=11.01[/tex]So the new wage per hour is $11.01.
show the prime factorisation of 49 :-;
thankyou.
Answer:
The prime Factorization of 49 is 7.7
Step-by-step explanation:
Hope this helps! :))
Answer:
7
Step-by-step explanation:
The factors of 49 are 1, 7, and 49
please help 40 points!!
Answer:
The midpoint is (-1,1)
Equation: y = -x -2
Step-by-step explanation:
Midpoint:
([tex]\frac{-5+3}{2}[/tex], [tex]\frac{-5 + 3 }{2}[/tex]) You are taking the averages of the x values and the y values.
([tex]\frac{-2}{2}[/tex],[tex]\frac{-2}{2}[/tex])
(-1,-1)
Equation:
The slope of the 2 points given is
[tex]\frac{3 - -5}{3- - 5}[/tex] = [tex]\frac{8}{8}[/tex] = 1 The slope is the change of y over the change in x. Points are given in the form (x,y) So, I subtracted the y values on top and the x values on the bottom of the fraction.
The equation that is created is perpendicular to the original line, so it slope is the negative reciprocal.
1 as a fraction is [tex]\frac{1}{1}[/tex]. negative reciprocal means turn the fraction upside down and take the opposite value. If I flip [tex]\frac{1}{1}[/tex] upside down, I get the same fraction which is equal to 1. Now I will take the opposite sign. Since it is positive, the new slope will be negative
slope -1
x = -1
y = -1
I am using the point that will be on the new line. This is the midpoint that we just found (-1,-1) I am going to plug in the number that I know and solve for b or the y=intercept.
y = mx + b
- 1 = -1(-1) + b
-1 = 1 + b Subtract 1 from both sides of the equation
-2 = b
y = mx + b
y = -1x -2
or
y = -x -2
Select the correct answer.If the zeros of a quadratic function are 3 and 8, what are the factors of the function?OA (X + 8) and (x-3)O B. (x-8) and (x+3)OC. (x+8) and (x+3)OD. (x-8) and (x-3)
The zero of x = 3 will be x - 3 = 0
The zero of x = 8 will be x - 8 = 0
Therefore, the quadratic equation will be
(x - 3) and (x - 8)
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Write the equation for a parabola with a focus at (-6,0) and a directrix at x = -2.
x=
y² = -8(x - 4), which is the required equation of the parabola.
What are a parabola's focus and directrix ?All points in a plane that are equally spaced out from a given point and a given line make up a parabola.
The line is known as the directrix, and the point is known as the parabola's focus.
A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.
The focus of the parabola is F(-6,0) and its directrix is the line x=−2 i.e., x+2=0
Let P(x,y) be any point in the plane of directrix and focus, and MP be the perpendicular distance from P to the directrix,then P lies on parabola if FP=MP
⇒(x+6)²+(y−0)² = ∣x+2∣÷1
⇒x² + 12x+36+y² = x² +4x +4
⇒y² + 8x = -32
⇒y² = - 8x - 32
⇒y² = -8(x - 4)
⇒ y² = -8(x - 4), which is the required equation of the parabola.
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Lisa is a software saleswoman. Let y represent her total pay (in dollars). Let “x”represent the number of copies of History is Fun she sells. Suppose that “x”and “y”are related by the equation 90x + 2200 =v.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Explanation
Part A
Given that x and y are related by the by the equation 90x + 2200 =y. We can find the change by comparing the formula with the original equation of a line.
[tex]\begin{gathered} y=mx+c \\ where\text{ m is the slope\lparen change in y for x\rparen} \end{gathered}[/tex]Comparing the above with the given question, m becomes change in Lisa's pay for each copy of history is fun. Therefore,
Answer: 90 dollars
Part B
If Lisa does not sell any copies of history is fun, therefore, the value of x becomes zero. We can then have the total pay as
[tex]\begin{gathered} y=90(0)+2200 \\ y=2200 \end{gathered}[/tex]Answer: 2200 dollars
PROGRESSIVEKayla ForshaeSupervisor: "Our goal is to make add-on sales during 85% of sales. If you make 35sales, how many add-on sales do you need to make to meet the goal?"
We are given that the total number of sales is 35.
According to the question, his goal is to make add-on sales during 85% of sales.
Therefore, the add-on sales would be:
[tex]\Rightarrow\frac{85}{100}\times35=29.75\approx30[/tex]Hence, we will need to make 30 add-on sales to meet the goal.
52. What is the 275th digit after the decimal point in therepeating decimal 0.6295 ?F. 0G. 2H. 5J. 6K. 9
Given:
The digit is 0.6295.
Required:
To find the 275th digit after the decimal point in the repeating decimal 0.6295.
Explanation:
For any non-negative integer, we have:
The 4n+1th digit after the decimal point is 6.
