Answer:
2(x-3)
Step-by-step explanation:
2x² - 2x - 12= 2(x²-x+6)= 2(x²+2x- 3x+6)= 2(x-3)(x+2)
(2x² - 2x - 12)/(x+2)= 2(x-3)(x+2)/(x+2)= 2(x-3)According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?
Answer:
Step-by-step explanation:
You didn't give your options, but it doesn't matter. We'll find all the possibilities and then you can pick it from your list.
When I teach this in Algebra 2, I call it the "the c over d thing" and all my students know EXACTLY to what I am referring. "c" is the constant and "d" is the leading coefficient. The combination of c/d give you the possibilities of roots for the polynomial. There are no real roots that a polynomial can have other than the possibilities we find when we do the c/d thing.
Our c is a 20. All the factors of 20 are as follows (notice that we have both the positive and negative factors):
20: ±1, ±2, ±4, ±5, ±10, ±20
Our d is a 3. All the factors of 3 are as follows (again, both the + and the -):
3: ±1, ±3 and that's it for 3.
c/d is as follows. Make sure you put ever c over every d!!!:
c/d: ±[tex]\frac{1}{1}[/tex], ±[tex]\frac{2}{1}[/tex], ±[tex]\frac{4}{1}[/tex], ±[tex]\frac{5}{1}[/tex], ±[tex]\frac{10}{1}[/tex], ±[tex]\frac{20}{1}[/tex], ±[tex]\frac{1}{3}[/tex], ±[tex]\frac{2}{3}[/tex], ±[tex]\frac{4}{3}[/tex], ±[tex]\frac{5}{3}[/tex], ±[tex]\frac{10}{3}[/tex], ±[tex]\frac{20}{3}[/tex]
Those are all the possibilities for your roots for that polynomial. As long as the roots are real (and they won't always all be real!), there are no roots but these.
Answer:
its D on edge
Step-by-step explanation:
What is the value of p?
Answer:
[tex]p = 43 \: \: \: degrees[/tex]
Answer A is correct
Step-by-step explanation:
[tex]90 + p = 133[/tex]
the sum of the exterior angles in a triangle is equal to the sum of opposite interior angles.
[tex]p = 133 - 90 \\ p =4 3 \: \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
At Barlow school, 4/9 of the 873 students are boys.
At Willow school, 2/3 of the 630 students are girls
Which school has a greater of boys and how many?
Answer:
Barlow School has the greater number of boys by 178.
Answer:
Barlow school by 178
Step-by-step explanation:
→ First let's work out the number of boys at Barlow school
[tex]\frac{4}{9}[/tex] of [tex]873[/tex] [tex]=[/tex] [tex](873/9)*4[/tex] [tex]=[/tex] [tex]388[/tex]
→ There is 388 boys in Barlow school. Now let's work out the number of boys at Willow school. Since we know that [tex]\frac{2}{3}[/tex] of the school is girls, it must mean that the remaining part must be boys so the fraction of boys at Willow school is [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{3}[/tex] of [tex]630[/tex] [tex]=[/tex] [tex](630/3)*1[/tex] [tex]=[/tex] 210
→ The question specifies to say which school has a greater number of boys and we can see Barlow school has more boys and the question says by how many so we take away the totals so 388 - 210 = 178
part 4. Find the measure of the indicated angle to the nearest degree
Answer:
hope this helps you
The lowest airport in the world is Atyrau Airport in Kazakhstan. Its
runway is 72 feet below sea level. A passenger in a small airplane on
the runway holds her phone exactly 4 feet above the runway. What
is the elevation of her phone? Use a negative sign where appropriate,
and don't include units when typing in the secret answer
Answer:
-72 + 4 = -68
If a polynomial function f(x) has roots 0, 4, and 3+ sqrt 11, what must also be a root of f(x)?
a. 3+i sqrt 11
b. -3+i sqrt 11
c. 3- sqrt 11
d. -3- sqrt 11
Answer:
The answer is C 3- sqrt 11
Step-by-step explanation:
Consider the following equations:
−x − y = 1
y = x + 3
If the two equations are graphed, at what point do the lines representing the two equations intersect?
a
(−1, 2)
b
(−2, 1)
c
(1, −2)
d
(2, −1)
Answer:
The Answer is: (-2,1)
Step-by-step explanation:
Please help ASAP! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
i think of a number , take away 1 and multiply the result by 3
Answer:
Step-by-step explanation:
Let the number be x
Take away 1: x -1
Then multiply the result by 3: (x- 1) * 3 = (x-1)3 or 3x - 3
Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h in total to paddle 2 km up a river and another 2 km back. Find the speed of the current, rounded to the nearest tenth.
