Answers
Solution:
Given:
[tex]f(x)=\frac{x+1}{x^2-6x+8}[/tex]The domain is the set of all possible x-values (inputs) that will make the function (output) to be real and defined.
To get the domain of the function given, we need to get the undefined or singularity points.
[tex]\begin{gathered} f(x)\text{ will be defined only when the denominator is equal to 0.} \\ \text{Hence, singularity or undefined points will occur when,} \\ x^2-6x+8=0 \\ \text{Solving to get these points,} \\ x^2-4x-2x+8=0 \\ x(x-4)-2(x-4)=0 \\ (x-2)(x-4)=0 \\ x-2=0 \\ x=0+2 \\ x=2 \\ \\ OR \\ x-4=0 \\ x=0+4 \\ x=4 \\ \\ \text{Hence, singularity occurs at;} \\ x=2,x=4 \end{gathered}[/tex]
The domain of the function will exist when;
[tex]\begin{gathered} x\ne2,x\ne4 \\ \\ \text{Hence, the solution to the domain of the function is;} \\ x<2\text{ OR }24 \end{gathered}[/tex]Hence, the solution to the domain is;
[tex]x<2\text{ OR }24[/tex]In interval notation, the domain is;
[tex](-\infty,2)\cup(2,4)\cup(4,\infty)[/tex]Therefore, the final answer is;
All real numbers except 2 and 4.
Related Questions
Max loves fishing. He and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour. Some time later a cruise ship left traveling in the same direction but at an average speed of 14 km/hour. After traveling for ten hours the cruise ship caught up with the fishing boat. How long did the fishing boat travel before the cruise ship caught up?
Answers
The fishing boat traveled for 14 hours before the cruise ship caught up.
In this question, we have been given Max and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an average speed of 10 km/hour.
After some time, a cruise ship left traveling in the same direction but at an average speed of 14 km/hour.
The cruise ship caught up with the fishing boat after traveling for 10 hours.
Let a cruise traveled 'm' km after 10 hours.
Using the formula of speed,
speed = distance / time
14 = m / 10
m = 14 * 10
m = 140 km
This means, a cruise traveled 140 km in 10 hours.
Now, we find the time needed for a fishing boat to cover 140 hours.
speed = distance / time
10 = 140/t
t = 140 / 10
t = 14 hours
Therefore, the fishing boat traveled for 14 hours before the cruise ship caught up.
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NEED THIS ASAP 50 POINTS UWU
Which property of equality should you apply to keep the equation 22 . a = 242 in balance when solving?
The division property of equality
The subtraction property of equality
The reflexive property
The substitution property of equality
Answers
A property of equality that you should apply to keep the equation 22 . a = 242 in balance when solving include the following: A. The division property of equality.
What is the subtraction property of equality?In Mathematics and Geometry, the subtraction property of equality states that the two (2) sides of an algebraic expression or equation would still remain equal even when the same number has been subtracted from both sides of an equality.
Based on the information provided above, we can logically deduce the following equation:
22 . a = 242
22 × a = 242
By applying the division property of equality, we have the following:
a = 242/22
a = 11.
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Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies. Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether. Graphically solve a system of equations in order to determine the number of donuts, x, and the number of cookies, y, that Autumn bought.
Answers
Autumn bought 4 Donuts and 2 Cookies worth of 5 dollars.
What are simultaneous equations?We know two simultaneous equations have a unique solution when they intersect at a point,
when they are parallel they have no solution and when they are coinciding they have an infinite no. of solutions.
Given, Autumn and her children went into a bakery and she bought $5 worth of donuts and cookies.
Each donut costs $1 and each cookie costs $0.50. She bought a total of 6 donuts and cookies altogether.
Let us denote no. of Donuts by x and no. of Cookies by y.
∴ x + y = 6...(i) and x + 0.5y = 5...(ii).
Subtracting eqn(ii) from eqn(i) we get y = 2 and substituting the value of y in eqn(i) we get x = 4.
Autumn bought 4 Donuts and 2 cookies with 5 dollars.
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To solve a system of equations _______________ means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: _______________ and _______________.
