Volume of a cylinder = base area x heigth
Volume = 603.2 in3
Height = 12 in
Replacing:
603.2 = base area x 12
603.2/12 = base area
Base area = 50.26 in2
Which expression has the fewest number of significant figures?A. 5,280B. 360C. 296.54D. 18.3
Concept
To determine the number of significant figures in a number use the following 3 rules:
1. Non-zero digits are always significant.
2. Any zeros between two significant digits are significant.
3. A final zero or trailing zeros in the decimal portion ONLY are significant.
Let's check through the options:
5,280
This has 3 significant figures
360
This has 2 significant figures
296.54
This has 5 significant figures
18.3
This has 3 significant figures
B) The value of the function decreased by ____ per year after 1990
From the question
We are given the function
[tex]y=-0.5x+29[/tex]Comparing the function with the equation
[tex]y=mx+c[/tex]Then the slope of the function is
m = - 0.5
Using the function
[tex]y=-0.5x+29[/tex]When x = 1
[tex]\begin{gathered} y=-0.5(1)+29 \\ y=28.5 \end{gathered}[/tex]When x = 2
[tex]\begin{gathered} y=-0.5(2)+29 \\ y=28 \end{gathered}[/tex]When x = 3
[tex]\begin{gathered} y=-0.5(3)+29 \\ y=27.5 \end{gathered}[/tex]By comparing the values of y, we will notice a decrease of 0.5
Hence,
The value of the function decreased by 0.5 per year after 1990
Given a Markup of $8.45 and a Selling Price of $42.25 find the Cost
Find measure angle ABD and measure angle CBD #C 2x A B
As we see in the figure, BD bisects the right angle ABC and thus, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.
From the given figure, we have
∠ABD = 4x° ---- (1)
∠CBD = 2x° ---- (2)
∠ABC = 90° ---- (3)
We have to find out the values of the ∠ABD and ∠CBD.
As given in the figure, we can see that BD bisects ∠ABC into ∠ABD and ∠CBD. So, we can say that -
∠ABD + ∠CBD = ∠ABC
=> 4x° + 2x° = 90° [From equation (1), (2), (3)]
=> 6x° = 90°
=> x° = 15° ---- (4)
Substituting equation (4) in equations (1) and (2), we get
∠ABD = 4x° and ∠CBD = 2x°
=> ∠ABD = 4*15° and ∠CBD = 2*15°
=> ∠ABD = 60° and ∠CBD = 30°
Since BD bisects the right angle ABC, we find out that ∠ABD = 60° and ∠CBD = 30°. Thus, option 1 is correct.
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Write an expression for the height of the flag after t seconds
Answer:
2t + 16
Explanation:
The graph shows that there is a linear relationship between height and time. So, we need to find the equation of a line with the form:
h = mt + b
Where m is the slope of the line and b is the y-intercept.
So, b is equal to the value of the height after 0 seconds, therefore, b or the y-intercept is equal to 16
b = 16
On the other hand, the slope can be calculated as:
[tex]m=\frac{h_2-h_1}{t_2-t_1}[/tex]Where t1 and t2 are two values of time in the table and h1 and h2 are their respective values of height.
So, if we replace t1 by 1, h1 by 18, t2 by 2, and h2 by 20, we get:
[tex]m=\frac{20-18}{2-1}=\frac{2}{1}=2[/tex]Therefore, the expression for the height of the flag after t seconds is:
h = 2t + 16
Waterworks is a company that manufactures and sells paddle boards. It's profit P, in hundreds of dollars earned, is a function of the number of paddle boards sold x, measured in thousands. Profit is modeled by the function P(x)=-2x^3+34x^2-120x. What do the zeros of the function tell you about the number of paddle boards that waterworks should produce?
areAs given by the question
There are given that the profit function
[tex]P(x)=-2x^3+34x^2-120x[/tex]Now,
The zeros are the x values where the graph intersects the x axis.
