Factorize:
x^4 - (x-z)^4
Answers
=(2x2 −2xz+z ^2 )(2x−z)(z)
Related Questions
An isosceles triangle has a base that is 3 times the length of its legs. The perimeter of the triangle is 45 cm. What is the length of the base?
Answers
Answer:
27cm
Step-by-step explanation:
[tex]s + s + s = p \\3x + x + x = 45 \\ 5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]
That's the length of one of its legs
The length of the base = 3x
= 3 x 9
= 45cm
The cost C in dollars of manufacturing x bicycles at a production plant is given by the function shown below.
C(x) = 5x²-1500x + 125,000
a. Find the number of bicycles that must be manufactured to minimize the cost.
b. Find the minimum cost.
a. How many bicycles must be manufactured to minimize the cost?
bicycles
Answers
Given function:
C(x) = 5x² - 1500x + 125000It has a positive leading coefficient, hence the parabola opens up. It means it has the minimum point at vertex.
The x-coordinate of the vertex is:
x = - b/(2a) = - (-1500)/(2*5) = 150The minimum cost is:
C(150) = 5(150)² - 1500(150) + 125000 = 12500Answer:
a) The minimum number of bicycles is the x-coordinate of the vertex, 150,b) The minimum cost is the value of C when x is 150, this is $12500.Write an equation in the form of y= mx for the proportional relationhip that pae through the point (2, -5) and (6, -45)
Answers
y=-10x+15 is the equation passing through the point which is in the form of y=mx+b
The equation of a line y = mx+b is called a straight line.
Where:
m is the slope, and b is the y-intercept.
given points are (2,-5) and (6,-45) consider these points as (x1,y1) and (x2,y2)
we have to find m: the slope of the line...
[tex]m=\frac{y2-y1}{x2-x1}[/tex]------------(1)
Now, plug the values into the formula of equation(1):
[tex]m=\frac{-45-(-5)}{6-2} \\\\m=\frac{-40}{4}[/tex]
m=-10
y=mx+b will become y=-10x+b
To find the b values:
for point(2,-5) consider x as 2,y as -5 and substitute in y=mx+b-5=-10*2+b
b=15
for point(6,-45) consider x as 6,y as -45 and substitute in y=mx+b-45=-10*6+b
b=15
so the final equation is y=-10x+15
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Many businesses and organizations insist that official communications use professional-looking fonts, such as times new roman. fonts characterized as less professional, such as comic sans, should be avoided. a student would like to determine if font choice makes a difference in the average grade on a typed response in english classes. there are currently four english classes available from which the student can collect data, and each class has a similar writing assignment. at the start of the assignment, students are randomly assigned a font, either times new roman or comic sans, and then complete the assignment. the teachers grade the assignments, and the mean grade for each font is found.Method A: At the start of the assignment, students choose a font, either Times New Roman or Comic Sans, and then complete the assignment.Method B: At the start of the assignment, students are randomly assigned one of two fonts, either Times New Roman or Comic Sans, and then complete the assignment.In both methods, the teachers grade the papers received, and the mean grade for each font is determined.Which method describes an experiment?a. Method A is an experiment because the students choose their own font.b. Method B is an experiment because the students are randomly assigned a font.c. Both methods describe experiments because both fonts are used on the assignment.d. Neither method describes an experiment because a third font should be included for comparison.
Answers
Hope this helps.
According to the United States Census Bureau, the state of Texas had a population of 16,986,510 in 1990. Census data shows that in 2000, the population of Texas was 20,851,820. Find the percent of change.
Answers
Answer:
22.7551745473%
Step-by-step explanation:
I could be very wrong but to find the percentage of change you have to divide the increase by the original number, and then multiply it by 100.
20851820-16986510=3865310
3865310/16986510=0.22755174547
0.22755174547*100=22.755174547
This answer can then be rounded up to 23%
Check for Reasonableness What is a good estimate for 380% of 60? Explain.