Answers
To solve a system of equations algebraically means that we will use some algebraic manipulation to find the solution(s). there are two techniques for solving algebraically: elimination and substitution.
The theory of linear systems serves as the foundation for the field of linear algebra, which is used in most branches of modern mathematics.
Computational methods for getting the solutions, which are essential to the disciplines of engineering, physics, biochemistry, computer science, and economics, are included in numerical linear algebra. It is useful to approximate a system of nonlinear equations by a linear system when developing a mathematical model or computational modelling of a relatively complex system (see linearization).The easiest method for resolving a system of linear equations is to repeatedly remove variables. This method is described in the sentences that follow.The first equation's variables should each be solved for in relation to one another.In the following equations, substitute this expression in its place. As a result, the system of equations contains one less equation and unknown.Hence the two ways an algebraic equation can be solved is by elimination and substitution.
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Choose four rational numbers at least two of your numbers should be between -1 and 1 one of which should be written as a decimal and the other should be written as a fraction
Answers
Any number that can be written as a fraction and in which the numerator and denominator are both integers is referred to as a rational number. In other words, p/q can be used to represent a rational number when p and q are both integers and q is 0. It will be 0.25 and 0.5.
Explain about the rational numbers?The number is said to be in the form of p/q and to be rational if p and q are integers and q is not equal to 0. Examples of rational numbers are 1/3, 2/4, 1/5, 9/3, etc.A rational number is any number that can be written as the difference between two integers. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1. This includes both ordinal and decimal fractions. A decimal fraction is one that has a denominator that is a power of 10. An example would be 0.25Hence, the rational numbers will be 0.25 and 0.5.
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Find the LCM of 4 and 14
Answers
Mia, this is the solution:
4 = 2 * 2
14 = 2 * 7
Therefore, we have:
2 = two ocurrences (the higher number)
7 = one ocurrence
LCM = 2 * 2 * 7
LCM = 28
if y=-2 when x=4, find y when x =7
Answers
As x and y vary inversely as each other , if x=7 then y = -8/7.
in the question ,
it is given that
x and y vary inversely ,
So , x * y = k
given that , when x = 4 , the value of y = -2 .
Substituting , 4 * (-2) = k
k = -8
so , the constant of variation (k) = -8 .
in order to find value of y when x = 7 ,
we substitute x=7 and k = -8 in the relation xy = k
we get , 7 * y = (-8)
Dividing both sides by 7 we get
7y/7 = -8/7
on simplifying we get ,
y = -8/7
Therefore , as x and y vary inversely as each other , if x = 7 then y = -8/7 .
The given question is incomplete , the complete question is
If y varies inversely as x, and y = -2 when x = 4 find y when x = 7 .
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Write an equasion of the line that passes through (0,-2) and (4,10)
Answers
Answer:
12.649
Step-by-step explanation:
we can use Pythagoras to solve this; simply by forming a triangle of the difference between the x and y values. (I added a lil-sketch of it).
So, we just need to find the length of the two sides:
Vertical side: 12
Horizontal side: 4
Thus;
[tex]4^{2} + 12^{2} = c^{2} \\160 = c^{2}\\Side c is equal to 12.649 (in whatever unit given)[/tex]
Rewrite 8-1/2 as an improper fraction.
Answers
Answer:
[tex]\frac{15}{2}[/tex]
Step-by-step explanation:
8 - [tex]\frac{1}{2}[/tex]
= [tex]\frac{16}{2}[/tex] - [tex]\frac{1}{2}[/tex]
= [tex]\frac{15}{2}[/tex]
Answer:
The answer is 17/2
Step-by-step explanation:
You get that by multiplying the whole number 8 by the denominator of the fraction, and that will be equal to 16 and the 1 from the numerator of the fraction 1/2, so the equation will look like 16+1=17. Your new numerator 17.
if a test yields almost identical scores when it is retaken after a two-month interval, we can say that the test is
Answers
Yield testing is a technique for figuring out the precise quantity of raw materials required to make a specific quantity of finished product.
