what is the solution of the system

Answer:

A) Distance time graph

B) d(t) = 25t

C) The expression shows the distance more clearly.

Step-by-step explanation:

A) A distance time graph as seen in the attachment provides a representation of the distance travelled.

We are told the car travels at a constant speed of 100 meters per 4 seconds. Which means that 100 m for each 4 hours. So, for 200m, it's 8 hours like seen in the graph and for 300m,it's 12 hours as seen in the graph.

B) And expression for the distance is;

d = vt

Where;

d is distance in metres

v is speed in m/s and t is time

We are told that the car travels at a constant speed of 100 meters per 4 seconds.

Thus, v = 100/4 = 25 m/s

Distance travelled over time is;

d(t) = 25t

C) Looking at both A and B above, it's obvious that the expression of the distance shows a more clearer way of getting the distance because once we know the time travelled, we will just plug it into the equation and get the distance. Whereas, for the representation form, one will need to longer graphs if the time spent is very long.

If the combination r = 5% and Y = $100 billion is on the Fed rule line, and the combination r = 7% and Y = $100 billion is considered, it would represent a movement up the Fed rule.

The Fed rule represents the relationship between the interest rate (r) and the level of real GDP (Y). As the interest rate increases from 5% to 7% while keeping the level of real GDP constant at $100 billion, it indicates a movement along the Fed rule line in an upward direction.

This implies that as the interest rate increases, the recommended level of real GDP decreases, based on the Fed rule. Therefore, the combination r = 7% and Y = $100 billion represents a movement up the Fed rule.

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In 1990, the average person in the United States consumed approximately 0.000532 lb (or 0.24 grams) of artificial sweeteners per year, based on USDA data.

In 1990, according to the USDA, each person in the United States consumed an average of 133 lb of artificial sweeteners per year.
To calculate the average consumption of artificial sweeteners per person, you can divide the total consumption by the population of the United States in 1990.
Let's assume that the population of the United States in 1990 was 250 million people.
To find the average consumption per person, you would divide the total consumption of 133 lb by the population of 250 million people:
133 lb / 250,000,000 people = 0.000532 lb/person
Therefore, in 1990, the average person in the United States consumed approximately 0.000532 lb (or 0.24 grams) of artificial sweeteners per year.

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Answer:

What kind of mathematics is this?

The total surface area of the given prism is: 381 yd²

The formula to find the area of a trapezium is:

Area = ¹/₂(a + b) * h

where a and b are parallel sides of the trapezium

Thus:

Area of 2 trapeziums = 2(¹/₂(11 + 5) * 6.3) = 100.8 yd²

Area of remaining sides = (2 * 7 * 6.3) + (11 * 6) + (5 * 6) = 184.2 yd²

Total surface area = 100.8 yd² + 184.2 yd²

Total surface area = 381 yd²

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The slope the line which divides the parabola and x-axis into two regions with equal area is 0

To find the slope of the line, we need to determine the point of intersection between the parabola and the x-axis.

Setting y = 0 in the equation y = x - x², we have:

0 = x - x²

Rearranging the equation:

x² - x = 0

Factoring out x:

x(x - 1) = 0

This equation is satisfied when x = 0 or x = 1.

Therefore, the line passes through the origin (0, 0) and the point (1, 0) on the x-axis.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

In this case, (x1, y1) = (0, 0) and (x2, y2) = (1, 0). Plugging these values into the slope formula:

Therefore, the slope of the line that divides the region bounded by the parabola y = x - x² and the x-axis into two regions with equal area is 0.

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The given series is 1 3 9 27 81

here, all the numbers are the multiplication of three.

it is the series of function f(x) = 3^x

substitute x= 1, 2 , 3 , 4 , 5......

Answer:

Step-by-step explanation:

Answer:

79.

Step-by-step explanation:

Replace the x by -5 and simplify:

f(-5) = 3(-5)^2 + (-5) + 9

       = 75 - 5 + 9

       =  79.

The value of f(-5) will be 79.

Step-by-step explanation:

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s) is called a polynomial.