Answers
A rectangular aquarium is 12 inches tall. The perimeter of the base is 80 inches. The length of the base is 4 times the width of the base. Enter the volume, in cubic inches, of the aquarium.
Answers
Answer:
Step-by-step explanation:
Okay so you have to multiple 12 x 80 which gives you 960, then you mulitply 960 x 4 to get your final answer which is 3840 cubic inches
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme out
Answers
There is no statistical support in the data for the claim that seeded clouds typically cover more than 300 acres per foot by average acrefeet.
Since the significance level is set at 0.10, the meteorologists can conclude that the data does not provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
This is because the calculated p-value is greater than the significance level. This means that there is not sufficient evidence to reject the null hypothesis, which states that the average acrefeet from seeded clouds is no greater than 300.
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12. Juan is a programmer going to school at
night to earn a higher degree. He starts the
month with $500 in his savings account. His
income is $4750. Each month he currently
spends $750 on food; $400 on clothes; $530
on video games and movies. His classes cost
$500 each month. His essential expenses
(rent, medical costs, insurance, tax) total
$2800. How much does Juan have for his Net
Cash Flow and Ending Cash at the end of the
month?
[A]Net Cash Flow: -$230
Ending Cash: $730
[B] Net Cash Flow: $2,570
Ending Cash: $3,070
[C] Net Cash Flow: -$230
Ending Cash: $270
[D] Net Cash Flow:-$270
Ending Cash: $230
[E] Net Cash Flow: $270
Ending Cash: -$770
Answers
Juan's Net Cash Flow at the end of the month is -$230 and his Ending Cash is $270.
To calculate Juan's Net Cash Flow and Ending Cash, you need to subtract his expenses from his income.
Juan's income is $4750 per month. His essential expenses, including rent, medical costs, insurance, and tax, total $2800 per month. He also spends $750 on food, $400 on clothes, and $530 on video games and movies, for a total of $2680 in non-essential expenses.
Therefore, his total expenses are $2800 + $2680 = $5480.
His Net Cash Flow is his income minus his expenses, which is $4750 - $5480 = -$730.
His Ending Cash is his Net Cash Flow plus his starting balance of $500, which is -$730 + $500 = $270.
Therefore, the correct answer is option C: Net Cash Flow: -$230, Ending Cash: $270.
In a series of transformations, which transformation would make two figures similar as opposed to congruent?a. dilationb. reflectionc. rotationd. translation
Answers
In a series of transformations, dilation would make two figures similar as opposed to congruent.
Rotation, reflection and translation are known as rigid transformations.
This means they do not change the size or shape of a figure, they simply move it.
These rigid transformations preserve congruence.
Dilation, however, are not rigid transformation, since they change the size of a shape.
Dilation would not change the shape, just the size: the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.
This would give us a similar, but not congruent.
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Solve for x. Round to the nearest tenth.
X= type your answer...
X
28
32
Answers
The value x is 28. By using Pythagorean theorem on the given triangle.
What is the meaning of the nearest tenth?
To write a decimal number up to one decimal place, round it to the nearest tenth. This is done in a way that leaves one digit after the decimal point after rounding.
Given that,
DC = 28
BC = 32
Assume that, AB = a and AD = b
Applying Pythagorean theorem on △BCD:
BC² = DC² + DB²
Putting BC = 32 and DC = 28 in the above equation:
32² = 28² + DB²
DB² = 32² - 28²
DB² = 32² - 28²
DB² = 240
The length of AC is CD + DA = 28 + b.
Now applying Pythagorean theorem on △ABC:
BC² = AB² + AC²
32² = a² + (28 + b)²
a² = 32² - (28 + b)² .....(i)
Now applying Pythagorean theorem on △ABD:
AB² = AD² + BD²
a² = b² + 240 ....(ii)
Now comparing equation (i) and equation (ii)
32² - (28 + b)² = b² + 240
1024 - (28² + 56b + b²) = b² + 240
1024 - 784 - 56b - b² = b² + 240
b² + 240 - 1024 + 784 + 56b + b² = 0
2b² + 56b = 0
2b(b + 28) = 0
Either,
2b = 0, b + 28 =0
b = 0, b = -28
Since the value of b can't be negative. Thus b = 0.