What exactly is a yield test?The amount of food material available for consumption after it has been prepared, processed, and changed into the completed product is referred to as yield.Yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of final product.AP weight minus waste equals EP weight.Calculate your yield percentage by dividing the edible product weight by 100. EP weight x AP weight x 100 = yield% is the formula.Therefore, yield testing is a method of determining the precise amount of raw materials needed to produce a certain amount of the final product.
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Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class?
Answers
it should be 14 students i think
Hope this help you
The perimeter of the rectangle is
A) 9.49
B) The p
C) 18.97
The area of the rectangle
A) 18.5
B) 20
C) 40
Please answer ASAP
Answers
The area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
What is termed as the rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and all four vertices that are 90 degrees apart. degrees. As a result, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal as well as parallel, it is also known as a parallelogram.For the given question;
To find the perimeter of the rectangle ABCD, first find the length of the sides.
Using the distance formula, find the length DA and DC,
DA = √(x2 - x1)² + (y2 - y1)²
Put the coordinate of the point D and A.
DA = √(8 - 1)² + (2 - 0)²
DA = √49 + 4
DA = √53 units.
Now, length DC
DC = √(3 - 1)² + (3 - 0)²
DC = √4 + 9
DC = √13 units.
For the rectangles;
DA = CB = √53 units.
DC = AB = √13 units.
Perimeter = DA + CB + DC + AB
Perimeter = 2√53 + 2√13 units
Perimeter = 2(√53 + √13) units.
Perimeter = 21.77 units.
Area = (1/2) base × height
Area = (1/2) CB × CD
Area = (1/2) × √53 × √13
Area = 26.24/2
Area = 13.12 sq. unit.
Thus, the area and the perimeter of the rectangle is found as 13.12 sq. unit and 21.77 units respectively.
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Solve for x and then give the m∠G?
Enter your answer in the box.
Answers
first the sum of all angles of in triangle is 180 degree.
x+(3x+25)+(x-5)=180
x+3x+25+x-5=180
4x+25+x-5=180
4x+x+25-5=180
5x+20=180
5x=180-20
5x=160
x=32 degree and
the angle of G is 3(32)+25=121 degree
i need to know if they are functions, please say
function A:(function or not a function)
function B:(function or not a function)
Answers
Answer:
First one is a function, second one is not, since it assigns more than one y value for x values.
Step-by-step explanation:
A function means for every x value, at most 1 y value exists. This is clearly not the case for the bottom figure. You can test it with an imaginary vertical line. There should be zero or one intersections.
What is the length of segment SR?
Answers
Applying the midsegment theorem, the length of segment SR is: 6 units.
What is the Midsegment Theorem?The Midsegment theorem states that if a segment is draw to connect the two midpoints of two sides of a triangle together, it is parallel to the third side of the triangle and also has a length measure that is half of the length of the third side of the triangle.
Segment SR is the midsegment of the triangle given and is parallel to the third side, FD.
SR = 2x - 14
FD = x + 2
Therefore:
SR = 1/2(FD) [midsegment theorem]
Substitute
2x - 14 = 1/2(x + 2)
2(2x - 14) = x + 2
4x - 28 = x + 2
4x - x = 28 + 2
3x = 30
x = 30/3
x = 10.
Length of SR = 2x - 14 = 2(10) - 14
Length of SR = 6 units
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Answer:
12 units
Step-by-step explanation:
Priya starts with $50 in her bank account. She then deposits $20 each week for 12 weeks. Write an equation that represents the relationship between the dollar amount in her bank account and the number of weeks of saving.
Answers
Answer: d=50+20w
D(deposit) = 50(starting amount)+20(added amount)w(multiply 20 by the amount of weeks, 12, and this is your equation.)
Which step shows the result of applying the subtraction property of equality? one-fourth (12 x 8) 4 = 3 step solution 1 3 x 2 4 = 3 2 3 x 6 = 3 3 3 x = negative 3 4 x = negative 1 step 1 step 2 step 3 step 4
Answers
The step 3 follow the subtraction property of equality.
Given,
The Equation is : 1/4 (12x + 8) + 4 = 3
There is some steps:
Step Solution
1 3x + 2 + 4 = 3
2 3x + 6 = 3
3 3x = -3
4 x = -1
To find the which step shows the result of applying the subtraction property of equality?
