When using the identity for the sum of two cubes to factor 125q^6-r^6s^3
Answers
Answer:
a = 5q²
b = r²s
Step-by-step explanation:
The given identity is \(a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})\)
we have to use this identity to factor of two cubes given as \(125q^{6}-r^{6}s^{3}=(5q^{2})^{3}-(r^{2}s)^{3}\)
As this expression is in the form of a³- b³
Here a is 5q² and b is r²s.
Answer:
a=5q2 b=r2s the expression factored is also (5q2-r2s) (25q4+5q2r2s+1r4s2)
Step-by-step explanation:
Related Questions
3 new books and 8 used books what is the ratio
Answers
Answer:
3:8
Step-by-step explanation:
brainlest???
Answer:
3:8
8:3
11:8
8:11
11:3
3:11
Step-by-step explanation:
i put all the possible answers
stay blessed and positive
what is the answer to my math problem. Evaluate 32^1/5
Answers
the answer is 2
Solution:
32⅕
(2⁵)⅕
Answer is 2
Question The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020. Find the percent decrease of the population of North Dakota. (Round to the nearest tenth of a percent.)
Answers
Answer: 6.25%
Step-by-step explanation:
Percent Decrease = ( ( Starting Value - Final Value ) / Starting Value ) * 100
So 672,000-630000 = 42,000
42,000 / 672,00 = 0.0625
Finally multiply by 100 soooooo 0.0625 * 100 = 6.25%
Henri necesita empacar en la menor cantidad de de cajas, cinta de color rojo y cinta de color verde si hay 120 metros de cinta de color rojo y 160 metros de cinta de color verde ¿que cantidad de cinta roja y verde deberá empacar Henri en cada caja?
Answers
Answer:
Step-by-step explanation:
Which transformations could have occurred to map △ABC to △A"B"C"?a rotation and a dilationa rotation and a reflectiona reflection and a dilationa translation and a dilation edg 2022
Answers
Answer:
D, dialation and rotation on edge
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Determine the amount of money you need to invest to accumulate $7,000 dollars in 4 years if you invest it at 2.5% annual interest, compounded quarterly.
Answers
An initial investment of $5,951.71 is needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly.
To determine the amount of money needed to accumulate $7,000 in 4 years with 2.5% annual interest compounded quarterly, we need to use the formula for compound interest.
The formula is A = P(1+r/n)^(nt), where A is the final amount, P is the initial investment, r is the interest rate, n is the number of times compounded per year, and t is the number of years.
Using the given information, we can plug in the values and solve for P. A = $7,000, r = 0.025, n = 4, and t = 4.
A = P(1+r/n)^(nt)
A = P(1+0.025)^4
$7,000 = P(1+0.025/4)^(4*4)
$7,000 = P(1.00625)^16
P = $5,951.71
To learn more about : investment
https://brainly.com/question/29227456
#SPJ8
f(x)=3x^0.4 find f(32)
Answers
Katie received a speeding ticket that incurred a $125 fine. After one month, she will also
be charged late fees for every month that she is delinquent. The amount she pays is
modeled by an exponential function, and the following table reflects the amount she will
have to pay each month.
Month Paid
Amount Paid
$125
1
2
3
$137.50
$151.25
$166.38
4
a. Write a function that models the fine Katie will pay in terms of the month it is paid. (5
points)
b. Using your function, predict how much Katie will pay if she waits until month 12 to pay
her fine. (5 points)
Answers
Answer:
Try A
Step-by-step explanation:
What is the completely factored form of this polynomial x^4 + 12x^2 + 32
Answers
ANSWER
\((x^{2}+4)(x^{2}+8)\)EXPLANATION
We want to completely factor the given polynomial:
\(x^4+12x^2+32\)To do this, we have to find two terms whose product is 32 and whose sum is 12.
The two terms are:
\(x^4+8x^2+4x^2+32\)Now, factor completely:
\(\begin{gathered} x^2(x^2+8)+4(x^2+8) \\ (x^2+4)(x^2+8) \end{gathered}\)That is the answer.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.
We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding
m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.
m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.
m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).
m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.
m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.
Based on the above analysis, the statements that are always true regarding the diagram are
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 = 180°
m∠2 + m∠3 + m∠5 = 180°
Therefore, the correct options are B, C, and E.
