The LCM of the polynomials is x(x + 3)(x^2 - 3x + 9).
How to determine the LCMFrom the question, we have the following parameters that can be used in our computation:
x^3+27 and x^3-3x^2+9x
Let's factor the first polynomial, x^3 + 27:
x^3 + 27 = (x + 3)(x^2 - 3x + 9).
Let's factor the second polynomial, x^3 - 3x^2 + 9x:
x^3 - 3x^2 + 9x = x(x^2 - 3x + 9)
Using the above as a guide, we have the following:
The LCM of these two polynomials is
LCM = x(x + 3)(x^2 - 3x + 9).
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a ball is thrown vertically upward. after seconds, its height (in feet) is given by the function . after how long will it reach its maximum height? h(t)
The ball reaches its maximum height after 2 seconds.
To determine when the ball reaches its maximum height, we need to find when its velocity changes from positive to negative. The velocity of the ball is given by the derivative of its height, which is the function h'(t) = -16t. The ball's velocity is 0 when h'(t) = 0, so we need to solve -16t = 0.
The solution to this equation is t = 0. When t = 2, h'(t) = -32, which is negative, indicating that the ball is moving downward. So, the maximum height is reached when the velocity changes from positive to negative, which is at t = 2 seconds.
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The manager of a local radio station wants to find out what type of music people in
the area like the most. She surveys every 10th person leaving a country music
concert held near the radio station.
Is this sample likely to be representative of the population? Explain.
Answer:
No, this sample is not likely to be representative of the population. The sample only includes people who attended a country music concert, which means it does not include people who prefer other genres of music. Therefore, the survey results would likely be biased towards country music, and not necessarily reflective of the general population's music preferences.
45 points!
The graph of $y = 2x^2 - 8x + 7$ is identical to the graph of $y = a(x-h)^2 + k$ for some real numbers $a, h, k$.
What is the value of $k$?
The value of k is 3.
What are Quadratic Functions?Quadratic functions are polynomial functions of second degree.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = 2x² - 8x + 7
This function is identical to some function y = a(x - h)² + k
We have to write the given quadratic function in the form y = a(x - h)² + k.
2x² - 8x + 7 = (2x² - 8x) + 7
= 2(x² - 4x) + 7
= 2(x² - 4x + 4) + 7 - 4
We have the algebraic identity, (a - b)² = a² - 2ab + b²
= 2 (x - 2)² + 3
a = 2, h = 2 and k = 3
Hence the value of k is equal to 3.
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hen reading a buret with graduated markings at every 0.1 ml, your recorded volume should read to which place? hundredths. thousandths. tenths.
When reading a buret with graduated markings at every 0.1 ml, your recorded volume should read to a) hundredths place.
Definition and Function of the BuretteA burette is a long tube-shaped glass instrument with scale lines like a measuring pipette or measuring cup with the same cross section from top to bottom. At the bottom of this tool is equipped with a faucet as a place for the solution to come out at the mouth of the burette.
The function of the burette is as a tool to measure the solution based on the volume released. The burette size usually has a volume of 25 / 50 ml.
If the burette is being used, it must be supported firmly with a stand equipped with clamps to clamp the burette. Make sure that when clamping the burette in the stand and clamp the position of the burette must be perpendicular so that the scale reading is correct and does not cause paralax errors.
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I need help!!! number says 5 btw
The car drive 36,666.66 miles in 5 year.
What is Speed?Speed = Distance/Time Distance = Speed X TimeTime = Distance / SpeedGiven:
A car drove 22, 000 miles in 4 months.
So, in one year the car drive
= 22,000 x 4/12
and, in 5 year the Car drove
= 22,000 x 4/12 x 5
= 36,666.66 miles
Hence, the car drive 36,666.66 miles.
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there are six members on a student council. two of these members will serve on a spring formal committee. how many possible spring formal committees are there?
There are 30 different combinations of two members who can be selected to serve on the spring formal committee.
Permutation is the arrangement of elements in a specific order. In this scenario, the elements are the six members of the student council, and the order in which they are arranged is important.