Now, According to the given steps:
From the table, we can know
From Step 2: 3x + 6 = 3
Subtract 6 on both sides
3x + 6 - 6 = 3 - 6
3x = -3
Hence, The step 3 follow the subtraction property of equality.
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8x^4+7x^3+2x^4+6+4x^3
Answers
You have the following algebraic expression:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ \end{gathered}[/tex]The previous expression can be simplified by taking into account, that for the simplification you sum or subtract (depending of signs) similar terms. Remind that similar terms are those one which has the same variable with the same exponent. In this case you have similar terms with variable x and exponent 4, furthermore you have similar terms with variable x and exponent 3. Then you sum this terms and you obtain:
[tex]\begin{gathered} 8x^4+7x^3+2x^4+6+4x^3 \\ =8x^4+2x^4+7x^3+4x^3+6 \\ =10x^4+11x^3+6 \end{gathered}[/tex]where you have summed 8x^4 + 2x^4 = 10x^4, and 7x^3 + 4x^3 = 11x^3.
Hence, the simplied expression is 10x^4 + 11x^3 + 6
What is the surface area of this rectangular pyramid? 4 mm
4 mm 4 mm
Answers
The formula for calculating the total surface area of a rectangular pyramid using its length, width, and height is provided as T.S.A. = lw + l[(w/2)2 + h2] + w[(l/2)2 + h2], where l is the length of the rectangular base, w is its width, and h is its height.
What is the Rectangular Pyramid?Pyramids are three-dimensional constructions with triangle-shaped faces and a base with a polygonal shape. A pyramid is referred to as a rectangular pyramid if its base is also rectangular. All pyramids have triangular sides, despite the fact that their bases are rectangular. The height of the pyramid is indicated by the top vertex, also known as the apex. The volume of a rectangular pyramid can be calculated using the formula V=1/3lwh, where l denotes the length of the base, w its width, and h its height.To learn more about Rectangular Pyramid refer :
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Jane is going to purchase a home that is $180,000, she makes the standard down payment (20%), then she is going to obtain a mortgage for the rest. How much will Jane have paid total for the house if she does a 30-year mortgage (360 months)? Interest rate for both is 4%(.04) How much will she have paid total for the house if she does a 15-year mortgage? Worth 5 points
Answers
Answer:
36000
Step-by-step explanation:
I think its that because the 20% of 180000 is 36000
what are the maximum dimensions of a div with the following properties?div.container { min-height: 150px; max-height: 600px; min-width: 300px; max-width: 900px;
Answers
Max width = 900px
600 x 900 or 540 000px
An A.P has 17 terms and a common difference of -4 determine the first and the last termif the A.P is 107.1
Answers
Answer:
Below in bold.
Step-by-step explanation:
The sum of 17 terms is 107.1.
Sn = (n/2)[2a + (n-1)d] where a = first term and d = common difference
(17/2) (2a + (17-1)(-4)) = 107.1
8.5(2a -64) = 107.1
17a - 544 = 107.1
17a = 651.1
a = 38.3 = First term
The last term is the 17th so
L = a + (n - 1) d
= 38.3 + 16*-4
= -25.7.
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles?
Answers
When a scale of 1 inch to 40 miles apart then distance = 112 miles .
We have been give that
If 1 inch = 25 miles,
Then 2.8 inches would be 25 miles multiplied by 2.8 since each of those 2.8 inches is 25 miles.
2.8 x 25 = 70.
70 miles.
The same two cities be on a map that has a scale of 1 inch to 40 miles
Then 1 inch= 40 miles,
then 2.8 inches would be 40 miles multiplied by 2.8 since each of those 2.8 inches is 40 miles.
2.8 x 40 = 112.
112 miles.
Hence , Distance equals 112 miles when measured on a scale of 1 inch to 40 miles apart.
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The cost of a banquet is represented by the equation C = 14p + 90, where C is the cost
and p is the number of people attending. What is the price per person attending?
Answers
The price per person attending is 104 .
