WORTH 45!!!
Use division to show that (x+5) is a factor given y= 2x^3 - x^2 - 41x + 70
Answers
```
2x^2 - 11x + 14
_______________________
x + 5 | 2x^3 - x^2 - 41x + 70
-(2x^3 + 10x^2)
---------------
-11x^2 - 41x
(-11x^2 - 55x)
-------------
14x + 70
(14x + 70)
--------
0
```
We can see that (x+5) evenly divides into 2x^3 - x^2 - 41x + 70, with no remainder. Therefore, we have shown that (x+5) is a factor of the polynomial y= 2x^3 - x^2 - 41x + 70.
Related Questions
in a series of coin flips, a run is a series of consecutive coin flips that are all the same. for example, in the sequence \[tt \textcolor{red}{hhh} tthhhth,\]the red letters form a run. if a fair coin is flipped four times, what is the expected length of the longest run?
Answers
The expected length of series of four coin flips is 1.
Given data:
To find the expected length of the longest run in a series of four coin flips, consider all possible outcomes and calculate their probabilities.
No runs: If all four coin flips result in alternating heads and tails, there are no runs.
The probability of this outcome is \((\frac{1}{2})^4 = \frac{1}{16}\)
One run of length 2: There are three positions where a run of length 2 can occur: HH, TT, or HT.
The probability of this outcome is \(3*(\frac{1}{2})^4 = \frac{1}{16}\)
One run of length 3: There are two positions where a run of length 3 can occur: HHH or TTT.
The probability of this outcome is \(2*(\frac{1}{2})^4 = \frac{1}{16}\)
One run of length 4: There is only one position where a run of length 4 can occur: HHHH or TTTT.
The probability of this outcome is \((\frac{1}{2})^4 = \frac{1}{16}\)
To find the expected length of the longest run, multiply the length of each possible run by its corresponding probability and sum them up:
Expected length of longest run = \((0 * \frac{1}{16}) + (2*\frac{3}{16}) + (3 * \frac{2}{16}) + (4 * \frac{1}{16})\)
= (0 + 6 + 6 + 4) / 16
= 16 / 16
= 1
Hence, the expected length of the longest run in a series of four coin flips is 1.
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Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.)
Answers
The integration by part is \(\frac{x^{3}In x }{3} -\frac{x^{3} }{9} +C\) with indicated choices of u and dv.
What is integration by parts?
The method Integration by Parts is known to be a special method of integration that is often useful. In calculus, definite integrals are referred to as the integral with limits such as upper and lower limits. It is also possible to derive the formula of integration by parts with limits.
Given: ∫ \(x^{2} In x dx\) ; \(u=In x\) ; \(dv=x^{2} dx\)
Consider \(u=In x\) and \(dv=x^{2} dx\)
⇒ \(u=In x\) ⇒ \(dv=x^{2} dx\)
⇒ \(du= \frac{1}{x} dx\) ⇒ \(v=\frac{x^{3} }{3}\)
Now, apply integration by parts to solve the integral
∫ u dv = uv - ∫ v du
the antiderivative of \(x^{n}\)\(=\frac{x^{n+1} }{n+1}\) and the derivative of In x = \(\frac{1}{x}\) .
⇒ ∫ \(x^{2} In x dx =\)\(\frac{x^{3} In x}{3} -\frac{x^{3} }{3} .\frac{1}{x} dx\)
= \(\frac{x^{3}In x }{3}\) \(-\frac{x^{2} }{3} dx\)
= \(\frac{x^{3}In x }{3}\) \(-\frac{x^{3} }{9} +C\)
Hence, the final integration is \(\frac{x^{3}In x }{3}\) \(-\frac{x^{3} }{9} +C\)
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Three cars are shown below, along with
their original prices.
The price of each car is then rounded to
the nearest £100.
a) Work out which car's price changes the
most.
b) By how much does this car's price
change?
Car X
£13,420
MATHS X
Car Y
£17,590
MATHS Y
Car Z
£12,860
MATHS Z
Answers
In linear equation , the car y's price changes the most.