Then,
To find the zeroes, replace P(x) with 0 and solve for x.
Then,
The zeroes of the given function is:
[tex]\begin{gathered} P(x)=-2x^3+34x^2-120x \\ 0=-2x(x^2-17x^{}+60) \\ x^2-17x^{}+60=0 \\ (x-12)(x-5)=0 \\ x=0,\text{ 12, 5} \end{gathered}[/tex]Hence, the zeroes of the function is 0, 12, 5.
Solve the formula for the indicated variable.surface area of cone; S=r^2+rl; solve for l.
Given:
The formula for the surface area of the cone is given as,
[tex]\begin{gathered} S.A\text{ = }\pi r^2+\pi rl \\ \end{gathered}[/tex]Required:
The modified formula for the surface area of the cone in terms of l.
Explanation:
The formula is given as,
[tex]S=\pi r^2+\pi rl[/tex]Taking common terms separately,
[tex]\begin{gathered} S\text{ = }\pi r(r\text{ + l\rparen}_{\text{ }} \\ \end{gathered}[/tex]Transposing the common terms to LHS,
[tex]r\text{ + l = }\frac{S}{\pi r}[/tex]Rearranging the equation for l,
[tex]\begin{gathered} l\text{ = }\frac{S}{\pi r}\text{ - r} \\ l\text{ = }\frac{S-\pi r^2}{\pi r} \end{gathered}[/tex]Answer:
Thus the required expression in terms of l is,
[tex]l=\frac{\text{S-\pi r}^2\text{{}}}{\text{\pi r}}[/tex]What is the distance between the points (9.0) and (0,5) on the coordinate plane?
( x 1 , y 1 ) = ( 9,0 )
( x 2 , y 2 ) = ( 0, 5 )
Distance between the points:
d^2 = ( x2 - x1 ) ^2 + ( y2 - y1 ) ^2
= ( 0 - 9 ) ^2 + ( 5 - 0 )^2
= 81 + 25
= 106
square root both sides, we have:
d = 10 . 296
d = 10. 3 units ( 1 decimal place)
Classify the following variables as quantitative or qualitative variables. If the variable is quantitative, identify whether it is discrete or continuous.The daily number of customers in a store.
A quantitative variable is the one who has a numerical significance such as number of items, time spent on playing a video game while a qualitative variable is the one who has not a numerical significance attached to it such as Gender , Eye color
Further in quantitative variable , discrete variable is the one which is a whole number and can not be broken down further , like number of items
while a continuous variable is the one which takes any value within an interval of values like between 1 and 2 , continuous variable can take any value like 1.21, 1.55556, 1.994 etc.
The daily number of customers in a store can take a whole number value.
Thus, the variable is discrete.
In a right triangle, the side opposite angle θ has a length of 80 inches, the side adjacent to angle θ has a length of 84 inches, and the hypotenuse has a length of 116 inches. What is the value of tan(θ)?
Solution:
The sides of a right triangle are hypotenuse, opposite, and adjacent.
The hypotenuse is the longest sides of the triangle.
The opposite is the side facing the angle.
The adjacent is the third side of the right triangle.
This sides are illustrated as shown below:
Thus, in the above right triangle ABC,
[tex]\begin{gathered} AC\Rightarrow hypotenuse \\ AB\Rightarrow opposite \\ BC\Rightarrow adjacent \end{gathered}[/tex]Given that the opposite side has a length of 80 inches, adjacent has a length of 84 inches, and the hypotenuse has a length of 116 inches, this implies that
[tex]\begin{gathered} AC=116 \\ AB=80 \\ BC=84 \end{gathered}[/tex]To evaluate the value of
[tex]\tan(\theta)[/tex]We use trigonometric ratios.
