Factors of a polynomial can divide it without leaving remainder. The other factor of [tex]6x^2 - 7x + 2[/tex] is given by Option D : [tex]3x + 2[/tex]
How to factorize a polynomial?Let the polynomial A(x) has one factor f(x).
Then, it means, we have:
[tex]\dfrac{A(x)}{f(x)} = g(x)[/tex]
Thus, A(x) can be written as [tex]A(x) = f(x) \times g(x)[/tex]
Thus, the other factor of that polynomial is
[tex]g(x) = \dfrac{A(x)}{f(x)}[/tex]
For given case, the polynomial [tex]A(x)[/tex] is
[tex]A(x) = 6x^2 - 7x + 2[/tex]
Its one factor f(x) is given [tex]f(x) = 2x - 1[/tex]
Thus, its second factor is obtained as:
[tex]g(x) = \dfrac{A(x)}{f(x)} = \dfrac{6x^2 - 7x + 2}{(2x - 1)} = \dfrac{6x^2 -4x -3x - 2}{2x - 1}\\\\g(x) = \dfrac{2x(3x + 2) - 1(3x + 2)}{2x - 1} = \dfrac{(2x - 1)(3x + 2)}{2x - 1}\\\\g(x) = (3x + 2)[/tex]
Thus, the second factor of the given polynomial is
Option D : [tex]3x + 2[/tex]
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HELP ANOTHER QUESTION, I REALLY NEED HELP. !!!!!!!!!!!!!!!!!!!!!
Answer:
i dont know Ecactly but i think mybe its 10 or 15
ill mark brainlest if correct
Tim's family is visiting Emeryville. They plan to see a movie and then explore the town. The
movie will cost the family $48, and parking costs $8 per hour.
How long will the family be able to spend in Emeryville if they want to spend less than $80 and
they don't have any other expenses?
Answer:
4 hours
Step-by-step explanation:
the cost of movie is $48
means they have $32 left with them
parking charge is $8 (32/8= 4)
means they can spend 4 hours in Emeryville
Subtract.
The difference is?
Answer:
11m^3+16m+16
Step-by-step explanation:
First, you have to subtract the m^3, then the m, and the 11 and -5.
Answer:
11m^3-21m^2+20m+16
Step-by-step explanation:
4 schools sent students to a languages course.
One of the schools sent both French and German students.
The ratio of French to German students it sent was 1 : 3
The school sent 21 German students.
The other 3 schools sent the same number of students.
Work out the total number of students sent to the languages course.
The first school sends 3 times as many German students as French students, so if they send 21 German students, they must also be sending 21/3 = 7 French students. The first school then sends a total of 21 + 7 = 28 students.
The other 3 schools send the same number of students. There are 4 schools, so the total number of students is 4 × 28 = 112.
A hot-air balloon has a 14-foot diameter that is being deflated at a rate of 0.25 feet per minute.
How many minutes, x, will it take before the balloon has shrunk to a diameter of 8 feet?
CLEAR CHECK
Write the equation that represents the situation.
−
x =
Solve for the time taken for the balloon to shrink to a diameter of 8 feet.
It will take
minutes.
Answer:
24 min
Step-by-step explanation:
14-8 is 6 so you need to shrink it 6 feet until it has a daimiter of 8.
6 divided by .25 is 24 so you have your answer
14-.25x=8
The equation is 14 - 0.25x = 8.
It will take 24 minutes for the balloon to shrink.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given:
A hot-air balloon has a 14-foot diameter.
Rate of 0.25 feet per minute.
Now, equation to represent the situation is
14 - 0.25x = 8
On further solving
6= 0.25x
x= 6/0.25
x= 24
Hence, it will take 24 minutes for the balloon to shrink.
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convert the following to powers first then simplify and then write answer as a radical
Answer:
[tex]\sqrt[15]{m^2n^4}[/tex]
Step-by-step explanation:
[tex](\sqrt[5]{m^2n^4} )^{\frac{1}{3}}\\\\\implies( (m^2n^4)^{\frac{1}{5}})^{\frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{5}\times \frac{1}{3}}\\\\\implies (m^2n^4)^{\frac{1}{15}}\\\\\implies (m^2)^{\frac{1}{15}} (n^4)^{\frac{1}{15}}\\\\\implies m^{\frac{2}{15}} n^{\frac{4}{15}}[/tex]
[tex]\sqrt[15]{m^2n^4}[/tex]
Suppose f(x) = = x. Find the graph of f(x - 2).
