Answers
Answer:
Step-by-step explanation:
Your difference of perfect cubes formula is given as
[tex](a-b)(a^2+ab+b^2)[/tex] and you have already correctly identified a as [tex]5q^2[/tex] and b as [tex]r^2s[/tex]. So we fill in the formula as follows:
[tex](5q^2-r^2s)((5q^2)^2+(5q^2)(r^2s)+(r^2s)^2)[/tex] and we simplify. Remember that
[tex](5q^2)^2=(5)^2*(q^2)^2=25q^4[/tex]. It's important that you remember the rules.
Simplifying then gives us
[tex](5q^2-r^2s)(25q^4+5q^2r^2s+r^4s^2)[/tex]
That's it, so fill it in however you need to on your end. Learn the patterns for the sum and difference of cubes and it will save you a ton of headaches...promise!!
Related Questions
HELP ME! In a complete sentence, describe the relationship between the three angles in the diagram below. Write and solve an equation to find the value of b and the measures of ∠QPS, ∠SPT, and ∠TPR.
Answers
Answer:
b = 17
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
Step-by-step explanation:
The sum of the three angles shown is a linear angle, with a measure of 180°.This fact can be used to write an equation:
(8b -12)° +b° +(2b+5)° = 180°
11b -7 = 180
11b = 187
b = 17
8b -12 = 8(17) -12 = 124
2b +5 = 2(17) +5 = 39
The value of b is 17.
The angle measures are ...
∠QPS = 124°
∠SPT = 17°
∠TPR = 39°
writing linear equations
Answers
Answer:
The graph in blue: y=4/3x-2
Step-by-step explanation:
Slope-intercept form is y=mx+b, m being the slope and b being the y-intercept.
To find the slope, you just put rise/run of the line.
Hope this helped :)
What is slope and how is it determined from a graph? How do you determine the intercepts from an equation or graph? How can linear equations and functions be written and graphed?
Answers
Hey there! I'm happy to help!
The slope is the steepness or incline of a line. From a graph, it is known as the rise over the run between two integer values. If you have a point at (1,1) and a point at (2,2), the rise (vertical difference) between them in 1 unit, and the run (horizontal difference) is 1 unit. 1/1 is 1, so the slope of a line that passes through these points is 1. This means that for every one unit to the right it goes, it goes one unit up.
The intercepts are where the line hits the x and y axes. By looking at a graph, you can find the y-intercept by seeing on what y-value the line intersects with the y-axis, and for the x-intercept you do so with the x-axis.
The slope-intercept equation is y=mx+b. This b is the y-intercept. To find the x-intercept, you plug in the value 0 for y and solve for x. This is because the x-axis is the line y=0, so you will see where the x is if y is equal to 0.
Linear equations and functions can be written in slope intercept form (y=mx+b), standard form (Ax+By=C), and point slope form [tex]y-y_{1} =m(x-x_{1} )[/tex].
They can be graphed by finding the y and x intercepts from the equation and then connecting the points to draw the line!
Have a wonderful day! :D
simplify: m–(a–k–b) HElp!
Answers
Answer: m-a+k+b
Step-by-step explanation:
m-(a-k-b)= m+-1*(a-k-b). Then, simply use distributive property to simplify the equation into m-a+k+b
Hope it helps <3
Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?
Answers
==================================================
Explanation:
Jane does the job alone and she can finish it in 5 hours. Her rate is 1/5 of a job per hour. By "job", I mean painting the entire fence. Notice that multiplying 1/5 by the number of hours she works will yield the value 1 to indicate one full job is done.
Through similar reasoning, Paul's rate is 1/6 of a job per hour.
Let x be the time, in hours, it takes Peter to get the job done if he worked alone. His rate is 1/x of a job per hour.
Combining the three individual rates gives
1/5 + 1/6 + 1/x = (6x)/(30x) + (5x)/(30x) + (30)/(30x)
1/5 + 1/6 + 1/x = (6x+5x+30)/(30x)
1/5 + 1/6 + 1/x = (11x+30)/(30x)
The expression (11x+30)/(30x) is the total rate if the three people worked together. This is assuming neither worker slows another person down.
Set this equal to 1/2 as this is the combined rate (based on the fact everyone teaming up gets the job done in 2 hours). Then solve for x
(11x+30)/(30x) = 1/2
2(11x+30) = 30x*1 .... cross multiply
22x+60 = 30x
60 = 30x-22x
60 = 8x
8x = 60
x = 60/8
x = 7.5
It takes Peter 7.5 hours, or 7 hours 30 minutes, to get the job done if he worked alone.