From trigonometric ratios,
[tex]\tan\theta=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} where \\ opposite\Rightarrow AB=80 \\ adjacent\Rightarrow BC=84 \\ thus, \\ \tan(\theta)=\frac{AB}{BC}\frac{}{} \\ =\frac{80}{84}=0.9523809524 \end{gathered}[/tex]Hence, the value of tan (θ) is
[tex]0.952[/tex]The first option is the correct answer.
Background Layout - Theme Transition 910 78 45 111 112 113 11 USE THE GIVEN INFORMATION TO ANSWER EACH QUESTION BELOW. 5(4) From the choices at the right, drag the expression that could be used to find the area of each piece 132 Andre needs to paint three square pieces of wood in the sizes shown. He has them arranged so that they meet to form a right triangle A: B: C: 13 Type to record the number of square centimeters Andre will need to paint on each piece 12(4) INTRO TO PYTHAGOREAN THEOREM A: B: C: 122 C 13 cm 123 A 5 cm 3 Add the area of piece A and the area of piece B together. What does this prove about the side lengths in a right triangle? 12 cm 52 B DRAG THESE Mong the Middle LLC, 2019
The area of a square is the squared side, it means
[tex]A=l^2[/tex]It means, for A, which has a side of 5, the area is
[tex]5^2[/tex]For B, which side is 12, its area is
[tex]12^2[/tex]For C, the area is
[tex]13^2[/tex]Andre has to paint (solve each power):
[tex]\begin{gathered} A=25 \\ B=144 \\ C=169 \end{gathered}[/tex]Once we add the areas of A and B we realize that the sum is equal to the area of C, it proves the pythagorean theorem that says that the sum of the squared length of the legs equals the squared length of the hypotenuse
Which of the following equations has roots x=3 (multiplicity 3) and x=−i, and passes through the point (1,-16)?
To verify that a value is a root of a function we use the following setup
F(x) = 0 and replace x by the value in this case 3 and -i.
Let's begin with x=3
[tex]\begin{gathered} f(x)\text{ = }x^3+3x^2+x+3 \\ f(3)\text{ = }3^3+3\cdot3^2+3+3 \\ f(3)\text{ = 60} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }x^5+9x^4+28x^3+36x^2+27x+27 \\ f(3)\text{ = 3}^5\text{+9}\cdot3^4\text{{}+28}\cdot3^3\text{+36}\cdot\text{3}^2\text{+27}\cdot3\text{+27} \\ f(3)\text{ = 2160} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }x^5-9x^4+28x^3-36x^2+27x-27 \\ f(3)\text{ = 3}^5-\text{9}\cdot3^4\text{{}+28}\cdot3^3-\text{36}\cdot\text{3}^2\text{+27}\cdot3-\text{27} \\ f(3)\text{ = 0} \end{gathered}[/tex][tex]\begin{gathered} f(x)\text{ = }x^3+3x^2+x+3 \\ f(3)\text{ = }3^3-3\cdot3^2+3-3 \\ f(3)\text{ = 0} \end{gathered}[/tex]Only options C and D pass the first filter.
Let's apply x=-i to those options
[tex]f(-i)\text{ = }(-i\text{\rparen}^5\text{ - 9}\cdot\left(-i\right)^4\text{ + 28}\cdot\text{\lparen-i\rparen}^3\text{ - 36}\cdot(-i)^2+27\cdot(-i)-27[/tex][tex]\begin{gathered} f(-i)\text{ = }-i\text{ - 9 + 28 i - 36}-27i-27 \\ f(-i)\text{ = 0} \end{gathered}[/tex][tex]f(-i)\text{ = \lparen-i\rparen}^3-3\left(-i\right)^2+(-i)-3[/tex][tex]\begin{gathered} f(-i)\text{ = i+ }3-i-3 \\ f(-i)\text{ = 0} \end{gathered}[/tex]both of the accomplish the equality f(x)=0
So to finish we replace the point to check which functions pass
Replacing f(1) = -16
[tex]\begin{gathered} \left(1\right)^5-9\cdot\left(1\right)^4+28\cdot(1)^3-36^{\cdot}(1)^2+27\cdot(1)-27 \\ f(1)\text{ = -16} \end{gathered}[/tex]This is equals to -16
[tex]\begin{gathered} \text{ f\lparen1\rparen= 1- }3+1-3 \\ f(1)=-4 \end{gathered}[/tex]So the answer is option C
What is an equation of the line that passes through the point (6,-2) and is parallel to the line y=2/3x+4?
