Answer:
answer is option C
Step-by-step explanation:
just take 6n as common and divine each value by it
The factored form of expression 6n⁴ - 24n³ + 18n is
6n (n² - 2n + 1) (n² - 2n + 3).
What is an expression?
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
First, we can factor out the greatest common factor of the expression, which is 6n:
6n(n³ - 4n² + 3n)
Next, we can factor the expression inside the parentheses by grouping:
n³ - 4n² + 3n = n²(n-4) + 3(n-4) = (n²+3)(n-4)
Substituting this back into the original expression.
6n (n² + 3) (n - 4)
However, we can further simplify by noticing that the expressions
(n² - 2n + 1) and (n² - 2n + 3) are both equivalent to (n - 1)² + 1 and (n - 1)² + 2, respectively.
Thus,
The factored form can also be written as 6n [ (n - 1)² + 1 ] [ (n - 1)² + 2 ]
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. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2)
Answer:
12
Step-by-step explanation:
Input interpretation: triangle | vertex coordinates (-3, 5) | (-3, 2) | (1, 2) | perimeter
Result: 12
Properties of Triangle:
edge lengths | 3 | 4 | 5 area | 6perimeter | 12interior angles | (cos^(-1)(4/5) rad | cos^(-1)(3/5) rad | π/2 rad)≈(0.643501 rad | 0.927295 rad | 1.5708 rad)interior angle sum | 180° = π rad≈3.142 radWhich expression is equivalent to \frac{r^9}{r^3}
Answer: [tex]\frac{r^9}{r^3} = r^{9-3} = r^6[/tex]
We subtract the exponents when dividing terms with the same base.
The general rule is [tex]\frac{a^b}{a^c} = a^{b-c}[/tex]
Hii!
___________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
r^6
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
To simplify this we need to use the division property of exponents:
[tex]\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}[/tex]. So if we divide two numbers with the same base, we subtract their exponents.
Let's apply this rule here.
[tex]\twoheadrightarrow\sf r^9\div r^3[/tex].
[tex]\bullet[/tex] Since these two numbers have the same base, we subtract their exponents
[tex]\twoheadrightarrow\sf r^6[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
show that the radius of B is 2.5cm
Answer:
how?
Please Attach Figure so someone can Solve...
Step-by-step explanation:
2^-4 simplified form
Answer:
1/16 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Answer:
Step-by-step explanation:
The table and the graph below each show a different relationship between the same two variables, x and y.
How much more would the value of y be on the graph than its value in the table when x = 12?
Answer:
240
Step-by-step explanation:
Using the straight line formula; y=mx+c, take two points, for example, (4, 80) and (5, 100)
m=change in y/change in x, so;
m=(100-80)/(5-4)= 20
Take point (4, 80)
80=20×4 + c
80-80=c=0
so y=20x
y=20×12=240
Triangle A B C is cut by line segment S T. Line segment S T goes from side A B to side C B. Lines S T and A C are parallel. The length of S B is 10 feet, the length of B T is 9 feet, and the length of C T is 2.7 feet.
What is the length of Line segment S A?
1.89 ft
2.43 ft
3 ft
7 ft
In the triangle ABC, the length of the line segment SA=3 ft ( 3rd option).
In triangle ABC,
SB=10ftBT=9ftCT=2.7ft &ST|| ABAccording to the triangle proportionality theory, we know that if a triangle has a line segment parallel to one of its sides, the line segment splits the other sides correspondingly.
Hence,
SA/SB=CT/BT
⇒SA/10=2.7/9
⇒SA=(2.7*10)/9
⇒SA=3
So, the length of SA is 3 ft.
Therefore the 3rd option is correct.
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Find the least common denominator for these
two rational expressions.
8
-9
3a²
-
a
The common denominator is 3a²
(Giving 45 points, and brainly if correct! Please hurry!)
Point A is on point −6 and Point B is on point 0. Let's use the Ruler Postulate to find the length of AB¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯ is 6. We can also write this as AB=6 or mAB¯¯=6.
Find the Length of CD¯¯
Now, let's find the length of CD¯¯. Point C is on point 4 and Point D is on point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯ is 4. We can also write this as CD=4 or mCD¯¯=4
Your Turn
1. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD¯¯?
The length of BC , AC and AD is 4 , 10 , 14.
What is Length ?Length is the distance between two points , It is measured in cm , m , km etc.
It is asked to calculate the length of BC , AC , AD
For BC
Point B is on point 0 and Point C is on point 4.