Answer:
the answer is graph 1
Step-by-step explanation:
3. Marcus had an average score of 90% on two biology tests about protists. If his first test score was 96%, which score did he receive on the second test? A.45% B.84% C.90% D.102%
Answer:
B: 84%
Step-by-step explanation:
How can you rewrite ( ^12 sqrt 12 ) ^5 without a radical?
Answer:
b
Step-by-step explanation:
Simplify and state the domain for x^2-x-12/x-4
The domain of a function is the set of input values the function can take
The domain is all set of real numbers
How to determine the domain
The expression is given as:
[tex]\frac{x^2 - x - 12}{x - 4}[/tex]
Factorize the numerator of the expression
[tex]\frac{(x - 4)(x + 3)}{x - 4}[/tex]
Simplify: Cancel out the common terms
[tex]x + 3[/tex]
The above expression can take any value of x.
Hence, the domain is all set of real numbers
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Can you help me please!
Answer: 0 = 0 and/or Infinitely Many Solutions
Step-by-step explanation:
When solving this equation we want to find x then substitute the answer we find for x to see if both sides are equal to the same number.
So once we find x replace x with that number: x = 8
Rewrite equation: [tex]-24+3(8)=16-2(8)[/tex]
So we solve [tex]-24+24=16-16\\0=0[/tex]
Since both sides are equal the answer would be Infinitely Many Solutions
how does 4(x + 2) = - 4 equals to x = -3
you have to get X alone
Answer:
Explained below
Step-by-step explanation:
4(x + 2) = - 4
Let's solve:
4(x + 2) = - 4
4(x) + 4(2) = - 4
4x + 8 = - 4
- 8 - 8
4x = -12
/4 /4
x = -3
Hope this helps!
Write the equation in slope-intercept from the two points given: (4,2) and (0,-5)
Explain. (step by step)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{4}}}\implies \cfrac{-7}{-4}\implies \cfrac{7}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{7}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{7}{4}x-7\implies y=\cfrac{7}{4}x-5[/tex]
I will give brainliest. Please help.
what percent of 610 is 457.5?
Answer:
75%
Step-by-step explanation:
457.7/610
divide it out
.75
make it a percentage
.75 × 100 = 75%
Hey guys! Person above me is correct, I made a mistke in my calculations!
Select each ordered pair that is a member of the function h(n)=3n^2-n
it's was helpful to you
# be careful#
A right triangle has legs measuring 16 in. And 28 in. What is the length of the hypotenuse? Round your answer to the nearest tenth. 23. 0 in. 32. 2 in. 44. 0 in. 1040. 0 in.
In a right-angled triangle, the Pythagoras theorem is used to find the hypotenuse. Then the hypotenuse is 32.2 inches.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
A right triangle has legs measuring 16 inches And 28 inches.
We know the Pythagoras theorem
[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2[/tex]
Then the hypotenuse will be.
[tex]\rm Hypotenuse ^2 = Base ^2 + Perpendicular^2\\\\\rm Hypotenuse ^2 = 16^2 + 28^2\\\\ \rm Hypotenuse ^2 = 256 + 784\\\\\rm Hypotenuse ^2 = 1040\\\\\rm Hypotenuse \ = 32.2[/tex]
Thus, the hypotenuse is 32.2 inches.
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help pls i really need it
Answer:
RHS
Step-by-step explanation: the hypotenuse and one side of the triangle is respectively equal to the hypotenuse and one side of the other triangle
so, its rhs
Find the value of (3 + 4) 2.
25
49
14
Answer:
14
Step-by-step explanation:
[tex](3 + 4)2 \\ add \: 3 \: to \: 4 = 7 \\ (7)2 \\ 7 \times 2 \\ 14[/tex]
Wyatt is going to a carnival that has games and rides. Each game costs $1. 25 and each ride costs $2. 75. Wyatt spent $20. 25 altogether at the carnival and the number of rides he went on is twice the number of games he played. Determine the number of games Wyatt played and the number of rides Wyatt went on.