To find the number of permutations, we use the formula nPk, where n is the number of elements and k is the number of elements we want to arrange.
In this case, n = 6 and k = 2,
so we have
=> 6P2 = 6!/(6-2)!
=> 6!/(4!) = 6 x 5/1 = 30.
So, there are 30 possible spring formal committees that can be formed from the six members of the student council.
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which figure is shown in the drawing
Need help with the picture attached, involving derivatives.
dy/dx = 0 when x = - 2, and x = 2/3 is not possible.
dy/dx = 0 when x = - 1, and x = 5.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
y = x³ - 6x² - 15x - 7
Differentiating w.r.t x.
[ d[tex]x^n[/tex]/dx = n[tex]x^{n - 1}[/tex] ]
[ dc/dx = 0 ]
dy/dx = dx³/dx - 6dx²/dx - 15dx/dx - d7/dx
dy/dx = 3[tex]x^{3 - 1}[/tex]dx/dx - 6 x 2[tex]x^{2-1}[/tex]dx/dx - 15 - 0
dy/dx = 3x² - 12x - 15
Now,
dy/dx = 0
3x² - 12x - 15 = 0
3(x² - 4x - 5) = 0
x² - 4x - 5 = 0
x² - (5 - 1)x - 5 = 0
x² - 5x + x - 5 = 0
x(x - 5) + 1(x - 5) = 0
(x - 5) (x + 1) = 0
x - 5 = 0
x = 5 _____(1)
x + 1 = 0
x = -1 _____(2)
Now,
For x = 2,
dy/dx = 3x² - 12x - 15
dy/dx = 3 x 4 + 24 - 15
dy/dx = 12 - 24 - 15
dy/dx = 12 - 39
dy/dx = -27 _____(3)
For x = 2/3,
dy/dx = 3x² - 12x - 15
dy/dx = 3 x 4/9 + 24 x 2/3 - 15
dy/dx = 4/3 + 16 - 15
dy/dx = 4/3 + 1
dy/dx = 7/3 _____(4)
From (1), (2), (3), and (4)
dy/dx = 0 when x = - 2 and x = 2/3 is not possible.
Thus,
dy/dx = 0 when x = - 1, and x = 5.
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use the day tool to graph f(x)=-|x+2|
The vertex of the absolute function is at (-2, 0). Then the graph of the absolute function f(x) = - |x + 2| will be drawn below.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The equation is given below.
f(x) = - |x + 2|
Then the absolute function is written as,
f(x) = - (x + 2), x ≥ -2
f(x) = - [- (x + 2)], x < -2
f(x) = (x + 2), x < -2
The vertex of the absolute function is at (-2, 0). Then the graph of the absolute function f(x) = - |x + 2| will be drawn below.
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consider this series. 16+24+36+54+... does the series converge or diverge? select answers from the drop-down menus to correctly complete the statement
The series 16+24+36+54+... diverges.
Divergent series are those that contain an infinite series that never converges and an infinite sequence of partial sums with no finite limit. In contrast, a series is considered to be convergent when its limits converge to its finite range of values. A limit that is finite in nature and exists for the partial sum of the series is crucial since only at that point will the series converge.
The given series in question 16 + 24 + 36 + 54 + deviates from the series. 16n, where n is the number of terms, can be used to denote the series' overall term. The total of the terms in the series also increases as n increases since 16n grows along with n, too. This indicates that the series diverges since it does not reach a particular finite value.
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Use the sentence to answer the question.
The toy is not fixable, so we will have to buy a new one.
What does fixable mean?
(1 point)
Responses
a person who fixes
a person who fixes
can be fixed
can be fixed
the result of fixing
the result of fixing
the act of fixing
Answer:
sjjejejejenenenwjjwnwnwnwnwnwn
Step-by-step explanation:
ewhw
Answer: can be fixed
Step-by-step explanation:
There were 50% more apples picked this year than last. If there were 230 pounds of apples picked this year, how many pounds were picked last year?