The 4n+2th digit after the decimal point is 2
The 4n+3th digit after the decimal point is 9
The 4n+4th digit after the decimal point is 5.
Since the repeating digit is 4 and we have to find the 275th digit.
Thus
[tex]\frac{275}{4}=68\text{ with remainder 3}[/tex]It can be written as:
275 = 4. 68 + 3
That is 275th digit after the decimal point in the repeating decimal is 9 with n= 68.
Final answer:
Thus option k is the correct answer.
A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).What is the Coordinates Of T
Given: A circle has a center point at the coordinates P(3,0) with a diameter line RT where R has the coordinates (-47,25).
Required: To determine the coordinates of T.
Explanation: The given circle is-
Let the coordinates of T be (x,y). Then the center of a circle is divided by the diameter in the ratio of 1:1. The section formula for a point (x,y) dividing a line segment in the ratio of 1:1 is-
[tex]\begin{gathered} x=\frac{(x_1+x_2)}{2}, \\ y=\frac{(y_1+y_2)}{2} \end{gathered}[/tex]Hence, for the given line RT, point P divided RT in 1:1. Thus-
[tex]\begin{gathered} 3=\frac{-47+x}{2}, \\ 0=\frac{25+y}{2} \end{gathered}[/tex]Further solving for x and y as-
[tex]\begin{gathered} x=6+47 \\ \Rightarrow x=53 \\ and\text{ }y=-25 \end{gathered}[/tex]Final Answer: The coordinates of T are (53,-25).
Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.) 5x + 4y = 24 2x – 7y = 26 7x – 3y = 50 7x + 3y = 50 3x - 3y = -2 36 x+ 11y = -2
Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.)
5x + 4y = 24
2x – 7y = 26
____
a) 7x – 3y = 50
b) 7x + 3y = 50
c) 3x - 3y = -2
d) 3 x+ 11y = -2
_____________________________
Try adding and subtracting the equations
5x + 4y = 24
+(2x – 7y = 26)
_______________
7x -3y= 50
5x + 4y = 24
-2x + 7y = -26
______________
3x + 11y = -2
Do you have any questions regarding the solution?
Im confused on what you have to do in order to find the answer
Given:
The ship is moved from (-10,9) to (-1,-5) in the coordinate plane.
To find:
The transformation rule
Explanation:
The initial point can be written to obtain the terminal point as follow,
[tex](-10+9,9-14)\rightarrow(-1,-5)[/tex]In general,
We write,
[tex](x,y)\rightarrow(x+9,y-14)[/tex]Final answer: Option C.
[tex](x,y)\operatorname{\rightarrow}(x+9,y-14)[/tex]
12)If the legs of a right triangle are 6 cm and 5 cm, find the area of the triangle.A)11 cm2B)15 cm2C)30 cm2D)60 cm2
What’s is the volume and surface area of the figure shown ?
• The total surface area of a cylinder is given by:
[tex]SA=2πr\left(r+h\right)[/tex]where r = 1.75 cm
h = 3 cm
Hence:
[tex]SA=2\times\pi\times1.75\times(1.75+3)=57.7\text{ }cm^2[/tex]• The volume of a cylinder is given by:
[tex]V=πr^2h[/tex]Hence:
[tex]V=\pi\times(1.75)^2\times3=28.9\text{ }cm^3[/tex]ANSWER
surface area = 57.7 cm²
volume = 28.9 cm³
The Ferris wheelThe community loves the Ferris Wheel because when they are at the top of the wheel they can look for their house and it has long been a family favorite. The company sent you a Ferris wheel that has a radius of 40 ft. and each car is 5 ft. tall. The people can’t start to look for their houses until they get above the tents of the carnival and those tents are 20ft tall. The Ferris wheel has 20 passenger cars and it takes 12 minutes to have all the cars filled. Once all cars are filled the Ferris wheel runs at 1 rotation for every 2 minutes for a total of 8 minutes.Once someone has boarded the Ferris wheel, how long will it take for them to be able to start looking for their house?How long will they have to search for their house?
Given:
radius of Ferris wheel = 40 ft
height of a car = 5 ft
height of a tent = 20 ft
no. of passenger cars = 20
time to load all cars = 12 minutes
time for 1 rotation = 2 minutes
time for all rotations = 8 minutes
What we want to know is how many degrees the car will have to travel along the circle before it reaches a height of 20 ft.
We can draw a triangle to represent the unknown and find the angle.
The total height from the ground to the center of the Ferris wheel is 45 ft (5ft car height + 40 ft radius). We deduct the 20ft height of the tent so we get the side of the right triangle we're using to solve for the missing angle. That height is 25 ft.
The radius also serves as the hypotenuse of the triangle.