The length of AC is CD + DA = 28 + b = 28.
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i need help desperately please don’t ignore!! :(
LN= 5x-8
NM= 12
m
find the value of x
Answers
The value of the missing part which is x is; x = 8
How to find the missing part of a triangle?
From the given triangle, we are told that;
LN = 5x - 8
NM = 12
∠KNL = (13x - 14)°
Now, since KN is an altitude in ΔKLM, it means that KN is perpendicular to LM and as such ∠KNL is a right angle which is 90 degrees. Thus;
(13x - 14)° = 90
1x = 90 + 14
13x = 104
x = 104/13
x = 8
This is the value of the missing value
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two planes flying at the same altitude are heading toward jwd airport. the paths of these planes form a right triangle. the jet is flying due east toward jwd at 450 mph. the turboprop is approaching jwd from the south at 275 mph. when each is 100 miles from the airport how fast is the distance between the planes changing?
Answers
The speed of the distance between the two planes is increasing at 325 mph as they approach JWD Airport.
The two planes form a right triangle, with the jet flying due east at 450 mph and the turboprop approaching from the south at 275 mph. The hypotenuse of the triangle is the distance between the planes, and the length of the hypotenuse is changing as the planes approach the airport. The rate of change of the length of the hypotenuse is equal to the sum of the rates of change of the two sides of the triangle, which are the speeds of the jet and the turboprop. As they are both 100 miles from the airport, the speed of the distance between the two planes is equal to the sum of the two speeds, or 450 mph + 275 mph = 325 mph. Therefore, the distance between the two planes is changing at a rate of 325 mph.
Rate of change of distance between the planes = Rate of change of jet + Rate of change of turboprop
= 450 mph + 275 mph
= 325 mph.
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There are no results for an airplane can carry a maximum of 36600 pound of cargo,passenger and luggage.On on the plane's next flight,it will carry 7,320 pounds of cargo.If each passenger with luggage weighs 220 pounds,what is the greatest number of passengers the plane can carry on its next fligh a 33 passenger b 133passenger c 166 passengers d 199 passengers
Answers
Answer:
b. 133 passengers
Step-by-step explanation:
The anount of weight taken by the passengers can be up to [tex]36600-7320=29280[/tex] lbs.
Dividing this by [tex]220[/tex] lb per passenger, we get there can be up to [tex]\lfloor 29280/220 \rfloor=133[/tex]
32 minutes and 2 seconds - 12 minutes and 15 seconds
Answers
32 minutes and 2 seconds - 12 minutes and 15 seconds
0 days 0 hours 32 minutes 2 seconds
- 0 days 0 hours 12 minutes 15 seconds
_________________________________
= 0 days 0 hours 19 minutes 47 seconds
[tex]=\fbox{19 minutes and 47 seconds or 19.783333 minutes}[/tex]
Select the correct answer from each drop-down menu. which if formulas are valid? and are valid if formulas.
Answers
Answer:
Step-by-step explanation:
Write the expression using exponents.
5.2 x y x y x y
The ( X ) stands for multiplication. So 5.2 times Y times Y times Y.
Answers
Calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1
Answers
The value of the double integral ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77
In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1
i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]
First we integrate the function (8x)/(1 + xy) as a function of y, treating the variable x as a constant.
G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy
G(x) = 8 ln(8x + 1)
Now we calculate the integral of the previous result as a function of x.
i.e., ∫_[0, 1] G(x) dx
= ∫_[0, 1] [8 ln(8x + 1)] dx
= 9 ln(9) - 8
= 11.77
Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77
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Vivian and her friends are planning a superhero movie marathon. Vivian is in charge of the
popcorn, so she buys a 2-pound jar of unpopped kernels. The jar's label says that 1 ounce of
kernels will make 1 quart of popcorn. How many cups of popcorn will her jar make?
