Final answer:
To find the product (f × g)(x), simply multiply the functions f(x) = 3x + 8 and g(x) = x^2 together. The result is (f × g)(x) = 3x^3 + 8x^2.
Explanation:
To find the product (f × g)(x), you need to multiply the function f(x) by the function g(x). Given f(x) = 3x + 8 and g(x) = x^2, the product (also known as the composition of functions) is obtained by multiplying these two functions together.
The product is calculated as follows:
(f × g)(x) = f(x)×g(x) = (3x + 8)×(x^2).
Now, distribute the x^2 term across the terms inside the parentheses:
(f × g)(x) = 3x^3 + 8x^2.
This is the simplified form of the product of the two functions.
Use power series to find two linearly independent solutions of y''-2xy'+4y = 0
Assume a general solution of the form
[tex]y(x)=\displaystyle\sum_{n\ge0}a_nx^n[/tex]
with derivatives
[tex]y'(x)=\displaystyle\sum_{n\ge0}na_nx^{n-1}=\sum_{n\ge1}na_nx^{n-1}[/tex]
[tex]y''(x)=\displaystyle\sum_{n\ge0}n(n-1)a_nx^{n-2}=\sum_{n\ge2}n(n-1)a_nx^{n-2}[/tex]
Substituting into the ODE gives
[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-2\sum_{n\ge1}na_nx^n+4\sum_{n\ge0}a_nx^n=0[/tex]
The first sum starts with degree 0; the second starts with degree 1; and the third starts with degree 0. So remove the first term from the first and third sums, then consolidate everything into one sum by shifting indices as needed.
First sum:
[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge3}n(n-1)a_nx^{n-2}[/tex]
[tex]\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}=2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n[/tex]
Third sum:
[tex]\displaystyle\sum_{n\ge0}a_nx^n=a_0+\sum_{n\ge1}a_nx^n[/tex]
So the ODE can be expressed as
[tex]\displaystyle\left(2a_2+\sum_{n\ge1}(n+2)(n+1)a_{n+2}x^n\right)-2\sum_{n\ge1}na_nx^n+4\left(a_0+\sum_{n\ge1}a_nx^n\right)=0[/tex]
[tex]\displaystyle2a_2+4a_0+\sum_{n\ge1}\bigg((n+2)(n+1)a_{n+2}+(4-2n)a_n\bigg)x^n=0[/tex]
Then the coefficients are given by the recurrence,
[tex]\begin{cases}a_0=a_0\\a_1=a_1\\2(2-n)a_n+(n+2)(n+1)a_{n+2}=0&\text{for }n\ge0\end{cases}[/tex]
Notice that we should have [tex]a_0\neq0[/tex] and [tex]a_1\neq0[/tex] in order to get non-zero solutions.
For [tex]n=2[/tex], we would find that [tex]a_4=0[/tex], which would imply that [tex]a_n=0[/tex] for all even [tex]n\ge2[/tex]. Then the even-indexed terms in the series contribute one solution,
[tex]y_1(x)=a_0+a_2x^2=a_0(1-2x^2)[/tex].
On the other hand, for odd [tex]n\ge1[/tex] we have
[tex]a_{n+2}=\dfrac{2(n-2)}{(n+2)(n+1)}a_n[/tex]
With [tex]n=1[/tex]:
[tex]a_3=\dfrac{2\cdot(-1)}{3\cdot2}a_1=-\dfrac2{3!}a_1[/tex]
With [tex]n=3[/tex]:
[tex]a_5=\dfrac{2\cdot1}{5\cdot4}a_3=-\dfrac{2^2\cdot1}{5!}a_1[/tex]
With [tex]n=5[/tex]:
[tex]a_7=\dfrac{2\cdot3}{7\cdot6}a_5=-\dfrac{2^3\cdot3\cdot1}{7!}a_1[/tex]
So the general pattern for [tex]n=2k+1[/tex], [tex]k\ge1[/tex], is
[tex]a_{2k+1}=-\dfrac{2^k\prod\limits_{i=1}^{k-1}(2i-1)}{(2k+1)!}a_1[/tex]
and we get a second (linearly independent) solution
[tex]y_2(x)=a_1x+\displaystyle\sum_{k\ge1}a_{2k+1}x^{2k+1}[/tex]
Which statements are true about a rectangular pyramid with a height of 9 centimeters and a base with the dimensions of 4 centimeters by 6 centimeters? Check all that apply.