point = (6,-2)
Parallel to y= 2/3x+4
If 2 lines are parallel, both have the same slope
Slope intercept form:
y= mx +b
where:
m= slope
b= y intercept
so, for y= 2/3x+4
slope = 2/3
So far we have
y= 2/3x +b
Replace x,y by the coordinate point given (6,-2) and solve for b:
-2 = 2/3 (6) + b
-2 = 4 + b
-2-4 = b
-6 = b
Final equation:
y= 2/3x - 6
If you are rolling two dice (numbered 1-6), what is the probability that the first die shows an odd number and the second die shows a number larger than 4?
Since we have two dices and we want to know the events where the first one shows an odd number and the second die shows a number larger than 4, we have that the following results are the ones that fit the requirement:
[tex](1,5),(1,6),(3,5),(3,6),(5,5),(5,6)[/tex]Now, we know that the sample space has 6x6=36 possible outcomes, therefore, the desired probability is:
[tex]P(\text{odd,x}>4)=\frac{6}{36}=\frac{1}{6}[/tex]therefore, the probability is 1/6
Translate the sentence into an equation.Twice the difference of a number and 9 equals 6.Use the variable y for the unknown number.
The difference of a number (y) and 9 is written as
[tex]y-9[/tex]Then, twice the difference of a number and 9 is
[tex]2(y-9)[/tex]Finally, set the later expression to be equal to 6,
[tex]\Rightarrow2(y-9)=6[/tex]The equation is 2(y-9)=6
Need Help Pls Answer
Answer:
5 yd
Step-by-step explanation:
A square is a quadrilateral with 4 sides of equal length.
The area of a square is found by squaring one side length:
[tex]A=s^2 \quad \textsf{(where $s$ is the side length)}[/tex]
Therefore, to find the side length of a square, simply square root its area:
[tex]\implies A=s^2[/tex]
[tex]\implies \sqrt{A}=\sqrt{s^2}[/tex]
[tex]\implies \sqrt{A}=s[/tex]
[tex]\implies s=\sqrt{A}[/tex]
Therefore, if the area of a square is 25 yd²:
[tex]\implies s=\sqrt{25}[/tex]
[tex]\implies s=5\; \sf yd[/tex]
Answer:
Length (s) = 5 yards
Step-by-step explanation:
Given information is,
→ Area (a) = 25 yd²
→ Length (s) = ?
Now we have to,
→ find the length of side of square.
Formula we use,
→ s² = Area of square
→ s² = a
Then the required length is,
→ s² = a
→ s² = 25
→ s = √(25)
→ [ s = 5 ]
Hence, the length is 5 yards.
suppose that GX equals FX +8+4 which statement best compares the graph of GX with the graph of FX
As given by the question
There are given that the value of g(x) is:
[tex]g(x)=f(x+8)+4[/tex]Now,
According to the rule of transformation,
y = f(x+c) the function f(x) is being shifted c units left
And, for y=f(x)+d, the function f(x) is being shifed d units up
So,
In the given functiong(x)= f(x+8)+4 the value of c is 8 and value of d is 4
So,
The graph of g(x) is the graph of f(x) shifted 8 units to the left and 4 units up.