We can then use the following to solve for the angle theta:
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \\ \cos\theta=\frac{25}{40} \\ \\ \cos^{-1}(\cos\theta)=\cos^{-1}(\frac{25}{40}) \\ \\ \theta=51.3\degree \end{gathered}[/tex]Now we know that the car must travel 51.3 degrees along the circle before it gets to a height where it can see above the tents. If one rotation is 360 degrees and it takes 2 minutes to complete one round, then to find the time it will take to travel 51.3 degrees, we use the following equation:
[tex]\begin{gathered} \frac{360\degree}{2minutes}=\frac{51.3\degree}{x\text{ }minutes} \\ \\ x=\frac{51.3(2)}{360} \\ \\ x=0.285\text{ minutes or }17.1\text{ seconds} \end{gathered}[/tex]It will take them 17.1 to be able to start looking for their house.
Now every time the car goes around the path of the Ferris wheel, for 17.1 going up and another 17.1 seconds going down, they will not be able to look for their house.
17.1 seconds x 2 x 4 turns = 136.8 seconds
8 minutes - 136.8 seconds = 480 - 136.8 = 343.2 seconds or 5 minutes and 43.2 seconds
They have 5 minutes and 43.2 seconds to look for their house.
when you isolate the variable, what must you do to keep the equation balanced x-3=7?
Answer:
To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced.
So x = 10
Explanation:
Given the below equation;
[tex]x-3=7[/tex]To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced;
[tex]\begin{gathered} x-3+3=7+3 \\ x=10 \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
The composition of the function, (g o h)(0) = 0.
How to Find the Composition of a Function?To find the composition of a function, first, find the value of the inner function by plugging in the given value of x. The output of the inner function would now be used as the input to evaluate the outer function.
We are given the following:
g(x) = 5x
h(x) = √x
To find the composition of the function, (g o h)(0), first, find h(0). To find h(0), substitute x = 0 into the inner function, h(x) = √x:
h(0) = √0
h(0) = 0
Find (g o h)(0) by substituting x = 0 into g(x) = 5x:
(g o h)(0) = 5(0)
(g o h)(0) = 0
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Pete Corporation produces bags of peanuts. Its fixed cost is $18,200. Each bag sells for $3.43 with a unit cost of $1.83. What is Pete’s breakeven point?
Let's call x to the bags of peanuts. One bag has a variable cost of $1.83, then the variable cost of x bags is 1.83x dollars.
The total cost of production for the corporation is obtained by adding fixed and variable costs. In this case, the total cost is 18,200 + 1.83x dollars.
The revenue for the corporation of 1 bag is $3.43, then of x bags is 3.43x dollars.
When the revenue and the total cost are equal, the breakeven point is reached, in this case:
18,200 + 1.83x = 3.43x
18,200 = 3.43x - 1.83x
18,200 = 1.6x
18,200/1.6 = x
11375 = x
The cost of production of 11375 bags is:
Total Cost = 18,200 + 1.83*11375
Total Cost = 18,200 + 20816.25
Total Cost = 39016.25
Pete’s breakeven point is (11375, 39016.25), or, 11375 bags and $39,016.25
HELP PLEASEEEEEEEE!!!
The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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The rational number is -91/100 or -0.91.
What is Rational number?Any number of the form p/q, where p and q are integers and q is not equal to 0, is a rational number. The letter q stands for the set of rational numbers.
The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
Given:
We have to find the rational number between -0.45 and -0.46
Now, make both decimal into fraction
-0.45 and -0.46
-45/100 and -46/100
Now, multiply 2
-45/100 x 2/2 and -46/100 x 2/2
-90/100 and - 92/100
Hence, the rational number is -91/100 or -0.91.
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In each of the following problems, how do I graph the line with the given slope m and y-intercept b.
m=5/3,b=-4
The graph is shown the following slope intercept formula y = 5/3x -4.
What exactly is a slope?A line's slope can be used to determine how steep it is.The slope is calculated mathematically as "rise over run" (change in y divided by change in x).When a line's equation is expressed as y = mx + b, the slope-intercept representation of the equation is used.M displays the slope of the line.B is the value of b where the y-intercept is located (0, b).For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.So, the slope-intercept formula: y = mx + b
Where, = 5/3x and b = -4.Now, substitute the values in the formula and graph the slope-intercept on the graph as follows:
y = 5/3x -4(Refer to the graph attached below )
Therefore, the graph is shown the following slope intercept formula y = 5/3x -4.
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Factor the polynomial completely if possible. If the expression cannot be factored, enter the expression as is
Given the polynomial:
[tex]w^2+7w-18[/tex]Let's factor the polynomial.
To factor, let's use the AC method.
Find a pair of numbers whose product is -18 and whose sum is 7.