A.The area of the base of the pyramid, B, is 8cm2.
B.The area of the base of the pyramid, B, is 24cm2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
D.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 1/3 of the volume of this pyramid.
E.The volume of this pyramid is 72cm3.
F.The volume of this pyramid is 216cm3.
Answer:
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
Step-by-step explanation:
Area of base of the pyramid = l × w = 4 × 6 = 24 cm^2
Volume of rectangular pyramid = (l × w × h)/3 = (4 × 6 × 9)/3 = 72 cm^3
Volume of rectangular prism = w × h × l = 9 × 4 × 6 = 216 cm^3
So according to these calculations, the correct answer options are:
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
Final answer:
The true statements about the rectangular pyramid are B, C, and E.
The base area is 24 cm² (Statement B), the volume of the pyramid is 72 cm³ (Statement E), and the volume of a similarly dimensioned rectangular prism is three times that of the pyramid (Statement C).
Explanation:
To determine which statements are true about the rectangular pyramid with given dimensions, we need to calculate the base area and the volume of both the pyramid and the rectangular prism and compare them.
The base area of the pyramid, denoted as B, is the area of the rectangle formed by the base's dimensions.
Therefore, B = length x width = 4 cm x 6 cm = 24 cm².
Thus, statement B is true.
For the volume of the pyramid (V), we use the formula V = (1/3) x B x height.
Plugging the values, we get V = (1/3) x 24 cm² x 9 cm, which equals 72 cm³.
So, statement E is true.
The volume of a rectangular prism with the same height and base dimensions is volume of the prism = length x width x height = 4 cm x 6 cm x 9 cm = 216 cm³.
Since the volume of the prism is three times the volume of the pyramid, statement C is true.
Statements A, D, and F are not true based on the above calculations and explanations.
Find the 7th term of the expansion of (3c + 2d)^9.
a.
760c^3d^6
c.
145,152c^3d^6
b.
760c^4d^5
d.
145,152c^4d^5
Answer:
c
Step-by-step explanation:
Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term. I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9). If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.
The expasion is as follows (up to the 7th term):
[tex]1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6[/tex]
That last term is the 7th term. You find out its value by multiplying all the numbers together and adding on the c^3d^6. Again those come from Pascal's triangle, and it's one of the coolest math things ever. I encourage you to take the time to explore how it works.
what was the total amount of all checks vera deposited
Answer:
(d) $1120.70
Step-by-step explanation:
You want the total of deposited checks as shown on the deposit slip.
TotalThe total value of checks is shown on the line "Subtotal." This is amount of the deposited checks. The same deposit slip shows a withdrawal of $80 cash, so the net deposit is $80 less than that subtotal.
Vera deposited $1120.70 in checks, choice D.
The correct total amount of all checks Vera deposited is $664.30, and the deposit ticket reflects a subtotal of $1040.70, which includes both checks and cash. Therefore, option (b) $664.30 is the accurate representation of the total amount of all checks.
To determine the total amount of all checks Vera deposited, we need to add the amounts of the individual checks listed on the deposit ticket.
1. Check #184: $138.09
2. Check #308: $312.15
3. Check #298: $214.14
Adding these amounts: $138.09 + $312.15 + $214.14 = $664.38
Therefore, the correct answer is option (b) $664.30. This represents the total amount of all checks Vera deposited. The deposit ticket indicates the subtotal of checks as $1120.70, but this includes the cash amount received as well. To find the total amount of all checks, we subtract the cash amount received, which is $80.00, from the subtotal: $1120.70 - $80.00 = $1040.70.