Hence, the correct option is A
solve for X in the equation
We are given the following equation
[tex]-\frac{3}{2}=\frac{x}{10}[/tex]Let us solve the equation for x
Firstly, apply the cross multiplication
[tex]\begin{gathered} -\frac{3}{2}=\frac{x}{10} \\ -3\cdot10=2\cdot x \\ -30=2x \end{gathered}[/tex]Now, divide both sides of the equation by 2 (so that the 2 on the right side gets canceled)
[tex]\begin{gathered} -30=2x \\ \frac{-30}{2}=\frac{2x}{2} \\ -\frac{30}{2}=x \\ -15=x \\ x=-15 \end{gathered}[/tex]Therefore, the value of x is -15
How can ️WXY be mapped to ️MNQ Translate vertex W to vertex M, then reflect across the line containing A WXB WYC XYD MQ
The answer is WX, because
A) Angle CDE measures 80 degrees.B)Angle CDE measures 100 degrees C) The sum of the measures of the arcs from E to C, one passing through D and passing through b is 360D)The arcs from E to C passing through D measures 100 degreesE) Angle BCD measures 50 degrees F) The arc from B to D passing through C measures 100
Given the figure of a cyclic quadrilateral
We will check whether the given statements are true or false.
A) Angle CDE measures 80 degrees.
True
Because the sum of the opposite angles has a sum of 180
B) Angle CDE measures 100 degrees
False
C) The sum of the measures of the arcs from E to C, one passing through D and passing through b is 360
True
Because the sum of the central angles of the circle = 360
The two arcs are forming the complete circle.
D)The arcs from E to C passing through D measure 100 degrees
False
Because the measure of the arc = 2 times the angle CBE = 200
E) Angle BCD measures 50 degrees
False
Because the measure of the angle BCD = 180 - 50 = 130
The sum of the opposite angles = 180
F) The arc from B to D passing through C measures 100
True
Because the inscribed angle opposite the arc = 50
So, the measure of the arc = 2 times the opposite inscribed angle
1. If I have at most $10 in my pocket what does this mean? What symbol would you use for "at most"?2. If I have at least $10 in my pocket what does this mean? What symbol would you use for "at least"?
ANSWER:
[tex]\begin{gathered} 1.\text{ }x\le10 \\ 2.\text{ }x\ge10 \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
1.
In this case it means that you actually have $10 or less, so an inequality that represents the situation would be:
[tex]x\le10[/tex]2.
In this case it means that you actually have $10 or more, therefore, an inequality that represents the situation would be:
[tex]x\ge10[/tex]match a graph with the story below.Writte the letter of the graph that corresponds with the story.Explain your answer.1. Opposite Tom’s home is a hill. Tom climbed slowly up the hill, walked across the top, and then ran quickly down the other side.2. Tom skateboarded from his house, gradually building up speed. He slowed down to avoid some rough ground, but then speeded up again.3. Tom walked slowly along the road, stopped to look at his watch, realized he was late, and then started running.4. This graph is just plain wrong. How can Tom be in two places at once?5. After the party, Tom walked slowly all the way home.
1. D
This graph shows an increase in speed. At first it's slow (Tom climbing up the hill), then it's a little faster (Tom walking across the top) and then it increases more (Tom running down the hill)
2. F
This graph shows a gradual increase of speed, then the speed it's almost zero -which means that in a long interval of time Tom did very little distance- and then the speed goes up again.
3. C
In this story, Tom stopped for a moment and then sped up. In graph C there's a horizontal line at a given distance. This means that Tom stopped walking and, naturally, the time kept going on.
4. H
There's a vertical line in this graph. It means that for a given time Tom was at one distance from home and at another distance from home at the same time. That's why this graph is wrong
5. J
Distance from home = 0 means he's home. He walked all the way home, so the graph has to start at a point that's not 0 and end at distance from home = 0
Anu wants to recover the cylindrical stool in his bedroom how much material does he need if there is no overlap and he does not recover the bottom of the store
Answer:
Given that,
Anu wants to recover the cylindrical stool in his bedroom how much material does he need if there is no overlap and he does not recover the bottom of the store.
