The required simplification of rational expression is (4 + x) / (x - 3).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression: x² + 2x - 8 / x² - 5x + 6
Given a rational expression,
x² + 2x - 8 / x² - 5x + 6
On simplifying, we get,
For numerator, x² + 2x - 8: (x - 2)(x + 4)
For denominator, x² - 5x + 6: (x - 2)(x - 3)
Now, x² + 2x - 8 / x² - 5x + 6 = (x - 2)(4 + x) / (x - 2)(x - 3)
= (4 + x) / (x - 3)
Restriction is that the denominator, x - 3 should not be 0.
Hence, the required simplification of rational expression is (4 + x) / (x - 3)
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PLS HELP QUICKLY
Point F is between points T and K.
The points are collinear.
Answer:
the answer issssssssssssss
first blank is - 12
2nd blank is -3
How can a graphical representation help you analyze data ?
Answer: It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision.
Step-by-step explanation To visualize the relationship between two numerical variables the most appropriate graph is a scatter plot. If there is a clear distinction between the independent (explanatory) and the dependent (response) variable, it is common to plot the independent variable on the x-axis and the dependent on the y-axis. The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data.
Choose the correct term to complete each sentence.
A radical expression can always be rewritten using a(n) (rational exponent/inverse relation).
A radical expression can always be rewritten using a rational exponent .
Radicals : The expressions which include a root ( [tex]\sqrt[n]{x}[/tex] ) are called radicals . For ex . [tex]\sqrt{2}[/tex] , [tex]\sqrt[3]{3}[/tex] , [tex]\sqrt[7]{5}[/tex] , and so on .
Rational Exponent : Numbers of the form ( [tex]a^{m}[/tex] ) are called rational exponents . For ex . [tex]7^{2}[/tex] , [tex]11^{3}[/tex] , [tex]5^{5}[/tex] and so on .
A radical can be converted into a rational exponent . This can be done by keeping the no . inside root as it is and reciprocating the index and raising it to the power of exponent .
( [tex]\sqrt[n]{x}[/tex] ) = ( [tex]x^{1/n}[/tex] ) where x is the base and 1 / x is the power of the exponent .
Hence , a radical expression can always be rewritten using a rational exponent .
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x)-g(x)+10
The domain value for f(x)-g(x)+10 = - x²- x + 17
What are the domain of the function f(x)-g(x)+10 ?Given : f(x)=2 x+5
g(x)=x²-3 x+2
Solution:
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+2 +10
f(x) - g(x) + 10 = 2 x+5 - x²-3 x+12
f(x) - g(x) + 10 = - x²- x + 17
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One year, Kim pays 9260 income tax work out how much she earned that year
Answer: Kim made roughly 46,300 that year.
Step-by-step explanation:
We know that income tax = 9260
Step 1 is to find out which tax bracket Kim comes under.
The min. tax for those in the 20% bracket is 7,500. (20% * 37,500)
The min. salary for those in the 40% bracket is 45,000. (40% * 112,500)
As Kim pays 9260 in tax, we know that she falls under the 20% bracket. As such, we can conclude that :
20% * (Kim's Salary) = 9260
Kim's Salary = 9260/20%(or 0.2)
Kim's salary = 46,300
Answer: About $55,000k
Step-by-step explanation:
Question 17 of 25
Which of the following values are in the range of the function graphed below?
Check all that apply.
Answer:
B, C, E
Step-by-step explanation:
Given a graph, you want to know the set of listed values that is included in the range of the graph.
RangeThe range of a function is its vertical extent, the set of output values the function may have. The graph shows a function with a range of ...
-6 ≤ y ≤ 0
Listed values that fall in that range are ...
-1 (B), -2 (C), and -6 (E)
Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75. Last week he ordered 4 pizzas and spent $41.50. Assume the price for each pizza is the same.
a) Does the pizza parlor charge a delivery fee? Explain.
b) Write an equation describing the total amount Luke spends, d, to get p pizzas delivered.
Yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75.
Last week he ordered 4 pizzas and spent $41.50.
