Complete the equation describing how
x and y are related.
х
0
1
2
3
4
Y
-6
- 10
-14
-18
-22
y = [? ]x + []
Enter the answer that belongs in [?].
Enter

(a) To compute the product h(x) of the polynomials f(x) and g(x) manually, we can use the distributive property of multiplication. Let's calculate the terms of h(x) step by step:

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f(x) = x^4 + 2x^3 + 3x^2 + 4x + 5

g(x) = x^2 + 2x + 4

We can use the following table T3 to show how each term of h(x) is computed:

Term of h(x)    | Computation

-------------------------------------

Constant term   | (Constant term of f(x)) * (Constant term of g(x))

x term           | (Constant term of f(x)) * (x term of g(x)) + (x term of f(x)) * (Constant term of g(x))

x^2 term         | (Constant term of f(x)) * (x^2 term of g(x)) + (x term of f(x)) * (x term of g(x)) + (x^2 term of f(x)) * (Constant term of g(x))

x^3 term         | (Constant term of f(x)) * (x^3 term of g(x)) + (x term of f(x)) * (x^2 term of g(x)) + (x^2 term of f(x)) * (x term of g(x)) + (x^3 term of f(x)) * (Constant term of g(x))

x^4 term         | (x term of f(x)) * (x^3 term of g(x)) + (x^2 term of f(x)) * (x^2 term of g(x)) + (x^3 term of f(x)) * (x term of g(x)) + (x^4 term of f(x)) * (Constant term of g(x))

Using this table T3, we can calculate the respective terms of h(x).

(b) To compute the quotient q(x) and remainder r(x) when f(x) is divided by g(x), we can use long division. Let's calculate q(x) and r(x) step by step:

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f(x) = x^4 + 2x^3 + 3x^2 + 4x + 5

g(x) = x^2 + 2x + 4

We can use the following table T4 to show how each term of q(x) and r(x) is calculated:

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Term of q(x)    | Computation

-------------------------------------

x^2 term         | Divide (x^4 term of f(x)) by (x^2 term of g(x))

x term           | Subtract (x^2 term of q(x)) * (g(x)) from f(x), then divide the result by (x^2 term of g(x))

Constant term   | Subtract (x^2 term of q(x)) * (g(x)) + (x term of q(x)) * (g(x)) from f(x), then divide the result by (x^2 term of g(x))

Using this table T4, we can calculate the respective terms of q(x) and r(x) using the long division method.

Note: The actual calculations for each term in the tables T3 and T4 are not provided here, but you can perform the calculations using the given polynomials f(x) and g(x) to obtain the specific values for each term.

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The volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.

What is volume of sphere?

The volume of a sphere is given by the formula:

V = (4/3)πr³

where r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159.

The volume of a sphere can be calculated using the formula:

V = (4/3)π\(r^3\)

where r is the radius of the sphere and π is the mathematical constant pi.

Using this formula, we can find the volumes of spheres a and b as follows:

Volume of sphere a:

V = (4/3)π(\(2^3\)) = (4/3)π(8) = 32π/3 cubic cm

Volume of sphere b:

V = (4/3)π(\(4^3\)) = (4/3)π(64) = 256π/3 cubic cm

Therefore, the volume of sphere a is 32π/3 cubic cm, and the volume of sphere b is 256π/3 cubic cm.

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Answer:

2 x 4 x 8 = 64

Step-by-step explanation:

Multiply all given lengths when finding the volume of a rectangular prism.

Answer:

8 km = 5 miles

88km= (5×88)/8 miles = 55 miles

Answer:

7,7, and 7

Step-by-step explanation:

If she vase is cubical we know that all 3 dimensions are the same. This means that x^3 = 343. So we know the answer is the cube root of 343, which is 7

The dimensions of the cubic vase are 7 by 7 by 7.

A three-dimensional object with six congruent square faces is called a cube. The cube's six square faces all have the same dimensions.

Given that the volume of the cubic vessel is 343 cubic inches.

The formula for the volume of a cube of side length a is:

V =a³

Substitute V= 343:

343 = a³

Or, a = ∛343

a = 7

Hence, the dimensions of the cubic vase are 7 by 7 by 7.

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A.) The rate of change of the water level with respect to time is (1/4) times the rate of change of the radius with respect to time. B.) The water level h as a function of time t is given by the equation h = 50t. C.) The rate of change of the radius of the cone with respect to time when the water is 8 meters deep is 200.

A.) To find the rate of change of the water level with respect to time, we need to use similar triangles. Let's denote the water level as h (the height of the water in the tank) and let's denote the radius of the water surface as r.