BC=|b−c|
BC=|0−4|
BC=4
For AC
Point A is on point -6 and Point C is on point 4.
AC=|a−c|
AC=|-6−4|
AC= 10
For AD
For AC
Point A is on point -6 and Point D is on point 8.
AD=|a−c|
AD=|-6−8|
AD= 14
Therefore the length of BC , AC and AD is 4 , 10 , 14.
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Here is a table giving the number of US households (in thousands) in 2013 by tenure and insurance status:
Insurance status
Owns home
Rents home
Insured
71
13
Uninsured
5
27
Find the marginal distribution of tenure in counts.
Owns home:
Rents home:
The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
For the given data the table can be made as shown below. The marginal distribution of tenure in counts can be calculated as,
Owns home = 71 + 5 = 76
Rents home = 13 + 27 = 40
Hence, The marginal distribution of tenure in counts who owns a home is 76, while those who rent a home is 40.
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Please hurry
How could you solve this problem?
2 × 3 × 4
Check all that are true.
Multiply 3 × 4 to get 12 and then multiply 12 × 6.
Multiply 2 × 3 to get 6 and then multiply 6 × 12.
Multiply 3 × 4 to get 12 and then multiply 12 × 2.
Multiply 2 × 3 to get 6 and then multiply 6 × 4.
Multiply 2 × 3 to get 6, multiply 3 × 4 to get 12, and then multiply 6 × 12.
Answer:
multiply 2×3 to get 6and then multiply 6×4 to get 24
Answer:
Multiply 3 × 4 to get 12 and then multiply 12 × 2.
Multiply 2 × 3 to get 6 and then multiply 6 × 4.
Explanation:
Original Answer : 2 × 3 × 4 = 24
1) 12 × 6 = 72
2) 6 × 12 = 72
3) 12 × 2 = 24
4) 6 × 4 = 24
5) 6 × 12 = 72
Hence, only option 3 and 4 is correct.
Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.” She then evaluated the expression when n = 2. Which statements are true about the expression and its value? Check all that apply.
The correct expression is 82 minus StartFraction 24 Over n EndFraction.
To evaluate the expression, subtract 26 from the quotient.
To evaluate the expression, subtract the quotient from 82.
The correct expression is StartFraction 82 Over n EndFraction minus 26.
The operations include division and subtraction.
To evaluate, substitute 24 for the variable in the equation.
The value of the expression is 15.
The correct expression is (82/n) - 26 ,The operations include division and subtraction , To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15 , Option D, E and F is the answer.
What is an Expression ?An expression is the mathematical statement consisting of variables , constant and mathematical operators .
It is given that the expression has to be formed from the data
the quotient of 82 and a number, decreased by 26
Let the number from which it is divided is n then
quotient * divisor = 82
quotient = 82 /n
(82/n) - 26 is the expression formed from the data
When n =2
the expression value is
41 -26
15
The correct expression is StartFraction 82 Over n EndFraction minus 26.
The operations include division and subtraction.
To evaluate, substitute 2 for the variable in the equation , the value of the expression is 15.
Therefore Option D, E and F is the answer.
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Answer:D.E.F
Step-by-step explanation:
Mei Mei left her house at time zero and drove for 4 minutes to the store, at a speed of 2 blocks per minute. Then she stopped and went into the store for 5 minutes. From there, she drove in the same direction at a speed of 5 blocks per minute until she got to the bank, which is 10 blocks away from the store. She stopped at the bank for 2 minutes. Then she drove home at a speed of 3 blocks every minute. Make a graph of showing the number of blocks away from home that Mei Mei is xx minutes after she leaves her house, until she gets back home.
The graph for Mei Mei' trip is attached accordingly. Also attached are the values derived from the question.
What is the explanation for the graph?The secret to comprehending the graph is to understand that every time Mei Mei spent while she was on the way to bank and back were are all computed cumulatively.
This means that when she stops at the store which is 8 blocks away from home (that is 2 blocks per min x 4 mins = 8blocks) the time spent is recorded as 4 + 5 at location 8 blocks, which is equals 9 minutes.
Also take note of the fact that the time spent is plotted on the x-axis and the blocks away from home on the y-axis.
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Need help and a better understanding
Find the value of x that makes the triangle a right triangle.
A
12
B
13
C
15
D
17
[tex]12^2+9^2=x^2\\144+81=x^2\\x^2=225\\x=15[/tex]
if f(x)=-3x-5 and g(x)=4x-2 find (f-g) (x)
If f(x)=-3x-5 and g(x)=4x-2, then the value of (f-g)(x) is -7x-3.