Triangle XYZ with vertices X(0, 0), Y(0, –2), and Z(–2, –2) is rotated to create the image triangle X'(0, 0),
Y'(2, 0), and Z'(2, –2).
Which rules could describe the rotation? Check all that apply.
R0, 90°
R0, 180°
R0, 270°
(x, y) → (–y, x)
(x, y) → (y, –x)
Answer:
The answer is R0, 90° and (x , y) → (-y , x) ⇒1st and 4th
Step-by-step explanation:
* Lets revise the rotation rules
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
(+90° or -270°)
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
(-90° or +270°)
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
(+180° or -180°)
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
* Lets solve the problem
∵ Δ XYZ has vertices⇒ X (0 , 0) , Y (0 , -2) , Z (-2 , -2)
∵ Δ X'Y'Z' has vertices X' (0 , 0) , Y' (2 , 0) , Z' (2 , -2)
* From them
# Y = (0 , -2) and Y' = (2 , 0), that means the image is (-y , x)
# Z = (-2 , -2) and Z' = (2 , -2), that means the image is (-y , x)
∴ The rotation is around the origin with angle 90° anti-clockwise
V.I.N: Anti-clock wise means positive angle , clockwise means
negative angle (90° means anti-clockwise , -90° means clockwise)
∴ The answer is: R0, 90° and (x , y) → (-y , x)
A coffee franchise is opening a new store. The company estimates that there is an 80% chance the store will have a profit of $100,000, a 10% chance of the store will break even, and a 10% chance of the store will lose $2,500. Determine the expected gain or loss for this store
The expected gain or loss for this store is a gain of $79,750.
What is gain and loss ?Gain is defined as the profit occurred by a store or a shopkeeper when an item is sold at a higher price than it was originally bought.
Loss is defined as the money lost by a store or a shopkeeper when an item is sold at a lower price than it was originally bought.
Both gain or loss is calculated by the formula -
Cost Price (CP) - Selling price (SP)
What is the expected gain or loss for this store ?It is given that the company estimates that there is an 80% chance the store will have a profit of $100,000, a 10% chance of the store will break even, and a 10% chance of the store will lose $2,500.
Calculating the net gain or loss or the company -
= (80% * $100,000) + (10% * $0) - (10% * $2,500)
= (80/100 * $100,000) - (10/100 * $2,500)
= $80,000 - $250
= $79,750
Thus the net gain involved in the business by the company is $79,750 .
Therefore, the expected gain or loss for this store is a gain of $79,750.
To learn more about gain and loss, refer -
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A sample proportion of 0.18 is found. To determine the margin of error for this statistic, a simulation of 100 trials is run, each with a sample size of 50 and a point estimate of 0.18.
The minimum sample proportion from the simulation is 0.28, and the maximum sample proportion from the simulation is 0.40.
What is the margin of error of the population proportion using an estimate of the standard deviation?
A) ±0.02
B) ±0.04
C) ±0.12
D) ±0.18
Answer:
The answer is B. 0.04
Step-by-step explanation:
too lazy to write
A TV has a listed price of $817.99 before tax. If the sales tax rate is 7.5%, find the total cost of the TV with sales tax included.Round your answer to the nearest cent, as necessary.
It should be $879.34, already rounded.
The length of Blake's rectangular living room is 6 meters and the distance between opposite corners is 10 meters. What is the width of Blake's living room?
Answer:8 meters
z^2=x^2+y^2
10^2=x^2+6^2
100-36=x^2
x=swrt(64)=8
By applying the Pythagorean Theorem, we find out that the width of Blake's living room is 8 meters. This theorem helps to calculate the unknown side of a right triangle when the other two sides are known.
Explanation:To answer this question, we can apply the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the diagonal across the rectangular room is the hypotenuse of a right triangle, with the length and width of the room as the remaining sides.