Answer:
115 apples were picked last year
Step-by-step explanation
It says there are 50% more apples picked this year than last year. So, we divide 230 by 2 because 50% is half of 100%. 230÷2 = 115
115 apples
The diameter of each wheel on a Formula
One race car is 26 in. If the tires must be
changed after 150,000 rotations, how many
miles will the race car travel on 1 set of tires?
Note: 12 in. = 1 ft; 5280 ft = 1 mile
A formula one race car will travel for 193.45 miles before changing its tires.
From the case, we know that:
tires diameter = 26 in.
1 set of tires = 150,000 rotations
12 in = 1 ft
1 miles = 5280 ft
We need to find the circumference of the tires before finding the total travel length.
Circumference = πd
Circumference = π(26in)
Circumference = 81.714 in.
We need to find the tires circumference in mile scale:
Circumference = 81.714 in : (12 inc/ft) : (5280 ft/miles)
Circumference = 0.0013 miles
Total travel distance = tires circumference x rotations
Total travel distance = 0.0013 x 150,000
Total travel distance = 193.45 miles
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pls help plssssss
it would really help
The measure of angle Y is given as follows
m < XYZ = 72.9º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For angle Y, we have that:
The adjacent side length is of 4 cm.The opposite side length is of 13 cm.Applying the tangent function, the measure is obtained as follows:
tan(Y) = 13/4
Y = arctan(13/4)
Y = 72.9º.
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A baby elephant at the zoo weighed 134134 kilograms at birth. She gained weight at a constant rate for the first 66 months until she weighed 362362 kilograms.
How much did the elephant gain each month? Simplify your answer completely.
The amount in weight the baby elephant grew each month is given by the equation m = 38 kilograms
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount in weight the baby elephant grew each month be m
Now , the equation will be
The initial weight of the baby elephant a = 134 kilograms
The final weight of the baby elephant b = 362 kilograms
Now , the number of months = n
The value of n = 6 months
So , amount in weight the baby elephant grew each month m = ( b - a ) / n
Substituting the values in the equation , we get
Amount in weight the baby elephant grew each month is
m = ( 362 - 134 ) / 6
On simplifying the equation , we get
m = 228/6
m = 38 kilograms
Hence , the baby elephant grew 38 kg every month
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Order these numbers from least to greatest.
4 7/11, 37/8, 4.427, 4.42
The order of given numbers is 4.42<4.427<4.625<4.64.
How to compare to decimals?Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.
The given numbers are [tex]4\frac{7}{11}[/tex] =4.64, 37/8 =4.625, 4.427, 4.42
From least to greatest is
4.42<4.427<4.625<4.64
Therefore, the order of numbers is 4.42<4.427<4.625<4.64.
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Find the value of x in the triangle shown below.
x=
The sum of the interior angles of a triangle is always 180°, using that we will see that x = 80°
How to find the value of x?The first thing you can notice is that we have a triangle with two equal sides, that means that the two bottom angles have the same measure.
Also, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write the equation:
50° + 50° + x = 180°
Solving that for x we will get:
x = 180° - 50° - 50° = 80°
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Naomi had a blast at the water park, even though she was 3 inches too short to ride the biggest slide, The Water Slinger. Naomi is 49 inches tall.
Let h represent the minimum height for The Water Slinger. Which equation models the problem?
Directions: Based on the information given in the following problem, compute the gross pay.
Regular salary: $1,100 per month
Overtime rate: $10.38 per hour (20 hours overtime to be paid)
Round your answers to two decimal places.
gross pay: $
The gross pay for the given service is $1307.6.
What is gross pay?Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages.
Given that, the regular salary of some service is $1100, we need to calculate the gross payment with over time rate, which is $10.38 per hour (20 hours overtime to be paid)
Therefore,
To find, gross payment, we will multiply by 10.38 by 20, and add to regular salary,
Gross payment = 10.38 × 20 = 207.6 + 1100
= 1307.6
Hence, the gross pay is $1307.6
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Two steps for solving 6x+6=-12
Answer:
Start by evening out the sides
6x + 6 = -12
-6 = -6
6x = 18
Divide by six (bc variable in front of x)
x = 3
Bob had $300 in his bank account. He wrote 3 checks for exactly $20, then deposited $50. What is the overall change to his bank account?