Answer: The speed of the current is 3.5 km/h.
Step-by-step explanation:
When they move in the river, the speed of the canoe is:
Sc is the speed of the canoe and Sr is the speed of the current.
Sc + Sr (when they move in the same direction as the current)
Sc - Sr (when they move in the opposite direction as the current)
So we have that in one hour, they moved 2km and then they returned other 2km.
Now, using the relation:
Velocity*time = distance
we can write 1hour = T1 + T2 such that:
(Sc + Sr)*T1 = 2km
(Sc - Sr)*T2 = 2km
T1 + T2 = 1hour -------> T2 = 1h - T1
Sc = 6km/h.
So we can write this as two equations:
(6km/h + Sr)*T1 = 2km
(6km/h - Sr)*(1h - T1) = 2km.
Now, the first step will be isolate one of the variables in one equation, we can get:
T1 = 2km/(6km/h + Sr)
and replace it in the second equation:
(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.
Now we solve this for Sr, i will ignore the units, so it is easier to read the math.
(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2
(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)
6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0
-Sr^2 + 36 -12 -12 = 0
-Sr^2 + 12 = 0
Sr = √12 = 3.5km/h
(where we take the positive value of the square root)
The speed of the current is 3.5 km/h
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:
(6 - a)(t₁) = 2 km
t₁ = 2 / (6 - a) (1)
(6 + a)(t₂) = 2 km
t₂ = 2 / (6 + a) (2)
t₁ + t₂ = 1 hour
[2 / (6 - a)] + [2 / (6 + a)] = 1
12 + 2a + 12 - 2a = 36 - a²
a² - 12 = 0
a = 3.5 km/h
The speed of the current is 3.5 km/h
Find out more at: https://brainly.com/question/22610586
Please answer correctly !!!! Will mark brainliest answer !!!!!!!!!
Answer:
functions f(x) and g(x) share one root in common that of x=2 and each have another different root
Step-by-step explanation:
Notice that function g(x) has for roots the values x = -1 and x = 2, (these are the crossings of the x axis that you see in the graph)
On the other hand, the function f(x) has two roots that are obtained by factoring it out:
[tex]f(x)=x^2+x-6\\f(x)= x^2-2x+3x-6\\f(x)=x(x-2)\,+\,3(x-2)\\f(x)=(x-2)\,(x+3)[/tex]
Therefore it has roots at x=2 and x= -3
So functions f(x) and g(x) share one root in common that of x=2 and each have another different root
the graph shows the speed of a vehicle during the final 50 seconds of a journey at the start of the 50 seconds the speed is k metres per second
Answer:
a) 27 m/s
b) 30 m/s
c) i) 3
ii) Deceleration
Step-by-step explanation:
The question is not complete, the correct question is given as:
The graph shows information about the speed of a vehicle during the final 50 seconds of a journey. At the start of the 50 seconds the speed is k metres per second. The distance travelled during the 50 seconds is 1.35 kilometres.
(a) Work out the average speed of the vehicle during the 50 seconds
(b) Work out the value of k.
(c) (i) Calculate the gradient of the graph in the final 10 seconds of the journey
(ii) Describe what this gradient represents
Answer:
The graph is attached. The total time = 50 seconds, total distance = 1.35 km = 1350 m
a) The average speed is the ratio of the total distance traveled to the total time taken to cover this distance. The average speed is given by the formula:
[tex]Average \ speed=\frac{total\ distance}{total\ time}\\ Substituting: \\ Average \ speed=\frac{1350\ m}{50\ s} = 27\ m/s[/tex]
b) From the graph, the total distance covered is the area of the graph. The graph is made up of a rectangle and triangle, the area of the graph is equal to the sum of area of rectangle and area of triangle.
[tex]Total \ distance=Total\ area=Area\ of \ rectangle+Area\ of \ triangle\\Total \ distance=(length *breadth)+\frac{1}{2}base*height\\1350 \ m=(40*k)+0.5*10*k\\1350=40k+5k\\45k=1350\\k=1350/45\\k=30\ m/s[/tex]c) i) The gradient in the last 10 seconds is the ratio of change in speed to change in time
[tex]Gradient=\frac{change\ in\ speed }{change\ in\ time}=\frac{0-k}{50-40} \\ bt \ k=30\\Gradient=\frac{0-30}{50-40}= \frac{-30}{10} =-3[/tex]
ii) Since the gradient is negative it means it is deceleration. That is in the in the last 10 seconds the vehicle decelerates at a rate of 3 m/s²
Answer:
Step-by-step explanation:
a)34 m/s
b) 40k=34
k=34/40
k=0.85 m/s
What is 2a+50=5a-4? Thank you for your time.