From the figure,
the diameter of the cylinder is 42 cm
height of the cylinder is 32 cm
we have that,
Curved surface area of the cylinder is,
[tex]=2\pi rh[/tex]where r is the radius of the cylinder and h is the height of the cylinder.
Radius of the cylinder is 42/2 cm =21 cm
Radius of the cylinder is 21 cm.
Substituting the values we get,
Curved surface area of the cylinder is,
[tex]=2\times\frac{22}{7}\times21\times32[/tex][tex]=4224cm^2[/tex]Area of the top is,
[tex]\begin{gathered} =2\pi r=2\times\frac{22}{7}\times21 \\ =132cm^2 \end{gathered}[/tex]Required area=Curved surface area+area of the top
we get,
Required area of the cylinder=
[tex]=4224+132[/tex][tex]=4356cm^2[/tex]The required amount of material is 4,356 cm square.
Solve the equation for the missing variable. Assume all variables are positive. Express your answer to nearest tenth.a^2+6^2=14^2
Here, we want to solve the given equation
We proceed as follows;
[tex]\begin{gathered} a^2+6^2=14^2 \\ a^2+36\text{ = 196} \\ a^2=\text{ 196-36} \\ a^2\text{ = 160} \\ a\text{ = }\sqrt[]{160} \\ a\text{ = +12.6 or -12.6} \end{gathered}[/tex]HelpHelp me with this thank you thank you thank you
Given
Quadratic equation
Find
Explain best method to solve equation
Explanation
I prefer the factorisation method to solve the equation.
to solve the equation with this method we take following steps
1. Put all the terms on one side.
2. then factor
3. now, set every factor equal to zero
4. next, solve the new equation which obtained by taking equal to zero
5. atlast, check the solution by puting values in main equation
Now, let us take an example
[tex]x^2-6x=16[/tex]now, use step 1st
[tex]x^2-6x-16[/tex]next, factor
[tex](x-8)(x+2)=0[/tex]now, put each factor equal to 0 and solve for x
[tex]\begin{gathered} x-8=0,\text{ x+2=0} \\ x=8.\text{ x=-2} \end{gathered}[/tex]Final Answer
Factorisation is the best method to solve quadratic equation
Hello, could you help me solve this question? Solve this answer using the sum of the geometric sequence formula.
Given that:
- Cory saves $30 in June.
- Each month he plans to save 10% more than the previous month.
- He saves money from June to December.
You can convert 10% to a decimal number by dividing it by 100:
[tex]10\text{ \%}=\frac{10}{100}=0.1[/tex]You already know that he has $30 in June. Then, you can determine that the amount of money (in dollars) he will save in July is:
[tex]30+(30\cdot0.1)=33[/tex]By definition, the formula for the Sum of a Geometric Sequence is:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]Where "r" is the Common Ratio, "n" is the number of terms, and this is the first term:
[tex]a_1[/tex]In this case, you can identify that the first term is:
[tex]a_1=30[/tex]And the second term is:
[tex]a_2=33[/tex]Therefore, you can find the Common Ratio as follows:
[tex]r=\frac{33}{30}=1.1[/tex]Since he saves money from June to December, the sequence has 7 terms. Then:
[tex]n=7[/tex]Now you can substitute values into the formula and evaluate:
[tex]S_7=\frac{30(1-(1.1)^7)}{1-r}\approx284.615[/tex]Hence, the answer is:
[tex]\text{ \$}284.615[/tex]
Rewrite in simplest terms: 10(7p + 6) – 5(5p + 4)
Answer:
Step-by-step explanation:
10(7p + 6) – 5(5p + 4)=70p+60-25p-20=45p+40=5(9p+8)
Question is down below. Please state the Claim, Evidence and reasoning to why the answer is correct.
