The division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
In this question,
we have been given a complex rational expression [tex]\frac{3x^{2} -9x}{x-2}\div \frac{x^2-9}{4x-8}[/tex]
We need to find the division of given rational expression.
We rewrite given rational expression as,
3x²-9 x / x-2 ÷ x² - 9 / 4 x-8
= 3x²-9 x / x-2 / x² - 9 / 4 x-8
= (3x²-9 x / x-2) × (4 x-8 / x² - 9 )
= [tex]\frac{3x(x-3)}{x-2}\times \frac{4(x-2)} {(x+3)(x-3)}[/tex]
= 12x / x + 3 .........(provided x ≠ -3)
Therefore, the division of given rational expression 3x²-9 x / x-2 ÷ x² - 9 / 4 x-8 is 12x / x + 3 provided x ≠ -3
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Convert 55°F to degrees Celsius.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C = (F-32)
9
F-C+32
=
Answer:
search up
Step-by-step explanation:
A
The art club raised $248 through fundraisers. then they spent $206 to set up an art show. they raised another $316 at the art show. how much money did the art club have after the show?
Using basic mathematical operations such as addition and subtraction, the art club have $358 after the show.
Basic mathematical operations includes addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If the art club raised $248 through fundraisers, spent $206 to set up an art show, and raised another $316 at the art show, adding the total amount they raised and subtracting the amount they have spent, we can solve how much money they have after the show.
$248 - $206 + $316 = $358
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Solve for x to the nearest tenth HELP
The value of x is 4.89 ≈ 5 units
Given,
The figure includes two right angled triangles.
Consider the first right angled triangle:
Hypotenuse = 7 units
Base = 3 units
Altitude = a
By using Pythagorean theorem, we can find a.
That is,
Hypotenuse² = Altitude² + Base²
7² = a² + 3²
49 = a² + 9
a² = 49 - 9
a² = 40
Altitude = [tex]\sqrt{40}[/tex] units
Now consider second right angled triangle:
Hypotenuse = [tex]\sqrt{40}[/tex] units
Altitude = 4 units
Base = x units
Apply Pythagorean theorem:
Hypotenuse² = Altitude² + Base²
([tex]\sqrt{40}[/tex])² = 4² + x²
40 = 16 + x²
x² = 40 - 16
x² = 24
x = [tex]\sqrt{24}[/tex]
Base, x = 4.89 ≈ 5 units.
Therefore, the value of x is 4.89 which is approximately equals to 5 units.
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How to solve? I tried but I found no answers.
Answer:
x=1
Step-by-step explanation:
Perimeter of the square is 4 times the side = 4*(4x-1)
Perimeter of Rectangle = 2 L + 2 W = 2*(2x+2) + 2*2x
4*(4x-1) = 2*(2x+2) +4x
16x-4= 4x+4+4x
16x-4 = 8x+4
16x-8x = 4+4
8x = 8
x = 8/8
x=1
Hope this helps!^^
two numbers to multiply to get -120
Answer:
-60 x 2= -120
Step-by-step explanation:
Answer:
-40 * 3
Step-by-step explanation:
Just one example of many
A
Write an equation and solve the scenario
4) The sum of three consecutive even
numbers is 42. What is the smallest of
these numbers?
Step-by-step explanation:
Combine like terms on the right side,
42= 3x+6.
Subtract 6 from each side
36=3x
Divide each side by 3
x=12, which is our lowest integer.
The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.
Hope this helps.
Question 2 of 10
What is the third quartile of the following data set?
20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44
OA. 37
OB. 42
OC. 35
OD. 29
The third quartile of the given data set is 42.
What is third quartile?The third quartile (Q3, or the upper quartile) is the 75th percentile, meaning that 75% of the data falls below the third quartile.
Given is a data set, 20, 21, 24, 25, 28, 29, 35, 37, 42, 43, 44 we need to find the third quartile of the data set,
To find the third quartile we will use the given below formula,
Q3 = 3/4 (n+1)th term,
n = 11
Q3 = 3/4 (11+1)
Q3 = 3/4 x 12
Q3 = 9th term
= 42
Hence, the third quartile of the given data set is 42.
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A stereo player is pricer at $1320 plus value added tax at 15% how much does the stereo player actually cost
Answer:
$1518
Step-by-step explanation:
Take the 1320 and multiply it by 0.15 (15% as a decimal) to get 198
Then add the 198 to the 1320 to get 1518
On which interval does h(t) have an average rate of change of zero?
