Find the quadratic polynomial that completes the factorization.
u^3 - 27 = (u - 3)

Find The Quadratic Polynomial That Completes The Factorization.u^3 - 27 = (u - 3)

Answers

Answer 1

Answer:

[tex]u^2+3u+9[/tex]

Step-by-step explanation:

The way to remember it, is like the square of a binomial, but all coefficients are 1.

So it's the square of the first term. The cross product. The square of the second. And you take only one of them.

In our situation is [tex]u^2+3u+9[/tex]

If you want a way to find it, the way you think is it. It's a second degree polynomial, so [tex]au^2+bu+c[/tex]. Then you multiply the terms together, and you have to get terms removing in a way that you're left with just [tex]u^3-27[/tex]. With some number crunching you'll end up with [tex]a=1; b=3, c=9[/tex]


Related Questions

Horatio weighs three times as much as Kimberly and together they weigh a total of 95

Answers

Answer:
option A:
h = 3k
h + k = 95

Step-by-step explanation:

let Horatio's weight be 'h' and Kimberly's weight be 'k'.

If
Horatio weighs three times as much as Kimberly
Then
h = 3k

Also if
together they weigh a total of 95
Then
h + k = 95

Therefore option A is correct.
Hope that helps...

1. Raphael bought eight pens and nine erasers from a shop and paid GHC 33. His friend, Yao bought five similar pens and six erasers from the same shop and paid GHC 21. Calculate the price of the pen and the erasers respectively.​

Answers

The price of the pen and the erasers Raphael and his friend bought are GHC 3 and GHC 1 respectively.

How to solve equation simultaneously

let

x = price of pen

y = price of erasers

The equation

8x + 9y = 33

5x + 6y = 21

multiply (1) by 6 and (2) by 9

48x + 54y = 198

45x + 54y = 189

subtract to eliminate y

48x - 45x = 198 - 189

3x = 9

x = 9/3

x = 3

substitute into (1)

8x + 9y = 33

8(3) + 9y = 33

24 + 9y = 33

9y = 33 - 24

9y = 9

y = 9/9

y = 1

How to solve simultaneous equation:

https://brainly.com/question/16863577

Can you help me? PLEASE

Answers

Hello!

Let's simplify the expression

6-2x+5+4x

Combine like terms:

6+5-2x+4x

11+2x

And that's the final answer, because 11 and 2x are not like terms (and that's Tyler's error. He shouldn't have combined 11 and 2x.

This is the correct way to simplify:

6+5-2x+4x

11+2x

Hope everything is clear.

Let me know if you have any questions!

#NeverGiveUp

:-)

fractions equivalent to 14/32

Answers

Answer:

7/16, 21/48, 28/64

Step-by-step explanation:

Hope this helps

Write an equation of a parabola with the given vertex and focus. Vertex (3,-2); focus (3,-3). Y=

Answers

Answer:

help mee

Step-by-step explanation:

i neddd heplp with my mathh thankyou

Which of the following is the correct factorization of this trinomial?

4x^2 - 0x - 9

A. (4x - 3)(x + 3)

B. (2x - 3)(2x + 3)

C. (2x - 9)(2x + 1)

D. (4x - 9)(x + 1)

Answers

Answer:

B. (2x - 3)(2x + 3)

Step-by-step explanation:

4x² - 0x - 9 = 4x² - 9 = (2x)² - 3² = (2x - 3)(2x + 3)

used: (a - b)(a + b) = a² - b²

Nayeli has a points card for a movie theater.
She receives 40 rewards points just for signing up.
• She earns 14.5 points for each visit to the movie theater.
She needs at least 185 points for a free movie ticket.

Answers

Answer: She would have to visit the movie theater 10 times.

Step-by-step explanation:

Step-by-step explanation:

I am not sure what the actual question is.

the general function for the amount of gathered reward points p with v visits to the theater is

p(v) = 14.5×v + 40 (40 starting points, 14.5 points per visit)

to know how many visits are needed for a certain amount of points (185) we need to solve that equation for v :

185 = 14.5×v + 40

145 = 14.5×v

v = 145/14.5 = 10

so, she needs at least 10 visits to gather the desired 185 points for a free ticket.

but that applies only to the first free ticket.

after that the function behavior kind of changes, because we have no more starting points :

so to get 2×185 = 370 points for 2 free tickets she will need

370 = 14.5×v + 40

330 = 14.5×v

v = 330/14.5 = 22.75862069...

we need to round up to the next whole number (because there can be no "part-visits").

so, she will need 23 visits for 2 free tickets (that means 13 more visits for the second free ticket).

Ahmed drive his car 4 hours continuously as average 80 Km/hr .if his speed was 60 Km in the 1st hour, 90 Km in the 2nd hour and 100 Km in the 3rd hour .Find his speed in the 4th hour ?