To know more about triangle:
https://brainly.com/question/28835566
#SPJ1
Oliver did the high jump three times. His scores were 7.016 feet, 5.42 feet, and 8.308 feet. How many feet did he jump in total? pleas help im in test
Answers
The total height of the three jumps is A = 20.744 feet
Given data ,
1st high jump score: 7.016 feet
2nd high jump score: 5.42 feet
3rd high jump score: 8.308 feet
On adding the scores , we get
7.016 + 5.42 + 8.308 = 20.744 feet
On simplifying the equation , we get
A = 20.744 feet
Hence , Oliver jumped a total of 20.744 feet in the three high jumps
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
Answers
The values of variables a to d are
a = 1 and c = 1, b = -3 and d = -5a = 1 and c = 1, b = 2 and d = -6a = 1, b = 2. c = 6 and d = 2How to determine the values of the variablesPolynomial 1
This is given as
x² - 8x + 15 = (ax + b)(cx + d)
The factors of 15 that add up to -8 are
-3 and -5
This means that
b = -3 and d = -5
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 2
This is given as
2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
Divide through by 2x
x² - 4x - 12 = (ax + b)(cx + d)
The factors of -12 that add up to -4 are
2 and -6
This means that
b = 2 and d = -6
Because the coefficient of x² is 1, then
a = 1 and c = 1
Polynomial 3
This is given as
6x² + 14x + 4 = (ax + b)(cx + d)
Factorize
(x + 2)(6x + 2) = (ax + b)(cx + d)
By comparison, we have
a = 1, b = 2. c = 6 and d = 2
Read more about polynomial at
https://brainly.com/question/7693326
#SPJ1
Help me with this question no explanation needed or just give it to me
Answers
Answer:
Step-by-step explanation:
No explanation is needed because there is no question.
Answer:
you got it
Step-by-step explanation:
no explanation needed
Write the equation of the line that goes through the points A(3,-2) and B(5,4)
Answers
Answer:
y = 3x - 11
Step-by-step explanation:
(3, -2) and (5, 4)
m = 4+2/5-3
m = 6/2
m = 3
y = 3x + b
4 = 3(5) + b
4 = 15 + b
b = -11
y = 3x - 11
What will be the
surface area of the
ramp
50 in.
60 in.
O 3672 inches squared
O 5760 inches squared
O 7392 inches squared
O 2880 inches squared
Answers
The surface area of the ramp is 3672 in².
Option A is the correct answer.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The ramp consists of three rectangular surfaces and two triangles.
Now,
Triangle.
Base = 48 in
Height = 14 in
Area of a triangle.
= 1/2 x base x height
= 1/2 x 48 x 14
= 48 x 7
= 336 in²
Rectangle.
Since the back and the bottom rectangle are not included.
Front rectangle.
Length = 50 in
Width = 60 in
Area = 50 x 60
Area = 3000 in²
Now,
The surface area of the ramp.
= 300 + 2 (336)
= 3000 + 672
= 3672 in²
Thus,
The surface area of the ramp is 3672 in².
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
Find the value of x in the diagram below. Classify
Answers
Answer:
x = 31.3
Step-by-step explanation:
100° and (3x + 6)° are vertical angles. Vertical angles are congruent.
To find the value of x, set both equal to each other.
3x + 6 = 100
3x = 100 - 6 (subtraction property of equality)
3x = 94
x = 94/3 (division property of equality)
x = 31.3 (nearest tenth)
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of
your response as Part A, Part B, and Part C.
Part A: Suppose event A and event B are mutually exclusive. Is the statement P(A and B)-0 true?
Part 9: Explain why or why not to support your answer to Part A.
Part C: Provide an example to support your explanation.
Answers
Part A :
Yes, the statement is true that P( A and B ) = 0 .
Given,
Event A and Event B are mutually exclusive.
Thus P ( A and B ) = 0
Part B:
A and B are mutually exclusive events if they do not occur at the same time.
This means that A and B do not share any common outcomes and
P(A and B) = 0.
Part C:
Let,
The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.
A and B do not have any numbers in common so P(A and B) = 0.
Hence, A and B are mutually exclusive.
Learn more about Probability,
https://brainly.com/question/29492440
#SPJ1
A car shop has 12 mechanics, of whom 8 can work on transmissions and 7 can work on brakes. a) What is the minimum number who can do both? b) What is the maximum number who can do both? c) What is the minimum number who can do neither? d) What is the maximum number who can do neither?
Answers
Answer:both a and b are correct
Step-by-step explanation:
Annabelle is going to a carnival that has games and rides. Each game costs $1.75 and each ride costs $3.50. Annabelle spent $28 altogether at the carnival and the number of games she played is 7 more than the number of rides she went on. Graphically solve a system of equations in order to determine the number of games Annabelle played, x,x, and the number of rides Annabelle went on, yy.
Answers
Answer:
$15.75
Step-by-step explanation:
1.75 x 7 = 12.25
28 - 12.25 = 15.75
Add dollar sign. Final answer is $15.75
Answer:
y=-1/2x+8
y=x-7
(10,3)
10 games played and 3 rides
Step-by-step explanation:
Which statement is false?
A. Linear pairs are two supplementary angles that are adjacent.
B. Complementary and supplementary angles must share a common side.
C. Acute angles measure between 0° and 90°.
D. Vertical angles are congruent.
Answers
The answer choice which represents a statement which is false among the given answer choices as required to be determined is; Choice B; Complementary and supplementary angles must share a common side.
