The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below. mc018-1.jpg How many roots of f(x) are rational numbers?
Answers
Answer: there are 3 root of f(x) which are rational numbers (2,0), (3,0) and (4.5,0)
Explanation:
Rational numbers are those that can be written in the form of p/q: q should not be equal to zero
since, the graph cuts x-axis at three points but rational are two
all integers are rational numbers
attached is the graph please have a look at it
Related Questions
A cookie recipe states for every 3 cups of flour, 1 1/2 teaspoons of vanilla are needed. How many teaspoons are needed for 5 cups of flour?
Answers
2x = 5
divide both sides by 2 to isolate x
x = 2.5
You need 2.5 teaspoons of vanilla for 5 cups of flour.
EXPERTS/ACE/GENIUSES
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and are similar. Find the value of x. A. 5 B. 15 C. 60 D. 240
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A geometric sequence is shown below : 2/3,2,6,18.. write the explicit formula
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now, we get the next term's value by simply multiplying the current term's value by the common ratio, so if we just divide any of the terms by the term before it, the quotient will just be the common ratio.
18/6 is just 3, so there you have it, and we know the first term is 2/3.
[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=3\\ a_1=\frac{2}{3} \end{cases}\implies a_n=\cfrac{2}{3}\cdot 3^{n-1}[/tex]
A prism with a base area of 3m^2 and a height of 4m^2 is dilated by a factor of 3/2 what is the volume of the dilated prism
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Why do clouds tend to form around 3:00 pm and 6:00 am
Answers
Lita,Kala, and Rose entered a typing competition. Lita typed 2 times as fast as Kala. The ratio of the number of words Kala typed to the number of words Rose typed was 4:1. If Rose typed 48 words, how many words did Lita type?
Answers
Then Lita types twice as fast so 192*2=384.
It should be 384 words.
Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = <1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =
Answers
- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t>
- parametric equations:
x = 1 + 6t
y = -1 + 7t
z = 7 - 6t
Explanation:
To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,
v = q - p
= (7,6,1) - (1,-1,7)
v = (6, 7, -6)
The vector equation of the line is given by
[tex]r(t) = v_0 + tv[/tex]
Where
[tex]v_0[/tex] = a point in the line (we choose point p(1,-1,7))
So, the equation of the line joining p and q is given by
[tex]r(t) = v_0 + tv \\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle \\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle \\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }[/tex]
In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.
Since the vector equation is given by
[tex]r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle[/tex]
The parametric equations of the line are given by:
[tex]x(t) = 1 + 6t \\y(t) = 1 + 7t \\z(t) = 7 - 6t[/tex]
The vector equation for the line segment joining the points p(1, -1, 7) and q(7, 6, 1) is r(t) = <1+6t, -1+7t, 7-6t> and the corresponding parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.
Explanation:To find the vector and parametric equations for the line segment joining two points p(1, -1, 7) and q(7, 6, 1), we first need to understand that the vector equation for a line segment in space is given by r(t) = p + t (q - p), where 0 ≤ t ≤ 1, and p and q are the coordinates of the points. The parametric equations are obtained by expressing the x, y, and z coordinates of r(t) as individual functions of t.
Substituting the given points into the vector equation we get: r(t) = <1+6t, -1+7t, 7-6t>. Then, the corresponding parametric equations will be x(t) = 1 + 6t, y(t) = -1 + 7t, and z(t) = 7 - 6t.
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3^2•3^n simplifies to 3^20 what is the value of the exponent n?
Answers
[tex]3^2 \times 3^n = 3^20 [/tex]
Solving for n.
Divide both sides by 3²
[tex] \frac{3^2 \times 3^n}{3^2} = \frac{3^{20}}{3^2} [/tex]
Simplify
[tex]3^n= 3^{20-2} \\ 3^n=3^{18} \\[/tex]
[tex]if \ a^{f(x)}=a^{g(x)} , \ then \ f(x)=g(x)[/tex]
So, n=18
Answer: n=18
53b−7b−6b+1 if b=25
Please help me with this problem! And what is the simplified expression?
Answers
Answer: 1001
B/c i said so
A slice is made perpendicular to the base of a right rectangular prism as shown.
What is the area of the resulting two-dimensional cross section?
Drag and drop the answer into the box.
mm²
48
28
84
144
16
Answers
Answer:
The correct option is 1. The area of cross section area is 48 mm².
Step-by-step explanation:
From the find it is noticed that the cross section is a rectangle with length 4 mm and width is 12 mm.
The area of a rectangle is the product of its dimensions.
[tex]A=l\times w[/tex]
Where, l is length of the rectangle and w is width of the rectangle.
The area of cross section is
[tex]A=4\times 12[/tex]
[tex]A=48[/tex]
Therefore the area of cross section area is 48 mm². Option 1 is correct.
Alicia buys a 5 pound bag of rocks for fish tank. She uses 1 1/8 pounds for a small fish bowl. How much is left
Answers
Here is your answer:
The proper answer to this question is "4".