Since the tank is in the shape of a cone, we know that the ratio of the change in radius to the change in height is constant. Therefore, we can write:

(r/40) = (h/10)

To find the rate of change of the water level with respect to time (dh/dt), we differentiate both sides of the equation with respect to time:

(d(r/40)/dt) = (d(h/10)/dt)

Now, let's express the rate of change of the radius with respect to time (dr/dt) in terms of the rate of change of the water level with respect to time:

(dr/dt) = (40/10) * (dh/dt)

Simplifying this expression, we get:

(dr/dt) = 4 * (dh/dt)

Therefore, the rate of change of the water level with respect to time (dh/dt) is (1/4) times the rate of change of the radius with respect to time (dr/dt).

B.) To find the water level h as a function of time t, we need to integrate the rate of change of the water level with respect to time (dh/dt) over time. Since water is flowing into the tank at a constant rate of 50m^3/min, we can write:

dh/dt = 50

Integrating both sides with respect to time, we get:

∫dh = ∫50 dt

h = 50t + C

Since we are given that the tank is initially empty at t = 0, we can substitute h = 0 and t = 0 into the equation:

0 = 50(0) + C

C = 0

Therefore, the equation for the water level h as a function of time t is:

h = 50t

C.) To find the rate of change of the radius of the cone with respect to time when the water is 8 meters deep (h = 8), we can use the relationship we derived earlier:

(dr/dt) = 4 * (dh/dt)

We know that the rate of change of the water level with respect to time is dh/dt = 50. Substituting this into the equation, we get:

(dr/dt) = 4 * 50

(dr/dt) = 200

Therefore, the rate of change of the radius of the cone with respect to time when the water is 8 meters deep is 200.

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From the probability, the quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit is 2,821,109,907,456 passwords

The most effective method to ascertain the probability

The accompanying information can be concluded:

Number of lower case letters = 26

Number of digits = 10

Total Characters = 26 + 10 = 36

Length of secret word = 8

The quantity of various passwords are conceivable assuming each character might be any lowercase letter or digit will be:

= (26+10)⁸ various passwords

= 2,821,109,907,456 passwords

The quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit, and something like one person should be a digit will be:

= 36⁸ - 26⁸

= 2,612,282,842,880 passwords

Finally, the probability that a substantial secret phrase will be produced will be:

= (36⁸ - 26⁸)/36⁸

= 0.93

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Answer: the perimeter is 214. AB's half is 32.5 and BC's whole is 65

Step-by-step explanation: 10x-5 and 12x-26 are equal, as shown by the marks on their lines, so we can set them equal to each other to solve for x. when solved x=7. then plug 7 into each equation to get 65. lastly add up 84+65+65 to get 214.

The area of the polygon is solved to be  1044 squared cm

The area of the composite polygon is solved by dividing the object into two sections. Then adding up the areas

Section 1 has dimensions:

length * width = 46 * 14 = 644

section 2 has dimensions:

length = 46 - 21 = 25

width = 30 - 14 = 16

Area = 25 * 16 = 400

Area of the composite figure

section 1  + section 2

= 644 + 400

= 1044 squared cm

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Answer:the rock would be at a point 12 m from water

Step-by-step explanation:

Answer: 5/4

Step-by-step explanation:

4/6

just add the numerators and denominators

If a and b set, then the cardinality of the Cartesian product of the two sets, |a × b|, is equal to the product of the cardinalities of the individual sets, |a| and |b|.

So, if |a| = 10 and |b| = 5, then |a × b| = 10 × 5 = 50.

Therefore, the cardinality of the Cartesian product of the two sets is 50.

In mathematical notation, this can be written as:

|a × b| = |a| × |b|

|a × b| = 10 × 5

|a × b| = 50

So the answer is 50.

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The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.

The given points are:

A(−2,3), B(4,3), C(4,−1)

When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.

Therefore, the diagonal points are B(4, 3) and D(-2, -1).

The equation of the line between these two points is:

(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)

(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)

y - 3 = (2/3) (x - 4)

3y - 9 = 2x - 8

3y = 2x + 1

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Answer:

An economic signal is described as any piece of data or information which allows people to optimize their decision-making process and make comparatively better decisions economically.

Step-by-step explanation:

hope it helps

mark me brainliest pls

Step-by-step explanation:

this is the answer

hopes it helps

Answer:

He makes £470 profit

Step-by-step explanation:

He pays $160 for 60 jumpers.