Answer:
2a+50=5a-4
5a-2a=50+4
3a=54
a=18
Answer:
[tex]a=18[/tex]
Step-by-step explanation:
[tex]2a+50=5a-4\\\mathrm{Subtract\:}50\mathrm{\:from\:both\:sides}\\2a+50-50=5a-4-50\\Simplify\\2a=5a-54\\\mathrm{Subtract\:}5a\mathrm{\:from\:both\:sides}\\2a-5a=5a-54-5a\\\mathrm{Simplify}\\-3a=-54\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3a}{-3}=\frac{-54}{-3}\\Simplify\\\frac{-3a}{-3}=\frac{-54}{-3}\\\mathrm{Simplify\:}\frac{-3a}{-3}:\quad a\\\frac{-3a}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3a}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1[/tex]
[tex]=a\\\mathrm{Simplify\:}\frac{-54}{-3}:\quad 18\\\frac{-54}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{54}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{54}{3}=18\\=18\\a=18[/tex]
Write the expression for the amount of wallpaper in square feet you need to cover the living room, which is the same height and width as the family room, but it has a length that is 5 times greater than the height. The living room has 2 doors.
Answer:
The expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]
Step-by-step explanation:
The necessary dimensions of the living room we need are the length and the height. We will not be needing the width because we will not be covering the floors with any wallpaper.
We will now assign variables to represent the surface areas of some features of the rooms.
Let the length of one wall of the living room be = l cm
Let the breadth of one wall of the living room be = b cm
Let the surface area of the doors be = d [tex]cm^{2}[/tex]
From the problem, we know that l = 5b
The area to be covered on one wall of the living room will be = length X breadth.
l X b
recall l = 5b
[tex]5b \times b = 5b^{2}[/tex]
this is the area to be covered on one wall.
For the four walls, we would have [tex]4 \times 5b^{2}= 20b^{2}[/tex]
Let us remember that the living room has two doors each covering a surface area of [tex]d cm^{2}[/tex] we will have to subtract these out since hey won't be covered.
[tex]20b^{2}- 2d[/tex]
Therefore, the expression for the amount of wallpaper needed is [tex]20b^{2}- 2d[/tex]
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
There are 50 sheets of drawing paper.
Larry divides the drawing paper between himself
and his younger brother John.
And Larry has 14 more sheets.
How many
sheets of drawing paper do Larry and his
brother have, respectively?
Answer:
John has 18 pieces of paper.
Larry has 32 pieces of paper.
Step-by-step explanation:
Let [tex]l[/tex] be how many pieces of paper Larry has and [tex]j[/tex] be how many pieces of paper John has.
We get:
[tex]j+14=l[/tex]
[tex]j+l=50[/tex]
[tex]j+j+14=50\\\\2j+14=50[/tex]
Subtract 14 from both sides
[tex]2j=36[/tex]
Divide both sides by 2
[tex]j=18[/tex]
John has 18 pieces of paper.
[tex]j+14=l\\\\18+14=l\\\\l=32[/tex]
Larry has 32 pieces of paper.
which of the following represents this function written in intercept form? y=-x^2-x+6
Answer:
Step-by-step explanation:
-(x-2)(x+3)
how many inches in 85937392 metres?
Answer:
3383361889.8
Step-by-step explanation:
1 meter = 39.3701 inches
85937392 x 39.3701 = 3383361889.8
Answer:
3,383,361,889.76 inches
Step-by-step explanation:
1 meter = 39.37 inches
multiply 85937392 by 39.37
answer is 3383361889.76
If m2 CBD = 42 and m2 DBE = 26, what is the measure of ZABE?
A. 26
B.42
C.112
D.124
72= 27+ 9s solve the equation
Answer:
s=5
Step-by-step explanation:
72=27+9s
Subtract 27 from both sides.
72-27=9s+27-27
45=9s
Divide 9 from both sides.
5=s
I need which other form can you represent the number 2 1/3
Answer:
You can also represent it as [tex]\sqrt[3]{2}[/tex]
Step-by-step explanation:
[tex](\sqrt[3]{2})^{3} =2\\2^{\frac{1}{3} } =2[/tex]
what is called circle
Answer:
A round plane figure whose boundary (the circumference)consists of points equidistant from a fixed point (the center)
Answer:
A round plane figure
Step-by-step explanation:
Clothing price (100 percent) is 26 dollars and 50 cents, Added tax is 5 percent, and total cost is blank. Darrien purchases some clothes for a total of $26.50, before tax. Sales tax in his state is 5 percent. What is the total price he has to pay for the clothes? Step 1: (Original Price)(Tax Percent) = Amount of Tax Step 2: Original Price + Amount of Tax = $
ANSWER PLS
Answer:
$27.83
Step-by-step explanation:
If Darrien spends 26.50, multiply that by 0.05 (26.50×0.05) which is 1.325 which rounds to 1.33. $1.33 is the amount of tax he has to add. For the full price you would do 26.50+1.33 to get 27.83.