The given functions are f(x)=-3x-5 and g(x)=4x-2.
We need to find the value of (f-g)(x)
What is a function?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now, (f-g)(x)=f(x)-g(x)=(-3x-5)-(4x-2)
= -3x-5-4x+2 = (-3x-4x)+(-5 + 2)
= -7x-3
Therefore, the value of (f-g) (x) is -7x-3.
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Evaluate if: A= -3 , B= -4, and c= 2/3
1. ABC - 15
2. B/C-|A|
(Pic included, must show work asap!)
Answer:
please mark me as brainlest
can you answer this question using simultaneous equations the substitution method
Answer:
a) a=17/16, b=3/8 (17/16, 3/8)
b) x=12/17, y=25/17 (12/17, 25/17)
Step-by-step explanation:
I attached the work for solving the equations with substitution method... Sorry it took a bit of time and this would've been easier if the question's asking for elimination lol
Joe kept track of how much TV she watched each day for two weeks how many hours did she spend watching TV
The total hours joe spent watching TV each day for two weeks is 12 1/2 hours
Total hours spent watching TVTotal hours spent watching TV for two weeks = Number of hours × days
= (0 × 1) + (1/4 × 1) + (1/2 × 1) + (3/4 × 3) + (1 × 3) + (1 1/4 × 4) + (1 1/2 × 1)
= 0 + 1/4 + 1/2 + 9/4 + 3 + 5 + 3/2
= 8 + (1+2+9+6) / 4
= 8 + 18/4
= 8 + 4 2/4
= 8 + 4 1/2
= 12 1/2 hours
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PLEASE HELP! I WILL MARK BRAINLIEST! Which type of lines is shown in the illustration above?
A. parallel lines
B. perpendicular lines
C. skew lines
D. intersecting lines
Answer:
D. Intersecting lines.
Step-by-step explanation:
The lines are intersecting each other.
The reason it is not perpendicular lines is because perpendicular lines have 90° angles.
Hope this helps!
If not, I am sorry.
Assessing the regression model on data other than the sample data that was used to generate the model is known as _____. Group of answer choices approximation cross-validation graphical validation postulation
Assessing the regression model on data other than the sample data that was used to generate the model is known as cross-validation
How to complete the blank?From the question, we have the following highlights:
Sample data, not usedThe model is a regression modelWhen the sample data is not used in a regression model, then the term is known as cross-validation.
Hence, the term that completes blank is cross-validation
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If sin(theta) = 4/7, what is cos(theta)? PLEASE HELP!
Step-by-step explanation:
sin(theta)=4/7
cos(theta)=√1-sin²theta
=√1-(4/7)²
=√1-16/49
=√(49-16)/49
= √33/49
=(√33)/7
Can someone please help me with this question?
The correct answer will be option D which is the value of D will be [tex]\left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right][/tex]
What is the matrix?A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.
The value of D will be calculated by multiplying the matrix if we get a unit matrix that will be the answer.
[tex]=\left[\begin{array}{cc}-9&-11&\\5&-6\\\end{array}\right]\times \left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right] \\\\\\=\left[\begin{array}{cc}(-54+55)&(99-99)&\\-(-30+30)&(55-54)\\\end{array}\right]\\\\\\=\left[\begin{array}{cc}1&0&\\0&1\\\end{array}\right][/tex]
Therefore the correct answer will be option D which is the value of D will be [tex]\left[\begin{array}{cc}-6&11&\\-5&9\\\end{array}\right][/tex]
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Henry leads a team of hikers for a full-day hike that takes 8 hours. Every hour, the hikers gain 250 feet in elevation. • The independent variable is ____, ________ in ________. • The dependent variable is _____, increased elevation in feet, or __________. A possible verbal description is “____ equals 250 times ____.” The equation ______ = ___________ corresponds to this relationship.
The missing blanks have been filled.
What is a Function ?A function is a mathematical statement used to relate a dependent and an independent variable.
It is given that
Total time taken to hike is 8 hours
Let the time taken in hours is represented by t
and the elevation is represented by h
Every hour, the hikers gain 250 feet in elevation.
The independent variable is t , time taken to hike , in hours .
The dependent variable is h , increased elevation in feet or elevation the hikers have gained .
A possible verbal description is Elevation at any given time equals 250 times the time taken to hike.
The equation h = 250 t corresponds to the relationship.
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5 m
2m
6 m
2 m
Mrs Phillips is going to cover the floor with floor boards.
