I really need hep please

I Really Need Hep Please

Answers

Answer 1

The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".

The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.

The Augmented matrix on which we have to perform the "row-operation" is

⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],

To get "1" in first row and first column,

The first row-operation is R₁ → 2R₁ + R₂

We get,

⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],

The second , row-operation to get a "1", is R₁ → R₁/2,

We get,

⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].

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Related Questions

A graph is shown.
6987654321
10
0 1 2 3 4 5 6 7 8 9 10
Which ordered pair describes a point that should be removed from the graph so that the graph represents a function?

Answers

An ordered pair that describes a point that should be removed from the graph so that the graph represents a function include the following: A. (1, 1).

What is a function?

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the graph shown below, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 1

1 → 1

In this context, we can reasonably infer and logically deduce that either (3, 1) or (1, 1) must be removed from the graph in order to represent a function.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

What is k? k - 9 < - 6

Answers

Answer:

Step-by-step explanation:

2

2-9=-7

In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.

Answer:

[tex]\mathrm{k < 3}[/tex]

Step-by-step explanation:

[tex]\mathrm{ k - 9 < - 6}[/tex]

Add both sides by 9 :-

[tex]\mathrm{ k - 9+6 < - 6+6}[/tex]

Simplify :-

[tex]\mathrm{k < -6+9}[/tex][tex]\mathrm{k < 3}[/tex]

___________________

Hope this helps!

pls answer asap

A traveler has 9 pieces of luggage.

How many ways can the traveler select 3 pieces of luggage for a trip?

Responses

84

84

504

504

60,480

60,480

362,880

Answers

Answer:

84

Step-by-step explanation:

Trust me

Answer:

84

Step-by-step explanation:

There are 9 pieces of luggage.

We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left.  The third piece can be selected 7 different ways.

9*8*7

504

But order doesn't matter since we are taking 3 pieces.

Divide by (3*2*1)

504/6 = 84

There are 84 different combinations of luggage

help pleaseeeeeeee

here is the picture is about Row Ops

Answers

The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

What is the result of the row multiplication?

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (see attached)

Answers

The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:

A. System A = Inconsistent (No solution)

B. System B = Consistent dependent (Indefinitely many solutions)

C. System C = Consistent independent (A unique solution)

How to identify the systems of linear equations

To identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.

Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.

Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.

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The graph shows the total weight of a fish tank, y, as a function of the amount of water in the tank, x

What is the weight of an empty tank?

Answers

The weight of the empty tank is given as follows:

4 pounds.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.

The weight of the empty tank is the intercept of the function, which is of b = 4, hence:

4 pounds.

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WY is a midsegment of AVXZ.
If VZ = 5t + 51 and WY = 11t, what is VZ?

Answers

VZ is 92.5. WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

what is midsegment  ?

A midsegment of a triangle is a line segment connecting the midpoints of two sides of the triangle. It is also known as a midline. The midsegment of a triangle is parallel to the third side of the triangle, and its length is half the length of the third side.

In the given question,

Since WY is the midsegment of AVXZ, it means that WY is parallel to AX and its length is half the length of AX.

Let's call the length of AX as L. Then, we have:

WY = 11t = 1/2 L

Multiplying both sides by 2, we get:

22t = L

Now, we can use this information to find VZ. Since WY is also parallel to VZ, we have:

WV = VZ

Substituting WV = L/2 and VZ = 5t + 51, we get:

L/2 = 5t + 51

Substituting L = 22t, we get:

22t/2 = 5t + 51

11t = 5t + 51

6t = 51

t = 8.5

Substituting t = 8.5 in the equation for VZ, we get:

VZ = 5t + 51 = 5(8.5) + 51 = 92.5

Therefore, VZ is 92.5.

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How to solve -10(x-1.7)=-3 by expanding first

Answers

To solve the equation -10(x-1.7)=-3 by expanding first, we need to apply the distributive property of multiplication.