Answer: He has 290 dollars.
Step-by-step explanation:
3 x 20 is 60
300-60 is 240
240 + 50 is 290.
The overall change is 110 dollars.
8 grades, help please!!!
Answer:
Step-by-step explanation:
no it isnt
 so does anyone know the answer to this image please show the steps along with it.
The transformations of the parent cube function to the function g(x) = -2(x + 4)³ - 5 are given as follows:
Reflection over the x-axis.Vertical stretch by a factor of 2.Translation left 4 units.Translation down 5 units.What are the transformations?The parent cube function is given as follows:
f(x) = x³.
The transformed cube function is given as follows:
g(x) = -2(x + 4)³ - 5.
Hence the transformations are given as follows:
Multiplication by -2: vertical stretch by a factor of 2 and reflection over the x-axis, due to the negative number with absolute value of 2.x -> x + 4: translation left 4 units.y -> y - 5: translation down 5 units.More can be learned about transformations at https://brainly.com/question/29209050
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One of the sides of a parallelogram has a length of 5 in. Can the diagonals
have the following lengths?
4 in. and 3 in.
with explanation, please !
Answer:
No, the diagonals of a parallelogram cannot have lengths of 4 in. and 3 in. The diagonals of a parallelogram bisect each other and have equal length. Therefore, if one diagonal has a length of 4 in., the other diagonal must also have a length of 4 in. and cannot have a length of 3 in.
Step-by-step explanation:
Yes, I know you pretty much
Ross goes on a hiking trip. He hikes 2000 feet before stopping to rest. He turns around and hikes back 1050 feet and rests again. After some time, he hikes the rest of the way back to his starting point. Sketch the graph to show the distance from his starting point compared to time. Use the graph to find the total distance that Ross hiked.
Helpp!
The total distance that Ross hiked is 4000 feet.
How to determine the total distance hikedFrom the question, we have the following parameters that can be used in our computation:
He hikes 2000 feet before stopping to rest. He hikes back 1050 feet After some time, he hikes the rest of the way back to his starting pointThis means that the total distance travelled is
Total distance = 2 * Initial distance hiked
Substitute the known values in the above equation, so, we have the following representation
Total distance = 2 * 2000
Evaluate
Total distance = 4000
Hence, the total distance hiked is 4000 feet
See attachment for the graph
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a certain forest coavers an area of 3900 km^2 suppose that each year this area decreases by 3.25% what will be the aera after 6 years
The solution is, the area after 6 years is 3198.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Rate of reduction = 100 - 3.25 = 96.75%
After 6 years, the reduction in trees =0 .9675^6
=0.820
Area after 6 years = 3900 x 0.820
= 3198
Hence, The solution is, the area after 6 years is 3198.
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Is `(2,5)` a solution to the system:
`x+y=7`
`2x-3y=-11`
Answer:
the answer is in the picture.. if you need to actually solve the system please tell me and i will send that too
7. Kiran iS playing a video game. He earns 3 stars for each easy level he completes and 5
stars for each difficult level he completes. He completes more than 20 levels total and
earns 80 or more stars.
The inequalities that represent the situation will be x + y > 20 and 3x + 5y > 80.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Kiran iS playing a computer game. He procures 3 stars for each simple level he finishes and 5 stars for each troublesome level he finishes. He finishes in excess of 20 levels altogether and procures at least 80 stars.
Let 'x' be the number of easy levels and 'y' be the number of difficult levels. Then the equations are given as,
x + y > 20
3x + 5y > 80
The inequalities that represent the situation will be x + y > 20 and 3x + 5y > 80.
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(1) I'm stuck with my math pls help me find the x and the y show ur steps
Answer:
Step-by-step explanation:
1=3x3)=9+2=11
2.01 Quiz Polygons and Symmetry 1
What is the value of x?
X= ___
Answer:
Step-by-step explanation:
112+120+133+128+100+x=720
593+x=720
x=720-593
x=127