Given that the length of the room is 6 meters and the hypotenuse is 10 meters, we can substitute these values into the formula of the Pythagorean Theorem:
Width² = Hypotenuse² - Length²
Substituting the known values gives:
Width² = 10² - 6²
Width² = 100 - 36
Width² = 64
Then, taking the square root of both sides:
Width = 8 meters
Therefore, the width of Blake's living room is 8 meters.
Learn more about Pythagorean Theorem here:https://brainly.com/question/28361847
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PLEASE HELP ASAP 50 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
3x^3 and 2x^3 should be combined because if numbers have an exponent combine only if they both have matching exponents and variables as well
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of the following function when x = 0?
Answer:
-2
Step-by-step explanation:
It's when the graph crosses the y axis
Find the Y value when the graphed line is at X = 0
When X is 0, the line crosses The X- axis at Y = -2
Aaron is in his math class. His teacher says that class will be dismissed when the minute hand makes a 90° clockwise rotation. What time will it be when the teacher dismisses the class?
4:05
3:35
3:25
3:20
3:55
Answer:
3:20
Step-by-step explanation:
The 360 degrees clockwise rotation of the minute hand corresponds to 60 minutes.
The 90 degrees clockwise rotation is one-fourth of the 360 degrees, and hence will corresponds to 15 minutes.
The time is now 3:05.
After 15 minutes the time will be 3:20
Therefore the teacher dismisses the class at 3:20
Two angles are complementary. The measure of the smaller angle is four less than the measure of the larger angle. What is the measure of the smaller angle?
Answer:
43 is the smaller angle
Step-by-step explanation:
greater angle is 47
43+47=90
43 is 4 less than 47
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The regular pentagon ABCDE rotates counterclockwise about its center to form pentagon A′B′C′D′E′. The angle of rotation at which point A′ coincides with point D is °.
Answer: 144°
Step-by-step explanation:
It is a regular pentagon which means all five sides are the same length. This also means that the angle between any two adjacent vertices is the same. So to find the angle between two adjacent vertices we take 360° and divide it by 5 which equals 72°. But A and D are not adjacent to each other, they have E in the middle (it also has B and C in the middle on the other side, but that's the bigger angle, and we usually label angles through their smaller angle. ex: a 30° angle is 30° if you look at it on the smaller angle (∠ ← here), but if you look at the bigger side of the angle (here →∠) it is 330°, yet we still call it a 30° angle). So, between A and D are two equal angles A to E, and E to D. So we multiply 72° by 2 which equals 144°.
So the answer is 144°.
Answer:
144
Step-by-step explanation:
plato
Calculate the rate of change for the quadratic function over the given interval: f(x)=x^2 + 4x +5 ; -4 =< x =< -2
Answer:
The average rate of change for this quadratic function is -2.
Step-by-step explanation:
In this question, we have f(x) = y = x^{2} + 4x + 5.
Given a function y, the average rate of change S of y=f(x) in an interval [x_s, x_f] will be given by the following equation:
S = \frac{f(x_{f}) - f(x_s)}{x_f - x_s}
So, in your problem, f(x) = x^{2} + 4x + 5, x_{f} = -2 and x_{s} = -4.
Applying these informations to the equation S above, we have:
S = \frac{f(-2) - f(-4)}{-2-(-4)}
Where
f(-2) = (-2)^{2} + 4(-2) +5 = 4-8+5 = 9-8 = 1
f(-4) = (-4)^{2} + 4(-4) +5 = 16-16+5 = 5
So, the average rate of change S will be
S = \frac{1-5}{2} = -4
how many ways can you order your favorite dessert from a menu of 8? A.) 6 B.) 40,320 C.) 6720 D.) 336
Can you tell me what do you mean exactly by menu of 8, so i can help you.