In the carnival the number of games number of rides Wyatt went on is 3 and 6 respectively.
What is system of equation?
A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
The number of unknown objects can be find using the system of solution.
Given information-
The cost of each game is $1.25.
The cost of each ride is $2.75.
Total amount of money spent by the Wyatt is $20.25.
The number of rides he went on is twice the number of games he played.
Suppose the number of games Wyatt played is x and the number of rides he went in the carnival is y.
As, the number of rides he went on is twice the number of games he played. Thus,
[tex]y=2x[/tex]
Let the above equation as equation one.
As total amount of money spent by the Wyatt is $20.25 and The cost of each game is $1.25 and the cost of each ride is $2.75. Thus,
[tex]1.25x+2.75y=20.25\\[/tex]
Put the value of y in the above equation from the equation one as,
[tex]1.25x+2.75(2x)=20.25\\1.25x+5.5x=20.25\\6.75x=20.25\\x=3[/tex]
Thus the number of games he played is 3.
Put this value of x in the equation one as,
[tex]y=2\times3\\y=6[/tex]
Thus the number rides Wyatt went on is 6.
Hence, In the carnival the number of games number of rides, Wyatt went on is 3 and 6 respectively.
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Sai reads 100 words each 1/2 minute. which statement is true
To buy a car, Rachel
borrowed $3,000 at
9% interest per
year for 3 years
How much money
did she have to pay
back?
You use the formula
3000*.09*3=810
She will have to pay back the amount of $3,810.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
We have been given data as:
Principal (P) = $3,000
Rate of Interest (R) = 9% = 9/100 = 0.09
Time (T) = three years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
⇒ Simple interest = 3,000× 9% × 3
⇒ Simple interest = 3,000× 9/100 × 3
⇒ Simple interest = 3,000× 0.09 × 3
Apply the multiplication operation, and we get
⇒ Simple interest = $810
The total payback amount = $3,000 + $810 = $3,810
Therefore, she will have to pay back the amount of $3,810.
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what is the equation of the linear function?
Answer:
yellow box
Step-by-step explanation:
if you follow the graph. it is a difference of 6 between each 2 points
so you don't have to solve with the formula
6/2 = 3 so 3 is your X
and you get larger as you go towards 0 so it is positive
and so add 6 to 10 because (-2,10) and you follow the 6 y for every 2 you go
so (0,16)
y = 3x + 16
Water is leaking out of an inverted conical tank at a rate of 7,000 cm^3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m.
Required:
Find the rate (in cm^3/min) at which water is being pumped into the tank. (Round your answer to the nearest integer.)
The inflow rate of water is given by the function of the volume of the
tank derived from the shape of the tank.
Response:
The rate water is being pumped into the tank is approximately 286,253 cm³/minWhich method can be used to find the rate at which water is pumped into the tank?
The given parameter are;
Shape of the tank = Conical
Rate at which water is leaking out of the tank = 7,000 cm³/min
Height of the tank = 6 m
Diameter of the tank = 4 m
Solution:
We have;
[tex]\dfrac{D}{h} = \mathbf{\dfrac{2 \cdot r}{h}}[/tex]
[tex]r = \mathbf{\dfrac{D}{2 \cdot h}}[/tex]
Which gives;
[tex]\dfrac{r}{h} = \dfrac{4}{6 \times 2} = \dfrac{1}{3}[/tex][tex]r= \mathbf{\dfrac{h}{3}}[/tex]
[tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h = \dfrac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{3} \right)^2 \cdot h = \mathbf{ \pi \cdot \dfrac{h}{27} ^3}[/tex]
Which gives;
[tex]\dfrac{dV}{dh} = \mathbf{\pi \cdot \dfrac{h}{9} ^2}[/tex]
By using chain rule of differentiation, we have;
[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \times \dfrac{dh}{dt}}[/tex]
Which gives;
[tex]\dfrac{dV}{dt} = \mathbf{\pi \cdot \dfrac{h}{9} ^2\times 20}[/tex]
[tex]\dfrac{dV}{dt} = \pi \cdot \dfrac{200}{9} ^2\times 20 \approx 279,252.68[/tex]
[tex]\dfrac{dV}{dt} = \mathbf{Inflow \ rate - Outflow \ rate}[/tex]
Therefore;
[tex]Inflow \ rate = \mathbf{\dfrac{dV}{dt} + Outflow \ rate}[/tex]
Which gives;
Inflow rate ≈ 279,252.68 + 7000 = 286,252.68 ≈ 286,253
The inflow rate = The rate water is being pumped into the tank ≈ 286,253 cm³/minLearn more about rate of change of a function here:
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If cosθ = [tex]\frac{2}{\sqrt{19} }[/tex] and angleθ is in Quadrant I, what is the exact value of tan2θ in simplest radical form???