Each pizza costs when ordered 3 pizzas
= 32.75/3 = $10.91
Each pizza costs when ordered 4 pizzas
= 41.50/4 = $10.37
Yes, the pizza parlor charges a delivery fee.
= (41.50+32.75)/(3+4) = 10.60
d = 10.60p
Thus, yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
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Solve each equation in the interval from 0 to 2π . Round your answer to the nearest hundredth.
cos2t = 1/2
Greetings from Brasil...
Jonathon collected 4 1/2 kg of seashells. If he gives 2 3/4 kg of seashells to his friend, what is the weight of the
remaining seashells that Jonathon has?
The remaining weight seashells that Jonathon has is 7/4 kg or [tex]1\frac{3}{4}[/tex] kg.
Define fractions.A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" derives from the Latin word "fractio," which means "to break." As the first civilization to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.
Weight of the remaining sea shells = [tex]4\frac{1}{2}[/tex] - [tex]2\frac{3}{4}[/tex]
Weight of the remaining sea shells = 9/2 - 11/4
Weight of the remaining sea shells = 18-11/4
Weight of the remaining sea shells = 7/4 kg
Weight of the remaining sea shells = [tex]1\frac{3}{4}[/tex] kg
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The weight of the remaining sea shells Jonathan has is 1¾ kg.
What exactly are fractions?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters. There are three major types of fractions in mathematics. Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator.So, the weight of the remaining sea shells: 4½ - 2¾
Now, solve the above fraction operation for the weight of remaining sea shells.
= 4½ - 2¾= 9/2 - 11/4= 18-11/4= 7/4kg= 1¾ kgTherefore, the weight of the remaining sea shells is 1¾ kg.
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Expand each logarithm. State the properties of logarithms used. log z²/5
The expanded form of the given logarithms (log z²/5) = 2logz + log 5
The Four Basic Properties of Logs:Four fundamental features are derived directly from the notion that logs are exponents. The first three can be recalled as follows: The log of a product equals the sum of the logs of the elements. A quotient's log is proportional to the difference in between numerator and denominator logs. The log of power is the power multiplied by the log of the base.
Briefing:Given : log z²/5
Applying the property (log a/b = log a +log b)
we get:
log z²/5
log z² + log 5
Applying the property
log z²
2 log z
replacing equation:
log z² + log 5
2logz + log 5
The expanded form of the given logarithms (log z²/5) = 2logz + log 5
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Diego evaluated 2 3/11−4/5. Each statement below is a way for Diego to check his answer. Use the drop-down menus to complete each statement. If his answer is the sum of 2 3/11 and 4/5, Diego's answer is too high or too low, or correct. If the sum of his answer and 4/5 is 1, Diego's answer is too high or too low, or correct. If the difference of 2 3/11 and his answer is 4/5, Diego's answer is too high or too low, or correct.
Simply solve the given equation and then evaluate according to the given situations. The answer is
a) Too high
b) Too high
c) Too low
Diego evaluated 2 3/11−4/5
Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. It is one of the essential mathematical functions we use in our everyday activities.
Subtraction is an operation used to find the difference between numbers. When you have a group of objects and you take away a few objects from it, the group becomes smaller
2 3/11 - 4/5 = 81/55 = 1.47
a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)
b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)
c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)
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Simply answer the supplied equation, then make a judgment call based on the scenarios. The response is
a) Excessive
b) Excessive
• Too little
Diego scored a 2 3/11/4/5.
In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. It is one of the fundamental mathematical operations we employ on a daily basis.
The operation of subtraction is used to calculate the difference between two numbers. If you remove a few items from a collection of things, the group will get smaller.
2 3/11 - 4/5 = 81/55 = 1.47
a) 2 3/11 + 4/5 = 169/55 = 3.07 (Too high)
b) (2 3/11 - 4/5) + 4/5 = 125/55 = 25/11 = 2.27 (Too high)
c) 2 3/11 - (2 3/11 - 4/5) = 25/11 - 81/55 = 44/55 = 4/5 = 0.8 (Too low)
Natalie is the creator of better brain, a new mindfulness app for teens. the app currently has 1,262 downloads, and natalie has set a goal of doubling the downloads every month. write an exponential equation in the form y=a(b)x that can model natalie's goal for the number of downloads, y, in x months. use whole numbers, decimals, or simplified fractions for the values of a and b.
