f(x) = x^4 + 2*x^3 + 3*x^2+4*x + 5
and g(x) = x^2 + 2*x + 4

Note that if we just use the coefficients of f(x) and g(x), then they look like 1 2 3 4 5 and 1 2 4

(5%) Compute the product h(x) of two polynomials f(x) and g(x) manually. In particular, show how the constant term, the x term, the x2 term, the x3 term etc. are computed from f(x) and g(x) respectively. Like Q7, use a table T3 to show line by line, how each term is computed (note the x2 term of h(x) comes from f(x)’s constant term and g(x)’s x2 term, plus f(x)’s x term and g(x)’s x term, and g(x)’s constant term and f(x)’s x2 term etc.
(5%) Compute the quotient q(x) and remainder r(x) when f(x) is divided by g(x), in other words compute q(x) and r(x) manually so that f(x) = g(x) * q(x) + r(x).

Answer:

D. 23

Step-by-step explanation:

m-12-(11)=0

m-23 = 0

m = 23

Answer:

Step-by-step explanation:

I will try my best to help you with algebra what is the question

The given set of vectors in R with the defined addition and scalar multiplication operations does not satisfy the closure properties, violating the vector space axioms.

In the first part, the set of vectors with the given operations does not satisfy all of the vector space axioms.

In the second part, let's examine the vector space axioms to determine which ones are not satisfied.

Closure under addition: The axiom states that for any vectors u and v in the set, the sum u + v must also be in the set. If we consider the vectors (1, 0) and (0, 1), their sum is (1, 1), which is not in the given set. Therefore, closure under addition is not satisfied.

Closure under scalar multiplication: The axiom states that for any scalar c and vector u in the set, the scalar multiple c * u must be in the set. If we consider the vector (1, 1) from the previous example, multiplying it by a scalar c will result in the vector (c, c). However, for certain values of c, such as c = 2, the resulting vector (2, 2) is not in the given set. Hence, closure under scalar multiplication is not satisfied.

Since the set does not satisfy closure under addition and closure under scalar multiplication, it does not satisfy the vector space axioms.

Learn more about scalar multiplication here:

https://brainly.com/question/30221358

#SPJ11

Answer:

C

90

Step-by-step explanation:

B is likely the center, I think. You can't do it otherwise.

The tangent and a radius of a circle meet at 90o

therefore the answer is 90.

All of this could be confirmed with a diagram.

Step-by-step explanation:

try to do 180 - 135 organise a 45-degree that is the first answer of a and b you're taking 180 - 144 you got the answer also 28 degrees

Answer:

1. y = 2x + 5

2. (-5) + 3 + (-8) = 3 - 5 - 8 = 3 - 13 = -10

3. given: 1/2, 3/4, 7/8, 0.55, 0.1

1/2, 3/4, 7/8 = 4/8, 6/8, 7/8

4/8 < 6/8 < 7/8

1/2 < 3/4 < 7/8

0.55 = 55/100 = 11/20

0.1 = 1/10 = 2/20

2/20 < 11/20

0.1 < 0.55

1/2 = 10/20

2/20 < 10/20 < 11/20

0.1 < 1/2 < 0.55

3/4 = 15/20

11/20 < 15/20

0.55 < 3/4

thus

0.1 < 1/2 < 0.55 < 3/4 < 7/8

Answer:

(5.1×10^15)×(8.1×10^5

Answer:

It goes up

Step-by-step explanation:

Step-by-step explanation:

a a reflex angle is more than 180° but less than 360° so in this case the reference angle of 95 degrees we are going to take 360° - 95 degrees to get255°

Answer:

100.571inches

Step-by-step explanation:

Perimeter. =2πr

Perimeter. =2×22÷7×16

Perimeter. =704÷7

Perimeter. =100.571inches

PLEASE GIVE BRAINLIEST

Answer:

C

Step-by-step explanation:

trust me if you really need this done

Answer:

Angelo needs to use the formula V = [tex]\frac{4}{3} \pi (8.5)^3[/tex].

Step-by-step explanation:

The formula for finding the volume of a sphere is [tex]V=\frac{4}{3} \pi r^3[/tex], wherein the variable, r, is the radius. Diameter is one half of the radius; thus, it would be 17/2 = 8.5. Substitute the values into the equation (i.e. V = [tex]\frac{4}{3} \pi (8.5)^3[/tex]).

Answer:

15 students.  30%

Step-by-step explanation:

(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection. (b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection. (c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.

Let's evaluate each given expression to determine if it is a function and, if so, determine its characteristics:

(a) Given f: Z → Z+, f(x) = |x − 2| + 1.