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.According to the question
a) Car x : £ 10320 ≈ £ 10300 10320 - 10300 = 20
Car y : £ 15430 ≈ £ 15400 15430 - 15400 = 30
Car z : £ 17490 ≈ £ 17500 17490 - 17500 = 10
10 < 20 < 30
so the car y's price changes the most.
b) this car's price change £ 30
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f(x +h)-f(x)
Find the difference quotient of f; that is, find
2,5*0, for the following function. Be sure to simplify.
h
f(x) = x² - 8x+5
f(x+h)-f(x)
= ()
(Simplify your answer.)
h
Answers
The difference quotient of the function f(x) = x² - 8x + 5 is given by (f(x + h) - f(x)) / h, and we need to simplify it.
To find f(x + h), we substitute x + h for x in the expression for f(x):
f(x + h) = (x + h)² - 8(x + h) + 5
= x² + 2hx + h² - 8x - 8h + 5
Subtracting f(x) = x² - 8x + 5 from f(x + h), we get:
f(x + h) - f(x) = (x² + 2hx + h² - 8x - 8h + 5) - (x² - 8x + 5)
= 2hx + h² - 8h
Dividing this expression by h, we obtain the difference quotient:
(f(x + h) - f(x)) / h = (2hx + h² - 8h) / h
= 2x + h - 8
Therefore, the difference quotient of the function f(x) = x² - 8x + 5 is 2x + h - 8. This expression represents the average rate of change of the function over the interval [x, x + h]. As h approaches zero, the difference quotient approaches the instantaneous rate of change of the function at x, which is the derivative of the function at x. The difference quotient is a fundamental concept in calculus and is used to define the derivative of a function.
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How many times should you multiply 8/7 by itself?
Answers
Answer:
to gain what result
Step-by-step explanation:
if u can please the full question
WILL GIVE BRAINLIST TO BEST ANSWER
Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
Show work
Find f(9)
11) f(n) = f(n - 1) x 4
f(1) = 4
Answers
Answer:
No solution
Step-by-step explanation:
Use the given functions to set up and simplify f(9)
which points are solutions to the linear inequality y<0.5x+2 select three options. (-3,-2)(-2, 1)(-1, -2)(-1, 2)(1, -2)
Answers
The given inequality: y < 0.5x + 2
The coordinates of they satisfy the given inequality than they are the solutions of the inequality y < 0.5x + 2
Plot the given points on the given line, The points which are passes through the line is the solution of the given inequality:
The point (-1,2)
The points doenot pss through the line and lie in the shaded region
So, (-1,2) are not the solution of the given inequality:
Solution are :(-2, 1)
(1, -2)
Answer :
(-2, 1)
(1, -2)
vx-w=2
rearrange it and make x the subject
Answers
Answer:
\(vx - w = 2 \\ vx = 2 + w \\ x = \frac{2 + w}{v} \)
What is the area of a rectangle with a base of 4 and a height of 7?
Answers
Answer:
28
Step-by-step explanation:
six times a number equals another while their sum is 28 find the numbers
Answers
Answer:
4 and 24Step-by-step explanation:
Let the numbers be x and y, then:
6x = yx + y = 28Substituting y in the second equation:
x + 6x = 287x = 28x = 4Then finding the value of y:
y = 6*4 = 24Claire owns a local bakery and sells boxes of muffins. Each box contains 6 muffins. If she sells 7 boxes of muffins by closing time on Thursday, how many muffins did she make to fill all the boxes that she sold?
42
0.9
1
13
Answers
Answer: Claire made 42 muffins by closing time
Step-by-step explanation:
Pretty simple math just multiply 6 muffins by 7 boxes and you get your answer.
Help plsss anyonnne plsss
Answers
Answer:
0.50
Step-by-step explanation:
The question states at least 2 which means 2 or more.
The only applicable numbers to look at would be 2 and 3.
First of all we find 2 since it's missing.
Now all probability distributions must add up to 1.