Which answer choice represents a statement which is false?It follows from the task content that the statement which represents na false statement is to be identified among the given answer choices.
First, acute angles have measures between 0 and 90° and hence, Choice C is correct.
Also, vertical angles are congruent and their measures are equal. Choice D is true.
Also, it is noteworthy to know that; If two supplementary angles are adjacent to each other; then they are called linear pair. Hence, Choice A is correct.
However, complementary and supplementary angles are angles whose sum amount to 90 and 180 respectively and do not necessarily need to share a side.
Therefore, Choice B represents a statement which is false.
Read more on complementary and supplementary angles;
https://brainly.com/question/14941189
#SPJ1
PLZ HELP WILL GIVE BRAINLYIST
Answers
Answer:
400 40
Step-by-step explanation:
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Answers
Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
The sides of which diagram are correctly labeled with respect to angle A?
A right triangle is shown. Angle A is opposite to the side labeled adjacent.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled opposite. The side labeled adjacent is opposite to the right angle.
A right triangle is shown. Angle A is opposite to the side labeled hypotenuse. The side labeled adjacent is opposite to the right angle.
Answers
9514 1404 393
Answer:
(b) Angle A is opposite to the side labeled opposite. The hypotenuse is opposite to the right angle.
Step-by-step explanation:
The hypotenuse is always opposite the right angle.
The side considered "opposite" is opposite the angle of interest, angle A in this case.
Answer:
Other person is correct
Step-by-step explanation:
What is the volumein cubic in, of a cylinder with a height of 20in and a base radius of 6in to the nearest tenths place ?
Answers
Answer:
\(Vc = 2,261.9\ in^3\)
Step-by-step explanation:
Volume of a Cylinder
The volume of a cylinder of radius r in and a height h can be calculated by:
\(Vc=\pi\cdot r^2\cdot h\)
The height of the cylinder is h = 20 in and the base radius is r = 6 in, thus:
\(Vc=\pi\cdot 6^2\cdot 20\)
\(Vc = 2,261.9\ in^3\)
in the expression 7a + b-12 which is a constant
Answers
Answer: Its -12
Step-by-step explanation:
In Algebra, a constant is a number on its own.
you bought a magazine for 6 dollars and three candy bars you spend a total of 12 dollars how much did each candy cost?
Plssss help
Answers
Answer:
$2
Step-by-step explanation:
step 1: 12-6=6
Step2: 6 divided by 3
what's the steps used to solve modeling problems in the correct order
Answers
Answer:
see below
Step-by-step explanation:
The first step is to read the problem
Then you need to make a plan
Implement the plan
Then evaluate the answer to see if it makes sense
Please see the attached
Answers
(a). The Tanakas paid a total of $523,906.40 for the townhome.
(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.
What is simple intresst?Simple interest is the type of interest that is calculated on the principal amount only.
It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.
(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.
Down payment = $41,000
Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40
Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40
(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.
Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000
Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40
To know more about interest visit:
https://brainly.com/question/29185625
#SPJ1
An isosceles triangle has an angle that measures 136°. What measures are possible for the other two angles? Choose all that apply.
Answers
Answer:
The other two angles are 22° , 22°
Step-by-step explanation:
To find the other angles, we can use angle sum property of triangle.
The given angle 136° cannot be base angles. Let the base angles be x.
x + x + 136 = 180°
2x + 136 = 180°
Subtract 136 from both sides,
2x = 180 - 136
2x = 44°
Divide both sides by 2,
x = 44 ÷ 2
\(\sf \boxed{x = 22^\circ}\)
Answer:42
Step-by-step explanation:
just addThe position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?
14 sec
15 sec
16 sec
17 sec
Answers
Answer: 15 seconds
Step-by-step explanation: Set both equations equal to each other to solve for the time when both trains would be side-by-side.
14t²=130t+1200
14t²-130t-1200=0
x=\(\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\\)and/or\(\frac{-b-\sqrt{b^{2}-4ac } }{2a} \\\)
a=14, b=-130, c=-1200
x=\(\frac{-(-130)+\sqrt{(-130)^{2}-4(14)(-1200) } }{2(14)} \\\)and/or\(\frac{-(-130)-\sqrt{(-130)^{2}-4(14)(-1200) } }{2(14)} \\\)
x=\(\frac{130+\sqrt{290^{2} } }{28} \\\) and/or \(\frac{130-\sqrt{290^{2} } }{28} \\\)
\(x_{1\\}\)=\(\frac{130+290}{28}\) and \(x_{2}\)=\(-\frac{40}{7}\)
\(x_{1\\}\)=15 seconds and \(x_{2}\)=\(-\frac{40}{7}\)
The value \(x_{2}\) can be discarded because it is negative. Both trains are parallel at 15 seconds.