Answers
If the jar level says that 1 ounce of kernels will make 1 quart of popcorn then 128 cups of popcorns will her jar make the popcorns.
The term ounce is a unit of measurement used in the Imperial system. It is mostly used in the United States. Ounces can be used to measure either liquid or dried goods. There are 32 ounces in one quart using the Imperial System of measurement. There are 4 cups in one quart. 1 quart is same as 32 ounces. Vivian and her friends are planning a superhero movie marathon. if Vivian buys 2 pound jar of unpropped kernels. then it will make 128 cups of popcorn. we know that 1 pound is equal to the 16 ounces so Vivian will make 32 ounces in 2 pound. A quart represented is a measuring unit used in the Imperial system and United States to measure liquids and dried goods. As per the leveling of the jar it will make 32 ounces in 32 quartz. then in 32 quartz it will make 128 cups of popcorn.
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9/2 * -(8/3) pls answer fast!...step by step explanation plss
Answers
Answer:
9 * -8
____ =-72/6
2 * 3
a van full of storm chasers is driving along a straight road at 94 kilometers per hour in hopes of filming a tornado. the tornado, 7 kilometers away, is traveling along the same road and moving directly toward them, traveling at 69 kilometers per hour. if neither the van nor the tornado changes course, how long will it be before they meet?
Answers
The time taken to traveled the van and the tornado before they meet as per the speed of the van and the tornado is equal to 2.6 minutes.
As given in the question,
Speed of the van along the straight road = 94 kilometers per hour
After travelling distance of 7 kilometers
Speed of the tornado along the same road = 69 km/hour
Total relative speed of van and tornado = 94 + 69
= 163km/hour
Distance travelled between two different speed = 7km
Time used to traveled before they meet = distance / speed
= 7 / 163
= 0.043 hours
= 2.58minutes
= 2.6minutes
Therefore, the time required to traveled the van and the tornado before they meet is equal to 2.6 minutes.
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Write an equation of the line that passes through P(3,3) and Q(1,-1).Write the equation in slope intercept form
Answers
Answer:
y = 2x-3
Step-by-step explanation:
Find slope from the two points (which is 2)
and then plug in one of the points (either (3,3) or (1,-1)) to find b in y=mx+b.
Combine everything, and there's your equation
pls help me in this homework id really appreciate it <3
Answers
Shota built a time travel machine, but he can't control the duration of his trip. Each time he uses the machine he has a 0. 80. 80, point, 8 probability of staying in the alternative time for more than an hour. During the first year of testing, shota uses his machine 202020 times. Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour? round your answer to the nearest hundredth. P(\text{at least one} < 1\text{ hour})=.
Answers
The Probability that at least one trip will last less than one hour =7/8
What is probability?It refers to the ratio of favorable outcome to the total possible outcome.
The possibility of happening an event is probability.
How to calculate probability of the given question?Probability of staying in the alternative time for more than an hour is 8
each trip is likely to last for more than one hour so probability of at least one trip will last more than an hour =1/8
Now, probability of at least one trip will last less than one hour = 1-1/8
7/8
hence, the result is 7/8
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Consider the function below. (If an answer does not exist, enter DNE.)h(x) = 5x3 − 3x5(a) Find the interval of increase. (Enter your answer using interval notation.)(−1,0)∪(0,1)
Answers
The interval in which the function h(x) = 5x³ - 3x^5 is increasing is given as follows:
(−1,0)∪(0,1).
How to obtain the intervals in which the function is increasing?The function in this problem is defined as follows:
h(x) = 5x³ - 3x^5.
To obtain the intervals for increase of decrease, the critical points of the function need to be obtained, which are the values of x for which the derivative is of zero.