--------------
Here's another equation to solve though its fairly the same idea as above
1/5 + 1/6 + 1/x = 1/2
30x*(1/5 + 1/6 + 1/x) = 30x*(1/2) ... multiply both sides by LCD
30x(1/5) + 30x(1/6) + 30x(1/x) = 30x(1/2)
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 15x-11x
30 = 4x
4x = 30
x = 30/4
x = 7.5
We get the same answer
Answer: 7 . 5 hrs
Step-by-step explanation:
It takes Jane 5 hours to finish the fence so she can get [tex]\dfrac{1}{5}[/tex] of the job done in 1 hour.
It takes Paul 6 hours to finish the fence so he can get [tex]\dfrac{1}{6}[/tex] of the job done in 1 hour.
It takes Peter x hours to finish the fence so he can get [tex]\dfrac{1}{x}[/tex] of the job done in 1 hour.
Together, it takes them 2 hours to finish the fence so they can get [tex]\dfrac{1}{2}[/tex] of the job done in 1 hour.
Jane + Paul + Peter = Together
[tex]\dfrac{1}{5}\quad +\quad \dfrac{1}{6}\quad +\quad \dfrac{1}{x}\quad =\quad \dfrac{1}{2}[/tex]
Multiply everything by 30x to eliminate the denominator:
[tex]\dfrac{1}{5}(30x) + \dfrac{1}{6}(30x) +\dfrac{1}{x}(30x) =\dfrac{1}{2}(30x)[/tex]
Simplify and solve for x:
6x + 5x + 30 = 15x
11x + 30 = 15x
30 = 4x
[tex]\dfrac{30}{4}=x[/tex]
7.5 = x
what is the mean devuation of the following numbers
Answers
Answer:
hi pls do enter the no.s
the diagrams shows a right-angled triangle. find the size of angle x. give your answer correct to 1 decimal place.
Answers
Answer:
1. 40.8 degrees
2. 65.6 degrees
Step-by-step explanation:
1.
sin(x) = opposite / hypotenuse = 17/26
x = arcsin(17/26) = 40.83 degrees
2. tan(x) = opposite / adjacent = 11/5 = 2.2
x = arctan(11/5) = 65.56 degrees
Question is the attached file.
Answers
Answer:
The critical points are 12 and 0.
Step-by-step explanation:
We have that the critical numbers are those values that result from equating the derivative of a function to zero. Also called roots or zeros of the derived function.
IF f is defined in x, it will be said that a is a critical number of f if f '(x) = 0 or if f is not defined in x.
Now the function is:
f (x) = x ^ 2 / (x -6)
we have that the derivative of the quotient is:
(f / g) '= (f' * g - g '* f) / g ^ 2
we replace and we have:
f (x) = [2 * x * (x-6) - 1 * x ^ 2] / (x -6) ^ 2
simplifying we have:
f (x) = [x ^ 2 - 12 * x] / (x -6) ^ 2
this must be equal to 0, like this:
[x ^ 2 - 12 * x] / (x -6) ^ 2 = 0
we solve:
x ^ 2 - 12 * x = 0
x * (x - 12) = 0
Thus:
x = 0
x - 12 = 0 => x = 12
The critical points are 12 and 0.
Can someone help me with these two questions I don’t know how to do it and it’s due at 11 I would really appreciate it
Answers
Answer:
6. Unit rate = 1.3 yards per second
7. Unit rate = 0.8 page per minute
Step-by-step explanation:
The unit rate is simply the comparison of 2 quantities, whereby dividing both, the denominator must be 1.
For example, in the graph given comparing distance walked over time, when x (time in s) = 3, y (distance in yd) = 4.
Unit rate represented by the slope is the yards covered per second.
Unit rate = [tex] \frac{4}{3} = 1.33 [/tex]
Unit rate ≈ 1.3 yards per second
For the second graph given, unit rate of the slope is the number of pages read per minute.
From the graph, 4 pages is read at 5 minutes.
Thus,
Unit rate = [tex] \frac{4}{5} = 0.8 [/tex]
Unit rate = 0.8 page per minute
What fraction is equal to six-sevenths times eight-fifths?