As we can see there are 0.20, 0.30 and 0.40 which is equal to 0.90. Therefore 1 - 0.90 = 0.10 which would be 2.
Hence, the peobability that x is at least 2 is 0.10 + 0.40 = 0.50.
2. The vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a. Find the equation of the perpendicular bisector of the side QR.
b. Find the slope of the median of the triangle that passes through point R.
c. Find the slope of the altitude of the triangle that passes through point Q.
Answers
The answers will be :
a. The equation of perpendicular bisector of QR is y = \(\frac{-5}{3}\) x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
What is slope of a line segment ?
Slope is the ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.
It is given that the vertices of a triangle are P(-6,1), Q(-2,-5) and R(8,1).
a.
The midpoint (M) of QR will be equal to
( \(\frac{-2 + 8}{2} , \frac{-5 + 1}{2}\) )
or
M = (-3 , 2)
Now , slope of line QR will be ;
\(m_{QR}\) = \(\frac{1+5}{8+2}\)
\(m_{QR}\) = 6 / 10
We know that :
m × \(m_{QR}\) = -1
m = -10 / 6
or
m = -5 / 3
Equation of line will be given as :
y + 2 = \(\frac{-5}{3}\) ( x - 3 )
y = \(\frac{-5}{3}\) x + 3
b.
The midpoint of PQ will be :
= (\(\frac{-6 - 2}{2} , \frac{1 - 5}{2}\))
= ( -4 , -2)
The slope of median of triangle that passes through point R will be ;
m = \(\frac{-2 - 1}{-4-8}\)
m = -3 / -12
m = 1/4
or
m = 0.25
c.
Slope of altitude of triangle that passes through point Q will be :
m = \(\frac{1 - 1}{-6-8}\)
m = 0 / -14
m = 0
The slope in this case doesn't exist.
Therefore the answers will be :
a. The equation of perpendicular bisector of QR is y = \(\frac{-5}{3}\) x + 3.
b. The slope of median of triangle passing through point R is 1/4.
c. The slope of the altitude of the triangle that passes through point R doesn't exists.
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You receive an $18 commission on a
$18 commission on a $300 TV that you
sold. What percent commission did you earn?
What the answer ?
Answers
Answer:
6%
Step-by-step explanation:
300 ÷ 3 = 100
18 ÷ 3 = 6
Solve the differential equation xy' = y + xe^8y/x by making the change of variable v = y/x.
Answers
This is the general solution to the given differential equation in terms of the variable v = y/x.
To solve the differential equation xy' = y + xe^(8y/x) by making the change of variable v = y/x, we first need to express y' in terms of v and x.
Using the product rule for differentiation, we have:
y' = (dv/dx)x + v
Substituting this expression for y' into the given differential equation, we get:
x((dv/dx)x + v) = y + xe^(8y/x)
Substituting v = y/x, we get:
x(dv/dx + v) = v + e^(8v)
Simplifying, we get:
xdv/dx = e^(8v)
Separating the variables and integrating, we get:
∫e^(8v)/v dv = ∫1/x dx
Using integration by substitution (u = 8v, du/dv = 8), we get:
(1/8)∫e^u/u du = ln|x| + C
Substituting back v = y/x, we get:
(1/8)∫e^(8y/x)/(y/x) dy = ln|x| + C
Simplifying and multiplying both sides by 8, we get:
∫e^(8y/x) dy/y = 8ln|x| + C
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Help, will rate brainlist if correct!!
y = x4 - 5x2
A.) What is the y-intercept of this graph? How do you know? (1 point)
B.) What are the x-intercepts/roots/zeros? Show your work. (4 points)
C.) Describe the end behavior of this function (2 points)
D.) Draw a graph of this function, carefully labeling your intercepts and showing the end behavior.
Answers
A. The y-intercept is at the point (0, 0).
B. The zeros are x = 0 or x = ±√5
C.
How to solve the expressionA) The y-intercept of this graph is the point where x = 0.
When x = 0, the value of y
= 0^4 - 5*0^2
= 0.