This expression represents a function. A function is a relation between two sets where each input value (x) maps to a unique output value (f(x)). In this case, for any integer input x, the function f(x) returns the absolute value of the difference between x and 2, plus 1. Since each input has a unique corresponding output, this function is one-to-one.

To determine if the function is onto or a bijection, we need to examine the range of the function. The range of f(x) is the set of all possible output values. In this case, the function returns only positive integers (Z+). Therefore, the function is onto since it covers the entire range of positive integers. However, it is not a bijection since the domain (Z) and the codomain (Z+) have different cardinalities.

(b) Given f: Z → Z+, f(x) = −3x + 2.

This expression also represents a function. It is a linear function that takes an integer input x and returns the value obtained by multiplying x by -3 and then adding 2. Since each input value maps to a unique output value, the function is one-to-one.

To determine if the function is onto or a bijection, we examine the range of f(x). The function f(x) returns positive integers (Z+). However, it does not cover the entire range of positive integers. Specifically, it only produces negative or zero values when x is positive. Therefore, the function is not onto, and it is not a bijection.

(c) Given f: R → R, f(x) = x² − 2x + 1.

This expression represents a function. It is a quadratic function that takes a real number input x and returns the value obtained by substituting x into the equation x² - 2x + 1. Since each input value maps to a unique output value, the function is one-to-one.

To determine if the function is onto or a bijection, we again examine the range of f(x). The quadratic function f(x) is a parabola opening upward, and its vertex is located at (1, 0). This indicates that the lowest point on the graph is at y = 0, and the range of f(x) includes all real numbers greater than or equal to 0. Therefore, the function is onto, and it is a bijection.

In summary:

(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection.

(b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection.

(c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.

Learn more about bijection here

https://brainly.com/question/32691273

#SPJ11

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Origibal data set

8, 11, 15, 22, 6

Rearranging The value :

x : 6, 8, 11, 15,22

Mean = Σx / n

n = sample size =5

Mean = (6+8+11+15+22) = 62

Mean = 62 / 5 = 12.4

Median = 1/2(n+1)th term

Median = 1/2(6)th term = 6/2 = 3rd term = 11

A.)

X = 4, 5, 15, 23, 19

MEAN = (4 +5 + 15 + 23 + 19) / 5 = 13.2

B.)

X = 2, 6, 5, 23, 34

Mean = (2+6+5+23+24) / 5

Mean = 60 / 2 = 12

C.)

X = 3, 7, 12, 21, 13

X = 3, 7, 12, 13, 21

Mean = (3+7+12+13+21) /5 = 11.2

Median = 1/2(6)th term = 6/2 = 3rd term = 12

The required answer is  [61.77, 69.23].

Given: Mean height of all 9th grade students at one high school is estimated as ≈65.5 Population standard deviation is σ = 3 inches. Number of samples n = 6Margin of error at 99% confidence level = 1.23Margin of error = E = z(σ/√n)Now, z = inv Norm(0.995) (as it is 99% confidence interval, α=0.01 and 1-α=0.99)⇒ inv Norm(0.995) = 2.58∴ E = 2.58(3/√6) = 3.73∴ The margin of error at the 99% confidence level is 3.73 inches .

Confidence interval = [sample mean - E, sample mean + E]=[65.5 - 3.73, 65.5 + 3.73] = [61.77, 69.23]

∴ The 99% confidence interval for the population mean height of all 9th-grade students at that high school is [61.77, 69.23].

Know more about confidence interval  here:

https://brainly.com/question/32546207

#SPJ11

(a) Inverse Laplace transform of F(s) = 4s/(s² - 81) is

[tex]f(t) = 2e^{(9t)} + 2e^{(-9t).[/tex]

We can rewrite F(s) as F(s) = 4s/[(s - 9)(s + 9)].

Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 9) + B/(s + 9), where A and B are constants.

Multiplying both sides by (s - 9)(s + 9), we get 4s = A(s + 9) + B(s - 9).

Expanding and equating coefficients, we have 4s = (A + B)s + 9A - 9B.

Equating coefficients of s on both sides, we get A + B = 4.

Equating constants on both sides, we get 9A - 9B = 0, which gives A = B.

From A + B = 4, we have 2A = 4, so A = B = 2.

Therefore, F(s) can be written as F(s) = 2/(s - 9) + 2/(s + 9).