Answers
Answer:
1 13/35 (mixed number) or 48/35 (simplified)
Step-by-step explanation:
6/7 times 8/5
= (6 times 8) / (7 times 5)
= 48/35 or 1 13/35
hope this helped :)
Answer:
48/35
Step-by-step explanation:
6/7*8/5=48/35
Calcule o valor dos produtos a) (-4). (-7/8) b) (-4). (-7/8) n sei pq tá repetido tá aqui na folha ;-; c) (-4).(+ 3,5) d) (-2).(-3/4). (-1/7) PRA HOJEE
Answers
Answer:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Step-by-step explanation:
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
É repetido talvez com sinal alterado para mostrar a diferença na resposta. Se o sinal for alterado, a resposta também se tornará negativa. Seria - 28/8.
Quando um número negativo é multiplicado por um número negativo, obtém um número positivo. Mas quando um número positivo é multiplicado por um número negativo, dá uma resposta negativa.
Sempre se lembre
negativo * negativo = positivo
positivo * negativo = negativo
negativo * positivo = negativo
positivo * positivo = positivo
Em palavras simples, dois sinais diferentes dão um sinal negativo e dois sinais semelhantes dão um sinal positivo na multiplicação.
English
a) (-4). (-7/8) = 28/8
b) (-4). (-7/8)= 28/8
c) (-4).(+ 3/5) = -12/5
d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28
Its repeated maybe with a changed sign to show the difference in the answer. If the sign is changed the answer would also become negative . It would become - 28/8.
When a negative number is multiplied with a negative number it gives a positive number. But when a positive number is multiplied with a negative number it gives a negative answer.
Always remember
negative * negative= positive
positive *negative=negative
negative *positive =negative
positive * positive = positive
In simple words two unlike signs give a negative sign and two similar signs give a positive sign in multiplication.
9. A solid rectangular block of copper 5 cm by 4 cm by 2 cm
is drawn out to make a cylindrical wire of diameter 2 mm.
Calculate the length of the wire.
Answers
Answer:
length = 1273.2 cm or 12.73 m
Step-by-step explanation:
Assume no loss.
diameter of wire, d = 2 mm
radius of wire, r = 1 mm = 0.1 cm
Volume of block, V = 5*4*2 = 40 cm^3
cross sectional area of wire, A = pi (r^2) = pi 0.1^2 = 0.01pi cm^2
Length of wire
= V/A
= 40 cm^3 / 0.01pi cm^2
= 4000/pi cm
= 1273.2 cm
= 12.73 m
Each CD at a music store is sold for $10. If n represents the number of CDs sold, which equation could be used to find the total number of dollars, d, the store receives from CD sales?
Answers
Answer:
10n = d
Step-by-step explanation:
We know that
Each CD is sold for 10 dollars
The music store has sold n amount of CD's
The total number of dollars 'd' depends on how many CD's were sold
The equation is: 10n = d
Hope this helps!
Answer:
D=10n
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each area of a circle to its corresponding radius or diameter.
Answers
Answer:
First box is 120.7016, second box is 63.585, third box is 28.26, and the fourth box is 12.56.
Step-by-step explanation:
You get these answers by using the area formula for a circle which is piR^2. If it says diameter divide it by 2 to get the radius.
What is the volume in cubic feet of the prism, rounded to the nearest cubic foot? Do not use units or commas in your answer.
Answers
Answer:
35.1
Step-by-step explanation:
There's a formula that i've linked as an image
Basically, substitute all 3 sides and the length into that formula, chuck it into the calculator and viola.
Or... we can use pythagoras' theorem and get the height of the triangle Height = [tex]3^{2}[/tex] - [tex]1.5^{2}[/tex] = 2.6
Area of triangle = (3 * 2.6) / 2 = 3.9
Volume = 3.9 * 9
Volume of prism = 35.1
Write a pair of negative integers whose difference is 8.
Answers
Answer:
(-5,-13) has a difference of 8
Answer:
-2 and -10
Step-by-step explanation:
negative integers are whole numbers below 0
difference is the same as (-)subtraction
x-y=8
if x= -2
-2-y=8
-y=8+2
-y=10
y= -10.
confirmation-2 - (-10)=8
-2+10=8
8=8
What is the following product?
Answers
Answer:
[tex]\boxed{6\sqrt{6} }[/tex]
Step-by-step explanation:
[tex]\sqrt{12} \sqrt{18}[/tex]
Multiply square roots.
[tex]\sqrt{12 \times 18}[/tex]
[tex]\sqrt{216}[/tex]
Simplify square root.
