Answer:
I'm pretty sure that this one is the correct factorization of the polynomial above: c) (3x+4)(9x^2-12x+16)
(3x−4)⋅(9x
2
+12x+16)
See steps
Step by Step Solution:
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STEP
1
:
Equation at the end of step 1
33x3 - 64
STEP
2
:
Trying to factor as a Difference of Cubes
2.1 Factoring: 27x3-64
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 27 is the cube of 3
Check : 64 is the cube of 4
Check : x3 is the cube of x1
Factorization is :
(3x - 4) • (9x2 + 12x + 16)
Trying to factor by splitting the middle term
2.2 Factoring 9x2 + 12x + 16
The first term is, 9x2 its coefficient is 9 .
The middle term is, +12x its coefficient is 12 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 9 • 16 = 144
Step-2 : Find two factors of 144 whose sum equals the coefficient of the middle term, which is 12 .
-144 + -1 = -145
-72 + -2 = -74
-48 + -3 = -51
-36 + -4 = -40
-24 + -6 = -30
-18 + -8 = -26
For tidiness, printing of 24 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(3x - 4) • (9x2 + 12x + 16)
Answer:
C
Step-by-step explanation:
When factorising the sum of cubes, we use the formula
a^3+b^3=(a+b)(a^2−ab+b^2).
In this case of 27x3+64,
27x^3=a^3
64=b^3
Find a:
27x^3=a^3
3^√27x^3=3^√a^3
3x=a
Find b:
64=b^3
3^√64=3√b^3
4=b
Substitute a=3x and b=4 into
(a+b)(a^2−ab+b^2)
(3x+4)((3x)^2−(3x×4)+4^2)
= (3x+4)(9x^2−12x+16)
(3x+4)(9x^2−12x+16) is the factorised form of 27x^3+64
A package of 4 pairs of insulated socks costs $22.36 . What is the unit price of the pairs of socks ?
Answer:
5.59
Step-by-step explanation:
22.36/4 = 5.59
hope this helps!
A store buys 19 sweaters for $190 and sells them for $532. How much profit does the store make per sweater?
Answer:
They made 342 dollars profit and only buyed them for 10 dollars each
Step-by-step explanation:
$2.80 each sweater
Step-by-step explanation:
Forget the 190, it is not necessary. We are focusing on 19, and 532.
To get the answer, divide 190 by 532. (532 / 190) you will get 2.80. That's how much profit the store makes per sweater.
HELPPPPPPP ME PLSSSSS
Answer:
first one i believe is D
Step-by-step explanation:
sending one should be B
Answer:
SU
R
Step-by-step explanation:
Q1 B is the answer
Q2 B is the answer
what is 2 to the power of 8 minus 10 minus 15 divided by 3
Answer:
241
Step-by-step explanation:
241
Answer:
241
Step-by-step explanation:
2^8 - 10 -15 / 3
256 - 10 - 15 / 3
256 - 10 - 5
246 - 5
241
Hope this helps!
three quantities that depend on time
Answer:
Velocity, Acceleration, Speed
Step-by-step explanation:
PLEASE HELP!! i will mark brainliest!!
Simplify.
(19) ×(12)2
Question 5 options:
118
1324
136
19
A book was $30. The book is now on sale for $15. What is the percent decrease?
Helpp please
Answer:
50%
Step-by-step explanation:
Answer:
The answer is.5 or 50%
Step-by-step explanation:
15 is half of 30 and that means it decreased by half or 50%.
Hopefully this helps you
pls mark brainlest
What is the solution to the equation 5x+0.25= 7x-0.05?
Answer: x=0.15
Step-by-step explanation:
5x+0.25=7x-0.05
5x+0.25-0.25=7x-0.05-0.25
5x=7x-0.3
5x-7x=7x-0.3-7x
-2x=-0.3
-2x/-2 = -0.3/-2
X=0.15
Hope this helps!
Find the volume of the cylinder with the info below.