Answers

Answer:

I would say 120 but that could be also be wrong but ill go with 120

Find the angle between vectors a=(1,2) and b=(1,-1/2).

Answers

Answer:

[tex]90^{\circ}[/tex]. In other words, these two vectors are perpendicular (orthogonal) to one another.

Step-by-step explanation:

Let [tex]\|a\|[/tex] and [tex]\|b\|[/tex] denote the magnitudes of vector [tex]a[/tex] and vector [tex]b[/tex]. The dot product between these two vectors is represented as [tex]a^{T}\, b[/tex].  Let [tex]\theta[/tex] denote the angle between the two vectors. The cosine of this angle would be equal to:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|}\end{aligned}[/tex].

The dot product between vector [tex]a = \langle 1,\, 2\rangle[/tex] and [tex]b = \langle 1,\, -1/2\rangle[/tex] is:

[tex]\begin{aligned}a^{T}\, b &= {\begin{bmatrix}1 \\ 2\end{bmatrix}}^{T}\, \begin{bmatrix}1 \\ -1/2\end{bmatrix} \\ &= 1 \times 1 + 2 \times \left(-\frac{1}{2}\right) \\ &= 0\end{aligned}[/tex].

The magnitudes of the two vectors are:

[tex]\begin{aligned}\| a \| &= \sqrt{1^{2} + 2^{2}} \\ &= 5\end{aligned}[/tex].

[tex]\begin{aligned}\| b \| &= \sqrt{1^{2} + \left(-\frac{1}{2}\right)^{2}} \\ &= \frac{1}{2}\, \sqrt{5}\end{aligned}[/tex].

Therefore:

[tex]\begin{aligned}\cos(\theta) &= \frac{a^{T}\, b}{\|a\| \|b\|} \\ &= \frac{0}{5 \times (\sqrt{5} / 2)} \\ &= 0\end{aligned}[/tex].

Among all angles between [tex]0^{\circ}[/tex] and [tex]180^{\circ}[/tex], the only angle with a cosine of [tex]0[/tex] is [tex]90^{\circ}[/tex]. Therefore, the angle between vector [tex]a[/tex] and vector [tex]b[/tex] must be [tex]90^{\circ}\![/tex]. Hence, these two vectors are perpendicular to one another.

04.04 SOLVING SYSTEMS OF EQUATIONS APPROXIMATELY
Need this badly

Answers

Answer:

See below ↓

Step-by-step explanation:

A) The Western Beach width decreases with increase in time whereas the Dune Beach width increases with increase in time.

B) Between Year 11 and Year 12

C) Find out the exact change in width per year for both beaches and plot them lines of change on a graph or as equations. Find where they intersect on the graph or solve the pair of equations to find out when they will both have the same width.

Solve for x
Can you pls help me?

Answers

Answer:

6x+50=92

Step-by-step explanation:

The x is for how much the classes cost plus the amount they charged her for the gear.

Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank contains 22,917 L at 2:45 PM and 8,077 L at 5:25 PM the same day, how much water will the tank contain at 6:10 PM that day?

Answers

The amount of water that the tank will contain at 6:10 PM that day is 4174 L.

What is a Conversion Rate?

The conversion rate of a physical quantity is the method by which a unit of measurement is changed from one process to another by following a standard conversion rate and dimensional analysis.

From the information given:

The difference in the time from 5:25 PM to 2:45 PM is 2 hours:40 minutesIf we convert 2 hours:40 mins to minutes, we have = 160 minutes

The difference in the water in the tank within these two periods is:

= 22917 L - 8077 L

= 14840 L

In one minute, the amount of Liter is:

= 14840/160

= 92.75 Liter/minute

Similarly, between 6:10 pm and 5:25 pm, there are 45 minutes difference.

Therefore, the amount of water that the tank will contain at 6:10 PM that

day is;
= 45 minutes × 92.75 Liter/minute

= 4174 Liters

Learn more about conversion rate here:

https://brainly.com/question/1810058

How many patients had more than 5 cavities?

Answers

Answer:

2 patients had more than 5 cavities.

step-by-step explanation:

5 cavities = 26 cavities = 07 cavities = 2

Here cavities > 5

so only 2 patients had more than 5 cavities also as had total 7 cavities.

Answer:

2 patients had more than 5 cavities

Step-by-step explanation:

Each dot represents a different patient.

"More than 5" means numbers greater than 5 (so from 6 onwards).

From inspection of the dot plot, there are 2 dots above all the numbers that are greater than 5.

Therefore, there are 2 patients who had more than 5 cavities.

**see annotated dot plot**

The area shaded with a pink rectangle is "more than 5 cavities"

Arcs and angles relay puzzle

Answers

Applying the angles of intersecting chords theorem, the value of x in the first figure is: x = 7.