[tex]\sqrt{36} \sqrt{6}[/tex]
[tex]6\sqrt{6}[/tex]
48 - 8x equivalent expression
Answers
Answer:
8(6-x)
Step-by-step explanation:
Both 48 and 8 can be divisible by 8.
48 ÷ 8 = 6
8 ÷ 8 = 1
Therefore you get the answer 8(6-x)
as the simplest form.
Hope this helps.
What is the slope of the line that passes through the points (1, 1) and (9, 7)? 3/4 4/5 5/4 4/3
Answers
Answer:
3/4
Step-by-step explanation:
We can use the slope of the line by using the slope formula
m = (y2-y1)/(x2-x1)
= (7-1)/ ( 9-1)
= 6/8
= 3/4
Answer: 3/4
Step-by-step explanation: To find the slope of this line, I will be showing you the graphing method.
To find the slope of the line using the graphing method,
we first set up a coordinate system.
Next, we plot our two points, (1, 1), which we label point A, and (9, 7), which we label point B, and we graph our line, as shown below.
Now, remember that the slope, or m, is equal to
the rise over run from point A to point B.
To get from point A to point B, we rise
6 units and run 8 units to the left.
So our slope, or rise over run, is 6 over 8, which reduces to 3/4.
Find the interquartile range for a data set having the five-number summary: 4.9, 12.4, 20.5, 28.8, 34.3
Answers
Answer:
16.4
Step-by-step explanation:
The interquartile range is the difference between the upper and lower quartiles.
Given the five figure summary, then
upper quartile = 28.8
lower quartile = 12.4
interquartile range = 28.8 - 12.4 = 16.4
The Interquartile range is 16.4.
What is an Interquartile range?When values are ranked from lowest to highest, the Interquartile range designates the middle 50% of those values.
Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3).
The interquartile range represents the variation between Q3 and Q1.
The interquartile range is calculated as follows:
The upper quartile is 28.8
The lower quartile is 12.4
The interquartile range is,
= 28.8 - 12.4
= 16.4
The value of the interquartile range is 16.4.
To know more about the Interquartile range
https://brainly.com/question/4135956
#SPJ1
The following box plot shows the number of years during which 40 schools have participated in an interschool swimming meet: A box and whisker plot is drawn using a number line from 0 to 10 with primary markings and labels at 0, 5, 10. In between two primary markings are 4 secondary markings. The box extends from 1 to 6 on the number line. There is a vertical line at 3.5. The whiskers end at 0 and 8. Above the plot is written Duration of Participation. Below the plot is written Years. At least how many schools have participated for more than 1 year and less than 6 years?
Answers
Answer:
Step-by-step explanation:
The box encloses data between the two quartiles, namely at least half of the data. If there are 40 schools, then half of them would be in the box, between 1 and 6.
see attached plot.
Answer:
really hard to tell what the box plot is like without an attachment so im gonna help u find it out anyway
Step-by-step explanation:
basically when u look at a box plot and the range the line in the middle is the median and then the max the lowest range the lower quartile and then the higher quartile you can find ur anser, simply find the median first, find where the lower quartile is and then the lowest number in the group thats in betweeen 1 and 6
x=y-y and 2x+4y=10 solve using substitution
Answers
Answer:
(0, 2.5)
Step-by-step explanation:
Well we substitute y-y into x in the following equation,
2x + 4y = 10
2(y-y) + 4y = 10
2y - 2y + 4y = 10
Combine like terms
2y - 2y = 0
4y = 10
10/4
y = 2.5
If y is 2.5 we can plug those into y.
2x + 4(2.5) =10
2x + 10 = 10
-10
2x = 0
0/2
x = 0
Simplify (2^3)^–2. PLEASE I NEED HELP U WILL GET 10 POINTS
Answers
Answer:
I won't give you the answer straight away so you take the time to read my answer and understand
Step-by-step explanation:
We knoe that 2 to the third is 8. when you square to a negative power, you do squaring normally, and then take the reciprocal of that number. so 8 to the second power is 64, and we flip it over, sp the answer is 1/64
Points A(-l, y) and B(5,7) lie on a circle with centre 0(2, -3y). Find the values of y. Hence, find the radius of the circle
Answers
Answer:
The answer is below
Step-by-step explanation:
Points A(-l, y) and B(5,7) lie on a circle with centre O(2, -3y). This means that AB is the diameter of the circle and OA = OB = radius.