Firstly we will analyze the question statement to determine the best possible answer.
So, the statement tells us about a person named Natalie,, the owner of an App designed for teenagers. Currently, the New Mindfulness app has One thousand two hundred and sixty-two downloads. Natalie sets a target to take her App downloads to double every month.
We are expected here to provide her with the best possible exponential equation to make her achieve the set goal.
We can use two variables for our exponential equation:
y for the number of downloads.
And x for the months.
We can use any value (Whole numbers, decimals, or fractions) in our exponential equation.
Now while keeping in mind all the necessary details, we can make the exponential equation as below:
Y= 1262 (2 x b) ^ x
Where Y are the downloads
X= 1 month or 30 days
By putting the values:
Y=1262 (2) ^ 1 month
Y=2524 after one month
So, the total number of downloads will double using the above exponential equation.
The pictures below show a relationship between the number of downloads Y and the month X.
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Answer: 1262(2)^x
Step-by-step explanation:
Lydia wants to ride her bicycle 34 miles this week. She has already ridden 7 miles. If she rides for 5 more days, which equation could be used to determine xx, the average number of miles she would have to ride to meet her goal?
Answer: Well i tried doing 7x5 but it is 35 and she has to ride her bike 34 miles so hope this helps if not then sorry
Step-by-step explanation:
The equation to determine the average number of miles she would have to ride to meet her goals is
5x = 34 - 7
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total miles = 34 miles
Number of days to ride = 5
The equation to determine the average number of miles.
5x + 7 = 34
Now,
Solve for x.
5x = 34 - 7
5x = 27
x = 27/5
x = 5.4 miles
Thus,
The average number of miles is 5.4 miles.
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f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
b. The inverse of f₁(x)=b x-h is equivalent to a translation of g .
If b^{h} < 1 then it will be a vertical stretch.
What authority possesses a power rule?
When a base is raised to a power and then the entire expression is raised to another power, the power of a power rule in exponents is used to simplify the algebraic statement.
A translation of function f is f₁ (x) = bˣ⁻h . It is equivalent to a vertical stretch or vertical compression of function f.
[tex]f_{1} (x) = b^{x - h}[/tex]
If we used the rules of powers, we know that when we have a subtraction in the power of an exponential, it can be split into a division. So the function can be rewritten as
[tex]f_{1} (x) = \frac{b^{x} }{b^{h} }[/tex]
Remember the original function was
f(x) = bˣ
therefore
[tex]f_{1}(X) = \frac{f(x)}{b^{h} }[/tex]
this means that if [tex]b^{h} < 1[/tex] then it will be a vertical stretch.
If b^{h} < 1 then it will be a vertical stretch.
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Which expression is equivalent to (5x^−5 y^3)^−2??
thanksss
Answer: I think its 1/5x^10y^-6
Step-by-step explanation:
please let me know if I'm wrong
a(cosb+cosc-1)+b(cosa+cosc-1)+c(cosa+cosb-1)=0
Answer:
Proved!
Step-by-step explanation:
Given Problem:
a(cosB+cosC-1)+b(cosC+cosA-1)+c(cosA+cosB-1) = 0
Solution:
Let ABC be any triangle.
1) Consider the L.H.S (left hand side) of the given equation:
LHS =
We know that,
Projection formula:
= 0 =RHS
(2) Consider the LHS of the given equation:
Hence Proved!!
The points (0, 0) and (1, 3) fall on a particular line. What is its equation in slope-intercept
form?
Answer:
y = 3x
Step-by-step explanation:
Slope-intercept form of an equation is a shortcut, fill-in-the-blank form you can use to write the equation of a line.
Slope-intercept eq:
y = mx + b
You fill in slope where the m is. And you fill in the y-intercept for the b.
In your problem they gave you two points. You can calculate slope with two points. Subtract the y's, 3-0, put that on top of a fraction. And subtract x's, 1-0, put that on the bottom of the fraction. The slope, m, is 3/1, which is 3.
slope:
m = 3-0 / 1-0 = 3/1 =3
The y-intercept is actually given in your problem. The y-intercept is the point where the line crosses the y-axis. The y-intercept is the point where the x is 0. They gave you the point (0,0) that is the y-intercept. So b = 0.
