The remainder of the equation is [tex]\rm x+1[/tex].
Given that,
When the equation is [tex]x^3+1[/tex] divided by [tex]x^2-x+1[/tex].
We have to determine,
The remainder for the equation?
According to the question,
The equation [tex]x^3+1[/tex] is divided by [tex]x^2-x+1[/tex].
On the division of the polynomial, the remainder is,
[tex]\dfrac{\rm x^3+1}{x^2-x+1}[/tex]
Factorize the equation to convert this into the simplest form,
[tex]\rm = x^3+1\\\\=x^3-x^2+x + x^2-x+1\\\\= x ( x^2-x+1) + 1(x^2-x+1)\\\\= (x+1) (x^2-x+1)[/tex]
Now, the equation can be written as,
[tex]\rm = \dfrac{(x+1) (x^2-x+1) }{ x^2-x+1}\\\\= x+1[/tex]
Hence, The required remainder of the equation is [tex]\rm x+1[/tex].
For more details refer to the link given below.
https://brainly.com/question/25880057
Answer: a
Step-by-step explanation:
on edge
If x < -4, then -4 is a solution.
True
False
Answer:
true
Step-by-step explanation:
the less than or equal to sign (≤) means that -4 is a solution. if it was the less than sign (<) then -4 would not be included
Answer:
i believe it would be true
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
carter construction has been asked to pave the parking lot of a local bank. how many square feet of pavement will they need to cover the whole parking lot?
Last month, Korey’s Comics had $4,350 in net sales with a gross profit of $3,320 and a net income of $1,850. Calculate Korey’s net profit margin. A. 42. 5% b. 55. 7% c. 76. 3% d. 179. 5%.
Korey's net profit margin is 42.5%.
Net profit margin is the ratio of net income to net sales. It is a profitability ratio. Profitability ratios measure the efficiency with which a company generates profit from its asset.
Net profit margin = net income / net sales
Net profit margin = $1850 / $4350 = 0.425 = 42.5%
A similar question was answered here: https://brainly.com/question/5990973
Answer:
A. 42.5%edge⬇️
Explain what similarity means in terms of congruence and proportionality.
Answer: Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size.
Step-by-step explanation: pls give brainlist
Can someone help me on this plzzz show work please
Answer:
That is the answer
The answer is
Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x inches, from each
corner and then fold each side up to form the box. If Jeremy wants the volume of the box to be 432 cubic inches, what should the minimum length
of the sides of the squares cut from each corner be? Find the volume of the box as a function of x. Given: V = length x width x height
a.
The volume of the box V = 4x³ - 72x² + 324x
Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.
Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x
= (18 - 2x)²x
= (324 - 72x + 4x²)x
= 324x - 72x² + 4x³
The volume of the box V = 4x³ - 72x² + 324x
b.
The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.
the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.Since the volume of the box is 432 cubic inches,
V = 324x - 72x² + 4x³
324x - 72x² + 4x³ = 432
4x³ - 72x² + 324x - 432 = 0
x³ - 18x² + 81x - 108 = 0
A factor of the expression is x - 3
So, x³ - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36
So, x³ - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0
Factorizing the expression x² - 15x + 36 = 0
x² - 3x - 12x + 36 = 0
x(x - 3) - 12(x - 3) = 0
(x - 3)(x - 12) = 0
So, x³ - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0
So, (x - 3)²(x - 12) = 0
(x - 3)² = 0 and (x - 12) = 0
x - 3 = √0 and x - 12 = 0
x - 3 = 0 and x - 12 = 0
x = 3 twice and x = 12
Since x = 3 is the minimum value, the minimum value of x = 3.
Since the length of the box, L = 18 - 2x
= 18 - 2(3)
= 18 - 6
= 12 inches
The width of the box = L = 12 inches
The height of the box = x = 3 inches.