Which statement best explains why this expression is equal to 46.8?
n+23.40
46.8 • ____________
23.40+n
Answer:
a, Addition is commutative, so n+23.4023.40+n equals 1.
Step-by-step explanation:
Find the direction of vector u shown
[tex]\vec u[/tex] starts at (1, 1) and ends at (-4, 3), so it's pointing in the same direction as the vector
[tex](-4, 3)-(1,1)=(-5,2)[/tex]
This vector terminates in the second quadrant, so its direction is
[tex]\pi+\tan^{-1}\left(-\dfrac25\right)\,\mathrm{rad}\approx158.2^\circ=(180-158.2)^\circ\,\text{N of W}=21.8^\circ\text{N of W}[/tex]
Answer:
C. 21.8 degrees N of W
Step-by-step explanation:
got it right on edge :)
Write the following integers in order from least to greatest. -1, +6, 0, +4, -2
ANSWER
-2,-1,0,+4,+6
EXPLANATION
The given integers are:
-1, +6, 0, +4, -2
To arrange from least to greatest means arranging in ascending order of magnitude.
We can observe that:
-2<-1<0<+4<+6
Therefore the numbers written in order from least to greatest is:
-2,-1,0,+4,+6
Donna bought 3 bags of dog treats for $6.75. What is the cost per bag of dog treats?
A. $2.25
B. $9.75
C. $3.38
[tex]6.75 \div 3 = 2.25[/tex]
A.$2.25
You take the total which is $6.75 and divide it by the number of dog treat bags she purchased and once you divide it you get the total of one bag which is $2.25 per bag.
Find the ratio of x to y, 2x+5y A.2 to 5 B. 5 to 2 C.2 to 7 D.5 to 7
Answer:
A. 2 to 5
Step-by-step explanation:
x is being multiplied by 2.
y is being multiplied by 5.
Although there is an infinite amount of ratios we can use when we know the values,we don't have that right now, so we have to stick to 2 to 5, which is our answer.
A student is attempting to sketch a graph of the function f(x)=3x−2−1. What are the values of the horizontal asymptote and the x− intercept of the graph?
The horizontal asymptote is y=−1 and the x-intercept is at (−2,0).
The horizontal asymptote is y=2 and the x-intercept is at (−1,0).
The horizontal asymptote is y=−1 and the x-intercept is at (2,0).
The horizontal asymptote is y=1 and the x-intercept is at (3,0).
Answer:
C
Step-by-step explanation:
y= -1 just like the other one
The horizontal asymptote is y=−1 and the x-intercept is at (2,0).
The answer is option C.
What is the horizontal asymptote?A vertical asymptote of a graph is a vertical line (x = a) where the graph tends toward positive or negative infinity as the inputs approach a.A horizontal asymptote of a graph is a horizontal line (y = b) where the graph approaches the line as the inputs approach ∞ or –∞.A slant asymptote of a graph is a slanted line (y = MX + c) where the graph approaches the line as the inputs approach ∞ or –∞.Learn more about horizontal asymptote here:-https://brainly.com/question/1851758
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A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 20? Also find the total number of grains of wheat on the board at this time and their total weight
Answer:
See below in bold.
Step-by-step explanation:
Here is 1 grain on square 1 , 2 on square 2, 4 on square 3 and so on. This is a geometric sequence with the nth term = a1r^(n - 1) where a1 = first term , r = common ratio.
So the 20th term (the number of grains on square 20) would be
1*2^(20-1) = 524,288.
Total = a1 * (r^n - 1) / (r - 1)
= (2^20 - 1) / 2-1 = 1.048,575
A card is drawn from a standard deck and a letter chosen from the word INCREDIBLE. What is the probability of drawing a king then getting an I
Answer:
2/10 simplify into 1/5
Step-by-step explanation:
Since there is a total of 10 cards in the deck, the denominator would be 10. As there is only two 'I's in the deck it would be the numerator.