The derivative of the function in this problem is given as follows:
h'(x) = 15x² - 15x^4.
Hence the critical points of the function are given as follows:
15x² - 15x^4 = 0
15x²(1 - x²) = 0.
Hence:
15x² = 0 -> x = 0.1 - x² = 0 -> x² = 1 -> x = -1, x = 1.Then the signals of the derivative in each interval is given as follows:
x less than -1: negative, as (1 - x²) < 0.x between -1 and 0: positive, as (1 - x²) > 0.x between 0 and 1: positive, as (1 - x²) > 0.x greater than 1: negative, as (1 - x²) < 0.The function is increasing when the derivative is positive, hence the interval is given as follows:
(−1,0)∪(0,1).
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Mustafa walks 15 km east and then 10 km south. How far is Mustafa from the starting point? Is in which direction
Answers
Answer:
25 kilometres West direction
suppose that a box contains 6 cameras and that 5 of them are defective. a sample of 2 cameras is selected at random ( without replacement). define the random variable x as the number of defective cameras in the sample. write the probability distribution for x .write your answer in fraction form or round to 3 decimal places.
Answers
If x is the number of defective cameras in the 2-size sample, that means that:
P(x = 0) = 0 (since there are no 2 cameras that can be selected without replacement that are not defective)
P(x = 1) = 5/15 = 1/3 (since there are 15 total ways to select a distinct sample and only 5 of these would have the non-defective one in them)
P(x = 2) = 10/15 = 2/3 (since there are 15 total ways to select a distinct sample and 10 of these would NOT have the non-defective one in them)
pete runs an ice cream stand that also sells snow cones served in paper cones. the paper cones he usually uses have a diameter of 6 inches and a height of 2 inches, but his supplier is out of them. as a replacement, he purchases paper cones with a diameter of 2 inches and a height of 6 inches. how do the volumes of the original and replacement cones compare?
Answers
Answer:
replacement is 1/3 the volume of the original
Step-by-step explanation:
You want to compare the volumes of a cone with diameter 6 in and height 2 in to one with a diameter of 2 in and height of 6 in.
VolumeThe volume of a cone is jointly proportional to the height and the square of the diameter:
V ∝ d²h
RatioThe ratio of the volume of the replacement cone to the original is ...
r = V2/V1 = ((2 in)²(6 in))/((6 in²)(2 in) = 2/6 = 1/3
The replacement cone has 1/3 the volume of the original.
Describe all the
positive integers that would make (32)x greater than 39. Explain your reasoning
Answers
The positive integers that will make (32)x greater than 39 must be greater than 39/32
How to find positive integers that will make (32)x greater than 39A whole number that is greater than zero is what is meant by the term "positive integer."
All counting numbers are included in the set of positive integers (that is, the natural numbers)
In the problem, the given expression is (32)x greater than 39 rewriting gives
(32)x > 39
solving for x
x > 39/32
the integer must be greater than 39/32
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part of a regression output is provided below. some of the information has been omitted. source of variation ss df ms f regression 3177.17 2 1588.6 residual 17 17.717 total 3478.36 19 the ss (residual) is a. 3177.17. b. 301.19. c. impossible to determine. d. 17.71.
Answers
The SS(residual) is - 301.19. Option (b) is the correct answer.
Given the table :
Source of Variation - - SS - - - df - - - MS - - - - F
Regression - - - - - -3177.17 - - -2 - - 1588.6
Residual - - - - - - - - ______ --17 - - -17.717
Total - - - - - - - - - - 3478.36 - - 19
Calculate the SSR, the Sum of the Square residual.
The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR), and Degree of Freedom RESIDUAL (DFR) are related by the formula :
MSR = SSR / DFR
Hence,
SSR = MSR × DFR
For the table ;
MSR = 17.717 ; DFR = 17
SSR = (17.717 × 17)
SSR = 301.19
So, the SS(residual) is - 301.19.
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