One pack of floor boards will cover 2.5 m².
How many packs of floor boards does she need?
You must show your working.
Diagram NOT
accurately drawn
Mrs. Phillips needs to buy 8 packs of floor boards
In contrast to a square, a rectangle is a planar figure having four equal neighboring sides, four straight sides, and four right angles. An enclosed 2-D form called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposing sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.
As per the figure attached Mrs. Phillips floor plan can divided into two rectangles
The area of rectangle is as follow:
Area = length(l) x Width(w)
Area of part 1 will be:
A = 6 x 2 = 12 m²
Area of part 2 will be :
a = 3 x 2 = 6 m²
Total area of floor = A + a
Total area of floor = 12 + 6
Total area of floor = 18 m²
Given one pack of floor boards will cover 2.5 m².
So total pack of floor block needed will be as follow:
Total pack of floor block = Total area of floor/Area covered by one pack of floor boards
Total pack of floor block = 18/2.5
Total pack of floor block = 7.2 packs ≈ 8 packs
Hence Mrs. Phillips needs to buy 8 packs of floor boards
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The line contains the point (5,0) and is parallel to the line defined by "-3x=4y"
Answer:
Step-by-step explanation:
The angle of depression from the hot-air
balloon to the car is 34°.
How high is the hot-air balloon flying?
Give your answer to 2 s.f.
6400 feet
Not drawn accurately
Answer:
Ans : 3578.83 feet from the ground
Step-by-step explanation:
You can use sine theory so
sine 32 = height/6400
6400 x sine 32 = height
Easy
Rewrite the polynomial in the form ax² + bx+c and then identify the values of a,
b, and c.
x
6
4x² +1
1. Identify your variables using let statements.
2. Determine the equations for the linear system.
3. Determine the solution to the linear system (point of intersection)
4. Explain the meaning of the solution using a therefore statement.
You own a catering company and are in charge of an engagement party. There are two dinners: a chicken dish, which costs $40, and a lobster dish, which costs $70. The 250 party guests have ordered their meals in advance, and the total cost to prepare the dinner is $13 570. How many of each type of dinner are you preparing?
The number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes
How to find the number of each type of dish.Let
x = number of chicken dish and y = number of lobster dishHow to determine the equations for the linear systemSince it cost $40 per dish for chicken dish, the total cost of chicken dish is 40x.
Also, since it cost $70 per dish for lobster dish, the total cost of lobster dish is 70y
So, the total cost of dish is T = 40x + 70y
Also, we know that the total cost of dish is $13,570.
So, 40x + 70y = 13570 (1)
Also, there are going to be 250 guest at the dinner and thus 250 dishes.
So, the total number of dishes is x + y = 250
So, x + y = 250 (2)
So, the equations of the linear system are
40x + 70y = 13570 (1)
x + y = 250 (2)
How to determine the solution for the linear systemSince
40x + 70y = 13570 (1)
x + y = 250 (2)
From (2), x = 250 - y
Substituting x into (1), we have
40x + 70y = 13570 (1)
40(250 - y) + 70y = 13570 (1)
10000 - 40y + 70y = 13570
30y = 13570 - 10000
30y = 3570
y = 3570/30
y = 119
Substituting y = 119 into x, we have
x = 250 - y
x = 250 - 119
x = 131
Therefore, the number of chicken dish is 131 dishes while the number of lobster dishes is 119 dishes
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A survey of 100 high school students provided this
frequency table on how students get to school:
Drive to Take the
Grade
Walk
School
bus
Sophomore
2
25
3
Junior
13
20
2
Senior
25
5
5
What is the probability that a randomly selected student
is a junior?
?
P (Junior)
=
Answer:
35/100
Step-by-step explanation:
You have to find how many juniors there are, so if you add 13, 20, and 2 you get 35. For the denominator you have to find the total number of students, so just add all of the numbers together to get 100. So there is a 35/100 chance that a randomly selected student is a junior.
Answer: 7/20
Step-by-step explanation:
The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?
The true statement is the circle has the radius equal to 7.
What is Equation of circle?The general equation for a circle is (x-h)² + (y-k)² = r², where ( h, k ) is the center and r is the radius.
As, standard form of equation of circle is
(x-h)² + (y-k)² = r²
At origin, equation of circle will be
(0-h)² + (0-k)² = r²
r² = x² + y²
Now, The line intersects the circle at (0,7)
r² = 0² + 7²
r² =49
r=7.
Hence, the circle has the radius equal to 7.
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