Answer:
In the interval (-∞, -5)
Step-by-step explanation:
Average rate of change of any graph is represented by the slope of the function in the given interval.
Rate of change =
= change in the y-coordinates
= change in the x-coordinates
If = 0, then the rate of change will be zero in that interval
From the graph attached,
From x = -∞ to x = -5, we find a flat line, showing
Therefore, average rate of change of h(x) in the interval (-∞, -5) is zero
In an examination 50 candidates sat for either Mathematics or English language 60% passed in Mathematics and 48% passed in English language. If each candidate passed in at least one of the subjects, how many candidates passed in (i) Mathematics (Ii) English language. Illustrate the information above in a Venn diagram. Use the Venn diagram to find the number of candidates who passed both subjects
A Venn diagram can be used to solve it.
Candidates passed in mathematics = 26Candidates passed in English = 20A Venn diagram is what?A Venn diagram is a type of diagram where the relationships between items or groups of objects are represented by circles. While circles that do not overlap do not share any features, overlapping circles do. Venn diagrams are used to illustrate the parallels and differences between two concepts visually.
The Venn figure shows that 4 students passed both courses and that 20 students succeeded in English while 26 students passed in mathematics.
P(A∪B) = P(A) + P(B) - P(A∩B)
50 = 30 + 24 - (candidates who passed both subjects)
(candidates who passed both subjects) = 4
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The profit from selling local ballet tickets depends on the ticket price. Using past receipts, the ballet company determines that the profit can be modeled by the function p = -15x2 + 600x + 60, where x is the price of each ticket. A) What unit price x should be charged to maximize revenue? B) what is the maximum revenue? C) between what two prices is a profit made?
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) The maximum revenue is 6060 dollars.
C) Two prices between which a profit is made are $19 and $21.
What are quadratic functions?f(x) = ax² + bx + c, where a, b, and c are numbers and are not equal to zero, is a quadratic function.A parabola is the shape of a quadratic function's graph.The graph's vertex, which is an extreme point, is one of its key characteristics. The vertex, or lowest point on the graph or minimal value of the quadratic function, is where the parabola will open up. The vertex is the highest point on the graph or, if the parabola opens downward, the maximum value.Given:
profit function P(x)= -15x² + 600x + 60
The value of a is -15, which is negative, so the graph is opening downwards.
The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola f(x) is given by
x-coordinate of the vertex = -b/2a
y-coordinate of the vertex = f(-b/2a)
We have the x-coordinate of the parabola as:
⇒ -600 / 2(-15)
⇒ -600/-30 = 20
A) x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.
B) y-coordinate of the vertex is given by
f(20) = -15(20)² + 600(20) + 60
= 6060
The maximum revenue is 6060 dollars.
C) f(21) = -15(21)² + 600(21) + 60
= 6045
f(19) = -15(19)² + 600(19) + 60
= 6045
at $21, the profit is $6045
at $19, the profit is $6045
Two prices between which a profit is made are $19 and $21.
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Work out the mean of these numbers 2 √18 √50 Give your answer in the form a√2 where a is an integer.
answer in the form a√2 where a is an integer. √18 √50= 4 root 2
Solution:
Mean
Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate the mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.
Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations
Observation :
An observation is a fact or figure we collect about a given variable. It can be expressed as a number or as a quality. An example of a number is the observation "25" for the age of a mother at the birth of her first child.
Using mean formula
Mean = {Sum of Observation} ÷ {Total numbers of Observations}
= [tex]\sqrt{18} +\sqrt{50}[/tex]
=[tex]3\sqrt{2} + 5\sqrt{2}\\ = 5\sqrt{2}[/tex]
sum of observation is 8[tex]\sqrt{2}[/tex]
total number of observation = 2
[tex]8\sqrt{2} /2\\=4\sqrt{2}[/tex]
Answer in the form a√2 where a is an integer. = 4 [tex]\sqrt{2}[/tex]
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ans = [tex]4\sqrt{2}[/tex]
Three hundred fifty seniors attended
the spring prom. If this number repre-
sents of the total senior class, then
how many seniors are in the class?
7
Answer:
there would be three hundred and fifty.
Let g(x)=-x^2+6x+2. Find and simplify g(-3)
Helpppp
The man in the video spent 9 minutes and 2 seconds to fill his bathtub before taking a bath. After taking the bath, his partner told him that taking a bath was wasting water, and he should shower instead.