What are linear equations?If a variable's highest power is always 1, an equation is considered to be linear. As a one-degree equation, it also goes by that name. An equation with one variable that has the usual form Ax + B = 0 is a linear equation. A coefficient, B is constant, and x is a variable in this situation. An equation with two variables that has the usual form Ax + By = C is a linear equation. Both a B are factors, C is a standard, and the variables in this solution are x and y. Linear equations are defined as equations with the maximum degree of 1. A linear equation cannot have a variable with an exponent greater than 1, according to this rule. A straight line is formed on the linear equation graph.
C = 14p + 90
Here p = 1 cause per person
So,
C = 14 (1) + 90
C = 104
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You have a function that takes in an X value and produces a Y value. The x value equals 7 times the y value, plus 18 more. What's the x value when the y value equals 6?
Answers
The value of x from the given function is 60.
Given that, the x value equals 7 times the y value, plus 18 more.
What is the function?A function in math means a correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to outputs.
Now, the x value equals 7 times the y value, plus 18 more
x=7y+18
Put y=6 in the obtained function, that is
x=7(6)+18
⇒ x = 42+18
⇒ x = 60
Therefore, the value of x from the given function is 60.
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Simplify as far as possible without a calculator.
5
√
3
(
2
√
3
−
3
√
7
)
Answers
After simplification this 5√3(2√3−3√7) we get, -38.71
5√3(2√3−3√7) is a linear equation.
What is linear equation?
An equation between two variables that, when plotted on a graph, produces a straight line or say first degree equation is known as linear equation.
Let's simply this 5√3(2√3−3√7)
=> 5√3 * 2√3 - 3√7 * 5√3
=> 5*2*√3*√3 - 3 * 5 √7 * √3
=> 10 * 3 - 15 * 1.732 * 2.645
=> 30 - 68.717
=> -38.717 or -38.71
Therefore, the value of 5√3(2√3−3√7), after simplification we get -38.71
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This Stem-and-Leaf Plot shows the number of books sold daily by a bookstore in the previous month. What is the mode of the data set?A.) 45 booksB.) 13 booksC.) 21 booksD.) 53 books
Answers
As you can see in the stem-and-leaf plot, the box with the most numbers is
[tex]\rightarrow2|00111122\leftarrow[/tex]And in this box, the number that is repeated the most is 1. So that, the data that is repeated the most is 21.
Therefore, the mode of the data set is 21.
Brady loves to go fishing he goes every weekend this weekend he caught 4 less fish than he did last weekend he caught 7 fish this weekend write and solve and equation to determine how many fish he caught last weekend let f represent the number of fish
Answers
Suppose n represents an integer. Then the next integer can be represented by the expression n+1. Write a linear expression that represents the sum of any two consecutive integers. Then use the expression to make an argument about whether the sum of any two consecutive integers is even or odd. Explain your reasoning.
Answers
The expression 2n + 1 will produce both odd and even numbers based on the choice we have made.
Expression:
An expression is a mathematical expression consisting of numbers, operations, and one or more variables.
Given,
Suppose n represents an integer. Then the next integer can be represented by the expression n+1.
Here we need to write the linear equation for these two consecutive integers.
Then we have to use the expression to make an argument about whether the sum of any two consecutive integers is even or odd.
Let n represents the first integer and n+1 is the second integer.
Then the linear equation for these two consecutive integer is
=> n + (n + 1)
=> 2n + 1
Now we have to take the value of n and n + 1 as, 2 and 3,
Then we apply the value to the expression,
=> 2(2) + 3
=> 4 + 3
Similarly, if we take the value as 5 and 6,
Then we get,
=> 2(5) + 6
=> 10 + 6
=> 16
So, based on the given details the equation givens both odd and even number based on the number our choices.
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2(2x - 7) = 22 solve for x and simplify your answer as much as possible
Answers
Answer: 9
Step-by-step explanation:
2(2x-7) = 22
4x - 14 = 22
4x = 36
x = 36/4
x = 9
Distribute the two to the 2x-7 in parentheses
Add 14 to 22
Divide 36 by 4