What is the Angles of Intersecting Chords Theorem?

If two chords of a circle intersect, the angles of intersecting chords theorem states that, the measure of the angle formed equals 1/2(sum of the measure of the arcs which are intercepted.

Thus, we can use the angles of intersecting chords theorem to find missing angles or value of x in the questions given.

For example, let's find the value of x in the first figure given:

12x + 5 = 1/2(83 + 95)

12x + 5 = 89

12x = 89 - 5

12x = 84

x = 7

Using same strategy, you can solve the rest of the problem given.

Learn more about the angles of intersecting chords theorem on:

https://brainly.com/question/1626547

How to change account to have access to tutor

Answers

You need to buy Brainly pro, it’s a monthly subscription.

go into settings and click on subscription

20 POINTS

Part E
How many of the 320 million Americans would you predict wear glasses?

Answers

About 164 million U.S. adults

If x and y vary inversely, and x = 8 when y = 1/4, what is y when x = -4?

Answers

[tex]y \propto \dfrac 1x\\\\\implies y = \dfrac kx \\\\\implies \dfrac 14 = \dfrac k{8}\\\\\implies k=2\\\\\text{When}~ x =-4\\\\y = \dfrac{k}{x} = \dfrac{2}{-4}= -\dfrac 12[/tex]

The quotient of seven and a number added to ten

Answers

Answer: 3

Formula: 21/7=3 3+7=10

Select the correct answer.
Which pair of statements correctly compares the two data sets?



A.
The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.
B.
The difference of the means is 1. This value is more than half of the mean absolute deviation of either data set.
C.
The difference of the means is 1. This value is 1 times the mean absolute deviation of either data set.
D.
The difference of the means is 1. This value is 2 times the mean absolute deviation of either data set.

Answers

Answer:

Step-by-step explanation:

Do you still need help?

Find the area of the shaded region. Use 3.14 for π.

Answers

Answer:  122 cm squared  (aprox)

Step-by-step explanation:

Area circle            pi* 10 squared   = 314 cm squared

Area rectangle  12x16 = 192 cm squared

                         314-192 = 122

In this figure, the coordinates of the vertices of quadrilateral PARK are (5, 5), (5, 1), (-2, 1), and (0, 5) respectively. The corresponding coordinates of the vertices in the image are (-10, -10), (-10, -2), (4, -2), and (0,-10). Which of the following statements is true? A. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a rotation and a dilation. B. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a reflection and a dilation. C. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a translation and a reflection. D. Quadrilateral P’A’R’K’ is the image of quadrilateral PARK after a rotation and a translation.

Answers

Answer:

B

Step-by-step explanation:

Answer:

The other personis wrong its answer A: a rotation and a dilation.

Step-by-step explanation:

I mean its kind of self explanatory but i hope it helps.

i got a 100% on my quiz with this question btw.

please solve the question to get brainliest with explanation​

Answers

Answer:

14) B. 9

15) C. (7 x 3)cm

Step-by-step explanation:

14) The area of of parallelogram ABCD is 63 and the altitude is 7

divide 63 by 7 = 9

15) The length of OC is twice the length of EO so CE = 1(7) + 2(7) = 3(7)

Answer:

14. B

15. C

Step-by-step explanation:

Question 14

Area of a parallelogram = base × altitude

Given:

area ABEF = 63 cm²base = ABaltitude = 7 cm

Substituting the given values into the formula and solve for AB:

⇒ Area = base × altitude

⇒ 63 = AB × 7

[tex]\sf \implies AB=\dfrac{63}{7}[/tex]

⇒ AB = 9cm

---------------------------------------------------------------------------------------------------

Question 15

Median:  the line segment from the vertex to the midpoint of the opposite side.

Median Theorem:  the medians of a triangle intersect at a point called the centroid.  The centroid is two-thirds of the distance from the vertices to the midpoint of the opposite sides.

Therefore,

[tex]\sf CO=\dfrac23CE \implies EO=\dfrac13CE[/tex]

Given:

EO = 7cm

Substituting the given values into the formula and solve for CE:

[tex]\sf \implies EO=\dfrac13CE[/tex]

[tex]\sf \implies 7=\dfrac13CE[/tex]

⇒ CE = (7 x 3) cm

Which equation does not represent a quadratic function?

Y = (x + 3)^2

y = 3x^2

y = 6x^2 - 1

y = x + 5

Answers

[tex]\text{A quadratic function is in the form of } ~ f(x)=ax^2 +bx+c.\\\\\\y=x+5 ~ \text{is linear so it is not in a form of quadratic function.}[/tex]

Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
O y-2 = 3(x +1/2)
O y-3 = 2(x + 1/2)
O y+ 1/2 = 3(x - 2)
o y + 1/2 = 2(x - 3)


Answers

Answer:

[tex]\displaystyle y + \frac{1}{2} = 3\, (x - 2)[/tex].