Question: How long would he need to run the shower to use the same amount of water as the bath that he took?
Please respond in one clear, succinct paragraph. Be sure to clearly state your final answer and include all of your mathematical reasoning that led you to your final answer. You will be graded on how accurate your final answer is and how clearly you were able to explain your answer. Make sure you write in complete sentences with proper writing conventions (i.e. grammar, punctuation, spelling).
Answer:
he will take the same time as its the same flow of water so he will spend 9 min and 2 sec
How much more would $10,000 earn in 3 years compounded daily at 1.33%, than compounded semi-annually at 4.33%? Round to the nearest cent. Please include the formulas used :)
The difference between $10,000 invested at 1.33% compounded daily and 4.33% compounded semi annually is $11,188.99.
What is the difference?When an amount earns interest that is compounded daily, it means that both the amount invested and the interest accrued increases in value every day over the 3 year period.
If an interest is compounded semi-annually, it means that both the amount invested and the interest accrued increases in value two times in a year.
The formula that can be used to determine the future value when the amount is compounded is:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years10,000 x [1.133^(3 x 365) ] - [1.0433^(2x3)]
10,000 x (2.4085 - 1.29)
10,000 x 1.119 = $11,188.99
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Find the coordinates of the orthocenter of each triangle with the given vertices. R(-4,8), S(-1,5), T(5,5)
The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.
The coordinates of the orthocenter of Δ RST is (–4, –4).
What is the orthocenter of the triangle?
An orthocenter of a triangle is the point at which altitudes drawn perpendicular from the vertex to the opposite sides of a triangle intersect. A triangle typically has three altitudes, and the intersection of all three altitudes is known as the orthocenter.
The orthocenter is the point where a triangle's three altitudes intersect, and the centroid is the point where the three medians intersect.
The slope of RS is (5-8)/(-1+4) or –1. So, the slope of the altitude, which is perpendicular to RS is 1.
Now, the equation of the altitude from T to RS is:
y - 5 = 1(x - 5)
y = x
Use the same way to find the equation of the altitude from R to ST. That is,
Y - 8 = -1/0 (X + 4 ) or x = -4
x = -4 and y = -4
Solve the equations to find the intersection point of the altitudes. So, the coordinates of the orthocenter of Δ RST is (–4, –4).
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HELPP I WILL MSRK YOU BRAINLIST…
Answer:
< - 9, 11 >
Step-by-step explanation:
consider the end points of the vector
(5, - 2 ) and (- 4, 9 )
x- direction is then - 4 - 5 = - 9
y- direction is 9 - (- 2) = 9 + 2 = 11
then vector in component form is < - 9, 11 >
You are given two metal cubes that look similar. One has an edge of 3. 2 cm long and a mass of 43. 63 g. The other has an edge of 8. 34 cm long and a mass of 683. 5 g. How can you determine if both cubes are made from the same material? select the true statements.
By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.
Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.
ρ = m/v
where ρ = density
m = mass
v = volume
Solving the density of each cube.
Cube 1 :
ρ = m/v
ρ = m/e^3
ρ = 43. 63 g/(3. 2 cm)^3
ρ = 1.3315 g/cm^3
Cube 2 :
ρ = m/v
ρ = m/e^3
ρ = 683. 5 g/(8. 34 cm)^3
ρ = 1.1783 g/cm^3
If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.
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Physical science
If a car travels 625 meters 15 seconds, how fast is it going?
Write an equation of each line in standard form with integer coefficients.
the line through (-4,6) and (2,-2)
The equation of the line in standard form passing through the points (-4 , 6) and (2 , -2) is 4x + 3y = 2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given two points, (-4 , 6) and (2 , -2), use the two-point form to generate the equation of the line.
y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)
y - -2 = [(-2 - 6)/(2 - -4)](x - 2)
y + 2 = (-8/6)(x - 2)
y + 2 = -4/3 x + 8/3
To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
y + 2 = -4/3 x + 8/3
4/3 x + y = 8/3 - 2
4/3 x + y = 2/3
Multiply both sides by 3 to have integer coefficients.