Distance from center to edge: 3 feet
Side length of the cylinder: 5 feet
Please help me out! I promise I will mark brainliest!
Answer: 141.3 in[tex]{3}[/tex]
1. V = πr[tex]{2}[/tex]h
2. V = (3.14)([tex]3{2}[/tex])(5)
3. V = 141.3 in.
Hope this answer helps you!
What are the slope and the y-intercept of the linear function that is represented by the table?
help me I will give brainiest 10 points
Answer:
1 solution
Step-by-step explanation:
-5(x-1)=25
-5x+5=25
-5x=20
x=-4
Multi-step Equations
5) 5n + 34 = -2(1 - 7n)
Answer:
4
Step-by-step explanation:
if you do all the steps right you should get 4
Help with questions 15. Please i need it ASAP ‼️‼️‼️‼️
Answer:
The first one and the thirds one. (I’m pretty sure)
Step-by-step explanation:
Ayuda por favor es para una tarea!!
Answer:
m<PAT = 41°
m<TAY = 41°
Please order the following from least to greatest! ASAP
0.71, 3/4, 78%, 0.775, 7/9
Answer:
0.71, 3/4, 0.775, 7/9, 78%
Asap plzz i need it in at least in 10 min
Answer:
Step-by-step explanation:
if 12x= 4(x+5), x equals...
distribute the 4 to the x and
12x = 4x + 20
subtract the 4x on both sides
8x = 20
divide by 8
x = 20/8
simplify
x = 5/2
5/2 = 2.5 so the answer is D
Lisa and Lori each dried 1/3 of the glasses. What fraction of the glasses
remains for Katie to dry?
How do you write 7,800 in scientific notation?
Answer:
7.8 x 10^3
Step-by-step explanation:
A rock is tossed vertically from a height of 2m with an initial velocity of 20 ms-1. The height of the rock, h, after t seconds can be modeled by the polynomial function :h(t)=−4.9t2+20t+2, t≥0. Calculate how many seconds, rounded to three significant figures, it takes for the rock to hit the ground.
Answer:
The rock takes 4.18 seconds to hit the ground
Step-by-step explanation:
Function Model
The height of a rock h, after t seconds, can be modeled by the polynomial function:
[tex]h(t)=-4.9t^2+20t+2, t\geq 0[/tex]
When the rock hits the ground, the height is 0, thus we need to find the value of t such as:
[tex]-4.9t^2+20t+2=0[/tex]
A quadratic equation can be expressed as:
[tex]at^2+bt+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The values for the given equation are:
a=-4.9, b=20, c=2
Applying the formula:
[tex]\displaystyle t=\frac{-20\pm \sqrt{20^2-4(-4.9)(2)}}{2(-4.9)}[/tex]
[tex]\displaystyle t=\frac{-20\pm \sqrt{400+39.2}}{-9.8}[/tex]
[tex]\displaystyle t=\frac{-20\pm 20.957}{-9.8}[/tex]
There are two possible solutions:
[tex]\displaystyle t=\frac{-20- 20.957}{-9.8}=4.18[/tex]
[tex]\displaystyle t=\frac{-20+ 20.957}{-9.8}=-0.1[/tex]
Since t > 0, the only solution is t=4.19 seconds
The rock takes 4.18 seconds to hit the ground
There are 90 males and 75 females that came to Jeff's house for a party. Jeff wants to split the males into equal groups and the females into equal groups to play a game. The groups of males and females must have the same amount of people. What is the greatest number of people that can be in each group?
Answer:
15 people
Step-by-step explanation:
We are told that there are 90 males and 75 females.
This question is a greatest common factor question.
We find the factors of 75 and 90
The factors of 75 are: 1, 3, 5, 15, 25, 75
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Then the greatest common factor is 15.