Fill the m and b in with the given numbers!
y = 3x + 0 Simplify.
y = 3x
a) The quadratic x^2-4-21 can be written in the form (x+a)^2+b find the values of a and b
b) Hence, or otherwise, solve the equation x^2-4x-21=0
According to the solving the value of a and b of the X² - 4X - 21 equation are:
a = -2
b= -25
What does quadratic signify in mathematics?A quadratic problem is a sort of problem in mathematics that deals with either a variable multiplied by itself – a process known as squares. The area of a square is defined as its side length multiplied by double itself in this language.
What is the purpose of quadratic?In everyday life, we employ quadratic formulas to calculate areas, determine the profit of a product, or calculate the velocity of an object. Furthermore, quadratic equations are defined as equations with at least one squared variable.
According to the given data:X² - 4X - 21
Expand to check:
For a.
(X - 2)² - 4 - 21 = (X - 2)² - 25
= X² - 4X + 4 - 25
= X² - 4x -21
= (X - 2)² - 25
a = -2 , b = -25
For b.
X² - 4X - 21 = (X - 2)² - 25 due to part a we can say that:
(X - 2)² - 25 = 0
X - 2 = ± 25
x = 7 , X = -3
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What is the horizontal asymptote for the rational function?
c. y=x²+2 x-3/x-2
AS we can see that there no degree in the given rational function, so, the value for horizontal asymptote will be 0.
What is the use of asymptotes?The asymptote of a curve is the location at which the curve converges. In other words, the curve and its asymptote are perpetually close, yet they never touch. Big O notation makes use of asymptotes, which are also simple approximations to complex equations and are useful for graphing rational equations among other things.
The asymptote(s) of a curve may often be found by looking at the limit of a value when the function is not defined. These points include and the point where the numerator of a rational function equals zero, as well as others.
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please help me with this
Applying the alternate interior angles postulate, the measure of angle HLI in the diagram is: 56°.
What is the Alternate Interior Angles Postulate?An example of interior angles that lie alternate to each other along a transversal are the angles shown in the image as angle HIL and angle MLI.
According to the alternate interior angles postulate, angle HIL is congruent to angle MLI.
Given that, the measure of angle MLI = 56°, since angles HIL and MLI are congruent angles based on the alternate interior angles postulate, therefore:
Measure of angle MLI = measure of angle HLI
Thus:
The measure of angle HLI = 56°
In conclusion, applying the alternate interior angles postulate, the measure of angle HLI in the diagram is: 56°.
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An auto repair shop records how far each vehicle they receive has been driven. The data for their
most recent 23 vehicles is shown in the histogram below.
What interval contains the 83rd percentile for this data?
The 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
What is a histogram ?
A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals.
It is given that , data for most recent 23 vehicles is shown in the histogram.
On the x-axis distance driven in thousands of kilometers and on the y-axis frequency is represented in the histogram.
For 23 vehicles , we have different ranges of distance driven i.e., 0 - 50 , 50 - 100 , 150 - 200 . 200 - 250 , 250 - 300.
We know that the 83rd percentile meant the distance driven is greater than or equal to 83 %.
i.e.,
Here , 83 lies between 50 - 100 , so , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
Therefore , 83rd percentile contains intervals which are 50 and 100 thousand kilometers.
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Find m
a. 24
b. 58
c. 37
d. 19
Answer:
24
Step-by-step explanation:
9 to the power of -3 as a fraction
Answer:
137174211/100000000000
Step by Step Explanation:
First, find the answer of 9^(-3), which would be 0.00137174211. Then, convert that into fraction form. Which would be 137174211/100000000000. Then simplify, which in order to simplify a fraction, there must be: 1. A number that will divide evenly into both the numerator and denominatior so it can be reduced. No such number exists for 137174211 and 100000000000. or 2. The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number. 137174211 is not greater than 100000000000, also meaning, this fraction is in it's simplest form.
A function consists of the pairs (2,3),(x,4) , and (5,6). What values, if any, may x not assume?