He sells 80% (48) for $12 each. Income of $576

He puts the remaining (12) on sale for one full one half off.

He sells 3 for half price ($6) and 3 for full price ($12) Income of $54

$576 + $54 = $630

$630 - $160 = $470

In pounds sorry about the USD

The best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar is using membership rules and arithmetic condition.

The Prolog interpreter warns that it can only find one occurrence of one or more variables, which is strange, since typically variables are used to perform unification, pass values from one predicate to another, etc.

Arithmetic in Prolog

In arithmetic expression, + - * / symbols are special type of infix operator, and these operators are also known as arithmetic operators. In Prolog, operators are used as predicates but here operators are functions and these operators return a numerical value.

Arithmetic expressions can include variables, numbers, operators, and arithmetic functions. These will be written in parentheses with their arguments. These will return numerical values just like the arithmetic operators.

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The probability that a randomly selected team from Little Town goes to both the city playoffs and the state playoffs is 0.02.

Let's denote the event of a team going to the city playoffs as C and the event of a team going to the state playoffs as S. We are given that P(C) = 0.20, which represents the probability of a team going to the city playoffs. We are also given that P(S|C) = 0.10, which represents the probability of a team going to the state playoffs given that they have already qualified for the city playoffs.

To find the probability of a team going to both the city and state playoffs, we can use the conditional probability formula: P(C and S) = P(C) * P(S|C). Substituting the given probabilities, we have: P(C and S) = 0.20 * 0.10 P(C and S) = 0.02. Therefore, the probability that a randomly selected team from Little Town goes to both the city playoffs and the state playoffs is 0.02.

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Answer:

0.02

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Volume= pi x radius squared x height

substitiute values

540π= π x r^2 x 15

divide 540π by π and 15

so thats 36= radius squared

so the radius is 6 as 6 squared is 36

so the diameter is radius x2

so the answer is 12

It has been proved that n²-5n is even for every n∈ℕ using induction.

Firstly, take the base case.
Check the base case for n = 1:
(1)² - 5(1) = 1 - 5 = -4, which is even since it's divisible by 2.

Now, assume the inductive hypothesis.
Assume that for some k ∈ ℕ, k² - 5k is even.

That means it can be represented as 2m, where m ∈ ℤ.

Now, consider the inductive step.
Prove that if the statement is true for n = k, it must also be true for n = k + 1.

Evaluate (k + 1)² - 5(k + 1):
(k + 1)² - 5(k + 1) = k² + 2k + 1 - 5k - 5

= (k² - 5k) + 2k - 4

We know from the inductive hypothesis that k² - 5k = 2m.

Substitute this into the expression:
2m + 2k - 4 = 2(m + k - 2)

Since m, k, and 2 are integers, m + k - 2 is also an integer. Let's call it p.

Now we have:
2(m + k - 2) = 2p

The expression is divisible by 2, which means it's even.

Therefore, (k + 1)² - 5(k + 1) is also even.

Therefore, by induction, we have proven that n² - 5n is even for every n ∈ ℕ.

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The equation will be y=10-x, where x is the number of days since Logan filled the nectar and y is the quantity of fluid ounces left.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party.

Here,

Let x be the number of days since the feeder is filled and y be the amount of nectar.

Capacity of the hummingbird feeder=10 ounces

Amount of nectar released each day=1 ounce

The equation will be,

y=10-1*x

y=10-x

The formula will be y=10-x, where x is the number of days since Logan filled it and y is the number of fluid ounces of nectar left.

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The median age of his friends is 13

From the question, we have the following parameters that can be used in our computation:

Age (years) 11 12 13 14 15 16

Frequency 3 5 4 2 4 2​

The median age is the age at the middle

So, we have

Median position = (20 + 1)/2

Median position = 10.5th

Here, we have

10.5th = 13

Hence, the median age is 13

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Answer:

48

Step-by-step explanation:

I do not have one sorry!

The value of the missing length in the triangle is b. 100

from the question, we have the following parameters that can be used in our computation:

The triangle

The height is calculated using the Pythagoras theorem as

h²= 60² - 36²

So, we have

h²= 2304

Evaluate

h = 48

Next, we have

(x -36) * 36 = 48 * 48

When evaluated, we have

x -36 = 64

So, we have

x = 64 + 36

Evaluate

x = 100

Hence, the value of x is 100

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Answer:

65.4

Step-by-step explanation:

5 × 6 = 30 square meter

30 × 2.18 = 65.4

Answer:

angle a is 73 and angle c is 180-(73+73)=34