Therefore, the y-intercept is at the point (0, 0).
B) The x-intercepts/roots of the function are the values of x that make y = 0.
To find these values, we need to set y = 0 and solve for x:
x⁴ - 5x² = 0
x⁴ = 5x²
x² = x⁴/5
x = ±√(x⁴/5)
We can simplify this expression by factoring x² out of both sides:
x²(x² - 5) = 0
x² = 0 or x² - 5 = 0
x = 0 or x = ±√5
hence the x-intercepts are at x = 0 and x = ±√5.
C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.
x → ∞ f(x) → ∞
x → -∞ f(x) → -∞
D) The graph is attached
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(q23) Find the volume of the solid obtained by rotating the region under the curve y = 2 - x about the x-axis over the interval [1, 2].
Answers
The volume of the solid obtained by rotating the region under the curve y=2-x about the x-axis over the interval [1, 2] is π units cubed.
How to calculate the volumeIn this case, the radius of each disc is r=2-x and the thickness of each disc is dx. The volume of each disc is then πr²dx=π(2-x)²dx.
The volume of the solid is then equal to the sum of the volumes of an infinite number of these discs, which is given by the following integral:
V = π∫_1² (2-x)²dx
V = π * 1
V = π
Evaluating this integral, we get V=π units cubed.
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In a normal distribution with mean 120.0 and stanciard deviation 30.0 there are 300 variates between 130 and 150 . How many varlates are there in the whole distribution? (Round your answer
Answers
In a normal distribution with a mean of 120.0 and a standard deviation of 30.0, there are 300 variates between 130 and 150.
Here is the breakdown-
To find the number of variates in the whole distribution, we need to calculate the area under the curve between the lowest and highest values of the distribution.
In this case, the lowest value is 130 and the highest value is 150.
We can use the standard normal distribution table or a statistical calculator to find the area under the curve between these two values. The area represents the proportion of variates within that range.
Once we have the proportion, we can multiply it by the total number of variates (300) to find the actual number of variates in the whole distribution.
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20% of the teachers at Francis Middle School teach science. If there are 6 science
teachers, how many teachers are at Francis Middle School?
Answers
Answer: A total of 30 teachers
Step-by-step explanation:
20% = 6 (science) teachers
20x5= 100
6x5=30 teachers
Hope this helps you!
Answer:
30 teachers
20% is 2/10 of 100
20 x 5 = 100
6 x 5 = 30
Therefore, 30 teachers.
The average of 15,19,23,41,and Z is 20. What is the value of x
Answers
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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How would you express the area of the rectangle using the Distributive Property?
A. 5(x + 3)
B. x(3 + 5)
C. 3(x + 5)
D. 3x + 5
Answers
PLease send explanation.
Answers
Answer:
Step-by-step explanation:
XY = 1/2 * QR (According to the midpoint theorem)
=1/2 * 15.6
=15.6/2
=7.8 m
HELP PLEASE!!!! SHOW WORK!!!
7) Kristof wants to build a new rectangular pen for Sven to live in. Kristof measures and finds that the width of the fence is 3x + 4. He also knows that he wants the length of the fence to be 4 times the width.
a) Create an expression that could be used to find the perimeter of the fence.
b) If Kristof knows that the perimeter of the fence is 280 feet, what is the length and width of the fence?
Answers
Answer: 5
Step-by-step explanation:
A factory can make 1,200 shirts in 6 hours. At this rate, how many shirts can the factory make in 9 hours?
Answers
Answer:
18000 shirts
Step-by-step explanation:
No of shirts in 6 hour = 1200
No of shirts in 1 hour = 1200÷6 = 2000
No of shirts in 9 hours = 2000×9
= 18000
3.) What would 9 gallons of gas cost at $2.12 per gallon? *
$18.80
O $17.56
$19.08
$11.12
Answers
Answer:
19.08
Step-by-step explanation:
each gal = $2.12
gals filled = 9
9 x 2.12 = 19.08
the distance from the ground of a person riding on a ferris wheel can be modeled by the equation where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?