For two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]), the coordinates of the midpoint (x, y) between the two points is given as:
[tex]x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex].
For A(-l, y) and B(5,7) with center O(2, -3y), the value of y can be gotten by:
[tex]For\ x\ coordinate:\\2=\frac{-1+5}{2}\\ 2=2.\\For\ y\ coordinate:\\-3y=\frac{y+7}{2}\\ -6y=y+7.\\-6y-y=7\\-7y=y\\y=-1[/tex]
The value of y is -1. Therefore A is at (-1, -1) and O is at (2, -3(-1))= (2, 3)
The radius of the circle = OA. The distance between two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]) is given as:
[tex]|OX|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Therefore\ the\ radius \ |OA|\ is :\\|OA|=\sqrt{(2-(-1))^2+(3-(-1))^2}=\sqrt{25}=5[/tex]
The radius of the circle is 5 units
Directions: For
1.what is the square root
361
Answers
Answer:
√361=19
Step-by-step explanation:
Helppppppppppppppppp
Answers
Answer/Step-by-step explanation:
Surface area of cylinder = 2πrh + 2πr²
Surface area of the cylinder with,
height (h) = 4 ft
radius (r) = 5 ft
Surface area = 2*3.14*5*4 + 2*3.14*5²
= 125.6 + 157
= 282.6 ft²
Surface area of the cylinder with,
height (h) = 12 yd
radius (r) = 3 yd
Surface area = 2*3.14*3*12 + 2*3.14*3²
= 282.74 yd²
Write the equation of a circle with center (7, -12) and radius 9.
Answers
Answer:
( x-7)^2 + ( y+12) ^2 = 81
Step-by-step explanation:
The equation of a circle can be written in the form
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
( x-7)^2 + ( y--12) ^2 = 9^2
( x-7)^2 + ( y+12) ^2 = 81
Answer:
(x - 7)² + (y + 12)² = 81
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Here (h, k) = (7, - 12) and r = 9, thus
(x - 7)² + (y - (- 12))² = 9², that is
(x - 7)² + (y + 12)²= 81
The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24.3 ounces of cereal (as labeled on the box). At various times in the packaging process, we select a random sample of 100 boxes to see if the machine is (on average) filling the boxes as labeled. On Tuesday morning, at 7:45 a.m., a random sample of 100 boxes produced an average amount of 23.6 ounces. Which of the following is an appropriate statement of the null hypothesis?
A) The machine fills the boxes with the proper amount of cereal.
B) The average is 24.3 ounces (H0: μ = 24.3)
C) The machine is not filling the boxes with the proper amount of cereal (H0: μ ≠ 24.3 ounces).
D) The machine is not putting enough cereal in the boxes.
E) The average is less than 24.3 ounces (H0: μ < 24.3).
F) The machine fills the boxes with an average of 23.6 ounces (H0: μ = 23.6).
Answers
Answer:
B.
Step-by-step explanation:
The null hypothesis will say that the mean is equal to what it is supposed to be. In this case, each box is supposed to have 24.3 ounces of cereal.
So, your null hypothesis would be that the average is equal to 24.3, or H₀ = 24.3. B.
Hope this helps!
Please help i will mark brainliest
Answers
Answer:
See below.
Step-by-step explanation:
To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:
[tex]y=mx+b[/tex]
From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.
Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]
Therefore, the equation of the line would be:
[tex]y=mx+b\\y=-1/4x-6[/tex]
An angle measuring 5.25 radians is equal to which of the measures given below? Check all that apply. - 300 degrees 48’ - 16.49 degrees - 16degree 24’ -300.8 degree
Answers
Answer:
300.8 degrees
Step-by-step explanation:
in a circle full angle is [tex]2\pi[/tex] radian
In degrees the value of angle is 360.
Thus
[tex]2\pi[/tex] radian is same as 360 degrees
thus
[tex]2\pi[/tex] radian= 360 degrees
dviding both side by [tex]2\pi[/tex]
[tex]2\pi[/tex] / [tex]2\pi[/tex] radian= 360/[tex]2\pi[/tex] degrees
1 radian= 360/[tex]2\pi[/tex] degrees
multiply both side by 5.25
1*5.25 radian= (360/[tex]2\pi[/tex]) * 5.25 degrees
using value of [tex]\pi[/tex] as 3.14 we have
5.25 radian= (360/2*3.14) * 5.25 degrees = 300.8 degrees