Answers
Answer:
4th option
Step-by-step explanation:
216p³ + 125q³ ← is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
then
216p³ + 125q³
= (6p)³ + (5q)³ → with a = 6p and b = 5q
= (6p + 5q)((6p)² - 6p(5q) + (5q)² )
= (6p + 5q)(36p² - 30pq + 25q²)
Related Questions
verify that the function satisfies the three hypotheses of rolle's theorem on the given interval. then find all numbers c that satisfy the conclusion of rolle's theorem. (enter your answers as a comma-separated list.) f(x)
Answers
The c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
The three hypotheses of Rolle's theorem are:
(a) f(x) is continuous on [a,b]
(b) f(x) is differentiable on (a,b)
(c) f(a) = f(b)
i) If you graph f(x), you can see that it is continuous that is no breaks on the interval [0,81]
ii) f(x) is differentiable on (0,81)
f '(x) = 1/(2√x) - 1/9 which exists on the open interval (0,81)
iii) f(0) = f(81) = √81 - 81/9 = 9-9 = 0
Rolle's Conclusion:
f'(c) = 0
f'(c) = 1/(2√c) -1/9 = 0
(9 - 2√c)/(18√c) = 0
√c = 9/2
c = 81/4
There is one number c = 81/4, which satisfies f '(c) = 0.
Therefore the c has only one number is c = 81/4 that satisfy the conclusion of rolle's theorem.
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Full question:
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)
f(x) =x − 1/9 x, [0, 81].
Please help ASAP and answer the whole thing please and thank you
Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:
Year Annual Tutoring Fee
2005 $1200
2008 $1350
A. What is the rate of change and initial value for Neil's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Neil charges each year. (10 points)
Answers
The equation in slope intercept form that represent the situation is y = 50x - 99050.
How represent linear equation in slope intercept form?Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptNeil charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount.
Using the table that shows the amount he charged for tutoring each year. we can find the rate of change.
The rate of change is the slope.
Therefore, (2005, 1200)(2008, 1350)
m = slope = 1350 - 1200 / 3
slope = 150 / 3
slope = 50
Therefore, let's represent the equation in slope intercept form. We will have to find the y-intercept of the equation.
Hence, using (2005, 1200)
y = 50x + b
1200 = 50(2005) + b
b = 1200 - 100250
b = - 99050
Hence, the equation is y = 50x - 99050.
where
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The length of a rectangular window is 5 feet more than its width. The area of the
window is 36 square feet. What are the dimensions of the window? Could a moving
company use that window to bring a standard upright piano into an apartment?
Answers
The dimensions of the window: Length = 9ft , width = 4ft
What are dimensions?
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
The homes we live in and the items we use on a daily basis all have three dimensions: height, length, and width.
Here, we have
l = w + 5
Area = length × width
The linear equation of the given dimension is:
36 = (w + 5)w
w² + 5w - 36 = 0
(w + 9)(w - 4) = 0
w + 9 = 0
w = -9
We only measure positive numbers so, we disregard this value.
we take,
w - 4 = 0
w = 4
l = 4 + 5
l = 9
The length of the window is 9 ft and the width of the window is 4 ft.
Hence, the dimensions of the window: Length = 9ft , width = 4ft
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I need help with this question too here is the question.
Fiona has 212 stickers to put in her sticker book. Page holds 18 stickers. How many pages does Fiona need for all of her stickers?
Again, please give me a valid answer. And show your work. Thank you. Have a good night.
Answers
Answer:
Fiona would need 12 pages to hold all 212 stickers.
Step-by-step explanation:
Since each page holds 18 stickers, and Fiona has 212 stickers, we need to divide.
212 / 18 = 11.7777778 pages
Because that we cannot have .77777778 of a page, we round to the nearest page, getting us 12 pages.
Have a good night, I hope my answer helped you!
12.0.5f-2.3g
f=12,g=2
Answers
Answer:14.1099
Step-by-step explanation:
4.2 = 16.7 - 5y solve for y
Answers
Answer:
y = 2.5
Step-by-step explanation:
To double check this, you can do 5 times (2.5), then do 16.7 minus that answer so you do, 16.7- 12.5 which does indeed equal 4.2
Answer:
y = 2.5
Step-by-step explanation:
[tex]4.2 =16.7-5y[/tex]
Subtract 16.7 from both sides of the equation you get:
[tex]-12.5=-5y[/tex]
Divide by -5:
[tex]2.5=y[/tex]
Hope this answers your question :)
solve for y
-8x+2y= -24
Answers
Answer:
y = -12 + 4x
Step-by-step explanation:
1. Add 8x to both sides of the equation.
2y = -24 + 8x
2. Divide each term in 2y = -24 + 8x by 2, then simplify.
• Simplify left side: cancel the common factor of 2
y = -24/2 + 8x/2
• Simplify right side: 2y/2 = -24/2 + 8x
y = -12 + 4x
3. Corey is playing a game in which he selects
all of the numbers that are less than -5 but
greater than -20. Shade the values that Corey
should choose.