we know that θ is in the I Quadrant, namely that cosine as well as sine are both positive, well, we know that
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{\sqrt{19}}}\qquad\qquad \textit{let's get the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{(\sqrt{19})^2-2^2}=b\implies \pm\sqrt{19-4}=b\implies \pm\sqrt{15}=b\implies \stackrel{I~Quadrant}{+\sqrt{15}=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\theta)=\cfrac{\stackrel{opposite}{\sqrt{15}}}{\underset{adjacent}{2}}~\hspace{10em} tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)} \\\\[-0.35em] ~\dotfill\\\\ tan(2\theta)=\cfrac{2\cdot \frac{\sqrt{15}}{2}}{1-\left( \frac{\sqrt{15}}{2} \right)^2}\implies tan(2\theta)=\cfrac{\sqrt{15}}{1-\frac{15}{4}}\implies tan(2\theta)=\cfrac{\sqrt{15}}{~~\frac{4-15}{4}~~} \\\\\\ tan(2\theta)=\cfrac{\sqrt{15}}{~~ \frac{-11}{4}~~}\implies tan(2\theta)=-\cfrac{4\sqrt{15}}{11}[/tex]
What is the simplified form of (4x^2)^3
Answer:
i guess the answer is 64x^5
Step-by-step explanation:
(4x^2)^3
=64x^5
Please help me with this question
Answer:
18
Step-by-step explanation:
House number:
1. has 3 people
2. has 2 people
3. has 3 people
4. has 2 people
5. has 3 people
6. has 2 people
7. has 3 people
looking at each rule, it all fits.
so now add it all up so its 18
Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3. X2 = –3y y2 = –3x x2 = 12y y2 = 12x.
The equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
What is the Equation of a parabola?y = a(x-h)² + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
As it is given that the focus of the parabola is at F(3,0) and its directrix is the line x=−3, therefore, we can write that
x=-3
x+3=0
Now, Let A(x,y) be any point in the plane of the directrix and focus, and MA be the perpendicular distance from A to the directrix, therefore, A lies on parabola if FA=MA,
[tex]FA=MA\\\\\sqrt{(x-3)^2 +(y-0)^2}=\dfrac{|x+3|}{1}\\\\{(x-3)^2 +(y-0)^2}={(x+3)^2}\\\\-6x^2+y=6x\\\\y=6x^2+6x[/tex]
Hence, the equation of the parabola whose focus is at (3, 0) and the directrix is at x = –3 is y=6x²+6x.
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andres is 1.65 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 40.15 meters. He stands 35 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
For the given data the height of the tree will be 12.86.
What is the triangle?A triangle is a three-sided polygon having three edges and three vertices in terms of geometry. The sum of the inner angles of the triangle is 180°.
Given that, Andrés is 1.65 meters tall, this is obvious. He determines the length of a tree's shadow at 2 p.m. to be 40.15 meters. The tip of his shadow touches the tip of the tree's shadow while he stands 35 meters away from the tree.
Since the triangle ABC and ADF are similar, their ratio will be the same.
Suppose the height of the tree to the nearest hundredth of a meter will be x.
5.15/40.15=1.65/x
5.15x=1.65× 40.15
5.15x=66.2475
x=66.24/5.15
x=12.86
Thus, the height of the tree will be 12.86.
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