Here is how:
First convert the mix number into a fraction:
1 1/8=9/8
5*8=40
1*8=8
-
9*1=9
8*1=8
40-8=32
32/8=4
8/8=1
Which means your answer is 4/1 or 4!
If you need anymore help feel free to ask me!
Hope this helps!
What is 3^2/3 equal to? A.3√9 B.2√9 C.3√27 D.2√27
Answers
[tex] 3^{\frac{2}{3}} = \sqrt[3] {3^2} = \sqrt[3] {9} [/tex]
how to do this 24:96 = 5:?
Answers
In that case, x=20
how much difference is there between investing $5,000 at 4% simple interest for 5 years and investing that same amount at 4% compounded quarterly
Answers
- Simple interest formula: [tex]A=P(1+rt)[/tex]
where
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex], so lets replace those values in our simple interest formula to find [tex]A[/tex]:
[tex]A=5000(1+(0.04)(5))[/tex]
[tex]A=5000(1.2)[/tex]
[tex]A=6000[/tex]
Now that we know the final investment value of our simple interest investment, lets use the compound interest formula to find the final investment value of the other one:
- Compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the time in years
For our problem we know that [tex]P=5000[/tex], [tex]r= \frac{4}{100} =0.04[/tex], and [tex]t=5[/tex]. Since we know that the interest is compounded quarterly (each 4 months), it mean that is compounded [tex] \frac{12months}{4months} =3[/tex] times per year, so [tex]n=3[/tex]. Now that we have all the vales, lets replace them in our formula:
[tex]A=5000(1+ \frac{0.04}{3} )^{(3)(5)} [/tex]
[tex]A=5000(1+ \frac{0.04}{3} )^{15} [/tex]
[tex]A=6098.95[/tex]
now that we know the final amounts of our investments, lets find how much difference is between them:
[tex]6098.95-6000=98.95[/tex]
We can conclude that the difference between invest $5000 in a compound interest investment vs a simple interest investment is $98.95.
At noon, ship a is 60 km west of ship
b. ship a is sailing south at 15 km/h and ship b is sailing north at 5 km/h. how fast is the distance between the ships changing at 4:00 pm?
Answers
base of our triangle if drawn is 60 km
to find dD/dt when t=4 hours we shall have:
(A+B)²+60²=D²
d/dt[(A+B)²+60²]=d/dt(D²)
[d(A+B)]/dt*2(A+B)(2)=dD/dt*2D
B=5km/h*4hr=20km
A=15km/hr*4=60km
20²+60²=D²
D=√4000
(15+5)*(2)*80*(2)=2*√4000*dD/dt
dD/dt=6400/√4000=101.192 km/hr
The two ships are sailing in opposite sides, Hence, the resultant speed is given by 15+5 = 20 km/hr.
Therefore, from the below triangle, we have
[tex]\frac{dx}{dt} = 20 \text{ km/hr}[/tex]
Let the distance between the ships is y. On applying Pythagorous theorem, we have
[tex]y^2=x^2+60^2\\ \text{On differentiating, we get}\\ 2y\frac{dy}{dt} =2x\frac{dx}{dt}\\\frac{dy}{dt}= \frac{x}{y} \frac{dx}{dt}[/tex]
On substituting the value of y as [tex]y=\sqrt{60^2+x^2}[/tex]
[tex]\frac{dy}{dt} =\frac{x}{\sqrt{60^2+x^2}} \frac{dx}{dt}[/tex]
Since, the at noon the ship is 60 km to each other. Hence, for 4 PM, i.e. t=4, we have
[tex]x=4 \times \frac{dx}{dt} \\ x= 4 \times 20 \\x=80[/tex]
On substituting the value in above, we get
[tex]\frac{dy}{dt} =\frac{80}{\sqrt{60^2+80^2}} (20[/tex]
[tex]\frac{dy}{dt} = 16.0 \text{ km/hr}[/tex]
Therefore, the distance between the ships changing at a rate of 16 km/hr at 4:00 pm
plz help ill give u branlist
Answers
so...
48 + 7(x + 1) = 90
7(x + 1) = 42
x + 1 = 6
x = 5
simplify the complex fraction
Answers
the final answer is (y+z)/(y-z)
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
Answers
It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65
Force angle x-component y-component
25 30 25cos(30)=21.65 25sin(30)=12.5
30 100 30cos(100)=-5.21 30sin(100)=29.54
Total Fx=16.44 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 °
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds
The region r is bounded by the parabola y = x2 and the line y = 4. set up definite integrals to find the moment mx of r about the x-axis and the area a of the region r. then find (x, y )
Answers
Volume is 256π/5, area is 32/3.
Details are in the attachment.
P.S. intersection points are (-2;4) and (2;4).
6 Bands were going to play at a concert. How many ways can the concert manager send them on stage?
Answers
there are two ways to resolve this task:
1. the 1st in this sequence is for 6 bands, the 2d in this sequence is for 5 rest bands, the 3d in this sequence is for 4 rest bands, the 4th in this sequence is for rest 3 bands, the 5th in this sequence is for rest 2 bands and the 6th in this sequence is for the last 1 band. Using the logical rule 'AND': A=6*5*4*3*2*1=720.