A relation between a collection of inputs and outputs is known as a function.
The order pairs can't be a function also,
f(x) = -√x → D: x ≥ 0
→ R: y ≤ 0
Which of the ordered pair sets defines a function?A relation is simply a collection of ordered pairs (x, y). In formal mathematics, a function is a relation in which x1= x2 if (x1,y) and (x2, y) are both in the relation. This simply states that two ordered pairs with the same x -value but different y -values cannot exist in a function.A function's range is the set of all its outputs. Example: Consider the function f: A B, where f(x) = 2x and A and B are both sets of natural numbers. In this case, A is the domain and B is the co-domain. The range is then the result of this function.If an x value has more than one y-value associated with it, as in the relation (4, 1), (4, 2), the x-value of 4 has y-values of 1 and 2, indicating that this set of ordered pairs is not a function. If each x-value has only one y-value, the relationship is a function.The order pairs can't be a function also,
f(x) = -√x → D: x ≥ 0
→ R: y ≤ 0
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Select all the equations by that have the same solution as 2x-5=15
Answer:
2x=20 i guess
Step-by-step explanation:
2x -5= 15
add 5 to both sides
you should get 20
it's 2x=20
Lesson Check (5.NBT.B.5)
1. There are 198 students in the soccer league.
There are 11 players on each soccer team. How
many soccer teams are there?
2
Solve the system of equations 8x- 3y =9 4x -4y=-8
Answer:
x = 3, y = 5.
Step-by-step explanation:
8x - 3y = 9
4x - 4y = -8
multiply the second equation by 2:
8x - 8y = -16
Subtract this from the first equation:
5y = 25
y = 5.
Substitute for y in equation 2:
4x - 4(5) = -8
4x = -8 + 20 = 12
x = 12/4 = 3.
Answer:
2
Step-by-step explanation:
1=1=2
If
LN
and
OQ
are parallel lines and mQPR = 115°, what is mLMP?
The measurement of angle ∠LMP is 65° when angle QPR is 115°.
What is corresponding angle ?
Any pair of angles that lie on opposite sides of two lines cut by a transversal on the same side.
Here, it is given that LN and OQ are parallel lines and ∠QPR = 115°
First, let us find the measurement of angle QPM as angle QPR and angle QPM are supplementary angles that is there sum will be 180° :
∠QPM + QPR = 180°
∠QPM + 115° = 180°
∠QPM = 180° - 115°
∠QPM = 65°
Now, angle QPM and angle LMP are corresponding angles there the measurement of both the angles will be same that is ;
∠QPM = ∠LMP = 65°
Therefore, the measurement of angle ∠LMP is 65°
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Help now...you have into 9/27/22 9:10
20 points BONUS IF YOU ANSWER QUICK!
Which phrase tells a major function of the endomembrane system?
producing and storing energy
directing the cell’s activities
manufacturing proteins
transporting substances in a cell
Answer: Transporting substances in a cell.
Step-by-step explanation: Transporting substances in a cell producing and storing energy.
Alonso fue al mercado con $55 para comprar huevos y azúcar. Sabe que necesita un paquete de 12 huevos que cuesta $2.75, Después de obtener los huevos, quiere comprar todo el azúcar que pueda con el dinero restante. El azúcar que le gusta viene en cajas que cuestan $11.50, 50 cada una. Hagamos que S represente el número de cajas de azúcar que compra Alonso.
1) ¿Cuál desigualdad describe este escenario?
2) Después de obtener los huevos, ¿cuántas cajas de azúcar puede comprar Alonso?
The expression that van be used to illustrate the quantities that Alonso will buy is 2.75e + 11.5s = 55.
How to illustrate the information?Total amount = $55
Cost of eggs = $2.75 per pack
Cost of sugar = $11.50 per box
Therefore, based on the information, it should be noted that the expression that can be used to illustrate the information will be:
Let s = sugar
Let e = eggs
Therefore, the expression will be:
(2.75 × e) + (11.50 × s) = 55
2.75e + 11.5s = 55
The expression that van be used to illustrate the quantities that Alonso will buy is 2.75e + 11.5s = 55.
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