3(4/3 x + y) = 3(2/3)
4x + 3y = 2
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-5+9-4-(-4)+(-9)-12+7
Answer:
Step-by-step explanation:
if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )
and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )
so -(-4) = 4 and +(-9) = -9
-5+9-4+4-9-12+7=-10
I hope this helps
|x+3| horizontail stretch by a factor of 4
g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
How do we find the function that was used to create the graph?A graph contains information about which input corresponds to which output.An examination of this leads to the relationships that were used to create it.If a function's graph rises after a certain value of x, the function must have an increased output for inputs greater than that value of x.If we know that the function crosses the x axis at some point, we can use those as polynomial roots for some functions.So, we must write a function g whose graph represents a horizontal stretch of f(x)=|x+3| by a factor of 4.
f(x) = |x+3|Now perform horizontal stretch 4:
g(x) = |¼x + 3|Therefore, g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
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The correct question is given below:
Write a function g whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.
g(x)=
What are the multiplication facts for 5? pls help marking brainly
Answer:
it is as follows:
5x2=10
5x3=15
5x4=20
5x5=25
5x6=30
5x7=35
5x8=40
5x9=45
Step-by-step explanation:
Answer: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150
Step-by-step explanation:
Sketch the solid that results when the region enclosed by the given equations is revolved about the x -axis.
y = x²
y = 0
x = 2
y = x², y = 0, x = 2 are region enclosed by the given equations is revolved about the x -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers. Use enclose, encloses, and enclosing rather than in close for other words that are similar to enclosed.Learn more about enclosed region
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James had $72 in his bank account. he bought a $75 painting from my local artist and paid with a check. he thought the artist will take a few days to deposit the check. he knows he will have enough money to cover the amount of the check once his paycheck is deposited, but he received a text notification the next day that his account balance was -$45. how much was james charge for an overdraft fee? make a claim. include textual evidence. show reasoning.
James was charged $42 for an overdraft fee for the purchase of the painting.
James had $72 in his bank, paying for a painting worth $75 with a cheque meant he had extra $3 for him to balance the local artist. Receiving an account balance was -$45 meant the bank helped James cover the extra $3 he was owing while charging him additional $42 for overdraft on the account. In mathematical relation, it is described as;
Cash in bank – cost of painting = ($72- $75)
= -$3
Thus, overdraft is calculated as;
Overdraft=Balance + amount to balance cost of painting = (-$45) + $3
=-$42
Therefore, James was charged an overdraft of $42 for the purchase of the painting.
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A honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day. How many times more eggs can an army ant queen lay?
Answer:
An army ant queen can lay 299,742 more eggs
The army ant queen will lay 120 times more eggs than the honeybee queen.
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 a honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day.
The ratio will be calculated as,
Army ant/honeybee queen = 300,000 / (2.5 x 10³)
Army ant/honeybee queen = 300,000 / 2500
Army ant = 120 x ( honeybee queen )
Therefore, the army ant queen will lay 120 times more eggs than the honeybee queen.
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Identify a pattern and find the next three terms in the pattern.
-4,-3,-2,-1, . . .
Pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
As given,
Given pattern is -4,-3,-2,-1, . . .
a₁ =-4
a₂ =-3
a₃ =-2 ….
d =a₂ - a₁
=-3 - (-4)
=1
Pattern is arithmetic progression with d=1.
aₙ =a₁ + (n-1)d
a₅ =a₁ + (5-1)d
=-4 +4(1)
=0
a₆ =-4 + 5(1)
=1
a₇ =-4 +6(1)
=2
Therefore, pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2
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.
Determine if the conjecture is valid by the law of detachment. given: if tommy made enchiladas tonight, then tommy must have an oven. tommy has an oven. conjecture: tommy made enchiladas tonight.
By determining the conjecture is not valid by the law of detachment.
A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.
Hypothesis: Tommy makes cookies tonight.
Conclusion: Tommy must have an oven.
Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.
Hence, the hypothesis is unfounded.
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Some people think that the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, resembles a golf ball. The building is a sphere measuring 165 feet in diameter. A typical golf ball has a diameter of approximately 1.5 inches.
a. Find the volume of Spaceship Earth to the nearest cubic foot.
The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.
Volume refers to the amount of space occupied by a three-dimensional object.
Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.
The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:
V = 4/3 π r^3
V = 4/3 π (82.5 feet)^3
V = 4/3 π (561,5151.625 cubic feet)
V = 2,352,071.15 cubic feet
Rounding off to the nearest cubic foot,
V = 2,352,071 cubic feet
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