The greatest number of people that can be in each group is 15
x-7(x-2)=10x+9-x
i need the answer asap pls
Step-by-step explanation:
x−7(x−2)=10x+9−x
Step 1: Simplify both sides of the equation.
x−7(x−2)=10x+9−x
x+(−7)(x)+(−7)(−2)=10x+9+−x(Distribute)
x+−7x+14=10x+9+−x
(x+−7x)+(14)=(10x+−x)+(9)(Combine Like Terms)
−6x+14=9x+9
−6x+14=9x+9
Step 2: Subtract 9x from both sides.
−6x+14−9x=9x+9−9x
−15x+14=9
Step 3: Subtract 14 from both sides.
−15x+14−14=9−14
−15x=−5
Step 4: Divide both sides by -15.
−15x−15=−5−15
x=13
Answer:
x=13
6-2x+x+8 giving 50 pts
Answer:
-2=3x
Step-by-step explanation:
Answer:
-2=3x
Step-by-step explanation:
Lamar ordered some books online for 6$ each. He paid a total of 3$ for shipping. The total cost of the purchase was 75$ . How many books did he buy?
Answer:
He bought 12 books.
Step-by-step explanation:
Here is your equation: 6 b+3=75
Step 1- Subtract 3 from both sides: 6 b+3-3=75-3
6 b=72
Step 2- Divide by 6: 6 b/6=72/6
b = 12 books in total.
There are 4 quarters in 1 dollar the total number of dollars is a function of the number of quarters does this situation represent a linear or nonlinear function? Explain why
Answer:
sample answer: If you make a table of values, you can see that 4 quarters equal 1 dollar and 8 quarters equal 2 dollars. If you graph the data, you will see a straight line. Therefore, this situation represents a linear function with a constant rate of change of 1/4
Step-by-step explanation:
The situation is a representation of the linear function.
What is meant by linear function?A linear function is one that, when graphed, produces a straight line. Thus, non-linear functions are any non-linear functions. Although graphing is the quickest way to determine whether a function is linear or non-linear, we can also determine linearity from its input/output table or equation. A straight line on the coordinate plane is represented by a linear function. For example, y = 3x - 2 denotes a straight line on a coordinate plane and, as such, a linear function.Given that,
One dollar is divided into four quarters.
The total number of dollars is a function of the number of quarters.
Based on the information presented above, we can conclude that when the dollar represents y value and the quarter represents x value
As a result, the slope should be 1/4.
y = 1/4x should be the linear function.
Hence, As a result, we can conclude that the situation is a linear function.
To learn more about linear function, refer to:
https://brainly.com/question/15602982
#SPJ2
help i need the answer ASAP
Answer:
you literly break down 10 to 6 then times the answer with 7
Step-by-step explanation:
answer:
i agree the answer is 7!
explanation:
hope this helped <3 also if wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)
What is the slope of the line represented by 5x – 2y = 24?
Answer:
the slope is y=5/2x-12
Find the slope of the line that contains the points:(-6, 3) and (-4,5).
Answer:
Slope:1
Step-by-step explanation:
When finding the slope from 2 points, you subtract them y/x
(-6,3)
(-4,5)
-2,-2
Slope: (-2,-2)=1
y=x+b
Insert on of the the points, in this case, I will choose -6,3
3=-6+b
b=9
So slope intercept form, the answer will be y=x+9.
Since you are just finding the slope, the answer is just 1.
The slope of the line that contains the points:(-6, 3) and (-4,5) is 1.
What is the slope of the line?You could be asked to determine a line's slope when working with linear equations. Knowing the slope formula in that situation is really helpful. Watch this lesson to learn the formula for calculating the slope of a line.
Given the coordinate of the line (-6, 3) and (-4,5).
Hence from the formula of the slope (m) = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
m = (5 - 3) / (-4 + 6)
m = 1
Therefore the slope of the line that contains the given points is 1.
Learn more about slope here:
https://brainly.com/question/15271574
#SPJ6
what is the inverse of function F f(x) 3-x/7
Answer: f^-1(x)=-7x+3 maybe ? i think
Step-by-step explanation:
help please can someone show me how to solve
Answer:
<DBC= 78
Step-by-step explanation:
since you already know what they equal all together
subtract 42 from 120