Answers
It will take the ferris wheel 5 seconds to make one revolution.
To determine how long it will take for the ferris wheel to make one revolution, we need to find the time it takes for d to return to its initial value.
Assuming that the ferris wheel starts at the lowest point, we know that the distance above the ground is 0 feet when t = 0. We can set the equation equal to 0 and solve for t as follows:
d = 50 sin(π/10 t) + 50
0 = 50 sin(π/10 t) + 50
sin(π/10 t) = -1
π/10 t = -π/2
t = -5 seconds
Since we are looking for the time it takes for d to return to its initial value, we can ignore the negative sign and take the absolute value of t, giving us the final answer of 5 seconds.
To find the time it takes for the ferris wheel to make one revolution, we need to determine the time it takes for the distance above the ground to return to its initial value. Assuming the ferris wheel starts at the lowest point, we can set the equation equal to 0 and solve for t. We get a negative value of t, but we can ignore the negative sign and take the absolute value of t, which gives us the final answer of 5 seconds.
It will take the ferris wheel 5 seconds to make one revolution.
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PLEASE ANSWER WILL MARK BRAINLIEST!
Answers
Answer:
3 and 4 can i please get brainliest i need one more to rank next level
Step-by-step explanation:
I really need help with this math problem
Answers
Step-by-step explanation:
The area with the highest inches receives most rainfall 1¼
The area with the lowest inches received lowest rainfall 1/8
1¼ location will have highest frequency using the ⅛line plot. There are 10 of ⅛ in 1¼
Add all the inches
1/8 + 3/8 +1/8 + 1/8 + 3/4+ 3/4 + 1/4 + 1¼ + 1/4 +1
6/8 + 2¼ + 1
6/8 + 3¼
6/8 + 13/4 = 32/8
Total rain = 4inches
if m<DEC= (12x-3)°, m<BCE= (7x-26)°, and m<DAE= 72°, find each angle measure.
Answers
The angle of each measure is:
m<DEC= 129°
m∠BCE = 51°
m∠ADE = 57°
m∠EDB = 123°
m∠DBC = 57°
What is meant by angle of measure in triangle?Angle of measure is the measure of an angle formed by two rays with a common endpoint. Angle of measure is important to many mathematical and scientific fields, including geometry, trigonometry, and physics.
In geometry, angles are used to define shapes and measure the size of an object. For example, angles are used to determine the angles of a triangle, or the angles between the sides of a rectangle. Angle of measure is also important in trigonometry, as it is used to calculate the lengths of sides and angles in a triangle, as well as the area of a triangle.
Angle of measure is also used in engineering, navigation, and surveying. When designing a building or structure, angles are used to determine the strength and stability of the structure, as well as the angles of the beams and walls. In navigation, angles are used to calculate the direction of a ship or aircraft. Finally, in surveying, angles are used to measure the angles between points on a map or a landscape.
Given,
m∠DEC= (12x-3)°, m∠BCE= (7x-26)°, and m∠DAE= 72°
∠DEC+∠BCE = 180°
12x-3+7x-26 = 180°
19x - 29 = 180°
19x = 180+29
x = 209/19
x = 11
Substitute x=11 in m∠DEC= (12x-3)°, we get
m∠DEC= 129°
Substitute x=11 in m∠BCE= (7x-26)°, we get
m∠BCE = 51°
To find m∠ADE,
m∠ADE + m∠DAE + m∠DEA=180°
m∠ADE + 72° + 51° = 180°
m∠ADE = 57°
To find m∠EDB,
m∠EDB + m∠ADE=180°
m∠EDB = 180° - 57°
m∠EDB = 123°
To find m∠DBC,
m∠DBC = m∠ADE are corresponding angles, so
m∠DBC = m∠ADE = 57°
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what is m if m + 16 = 31
Answers
Answer:
15
Step-by-step explanation:
m + 16 = 31
m = 31 - 16
m = 15
Answer:
m = 15
Step-by-step explanation:
15 + 16 = 31