So,
The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.
the length of the box, L = 12 inches, the width of the box = 12 inches and the height of the box, x = 3 inches.Learn more about volume of a box here:
https://brainly.com/question/13309609
Given points A(6,4),B(-2,1)and C(5,0), graph triangle ABC and its reflection image across each line. The x-axis
Answer:
A’ (6, -4)
B’ (-2, -1)
C’ (-5, 0)
Step-by-step explanation:
When reflecting anything across the x, the x values stay the same and the y values become opposites. When reflecting anything across the y, the x values become the opposites and the y values stay the same.
The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Reflection is the flipping of a figure. If a point A(x, y) is reflected across the y axis, the new point is at A'(x, -y). Given the vertices of the triangle at A(6,4), B(-2,1) and C(5,0).
The reflection of triangle ABC across the x axis has vertices at A'(6,-4), B'(-2,-1) and C'(5,0).
Find out more on reflection at: https://brainly.com/question/14062035
Place the steps to solve 2(x + 3) - 5x > 18 in order.
Answer:
-4
Step-by-step explanation:
That's the answer above
Luke cut down a tree that was 27.6 feet tall. Then he cut the tree into 6 equal pieces to take it away. What is the length of each piece?
Answer:
4.6 feet (explanation of division)
Answer:
The length of each piece is 4.6 feet
Step-by-step explanation:
You have an account that starts at $2500 with an interest rate of 3.25% compound yearly. How much is in the account after 10 years? Round your answer to the nearest hundredth.
Answer:3,312.50
Step-by-step explanation:1. We assume, that the number 2500 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 2500 is 100%, so we can write it down as 2500=100%.
4. We know, that x is 3.25% of the output value, so we can write it down as x=3.25%.
5. Now we have two simple equations:
1) 2500=100%
2) x=3.25%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
2500/x=100%/3.25%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
2
Question 7(Multiple Choice Worth 1 points)
(04.04LC)
Point P on the coordinate grid below shows the location of a stage light. A second stage light is 6 units above P. The length of each square on the grid is
2 units. What are the coordinates of the location of the second stage light?
2
16-14-12-1046
012101
O (8.-10)
O (8,2)
(14,2)
(14.-10)
Answer:
Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)
write the equation of the line in fully simplified slope-intercept form
y= -4x-5 you can find this by seeing how far it goes up/down and where it starts:)
If f(x) = x2 - 1 and g(x) = 2x - 3, what is the domain of (fog)(x)?
Answer:
domain will be ( -∞, ∞)
Step-by-step explanation:
The given functions are f(x) = x² - 1 and g(x) = 2x - 3
We have to find domain of (fog)(x)
We will find the function (fg)(x) first.
(fog)(x) = f[g(x)]
= (2x - 3)²
= 4x² + 9 - 12x - 1
= 4x² - 12x + 8
= 4 (x² - 3x + 2)
The given function is defined for all values of x.
Therefore, domain will be ( -∞, ∞)
https://brainly.com/question/2458431
What is the next term of the geometric sequence?
192, 48, 12,
Answer:
3
Step-by-step explanation:
The pattern is dividing 4 each time.
192/4=48
48/4=12
12/4=3
Hope this helps! Plz give brainliest!
How do you write 9,200 in scientific notation?
Answer:
9.2 x 10^3
Step-by-step explanation:
HOPE THIS HELPS and if it does brain pls thx
12 5 x-10 what is the value of x
Answer:
X=23
Step-by-step explanation:
12²+5²=(X-10)²
144+25=(X-10)²
169=(X-10)²
√169=√(X-10)²
13=X-10
X=23
Do the ratios 18 7 and 2 1 form a proportion?
Hi!
There are a few ways we can do this. The first one is this:
The ratios 18:7 and 2:1 can be represented as fractions: [tex]\frac{18}{7}[/tex] and [tex]\frac{2}{1}[/tex]
To see if they are proportions, we can put the fractions in their simplest form and see if they are equal. However, they are already simplified, and we can see that they are not equal.
Therefore they are not proportions.
The second way we can see is to use cross products. Once again we'll put them as fractions, except we'll set them side by side, like so:
[tex]\frac{18}{7}[/tex] [tex]\frac{2}{1}[/tex]
To see if they are proportions, we simply multiply the diagonals. These would be 18 x 1 and 7 x 2 which equals 18 and 14. These are not equal.