Expanding -10(x-1.7), we get

-10x + 17 = -3

Now we can solve for x by isolating the variable on one side of the equation. To do this, we'll add 10x to both sides of the equation

-10x + 17 + 10x = -3 + 10x

Simplifying, we get

17 = 10x - 3

Next, we add 3 to both sides of the equation

17 + 3 = 10x - 3 + 3

Simplifying, we get

20 = 10x

Finally, we divide both sides of the equation by 10 to isolate x

20/10 = 10x/10

Simplifying, we get

2 = x

Therefore, the solution to the equation -10(x-1.7)=-3 by expanding first is x = 2.

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Can you please help me with this please please

Answers

Answer:

a. 14:8

b. 6:14

Step-by-step explanation:

all books on the shelf = 6+8=14

a. 14:8

b. 6:14

A triangle has side lengths of (6.1w + 7.8) centimeters, (1.4w + 8.1) centimeters
and (8.7x + 2.5) centimeters. Which expression represents the perimeter, in
centimeters,
of the triangle?

Answers

The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:

(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)

Simplifying and combining like terms, we get:

7.5w + 11.2x + 18.4

Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

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what is – 7n + –3 – 6n + 3 + 5 is simpified

Answers

Answer:

-13n + 5

Step-by-step explanation:

Give:

– 7n + –3 – 6n + 3 + 5

To Find:

simplify

Explanation:

– 7n + –3 – 6n + 3 + 5

= (-7n - 6n) + (-3 + 3 + 5)

=  - 13n + 0 + 5

= -13n + 5

Final Answer:

-13n + 5

Find the length of the missing side

Answers

Answer:

x = 45°

Because there are 180° in a triangle

Prove the following this:The number of left cosets of a subgroup is equal to the number of its right cosets?

Answers

To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.

Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.

First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.

Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.

Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.

2. How does making tables help you
identify relationships between terms in
patterns?

Answers

Answer:

Step-by-step explanation:

well if you know the term than you know the pattern

Please help me with this question

Answers

Answer:

Your answer is E) 1/2 , -6 , 5

Step-by-step explanation:

Find the slope between (-6,5) then simplify and you will get 1/2

With Bonds, banks pay you back with
O free banking
O a fixed amount
O interest
O stocks

Answers

The answer is c INTEREST

Plot the foci of this ellipse.

Answers

The equation of the ellipse  derived as is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.

The equation of foci is

F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)

What is an ellipse?

An ellipse is  described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.

We can write the equation of an ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) = the center of the ellipse,

a = the semi-major axis,

and b = the semi-minor axis.

The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).

we know also the formula to find the foci of an ellipse is:

F₁ = (h - √(a^2 - b^2), k)

F₂ = (h + √(a^2 - b^2), k)

The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:

2a = √((x - h + √(a^2 - b^2))^2 + (y - k)^2) + √((x - h - √(a^2 - b^2))^2 + (y - k)^2)

Simplifying, we then can write  the equation of the ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

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Help please!!!!
Whoever answers right gets brainliest!

Answers

The simplified form of given expression a³/a⁶b⁻¹ is b/a³.

Hence, the correct option is C.

Exponents are a shorthand notation used in mathematics to represent repeated multiplication of a number by itself. The exponent is a small number written to the right and above a base number, and indicates how many times the base should be multiplied by itself.

In the given expression, a³/a⁶b⁻¹

We can apply the rules of exponents, and we get

= a³⁻⁶/b⁻¹

= a⁻³/b⁻¹

= b/a³

Hence, the correct option is C.

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In order to save the world. Monnor must find the square of the sum of the roots of the equation: x^2-7x+5=0. What is the answer to Monnor's problem?

Answers

The answer to Monnor's problem is NOTA

How to find the answer to Monnor's problem?

For any quadratic equation of the form ax² + bx + c, the sum of roots is given by:

sum of roots = -b/a

In this case, x² - 7x + 5 = 0. Where a = 1 and b = -7. Thus:

sum of roots = -(-7)/1 = 7

Since Monnor must find the square of the sum of the roots of the equation, we have:

square of the sum of the roots = 7² = 49

Thus, the answer to Monnor's problem is NOTA

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Rewrite the quadratic function as a product of linear factors.

f(x) = 16x^2 - 3

help pls

Answers

Answer: (4x - √3)(4x + √3).

Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.

So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).

Find the slope of the line with a y-intercept = 4, passing through the point (2,8)

Answers

Answer: d. m = 2

Step-by-step explanation:

First, we will write a slope-intercept equation using the y-intercept given.

       y = mx + 4

Next, we will substitute the given point and solve for m, the slope.

       y = mx + 4

       (8) = m(2) + 4

       4 = 2m

       m = 2

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Answer:

[tex]\boxed{\sf m=2}.[/tex]

Step-by-step explanation:

1. Identify the 2 given points.

In order to find the slope of any linear equation you need at least 2 points the line passes through. We're explicitly provided one, (2, 8), we just need to figure out the other one.

When the statement says that the line has a y-intercept of 4, it means that at a point with y=4 the function touches the y axis. The only way to touch the y-axis is if the x value is 0. Hence, another given point is (0, 4).

2. Calculate the slope.

Formula: [tex]\sf m=\dfrac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

Naming the variables (can be done arbitrarily but always make sure the y's are actual y values from the ordered pairs and that x₁ goes with its corresponding y₁ value from the ordered pair):

[tex]x_{1} =2;\\x_{2} =0;\\y_{1} =8;\\y_{2} =4.[/tex]

Now substituting these values in the formula:

[tex]\sf m=\dfrac{(4)-(8) }{(0) -(2) }=\dfrac{-4}{-2} =\boxed{\sf 2}.[/tex]

Check out the attached image to see the graphed line.

I really need help please

Answers

Valid row operations are:

6R₁+ R₂ → R₃-(1/2) R₁ → R₁R₁ ↔ R₂R₁ ÷ 2 → R₁2R₂ → R₂-1R₃+ R₂ → R₂2R₁ → R₂R₁ + R₂ → R₂

What are invalid row operations?

Invalid row operations are:

0R₁ → R₁ (this is equivalent to multiplying a row by zero, which is not a valid row operation)

R₃ ÷ 0 → R₃ (division by zero is undefined)

-2 ÷ R₁ → R₁ (division by a variable is not a valid row operation)

2R₁ + R₂ → R₂ (the row operation should be adding multiples of one row to another row, not a combination of multiple rows)

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how do you find the base of a rectangle if you only know the height

Answers

Step-by-step explanation:

You will have to know more....like the area or the perimeter or the diagonal measure to determine the base if you only have the height.

what are the answers to these questions?

Answers

a) The volume of the box can be expressed as V = x(20-2x)(6-2x) cm³.

b) The domain of V is [0, 3) in interval notation.

c) The dimensions of the box that maximize the volume are L = 40/3 cm, W = 2/3 cm, and H = 10/3 cm.

d) The maximum volume is 160/27 cm³.

(a) To form the box, squares of side x are cut out of each corner. So, the length of the box will be (20-2x) cm and the width of the box will be (6-2x) cm.

Since the height of the box is x cm, the volume of the box can be expressed as

V = x(20-2x)(6-2x) cm³.

(b) The domain of V is the set of all possible values of x for which the length, width, and height of the box are positive. This is equivalent to the condition that 0<x<3. So, the domain of V is [0, 3) in interval notation.

(c) To maximize the volume, we need to find the critical points of V. Differentiating V with respect to x, we get

dV/dx = 4x³ - 52x² + 120x.

Setting dV/dx = 0, we get

x = 0 or x = 3 or x = 10/3.

Since the domain of V is [0, 3), we need to check the values of V at x = 0 and x = 3.

We also need to check the value of V at the critical point x = 10/3. Evaluating V at these values, we get

V(0) = V(3) = 0

and

V(10/3) = 160/27.

(d) To find the dimensions of the box that maximize the volume, we substitute the value of x = 10/3 into the expressions for the length, width, and height of the box.