Answer:
The answer is 27.83
Step-by-step explanation:
Thank the person above me.
What fraction is equivalent to 5%?
A: 50/100
B: 1/20
C: 5/10
D: 1/5
Answer:
1/20
Step-by-step explanation:
5%
Percent means out of 100
5/100
Divide top and bottom by 5
1/20
Answer:
HI THERE,THE ANSWER IS
B
Step-by-step explanation:
[tex]\frac{1}{20} \\[/tex] X 100%=5%
Sean is drinking a slushy as fast as he can.
The amount of slushy left in the cup (in milliliters) as a function of time in seconds) is graphed.
How much slushy did sean drink every 5 seconds
Answer:
40 millimetres
Answer:
40
Step-by-step explanation:
Select the graph for the solution of the open sentence. Click until the correct graph appears.
4|x| - 1 < -4
Answer:
No solution!
Just turned it in <3
Answer:
tis indeed no solution your honor
Step-by-step explanation:
A baker is folding up open-topped boxes to package up her baked goods. She has
flat, rectangular pieces of cardboard that are 10 inches by 6 inches. She wants to
maximize the volume of the box. What size squares should she cut from the corners
of the cardboard?
Answer:
She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume
Step-by-step explanation:
Length = L = 10 inches
Width = W = 6 inches
Suppose x is cut from the 4 corners to make a box.
Dimensions of the Box:
L= 10 - 2x
W = 6 - 2x
H = x
Volume of the Box:
V = (L)(W)(H)
V = (10-2x)(6-2x)(x)
V = 4x³ - 32x² + 60x
For Maximum value:
[tex]\frac{dV}{dx}=0[/tex]
[tex]\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0[/tex]
The values of x found are:
x= 4.12 , x = 1.21
If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.
We discard 4.12. Now x=1.21
So,
If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V
*Giving brainliest* Over what interval is the function in this graph constant?
Answer:
C
Step-by-step explanation:
Constant means unchanging. You can see that there is a portion in the graph where the line is just flat. That means that the graph is constant in that interval. Find where the constant line starts and ends. Since the coordinates are increasing by 2, and the constant line starts between 0 and the first tick (2), the constant line starts at 1. Do the same thing to find where it ends(the last point where the line is flat). This should be 6.
That means the line is unchanging(constant) from 1 to 6, which can be represented by C.
Need HELP!!!! Write the point-slope form of the line that passes through (5, 5) and is perpendicular to a line with a slope of 1/4. Include all of your work in your final answer.
Answer:
[tex]y - 5 = -4(x-5)[/tex]
Step-by-step explanation:
Given
Line coordinates: (5,5)
Perpendicular slope = [tex]\frac{1}{4}[/tex]
Required
Find the point slope form of the line
First, the slope of the line has t be calculated;
Given that two lines are perpendicular;
The relationship between there slopes is given as [tex]m_1.m_2 = -1[/tex]
Let m_2 represent the slope of the second line;
such that [tex]m_2 = \frac{1}{4}[/tex]
So;
[tex]m_1 * \frac{1}{4} = -1[/tex]
Multiply both sides by 4
[tex]m_1 * \frac{1}{4} * 4 = -1 * 4[/tex]
[tex]m_1 = -1 * 4[/tex]
[tex]m_1 = -4[/tex]
Now, the equation of the line can be calculated using slope formula;
[tex]m = \frac{y - y_1}{x- x_1}[/tex]
Where
[tex](x_1,y_1) = (5,5)\\m_1 =m = -4[/tex]
So; [tex]m = \frac{y - y_1}{x- x_1}[/tex] becomes
[tex]-4 = \frac{y - 5}{x- 5}[/tex]
Multiply both sides by x - 5
[tex]-4(x-5) = \frac{y - 5}{x- 5} * (x-5)[/tex]
[tex]-4(x-5) = y - 5[/tex]
Reorder
[tex]y - 5 = -4(x-5)[/tex]
Hence, the line in point-slope form is [tex]y - 5 = -4(x-5)[/tex]
A sugar cookie recipe that makes 3 dozen cookies calls for 1.5 cups of white sugar. How much white sugar would you need to make 5
dozen cookies?
Answer:
Brainliest here!
Step-by-step explanation:
3 dozen cookies = 1.5 cups
one dozen cookies= 0.5 cups
5 dozen cookies = 2.5 cups of sugar