The following table gives special names given to polynomials of low orders.

polynomial order polynomial name

2                         quadratic polynomial

3                         cubic polynomial

4                        quartic

5                         quintic

6                         sextic

Here, the given polynomial: f(x) = 3x² + x + 9

by putting value of x = -5

\(3*(-5)^{2} + (-5) + 9\)

after putting we get,

\(75 - 5 + 9\)

On solving the above numerical we get,

\(79\).

So our final answer would be 79 on putting x = -5 in the given polynomial : f(x) = 3x² + x + 9

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Answer:

6.T

7.F

8.F

9.T

10.T

Step-by-step explanation:

I also took the test and these where my correct answers

Answer:

I think it is D , but if it not plz forgive me

Answer:

d

Step-by-step explanation:

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

A binary tree is a structure in which each node is capable of having two successor nodes, called left and right child nodes. The unique starting node is called the root.

In a binary tree, each node can have at most two successor nodes, namely the left child and the right child. These successor nodes are positioned below the parent node. The binary tree structure allows for branching and hierarchical organization of the nodes. The root node is the topmost node in the tree and serves as the starting point from which the tree branches out. Each node can have a left child, a right child, both, or none, depending on the specific configuration of the tree. This hierarchical arrangement of nodes and their successors allows for efficient data storage and retrieval in various algorithms and data structures.

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Answer:

Step-by-step explanation:

25% it means 1/4 of the total

1/4 of 80 is 20 (80/4=20)

answer B

The rate of increase of the y-coordinate as it approaches the point (1, 5) is 4 cm/s.At that instant, the x-coordinate of the point is not changing; it is staying at 1.

When a point reaches a certain coordinate, it means that the point is not changing anymore. In this case, the point has reached the coordinate (1, 5), which means that the x-coordinate (1) is not changing, while the y-coordinate (5) is increasing at a rate of 4 cm/s. Therefore, the x-coordinate of the point is not changing at that instant.

x = 1

Rate of Change (x-coordinate) = 0 cm/s

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The correct answer is option b. 15.77%. The annual discount rate, also known as the discount rate or the rate of return, can be calculated using the present value formula.

Given that a cash flow of £52 million in 5 years' time is currently valued at £25 million, we can use this information to solve for the discount rate.

The present value formula is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

In this case, we have PV = £25 million, CF = £52 million, and n = 5. Substituting these values into the formula, we can solve for r:

£25 million = £52 million / (1 + r)^5.

Dividing both sides by £52 million and taking the fifth root, we have:

(1 + r)^5 = 25/52.

Taking the fifth root of both sides, we get:

1 + r = (25/52)^(1/5).

Subtracting 1 from both sides, we obtain:

r = (25/52)^(1/5) - 1.

Calculating this value, we find that r is approximately 0.1577, or 15.77%. Therefore, the annual discount rate is approximately 15.77%, corresponding to option b.

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Answer:

\(y=4x-5\)

Step-by-step explanation:

Slope-intercept form is given as \(y=mx+b\). We can simply manipulate and rearrange the given function to be in this form:

\(8x-2y=10,\\-2y=-8x+10,\\\boxed{y=4x-5}\)

Answer:

Step by Step Explanation:

Pythagorean theorem tells us how the side lengths of right triangles are related.

The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.

This relationship can be written as the equation:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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In the expression 2*4 + 3y, the coefficient of y is 3. The coefficient is the number next to the variable.

Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.

We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:

=>  1-2-3-4

=>  1-2-4-3

=>  1-3-2-4

=>  1-3-4-2

=>  1-4-2-3

=>  1-4-3-2

Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:

=> 6/16 = 0.375

This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

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The number of downloads of the high quality version that was made was 600.

This is a great system of equations problem

If we call the number of standard version downloads (S)  

The high quality downloads (H).

To find S, we can rearrange the first statement to H = 910 - S,

Then we would substitute (910 - S) wherever you see an H in the second equation so that you have only S's in your equation.

Thus:

2.8(S) + 4.4(910 - S) = 3044

2.8S + 4004 - 4.4S = 3044

-1.6S = -960

s = 600

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Answer:

Breadth= 4.5cm

Step-by-step explanation:

Area= length x breadth

54cm²=12× b

b=54cm²÷12

b=4.5cm