So, the length of the box is

20-2(10/3)

= 40/3 cm,

the width of the box is

6-2(10/3)

= 2/3 cm, and

the height of the box is 10/3 cm.

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Another Statistics question pls help me

Answers

Answer:

55

Step-by-step explanation:

0* .4

28*.5

410*.1

C & J Realty has received 16 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any two of the firm's real estate agents if each agent handles eight inquiries?

Answers

There are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

What is combinations?

Combinations are a mathematical concept used to count the number of ways that a certain number of items can be selected from a larger set of items without regard to the order in which they are selected.

We can use combinations to solve this problem. We need to choose 8 inquiries out of 16 for the first agent, and the remaining 8 inquiries will be handled by the second agent.

The number of ways to choose 8 inquiries out of 16 is:

C(16, 8) = 16! ÷ (8! * (16-8)!) = 12870

This is the number of ways the inquiries can be directed to one agent. Since there are two agents and each handles 8 inquiries, we need to divide this number by 2 to avoid counting each arrangement twice:

12870 ÷2 = 6435

Therefore, there are 6435 ways to direct the inquiries to any two of the firm's real estate agents.

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If 2X = 25 then X = 5, true are false.

Answers

Answer:

False

Step-by-step explanation:

The reason for it being false is because 2X = 25 should be divided to by 2 to get to X, which should be half of 25.

therefore X should equal 12.5

the front of a refrigerator with a freezer on the bottom . The freezer part on the bottom has a height of 2 feet. The top part has a height of 5 feet.Explain how you find the total area of the front of the frig

Answers

The total area of the front of the figure is 21 [tex]feet^{2}[/tex].

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

To find the total area we need to add the area of the refrigerator and the area of the freezer.

The top part i.e refrigerator has a height of 5 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 5 * 3

                                                       = 15 [tex]feet^{2}[/tex]

The bottom part i.e freezer has a height of 2 feet and 3 feet width

Area of the refrigerator section = height * width

                                                       = 2 * 3

                                                       = 6 [tex]feet^{2}[/tex]

The total area of the front of the figure is = Area of the refrigerator section + Area of the freezer section

                                                                   = 15 + 6 = 21[tex]feet^{2}[/tex]

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X 2 3 4 5 6 p(x=x) find the value of p(x>3)

Answers

From the given data, we have:

| x   | 2   | 3   | 4   | 5   | 6   |

| --- | --- | --- | --- | --- | --- |

| p(x) |    |    |    |    |    |

We need to find the value of p(x > 3).

We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.

p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1

We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).

p(x ≤ 3) = p(x = 2) + p(x = 3)

To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:

p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))

Now we can substitute this into the equation for p(x ≤ 3) and solve:

p(x ≤ 3) = p(x = 2) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)

p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))

Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):

p(x > 3) = 1 - p(x ≤ 3)

p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))

p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)

Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.

NEED HELP ASAP! (10POINTS)

Answers

The statement that is true on the linear relationship between the brochures and cost of printing is A. the printing fee is $ 2.50.

How to find the printing fee ?

To find the printing fee, find the difference between the total cost of two different numbers of brochures printed.

The printing fee is:

= ( Total cost of 43 - total cost of 40 ) / ( Difference between 43 and 40 )

= ( 607.50 - 600 ) / ( 43 - 40 )