Step-by-step explanation:

Consider a line in a cartesian plane that goes through the point [tex](x_{0},\, y_{0})[/tex]. If the slope of this line is [tex]m[/tex] (a real constant,) the equation of this line in point-slope form would be:

[tex]y - y_{0} = m\, (x - x_{0})[/tex].

The line in this question goes through the point [tex](2,\, (-1/2))[/tex]. Thus, [tex]x_{0} = 2[/tex] whereas [tex]y = (-1/2)[/tex]. The slope of this line is [tex]m = 3[/tex]. Thus, the equation of this line in point-slope form would be:

[tex]y - (-1/2) = 3\, (x - 2)[/tex].

Simplify to obtain:

[tex]y + (1/2) = 3\, (x - 2)[/tex].

Factor z3 + 2z2 - 9z - 18. (z - 3)(z + 3)(z + 2) (z 2 + 9)(z - 2) (z 2 + 2)(z - 9)

Answers

Answer:

Read the explanation

Step-by-step explanation:

look at the photo

[tex] \rm \int_{0}^ \infty \frac{ \sqrt[ \scriptsize\phi]{x} \tan^{- 1} (x)}{(1 + {x}^{ \phi} {)}^{2} } {}^{} {} \: dx\\ [/tex]​

Answers

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

[tex]I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx[/tex]

Replace [tex]x \to x^{\frac1\phi} = x^{\phi-1}[/tex] :

[tex]I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

Split the integral at x = 1. For the integral over [1, ∞), substitute [tex]x \to \frac1x[/tex] :

[tex]\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

The integrals involving tan⁻¹ disappear, and we're left with

[tex]I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}[/tex]

Airplane X left the airport, flying at a rate of 400 miles per hour. Airplane Y left 2 hours later, flying at a rate of 450 miles per hour. How long will it take airplane Y to catch up to airplane X?

Answers

Answer:   i think it will take 48 hours

Step-by-step explanation:

here's how to get 48 so basically 450-400-2= 48

now if you end up doing 400 - 450 then you will get -50 if you do 400-450-2 you will get a -52 so you want to make sure you do the biggest number first and then do the smaller numbers to get 48 like 450 - 400 - 2 and then you will have 48

i hope this helps!

Find the value of x.

Answers

Answer:

Maybe 8

Step-by-step explanation:

because its the same side

Jennifer is a wedding planner. She set up six chairs at each table for the reception. If t represents the number of tables, which of the following expressions represents the total number of chairs that she set up?
A. 6 + t
B. t + 6
C. 6t
D. t - 6

Answers

Answer: C. 6t

Step-by-step explanation:

T is unknown, but because you are only asked for the equation to figure out the total,  you simply multiply the 6 chairs per t, or table together, 6t

(12 pts) Choose whether the graphs of the following situations would have a positive slope, a negative slope, or a slope of zero
a. The amount of water in a bathtub as it is being filled
b. The temperature of a hot drink that you left sitting on your desk
c. The number of light bulbs on the Halloween string lights around your window
d. Power in your cell phone battery as you stream a video

Answers

Answer:

  a. positive

  b. negative

  c. zero

  d. negative

Step-by-step explanation:

You want a description of the sign of the slope of a graph of ...

amount of water in a filling bathtubtemperature of a cooling drinknumber of lights in a stringpower in a battery being used

Slope

The slope of a graph is the "rise" divided by the "run." Generally, we choose the direction of "run" to be to the right, so the "rise" will be positive when the graph shows an increasing value, and it will be negative when the graph shows a decreasing value. When the rise is zero (the value is neither increasing nor decreasing), the slope is zero.

Water

A graph of the volume of water in a filling tub will show it starts at some low value and increases over time. Generally such a graph will have volume on the vertical axis, and time on the horizontal axis. Since the volume is increasing, the slope is positive.

Temperature

As a hot drink cools, its temperature decreases. The graph of temperature will generally be drawn with temperature on the vertical axis, and time on the horizontal axis. Since the temperature is decreasing, the slope will be negative.

Lights

We presume there is no process going on that is changing the number of light bulbs in the string of lights, so the value is constant. It is neither increasing nor decreasing, so the slope of its graph will be zero.

Power

If we presume your cell phone is not connected to a charger while it is streaming video for you, then we can assume the power in the battery is decreasing. The slope of the graph of battery power will be negative.

(If the phone is connected to a charger, the slope may be zero or positive, depending on the power output of the charger. One of my phone chargers is "low power," so the battery power does not increase unless the phone is turned off (not playing video).)

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