Hope this will help :)
Answer:
2/130 = 1/65
Step-by-step explanation:
There are 4 kings out of 52 cards total. Your chances of drawing a king are 4/52
Incredible has 10 letters 2 of which are 'i's' So your chances of picking 2 eyes is 2/10
Combined you have
4/52 * 2/10 = 2/ 130 = 1/65
What is the surface area of the regular pyramid given below?
For this case we have by definition, that the total surface area of a regular pyramid with a square base is given by:
[tex]SA = \frac {1} {2} p * S + A_ {b}[/tex]
Where:
p: It is the perimeter of the base
S: It's the inclination
[tex]A_ {b}:[/tex] It is the area of the base
Substituting:
[tex]A_ {b} = 7 ^ 2 = 49units ^ 2\\p = 7 + 7 + 7 + 7 = 28units\\S = 10units\\SA = \frac {1} {2} 28 * 10 + 49\\SA = 140 + 49\\SA = 189 \ units ^ 2[/tex]
ANswer:
Option B
Answer:
B. 189 units squared
Step-by-step explanation:
ap3x
PLEAAAASEEEE HELPPPPP 1. Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces the previous height. Find the height the ball will bounce after hitting the ground the fourth time. (SHOW WORK)
2. The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7. The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8. (SHOW WORK) Suppose an architect has designed a building strong enough to withstand an earthquake 70 times as intense as the Denali quake and 30 times as intense as the Rat Islands quake. Find which structure is strongest. Explain your finding. (SHOW WORK)
Answer:
1) The height the ball will bounce after hitting the ground the fourth time = 2.0736ft
2) The building is strong enough to withstand the Denali earthquake
Step-by-step explanation:
1) According to the given statement Bradley dropped the ball from a roof 16 feet high.Each time the ball hits the ground, it bounces3/5 the previous height
Therefore,
First bounce = 16*3/5 = 9.6
Second bounce = 9.6 *3/5 = 5.76
Third bounce = 5.76*3/5=3.456
Fourth bounce = 3.456*3/5=2.0736
The height the ball will bounce after hitting the ground the fourth time = 2.0736ft....
2) The 2002 Denali earthquake in Alaska had a Richter scale magnitude of 6.7.
Denali earthquake = 6.7 * 70 =469
It means that the building in Denali should be strong enough to withstand an earthquake of that magnitude
The 2003 Rat Islands earthquake in Alaska had a Richter scale magnitude of 7.8
Rat Islands earthquake = 7.8 * 30 = 234
It means that the building in Rat Islands should be strong enough to withstand an earthquake of that magnitude....
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6
Given:
A polynomial of the 5th degree A leading coefficient of 7A constant term of 6Problem-solving:
Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.
[tex]\boxed{ \ 7x^5 + bx^4 + cx^3 + dx^2 + ex + 6 \ }[/tex]
Now we make the first polynomial, for example:
b = 3c = -2d = 2e = -5Thus, the result is [tex]\boxed{\boxed{ \ 7x^5 + 3x^4 - 2x^3 + 2x^2 - 5x + 6 \ }}[/tex]
Then we make the second polynomial as an alternative. For example:
b = -6c = 0d = -2e = 0Thus, the polynomial is [tex]\boxed{\boxed{ \ 7x^5 - 6x^4 + 4x^2 + 6 \ }}[/tex]
Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.
Notes:
Let us rephrase the following definitions.