= 7. 50 / 3

= $ 2. 50

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Households with a computer by region graph of households with a computer by region. which region had the greatest growth in percentage of households with a computer between 2008 and 2018? africa asia western europe the americas Describe three characteristics of the first factories. Please help Use Mean value theorem to prove 6a + 3 < a + 2 for all a > 1.Using methods other than the Mean Value Theorem will yield no marks. {Show all reasoning). Your doing practice 5 Which stanza best expresses the societal changes that occurred during the Victorian Age as they relate to the tone of Dover Beach?A The Sea of Faith/Was once, too, at the full, and round earths shoreB . . . on the French coast the light/Gleams and is gone;C But now I only hear/Its melancholy, long, withdrawing roar,D . . . for the world, which seems/To lie before us like a land of dreams,/ . . .Hath neither joy, nor love, nor light . The given program reads a list of single-word first names and ages (ending with -1), and outputs that list with the age incremented. the program fails and throws an exception if the second input on a line is a string rather than an integer. at fixme in the code, add try and except blocks to catch the valueerror exception and output 0 for the age.ex: if the input is:lee 18lua 21mary beth 19stu 33-1 Performance taskspeaking activity: informative presentation colin powells advice to readers is "always do your very best." today, you will proceed to write a speech that you will present to the class through flipgrid. in your speech, you will need to explain how this principle helped shape powells life and career. as you write your speech, include information from the texts that indicates how experiences, people, and events influenced powell. be sure to present your ideas in a logical order. include details that support each idea. once you are done writing your speech, practice delivering it in a formal way, using appropriate eye contact, correct volume, and clear pronunciation. check that you have not used any vague pronouns that might confuse listeners. when you present your speech, remember powells principle and do your very best! what is the complementary strand for the following template strand of DNA: AAA TCG? A force compresses a bone by 1.0 mm. A second bone has the same cross-sectional area but twice the length as the first. By how much would the same force compress this second bone? 0.50 mm 0 1.0 mm 2.0 mm 4.0 mm 8.0 mm Compute the area of the following triangle. (Express answer in cm^2)b= 20in h= 4in A= ? Cm^2 True or False Deductive reasoning is when someone uses lots of data to make a conjecture. Read the quote from the Quran.Based on what you know aboutMuhammad's teachings, explainwhat man "did not know." The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 8.2 mg and a standard deviation of 1.45 mg. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 42 cigarettes with a mean nicotine amount of 7.73 mg.Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 42 cigarettes with a mean of 7.73 mg or less.P(M < 7.73 mg) = ??? Determine the intercepts of the line.Do not round your answers.-5x - 4y = 10 A ninja star, or shuriken, is usually constructed using four congruent isosceles triangles that are placed along the sides of a square. What is the value of x?a.) 46b.) 56c.) 62d.) 118 110 Percent is Too Much to Give 1 expect every member of this team to give 110 percent," said our new men's track coach "110 percent of practice, 110 percent at every meet, 110 percent in every race "While ! knew no one could give more than 100 percent, the message that our coach expected our best effort all the time came through clearly I tried to live up to his expectations, but by the and of the season, I was exhausted from training so hard all the time. Sul, I was determined to do well that day in the district relay race. When I got the baton for the anchor leg, I began running as hard as I could and easily took the lead. The runner to my left was more relaxed. He kept up with me but didn't try to pass. As we neared the finish line, his kick became more powerful, and he started to pass me. I tried to speed up, but f was already going as fast as I could, and my legs were getting tired. The other runner, however, seemed to have plenty of energy left. As I crossed the finish line behind him. I heard him say to his coach through heavy breaths, "You were right, Coach, pacing yourself is the key to victory!" 1. What is the central idea of this passage? Support your response with evidence from the excerpt. 2. How does the title summarize the lesson the writer learned? 3. How are the coach's words to the team in the first sentence an appeal to ethos? The monthly demand function for product sold by monopoly is p 2,220 1x2 dollars, and the average cost is C = 900 + 14x + x2 dollars. Production is limited to 1,000 units, and x is in hundreds of units_ Find the revenue function, R(x)_ R(x) Find the cost function, C(x): C(x) Find the profit function, P(x) P(x) (a) Find P'(x) . P'(x) Considering the limitations of production, find the quantity (in hundreds of units) that will give the maximum profit. hundred units (b) Find the maximum profit The author makes several references to goldilocks throughout the article. To whom or what does the author compare goldilocks? How does these comparisons contribute to the development of the article as a whole. Article's here:file:///C:/Users/shirl/Downloads/Ready+Unit+3+Interim+Assessment+Student%20(1). Pdf Convert the rectangular coordinates (0, 63) into polar form. Express the angle using radians in terms of over the interval 0 0 < 27, with a positive value of r. Haw many valance electrons in the following atoms.O Na Sr