-9
7 -5
6
-3 -11
-15
18
0
Answers
The numbers that will be chosen when Corey selects all of the numbers that are less than -5 but greater than -20 include -9, -11 and -15.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Based on the information, the inequality will be expressed as:
-20 < x < -5
In this case, the numbers have to be from -6 to -19. The numbers illustrated in the options are -9, -11 and -15.
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ASAP PLEASE!
A particular dishwasher uses 4 gallons of water per load. Their advertising claims that hand washing the dishes uses 6 times as much water. According to this estimate, how many gallons of water would it save to wash 215 loads using the dishwasher instead of by hand?
Answers
Answer: 4,300 gallons of water
215 x 4 = 860 gallons of water using the dishwasher
215 x 6 x 4 = 5,160 gallons of water by hand
5,160 - 860 = 4,300 gallons of water saved by using the dishwasher.
- Your welcome, keep it up champ.
Find the slope of the line shown on the graph to the right.
Answers
The slope of the line is 5/6.
From the graph:
Slope : a surface of which one end or side is at a higher level than another rising or falling surface.
Points are (-3,-2) and (3,3)
slope m = y2-y1 / x2-x1
= 3 - (-2) / 3 - (-3)
= 3 + 2 / 3 + 3
m = 5/6.
Therefore the slope of the line is 5/6.
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Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) ln x^2-1/x^7 , x>1
Answers
By using property of logarithms, We get the answer
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
Given,
In the question:
The equation is :
In [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1
To solve by using by using property of logarithms to expand the expression as a sum, difference, and / or constant multiple of logarithms.
Now, According to the question:
We know that:
The property of logarithms is:
[tex]log_{a}{\frac{m}{n} } = log_{a}m - log_{a}n[/tex]
The given equation is :
In [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1
In [tex]\frac{x^{2} -1}{x^7}[/tex] = In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex]
Again, Using the another property of logarithms.
[tex]log_am^x = nlog_am[/tex] {x∈ R}
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [tex](x^2 -1)[/tex] - 7 In x
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [ (x + 1)(x - 1)] - 7In x
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
{Log (mn) = [tex]log_{a}m - log_{a}n[/tex]}
Hence, By using property of logarithms, We get the answer
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
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Find the xx-intercept of each line defined below and compare their values.
Equation of Line A:
y-2=-(x+1)
Select values from Line B:
x y
−2 0
-1− -3
0 -6
Answers
The x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).
Given:
Equation of Line A: y-2=-(x+1)
on finding x intercept put y = 0
0 - 2 = -x - 1
-2 = -x - 1
-x = -2 + 1
-x = -1
x = 1.
The x intercept is (1,0)
The x intercept for the line B is (-2,0).
Therefore the x-intercept of line A is (1,0) and the x - intercept of line B is (-2,0).
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4x + 9 > 1. Pls help
Answers
x>-2
Explanation:
So in this question, you need to isolate the variable x on one side of the equation. In order to do this, you need to subtract 9 from both sides and then divide by 4:
4x+9>1
4x>-8
x>-2
4x+9>1
4x-9>-9
4x>-8
divide by 4
X>-2
A jeweler is dividing 3/8 a pound of rubies among 4 lots. What part of a pound will each lot weigh?