Therefore they are not proportions.
Hope this helps! Have a great day! Let me know if you need any other help :D
Please help solve this question!
Answer:
[tex]\sqrt{49 - x^{2}}[/tex]
Step-by-step explanation:
Pythagorean theorem [tex]c^{2} = a^{2} + b^{2}[/tex] Then:
[tex]7^{2} = x^{2} + y^{2}\\y^{2} = 7^{2} - x^{2}\\y^{2} = 49 - x^{2}\\y = \sqrt{49 - x^{2}}[/tex]
the lenght of the third side = [tex]\sqrt{49 - x^{2}}[/tex]
Ф = [tex]sin^{-1} (\frac{x}{7} )[/tex]
Ф = [tex]cos^{-1} (\frac{y}{7} )[/tex]
Ф = [tex]tan^{-1} (\frac{x}{y} )[/tex]
Y-5=0.5x^2+6x-3 how many x-intercepts does the graph of this quadratic have ?
we have that
Y - 5 = 0.5x2 + 6x - 3--------------- > y=0.5x2 + 6x -3+5=0.5x2 + 6x+2
y=0.5x2 + 6x +2
using a graphic tool
see the attached figure
the graph have two x-intercepts----------> (-11.657,0) and (0.343,0)
5. A quarter is tossed in the air 300 times.
About how many times would you expect the quarter to land on heads?
A 50
E 200
B 110
C 150
D 180
Answer:
C
Step-by-step explanation:
The probability of getting heads or tails is 50%.
300*50% = 150
Answer:
C. 150 times
Step-by-step explanation:
Because a coin only has tails and heads, you can say that the probability would be half. Because it was tossed 300 times, you can say: 300*0.5=150
Find the quotient of 1/6 and 2/9
Answer:
3/4 or 0.75
Step-by-step explanation:
When dividing- quotient- fractions, remember keep, change, flip
Keep- keep the first fraction
Change- change the division sign into a multiplication sign
Flip- flip the second fraction
So your problem really is:
[tex]\frac{1}{6} *\frac{9}{2}[/tex]
Which is: 9/12 or 3/4
RS is the perpendicular bisector of TU. Find x and y
Answer:
x = 1
y = 30°
Step-by-step explanation:
is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':
20x-3 = 5x+12
15x = 15
x = 1
we also know that RS intersecting with TU creates a 90° angle
if 3y = 90 then y = 30
Help me with this please!!!
Write the function for the graph!?!??
The y intercept is the y value when x is 0 which is shown on the graph as (0,4) making the y intercept is 4
The next point given is (1,8) which shows for every 1 increase in x (1-0 = 1) the y value increases by a multiple of 2 (4 x2 = 8)
The equation would be f(x) = 4 * (2)^x
The answer is B
is this correct ? if not what’s the correct answer?
Answer:
No. The correct answer would be C.
Step-by-step explanation:
AAS: The side cannot be in between the two angles.
ASA: The side is in between the two angles.
What are the factors of 14 and 7?
Sasha practices piano for 45 minutes, 6 days a week. How many minutes does Sasha practice in a week? Use an area model to solve.
Answer:
270
Step-by-step explanation:
Because i multiple 45 by 6
can i have some help on both of these questions for brainlist !!!!!!!!!!!
Answer:
B and A
Step-by-step explanation:
What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).
The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…
I hope this helps :)!
how many feet are in 306 inches
Answer:
25.5
Step-by-step explanation:
There are 12 inches in a foot and therefore...
306/12=25.5
306 inches is 25.5 feet
Which table represents the same proportional relationship as the equation Y= 36x?
Answer:
C
Step-by-step explanation:
It does what the equation says. It multiplies x by 36
I hope this helps!
ANSWER ALLL PLEASEEEEEEEEE ILL GIVE BRAINLIST !!!!!!!!!
Answer:
question 3 is $9.99
question 4 I believe is the third option