A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example, [tex]\boxed{-2} \boxed{3x^2} \boxed{4a^3b^4} \boxed{-5xy^3z^2} \boxed{\frac{3}{5}}[/tex]A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above [tex]\boxed{ \ -2, 3, 4, -5, \frac{3}{5} \ }[/tex] are the coefficients.A polynomial is the sum or difference of a set of monomials. For example, [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex]Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial [tex]\boxed{ \ 2x^2 - 3xy^2 + 4x^2y \ }[/tex] are [tex]\boxed{ \ 2, - 3, and \ 4. \ }[/tex]The constant term is the term of polynomial that does not contain a variable.The leading coefficient is the coefficient of the term containing the variable raised to the highest power.For example, consider the polynomial [tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex]
[tex]\boxed{ \ 2x^4, - 3x^2, - 4x, and \ - 5 \ }[/tex] are the terms of polynomial.[tex]\boxed{ \ 2, - 3, - 4 \ }[/tex] are the coefficients.- 5 is the constant term.2 is the leading coefficient.A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:
[tex]\boxed{ \ 2x^4 - 3x^2 - 4x - 5 \ }[/tex] is a polynomial in standard form.[tex]\boxed{ \ - 3x^2 + 2x^4 - 5- 4x \ }[/tex] is the polynomial, but it is not in standard form.Learn moreThe remainder theorem https://brainly.com/question/950038768.32 divided by 2.8 is divisible https://brainly.com/question/5022643#Determine whether each algebraic expression is a polynomial or not https://brainly.com/question/9184197#Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer
A polynomial of the 5th degree with a leading coefficient of 7 and a constant term of 6 could take the form of 'f(x) = 7x^5 + 6'. The other coefficients (b, c, d, e) can be any real numbers, but for simplicity, they can be set to zero in this instance.
Explanation:The student's question relates to constructing a polynomial of the 5th degree with specific characteristics in the field of Mathematics, specifically in algebra. One can present such a polynomial with the general form:
f(x) = ax^5 + bx^4 + cx^3 + dx^2 + ex + f
Where the leading coefficient a is 7 and the constant term f is 6. In this case, since the only information provided is the leading coefficient and the constant term, and not any constraints on the other coefficients (b, c, d, e), they can be any real numbers, including zero. Thus, one example of a polynomial fitting these constraints is:
f(x) = 7x^5 + 0x^4 + 0x^3 + 0x^2 + 0x + 6
To simplify the algebra and make calculations easier, one can eliminate terms wherever possible, which in this example has been executed by setting the coefficients of x^4, x^3, x^2, and x to zero. After forming any polynomial, it is also important to check the answer to ensure that it matches the given criteria, which in this case it does.
Learn more about polynomial of the 5th degree here:https://brainly.com/question/12850541
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Please help me out please
By comparing the perimeters, we can deduce the scaling factor:
[tex]k = \dfrac{34}{20} = 1.7[/tex]
The areas scale with the square of the scaling factor, so the new area is
[tex]19.6 \cdot 1.7^2 = 56.644[/tex]
What segment is the projection of ST on QT?
UT
QU
QT
Answer:
UT
Step-by-step explanation:
The projection of ST on QT is found by locating the points on QT that are nearest the endpoints S and T of the original segment. On QT, U is the point closest to S, and T is the point closest to T. Then the projection is the segment between those identified points: UT.
Answer:
UT
Step-by-step explanation:
F(x) = 3x-1 and g(x)=2x^2
a. Find (f g) (x).
b. Find (f-g) (x).
c. Find f(g(x)).
d. Find g(f(x)).
Answer:
See below
Step-by-step explanation:
a. here you are to multiply the two functions together:
[tex](3x-1)(2x^{2} )=6x^{3}-2x^{2}[/tex]
b. here you are to subtract g from f:
[tex](3x-1)-(2x^{2})=-2x^{2}+3x-1[/tex]
c. here you are to compose g into f. In other words, pick up the whole g function and plug it into f wherever you see an x:
[tex]3(2x^{2} )-1=6x^{2} -1[/tex]
d. here you are compose f into g. In other words, pick up the whole f function and plug it into g wherever you see an x:
[tex]2(3x-1)^2[/tex]
You now have to FOIL out the (3x-1) like so:
[tex]2[(3x-1)(3x-1)][/tex]
which gives you
[tex]2(9x^{2} -6x+1)[/tex]
Distribute in the 2 and you'll end up with the answer:
[tex]18x^{2} -12x+2[/tex]