A 1/16
B 3/32
C 1/8
D 1/4
Answers
Answer:
B 3/32
Step-by-step explanation:
3/8 divided by 4
do the keep change flip method and solve
3/8 x 1/4
I Given:
2x-9
5
= 1
Prove: x = 7
Answers
It is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
Given: 2x-9 -5 = 1
We need to prove that x = 7
2x - 9 - 5 = 1
2x - 13 = 1
2x = 14
x = 7
Therefore, it is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
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Determine which set of side measurements could be used to form a triangle. 4, 6, 12 5, 19, 24 6, 10, 17 8, 9, 15
Answers
The set of side measurements that could be used to form a triangle is 8, 9 and 15
If a, b and c are the sides of the triangle
Then a + b > c
b + c > a
c + a> b
The first set of sides are
4, 6, 12
4 + 6 > 12
10 < 12
It will not form a triangle
The second set of sides are
5, 19 and 24
5 + 19 > 24
24 = 24
It will not form a triangle
The third set of sides are
6, 10 and 17
6 + 10 > 17
16 <17
It will not form a triangle
The fourth set of sides are
8, 9 and 15
8 +9 > 15
17 > 15
8+15 > 9
23 > 9
9 + 15 > 8
24 > 8
It will from a triangle
Hence, the set of side measurements that could be used to form a triangle is 8, 9 and 15
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if the domain of f(x) = 2x + 3 is {-3 ≤ x ≤ 0}, which number is not in the range -1,3,0, or 6?
Answers
Answer: 6
Step-by-step explanation:
If the domain is {-3 ≤ x ≤ 0}, then we will decide which of the given values is not in the range.
6 is not between, including the values of, -3 and 0, so the number not in the range is 6.
[tex]2x^{2} +7x-4=0[/tex]
Answers
Hence the answer would be (2x -1)(x+4)
13 out of 20 jellybeans are green what percent of jellybeans are green
Answers
Answer:
65
Step-by-step explanation:
What is the factored form of n2 + n
Answers
The factored form of n2 + n is: n(n+1).
How to find the factored form?Given data:
n²+n
Now let find the factored form of n²+n
n²+n
Rewrite in factored form
n(n+1)
Hence,
n²+n = n(n+1)
Therefore n(n+1) is the factored form.
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Lines j and k are parallel. m∠3 = (3x − 18)° and m∠4 = (y + 25)° and m∠7 = 75°. Find the values of x and y.
Answers
Answer:
x = 31 , y = 80
Step-by-step explanation:
∠ 3 and ∠ 7 are corresponding angles and are congruent , so
3x - 18 = 75 ( add 18 to both sides )
3x = 93 ( divide both sides by 3 )
x = 31
then
∠ 3 = 3x - 18 = 3(31) - 18 = 93 - 18 = 75°
∠ 3 and ∠ 4 are a linear pair and sum to 180° , then
75 + y + 25 = 180
y + 100 = 180 ( subtract 100 from both sides )
y = 80
Somebody please help.
Select the correct answer.
What is the exact value of cos 105°?
Answers
Check the picture below.
[tex]\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}~~ - ~~\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{2}-\sqrt{6}}{4} \end{array}}[/tex]
a group of friends wnats to go to the amusement park.They have no more than $110 to spend on parking and admission.parking is $8 and tickets cost $23 per person including tax
Answers
Answer:
Step-by-step explanation:
Based on the information given in the question, the inequality which can be used to determine x, the number of people who can go to the amusement park will be:
8 + 23(x) ≤ 100
8 + 23x ≤ 100
23x ≤ 100 - 8
23x ≤ 92
x ≤ 92/23
x ≤ 4
The number of people that can go to the amusement park will be at most 4
One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answers
Answer:
∴ The measure of the hypotenuse is 20cm (to the nearest tenth).
Step-by-step explanation:
Let the length of the hypotenuse be x cm.
x² = 11² + 14²
∴ x = 20cm (to the nearest tenth)
5. A sprinter runs at 12m/s. Convert this to km/h.
a) 2 km/h b) 12 km/h C) 3.6 km/h d) 43.2 km/h
Answers
Answer:
43.2km/h
Step-by-step explanation:
1km = 1000m
1h = 3600s
1km/h to m/s
= 1 × 1000/3600
= 1000/3600
1m/s to km/h
= 1 ÷ 1000/3600
= 1 × 3600/1000
Hence, 12m/s = 12 × 3600/1000
= 43.2km/h
Bijou says the following steps can be used to find 0.62 of 7:
Step 1 Change "of” to the multiplication symbol.
Step 2 62×7=434
Step 3 There are 0 decimal places in 7 and 2 decimal places in 0.62 for a total of 2 decimal places in the factors.
Step 4 Move the decimal place in the product 2 places to the right to find the solution: 0.62 of 7 is 43,400.
In which step did she make her first error?
Answers
Bijou made her first decimal place error in Step 4 because the answer is supposed to be 4.34, not 43,400.
How is the decimal place determined?The decimal place of a product of two numbers should be determined based on the number of decimal places the multiplier and the multiplicand originally have.
A decimal place error is committed when the result bears a decimal place in the wrong position.