the distance the ship travelled from point A to D is 582 ft
Explanation:To dtermine the distance from point A to D, we need to find the distance from point A to C and distance from point C to D
To get the distance from point C to D, we will consider triangle BCD:
opposite = 125 ft
DC = ?
angle = 16°
To get DC (adjacent), we will use tan ratio:
[tex]\begin{gathered} \tan \text{ 16}\degree\text{ = }\frac{opposite}{adjacent} \\ \tan \text{ 16}\degree\text{= }\frac{125}{DC} \\ DC(\tan \text{ 16}\degree)\text{ = 125} \\ DC\text{ = }\frac{125}{\tan\text{ 16}\degree} \\ DC\text{ = }435.93\text{ ft} \end{gathered}[/tex]To get the distance from point A to C, we will consider triangle ABC:
opposite = 125 ft
AC = ?
angle = 7°
To get AC (adjacent), we will use tan ratio:
[tex]\begin{gathered} \tan \text{ 7}\degree\text{ = }\frac{opposite}{adjacent} \\ \tan \text{ 7}\degree\text{= }\frac{125}{AC} \\ AC(\tan \text{ 7}\degree)\text{ = 125} \\ AC\text{ = }\frac{125}{\tan\text{ 7}\degree} \\ AC\text{ = }1018.04\text{ ft} \end{gathered}[/tex]Distance AC = Distance DC + Distance AD
[tex]\begin{gathered} 1018.04\text{ = 435.93 + Distance AD} \\ \text{Distance AD = 1018.04 - 435.93} \\ \text{Distance AD = 582.11 ft} \end{gathered}[/tex]The distance the ship travelled from point A to D = Distance AD
To the nearest foot, the distance the ship travelled from point A to D is 582 ft
I need help with this question please Identify the binomial that is a factor of the polynomial
(x-2)
1) Let's use the Rational Roots Theorem so that we can factor this Polynomial and find the factors that make up this Polynomial.
2) Taking all the factors of the constant and the leading coefficients we have:
[tex]P(x)=3x^3-11x^2-2x+24[/tex]
Let's enlist these factors:
[tex]\begin{gathered} 24\colon\pm1,\pm2,\pm4,\pm3,\pm6,\pm8,\pm12,\pm24 \\ 3\colon\pm1,\pm3 \end{gathered}[/tex]2.2) Let's pick any number on the numerator and divide it by any number of the denominator, to get possible roots:
[tex]\begin{gathered} \frac{\pm1,\pm2,\pm4,\pm3,\pm6,\pm8,\pm12,\pm24}{\pm1,\pm3}=\pm1,\pm2,\pm\frac{4}{3}, \\ \end{gathered}[/tex]Proceeding with that let's do a Synthetic Division, testing 2
[tex]\begin{gathered} \frac{3x^3-11x^2-2x+24}{(x-2)}= \\ (x-2)(3x^2-5x-12) \\ (x-2)(3x+4)(x-3) \end{gathered}[/tex]Note that we have three factors. After factoring out
3) Hence, the answer is (x-2)
Find the least common multiple of these two expressions. 12x^2w^6v^8 and 8x^5w^3
Given
[tex]12x^2w^6v^8\text{ }and\text{ }8x^5w^3[/tex]To find:
The Least Common Multiple of the above expressions.
Explanation:
It is given that,
[tex]12x^2w^6v^8\text{ }and\text{ }8x^5w^3[/tex]That implies,
[tex]\begin{gathered} 12x^2w^6v^8=4\cdot3\cdot x^2\cdot w^3\cdot w^3\cdot v^8 \\ 8x^5w^3=4\cdot2\cdot x^2\cdot x^3\cdot w^3 \\ \therefore LCM=4\cdot3\cdot2\cdot x^2\cdot x^3\cdot w^3\cdot w^3\cdot v^8 \\ =24x^5w^6v^8 \end{gathered}[/tex]Hence, the Least Common Multiple of the given expressions is,
[tex]LCM=24x^5w^6v^8[/tex]