2. According to arrangement rules it is the formula: A=n!, where n - number of bands.
A=6!=720.
answer: 720.
determine the area of a 21ft circle
Answers
.. = (π/4)*(21 ft)^2
.. = 110.25π ft^2
.. ≈ 346.36 ft^2
The prism is completely filled with 1750 cubes that have edge length of 1/5 feet. What is the volume of the prism,
Answers
the volume one cube=(1/5)*(1/5)*(1/5)=(1/125) ft³
the volume of prism=1750*(1/125)=14 ft³
the answer is 14 ft³
Using synthetic division, find the quotient Q(x) and the remainder R if the polynomial P(x) = x3 − 2x2 − 3x + 18 is divided by (x + 2).
Answers
quotient: x^2 - 4x + 5
remainder: 8
Explanation:
1) Given
p(x) = x^3 - 2x^2 - 3x + 18
divisor: x + 2
2) Write the coefficients of p(x) in order:
1 -2 -3 18
3) dividing by x + 2 => run the division for x = - 2
4) division
| 1 -2 -3 +18
|
-2 | -2 +8 - 10
-----------------------------------
1 -4 +5 +8
The last digit is the remainder, the others are the coefficients of the quotient:
=>
quotient = x^2 - 4x + 5
remainder = 8
The quotient Q(x) is found to be x² - 4x - 11 and the remainder R is 4.
The question involves using synthetic division to find the quotient Q(x) and the remainder R when the polynomial P(x) = x³ − 2x² − 3x + 18 is divided by (x + 2).
To perform synthetic division, we first write down the coefficients of P(x): 1, -2, -3, and 18. The divisor is (x + 2), so we use -2 for the synthetic division.
Write the coefficients of P(x): 1, -2, -3, 18.
Write the root of the divisor (x + 2) = -2 on the left side of the synthetic division setup.
Bring down the first coefficient (1).
Multiply -2 by 1, place the result (-2) under the second coefficient (-2), and add the two numbers yielding -4.
Repeat the multiplication and addition process for the rest of the coefficients.
The results of the synthetic division process give us the coefficients of the quotient Q(x) and the remainder R.
In performing the synthetic division, we find that the quotient Q(x) is x² - 4x - 11 and the remainder is R = 4.
One angle of a rhombus measures 108°, and the shorter diagonal is 9 inches long. Approximately how long is the side of the rhombus? (Hint: Diagonals of a rhombus bisect the angles.) 7 in. 8 in. 11 in.
Answers
cos θ=adjacent /hypotenuse
θ=108/2=54°
adjacent = 9/2=4.5 inch
hypotenuse=length of the rhombus
thus
cos 54=9/x
x=4.5/cos 54
x=7.6558~8 inches
the answer is 8 inches
Answer:
8 in.
Step-by-step explanation:
Let's find the rhombus's length...
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine = ° = 54°
adjacent = = 4.5 in
Length of Rhombus = Hypotenuse
So...
cos54 = [tex]\frac{9}{x}[/tex]
x = [tex]\frac{4.5}{cos 54}[/tex]
x = 7.6558... about 8 inches
A math test took 50 minutes to complete. The test ended at 3:55. What time did the test begin?
Answers
A math test ended at 3:55 and it took 50 minutes to complete. What time did the math test start?
The math test started at 3:05.
If we know that the math test ended at 3:55 and lasted 50 minutes, we can subtract 50 minutes from 3:55 and we will get an answer of 3:05.
Therefore, the math test started at 3:05.
A square playground has an area of 175 m2. What is the approximate length of each side of the playground? Round your answer to the nearest meter
Answers
Therefore, for a known area A, the side length is
side = √ (area)
= √ (175)
= 13.2288 (to 4 places of decimals).
If the area of a square playground is 175 [tex]m^{2}[/tex] then the approximate length is 13 meters.
What is square?A square is a two dimensional figure having four vertices, four edges, four angles and all the sides are equal to each other. The perimeter is equal is equal to 4*side and the area is side*side.
How to find side of square?We have been given the area of the square playground equal to 175 meter square. We know that the area of a square is side*side means [tex]side^{2}[/tex].
Put the value of 175 equal to side square and we will get the value of slide.
Area =[tex]side^{2}[/tex]
175=[tex]side^{2}[/tex]
side=[tex]\sqrt{175}[/tex]
Side=13.22m
If we round to nearest meter then it will be equal to 13m.
Hence if the area of a square playground is 175 meter square then the side will be equal to 13m.
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a parallelogram has an area of 108 square inches. The base of the parallelogram is 18 inches. Explain how you could find the height of the parallelogram, then find the height. Show your work.
Answers
A=bh
108=18h
divide both sides by 18 to find h
6=h
The height is 6 inches.
Answer:
Height=6in
Step-by-step explanation:
Took test and got it correct
Please help me with this question
Answers
1. S=12²-10²=44 sq. ft.
2. S=10*12-6*8=120-48=72 sq. ft.
answers: 1-C; 2-C.
find the product 3012 and 4