In this situation, 0.62 of 7:
= 0.62 x 7
= 62 x 7 ... removing the two decimal places
= 434
= 4.34 ... putting back the two decimal places in the final result.
Thus, Bijou did not commit any decimal place or multiplication error in Steps 1 through 3 but in Step 4.
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a study of elephants is conducted to determine the average weight of a certain subspecies of elephants. the standard deviation for the population is 1500 pounds. at a 99% level, how many elephants need to be weighed so the average weight will be accurate to within 200 pounds?
Answers
The birth weight of elephants at the 99% confidence level is 3820 pounds
What is the standard deviation?
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The average birth weight of elephants is 200 pounds = 200
The deviation of 60 pounds. = 1500
The birth weight of elephants is at the 85th percentile. z = 99%= 1.645
Now from the formula of z-score:-
[tex]z=\sqrt{\frac{x-\mu}{\sigma} }[/tex]
[tex]1.64 =\sqrt{\frac{x-200}{1500} }\\[/tex]
[tex]1.645^{2} =\frac{x-200}{1500}[/tex]
2.68 = (x-200)/1500
2.68×1500=x-200
4020-200=x
3820=x
Hence the birth weight of elephants at the 99% level percentile is 3820 pounds
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Noah borrows \$2000$2000dollar sign, 2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. The relationship between the amount of money, aaa, in dollars that noah owes his father (including interest), and the elapsed time, ttt, in years, is modeled by the following equation. A=2000e^{0. 1t}a=2000e 0. 1t a, equals, 2000, e, start superscript, 0, point, 1, t, end superscript how long did it take noah to pay off his loan if the amount he paid to his father was equal to \$2450$2450dollar sign, 2450? give an exact answer expressed as a natural logarithm.
Answers
Two years , is the time in which Naoh had to pay off his loan when the ammount he paid to his father was equal to $2450.
In the question we have given,
Amount borrowed by Naoh from his father
= $2000
The relationship between amount of money A in dollars with interest and elapsed time t is
A = 2000 e⁽⁰·¹⁾ᵗ
let Naoh pay $2450 after elapsing "t" years .
that is A = $2450 after time t years of borrowing.
We shall calculate the time which elapsed after borrowed by Naoh for paying $2450.
So, putting A = 2450 in above equation we get
2450 = 2000 e⁽⁰·¹⁾ᵗ
=> e⁽⁰·¹⁾ᵗ= 2450/2000 = 49/40
Taking logarithm both sides
=> ln ( e⁽⁰·¹⁾ᵗ) = ln (49/40)
=> (0.1 )t = 0.203
=> t = 2.023 ~ 2
Hence, after 2 years , Naoh will pay $2450 with including interest to his father.
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HELP HELP HELP HELPP
ONLY ANSWER IF YOU KNOW
Answers
Answer:
Step-by-step explanation:
1(x1)+ (-4)x2+ (-10)x3 = -40 Eq 1
0 + (1)x2 + 3(x3) = 14 Eq 2
0 + (-2)x2 + (-5)x3 = -23 Eq 3
from the 2nd equations we get
x2 + 3*x3 = 14
x2 = 14 - 3*x3
plug this into equation 3
(-2)*(14-3*x3) + (-5)x3 = -23
now solve for x3 :)
-28+6*x3-5*x3 = -23
-28 +x3 = -23
x3 = 5
nice !
now find x2
x2 = 14-3*(5)
x2 = -1
now find x1
x1 + (-4)*(-1) + (-10)*5 = -40
x1 +4 -50=-40
x1 = 6
X = [ 6 ; (-1) ; 5 ]
a random sample of high school seniors were asked whether they were applying for college. the resulting confidence interval for the proportion of students applying for college is (0.65,0.69). what is the margin of error?
Answers
Using the confidence interval, the margin of error is 0.02.
In the given equation we have to find the margin of error.
The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).
Let p = population proportion of students applying for college
P = Sample proportion of students applying for college
ME = margin of error
So the confidence interval
CI = (P-ME, P+ME)
From the given question;
(P-ME, P+ME) = (0.65,0.69)
So lower bound= P-ME = 0.65............................(1)
Upper Bound = P+ME = 0.69............................(2)
Simplifying the Equation 1 and 2
Add equation 1 and 2 we get
2P = 1.34
Divide by 2 on both side we get
P = 0.67
Putting the value of P in the equation 2
P+ME = 0.69
0.67+ME=0.69
Subtract 0.67 on both side we get
ME = 0.02
Hence, the margin of error is 0.02.
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