Now, using the inverse Laplace transform formulas:

[tex]L{e^{at}} = 1/(s - a),\\L{e^{(-at)}} = 1/(s + a),[/tex]

we can find the inverse Laplace transform of F(s):

[tex]f(t) = L^{(-1)}{F(s)} = 2L^{(-1)}{1/(s - 9)} + 2L^{(-1)}{1/(s + 9)}\\= 2e^{(9t) }+ 2e^{(-9t).[/tex]

Therefore, the inverse Laplace transform of F(s) = 4s/(s² - 81) is f(t) = 2e^(9t) + 2e^(-9t).

(b) Inverse Laplace transform of F(s) = (7s + 52)/(s² + s - 1):

We can rewrite F(s) as F(s) = (7s + 52)/[(s - 1)(s + 1)].

Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 1) + B/(s + 1), where A and B are constants.

Multiplying both sides by (s - 1)(s + 1), we get (7s + 52) = A(s + 1) + B(s - 1).

Expanding and equating coefficients, we have 7s + 52 = (A + B)s + (A - B).

Equating coefficients of s on both sides, we get A + B = 7.

Equating constants on both sides, we get A - B = 52.

Solving these equations, we find A = 29 and B = -22.

Therefore, F(s) can be written as F(s) = 29/(s - 1) - 22/(s + 1).

Using the inverse Laplace transform formulas:

[tex]L{e^{at} = 1/(s - a),\\L{e^{(-at)} = 1/(s + a),[/tex]

we can find the inverse Laplace transform of F(s):

[tex]f(t) = L^{(-1)}{F(s)} = 29L^{(-1)}{1/(s - 1)} - 22L^{(-1)}{1/(s + 1)}\\= 29e^t - 22e[/tex]

To know more about Inverse Laplace transform refer here:

https://brainly.com/question/30404106

#SPJ11

Answer:

43

Step-by-step explanation:

A is the answer

Answer:

Ima steal your points

Step-by-step explanation:

Answer:

201.1 square feet

Step-by-step explanation:

The radius (r) of the patio is 16/2 = 8

Area of a circle is π[tex]r^{2}[/tex] so [tex]8^{2}[/tex]π = 201.0619298 or 64π

Answer:

It will take 113.10 ft² of tiles to cover the patio.

Step-by-step explanation:

area of a circle formula: A = πr²

The diameter is twice the length of the radius. To find the radius, divide the diameter by 2:

16/2 = 8

To find the area of the circular patio, apply the radius to the formula A = πr²:

A = π6²

A = 113.10 ft²

Answer:

6283 in³

Step-by-step explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch

A number system is a system for the presentation of numbers into groups or categories

The true statement is the option;

C. All irrational numbers are real numbers

Reason:

The number system is composed of two types of numbers, which are;

Imaginary Numbers;

The imaginary numbers are the numbers that have the value √(-1), within them

Real Numbers:

There are two types of real numbers which are;

Rational numbers; Numbers that can be written in the form [tex]\dfrac{a}{b}[/tex], where a, and b, are integers

Irrational numbers; Numbers that cannot be expressed in the form [tex]\dfrac{a}{b}[/tex], such as π, √2, e

Therefore;

All irrational numbers are real numbers

Learn more here:

https://brainly.com/question/9842110

The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2

Variation of weight = Between 6 to 12.

It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.

Calculating the total range of weight -

Range = Higher weight - Lower weight

= 12 - 6

= 6

Similarly, calculating the total range of weight for 8 pounds and 11 pounds

Range = Higher weight - Lower weight

= 11 - 8

Calculating the probability -

Probability = Range of interest / Total range

= 3 / 6

= 1/2.

Read more about probability on:

https://brainly.com/question/25839839

#SPJ4

Complete Question:

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost between 8 pounds and 11 pounds

a. 1/2

b. 1/4

c. 2/3

d. 1/3

Answer:

8km

Step-by-step explanation:

there are 4 unit between Gabe's house and the library so distance is 4×2=8km

Answer:

3

Step-by-step explanation:

Since it's at the same time of the day, the ratio between the height of the person and the shadow they cast will stay the same. So the man's height to shadow ratio is 6:8 = 3:4. The son's height to shadow ratio would be the same so x:4 = 3:4 therefore his height is 3 feet.

Answer:

c the right tail is longer than the left

Step-by-step explanation:

Answer:

3a-12c

Step-by-step explanation:

(5a-7c)-(2a+5c)

5a-7c-2a-5c

(5a-2a)+(-7c-5c)

3a-12c

Answer:

3a - 12c

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

the ratio of base1 ABCD to base 1 of WXYZ is        

                      8                 to      12

     8/12    = 2/3      

Answer:

Gavin has 3 parts left.

Step-by-step explanation:

8-3-2=3. The time was not important.

Answer:

it's 75 feet above sea level

Answer:

75 feet

take 125

minus

50

which give you 75.