We have the pair:
9 and -2
We have the factors:
(w + 9)(w - 2)
Therefore, the factored form of the polynomial is:
[tex](w+9)(w-2)[/tex]ANSWER:
[tex](w+9)(w-2)[/tex]write the equation of the line with the points (0,2) and (4,10) standard form
A study found that 36% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-six percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.(c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
assisted reproductive technology (ART) cycles:
pregnancies = 36%
pregnancies resulted in multiple births = 26%
Step 02:
a.
p (pregnancies) = 36% = 36/100 = 0.36
pregnancies resulted in multiple births = 26% = 26/100 = 0.26
p(pregnancies resulted in multiple births) = 0.36*0.26 = 0.0936
b.
p (pregnancy did not produce a multiple birth) = 1 - 0.0936 = 0.9064
c.
Indeed, the probability of multiple pregnancies is low 9.36%.
That is the full solution.
3. Two companies charge differently for canoe rentals, as shown below.
Company A: c= 8h+ 10, where cequals the total cost (in dollars) and hequals number of
hours.
Company B: $15 per hour.
a. What is Company A's rate of change? How much would it cost for a 4 hour rental?
b. What is Company B's rate of change? How much would it cost for a 4 hour rental?
c. Which is the better buy? By how much for a 4 hour rental?
The rate of change for company A is 8.
The rate of change for company B is 15
Company A is better as it is charging less by a value of $18
What is rate of change?
Rate of change is the changes in the dependent variable when the independent variable changes by a unit value.
We are given 2 companies
A) equation for charges applied by company A is given by c=8h+10
Cost is a function of hours
To find the rate of change we differentiate the function
We get c' = 8
Rate of change for company A is 8
The cost for 4 hour rental is
c= 8(4)+10
c=32+10
c=$42
B) Company B charges $15 per hour
Rate of change for company B is 15
The cost for 4 hour rental is
c= 15(4)
c=$60
C) Company A is better to buy by $18 as the difference between the four hours price between company A and company B is $ 18
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are natural numbers closed under theoperation of subtraction? why or why not?
Firstly, let us define natural numbers.
Natural numbers are simply positive intergers, that is integers that are greater than zero e.g 1,2,3,4...
Secondly, when is a set said to be closed under a particular operation?
A set is said to be closed under an operation if and only if the operation on any two elements of the set produces another element of the same set. for example when you perform an operation (like addition) on a set of number (like natural numbers) it must give you a number from that same set.
E.g
let's check whether natural numbers are closed under the operation of adddition.
taking two numbers 3 and 5.
[tex]3+5=8[/tex]since the operation gives us 8, which is a natural number, it means natural numbers are closed under the operation of addition.
Back to the main question, which is to check whether natural numbers are closed under the operation of subtraction.
taking two cases.
case 1; taking numbers 3 and 5
[tex]3-5=-2[/tex]case 2: taking numbers 7 and 2
[tex]7-2=5[/tex]From the two cases, case 2 gave us a natural number while case 1 does not give us a natural number.
This means that Natural numbers are not Closed under subtraction.
Because subtraction operation on natural numbers does not necessarily produce another natural number.
On a general note;
Natural numbers are closed under Addition and Multiplication operations
while They are not closed under subtraction and division operation
Determine the domain and the range of the function.C. Determine where the function is increasing and where it is decreasing.
Given:
[tex]f(x)=2x^2-x+1[/tex][tex]a=2\text{ ; b= -1 ; c=1}[/tex]Graph opes upwards.
Let the vertex be (h,k)
[tex]h=-\frac{b}{2a}[/tex][tex]h=-\frac{(-1)}{2(2)}[/tex][tex]h=\frac{1}{4}[/tex][tex]k=f(h)[/tex][tex]k=2(\frac{1}{4})^2-\frac{1}{4}+1[/tex][tex]k=2(\frac{1}{16})-\frac{1}{4}+1[/tex][tex]k=\frac{1}{8}-\frac{1}{4}+1[/tex][tex]k=\frac{1-2+8}{8}[/tex][tex]k=\frac{7}{8}[/tex][tex]\text{Vertex}=(\frac{1}{4},\frac{7}{8})[/tex]Axis of symmetry is
[tex]x=\frac{1}{4}[/tex]y- intercept
x=0,
y=1
There is no x intercept .
Domain:
[tex](-\infty,\infty)[/tex]Range:
[tex]\lbrack\frac{1}{4},\infty)[/tex]The function is increasing:
[tex](\frac{1}{4},\infty)[/tex]The function is decreasing:
[tex](-\infty,\frac{1}{4})[/tex]
Type your solution out or write it as anordered pair.
Answer:
No Solution
Explanation:
Given the system of equations:
[tex]\begin{gathered} y=-x+3 \\ y=-x+5 \end{gathered}[/tex]Using elimination, on subtracting, we have:
[tex]\begin{gathered} 0=-2 \\ \text{But:} \\ 0\neq-2 \end{gathered}[/tex]Therefore, the system of equations has No Solution.