Casey's Mail Manufacturing is a company that produces chain mail. Their most popular product is saw-cut metal links that hobbyists can use to make their own creations. The company recently spent $100 on advertising, which they hope to make back quickly. The wire used to produce one gram of links costs $2, but the finished links sell for $3 per gram. Eventually, the company will make back its investment and break even. How many grams of links must be sold?

We need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

As per the question statement, we are provided with a binomial (n² - 18n),

And we are required to add a proper constant to the above mentioned binomial so that the resulting trinomial is a perfect square, and then factorise the resulting trinomial.

To answer question, first we need to know the standard form of expanding a perfect square into a trinomial, which goes as,

[(a - b)² = {(a)² + (b)² - (2 * a * b)]

Here, if we compare our concerned binomial (n² - 18n), or, [(n)² - (2 * n * 9)], with the above mentioned standard expansion of a perfect square into a trinomial, we get, (a = n) and (b = 9), and the (b²) term is missing.

Adding [(b²) = (9²) = 81] which is a constant term, to our concerned binomial (n² - 18n), we get, (n² - 18n + 81),

Or, [(n)² + (9)² + (2 * n * 9)],

Which is a trinomial and matches with the standard expansion of a perfect square into a trinomial, and hence,

[(n² - 18n + 81) = (n - 9)²]

That is, we need to add 81 as the constant term to the binomial (n² - 18n) so that the resulting trinomial is a perfect square, and factorization of that resulting trinomial will be (n - 9).

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The fifth graders are read for total 180 minutes.

What do you mean by minutes?

A 60-second interval of time. In an hour, there are 60 minutes. For illustration, the time 10:35 is 35 minutes after 10 o'clock. A minute is equivalent to 1/60th of a degree in terms of angles.

According to the given question,

First 5 students read for 100 minutes.

Then, next 25 studenda read for 50 minutes.

And the rest of the fifth graders read for 30 minutes.

Now, we will adding all the minutes to obtain the answer or total minutes of fifth grader read,

Total minutes of fifth graders read= 100+50+30

                                                        =180 minutes.

Therefore, the fifth graders take 180 minutes to read.

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Puzzle:

A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?

The initial  distance is 10 miles

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Puzzle:

A man walked certain distance first. Then, walked 12 miles. Again walked twice the distance he walked at first. Now, the total distance is 42 miles. what is the initial distance?

Let x=  initial distance

x+12+2(x)=42

3x+12=42

3x=42-12=30

x=30/3=10 miles

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Answer:

Step-by-step explanation:

You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.

Let x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:

  x +y = 36 . . . . . total number of vases

  3x +4y = 125 . . . total number of flowers

Substituting for x, we have ...

  x = 36 -y

  3(36 -y) +4y = 125

  108 +y = 125

  y = 13

  x = 36 -13 = 23

There are 23 vases of daisies and 13 vases of lilacs.

Answer:

  105 N

Step-by-step explanation:

You want the force exerted on an area 2 m by 1.25 m by a pressure of 42 N/m².

The area is ...

  A = LW

  A = (2 m)(1.25 m) = 2.50 m²

The force is the product of the pressure and the area:

  F = PA

  F = (42 N/m²)(2.5 m²) = 105 N

The box exerts a force of 105 N on the table.

A word problem that uses mixed numbers and asks to find the unit price of an item is " The price of a cup of rice is $2. Find the price of 3 1/2 cups.

From the information given, we want to find the word problem that uses mixed numbers and asks to find the unit price of an item.

This can be illustrated as the price of a cup of rice is $2. Find the price of 3 1/2 cups.

Therefore, the price of the cups of rice will be:

= 3 1/2 × $2

= $7

The price is $7.

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For the period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

According to the specified question-

Rate of change = (final number - initial number)/(final year - initial year)

Rate of change = (12,458 - 968)/(2010 - 2005)

Rate of change = -11490/5

Rate of change = -2298 fishes per year.

Negative sign shows there is a decline in the number.

Thus, for the time period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

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The equation D show the multiplication property of inequality if n+4 =11

What is inequality?

inequality, In mathematics if a statement of an order relationship—greater or greater than or equal to, less than, or less than or equal between two number or algebraic expressions.

An inequality show the relationship between two values in an algebraic equations that are not equal.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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The line with no slope will be a horizontal line the correct option is line b.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that on a coordinate plane, line A has a negative slope, line b is horizontal, line c is vertical, and line d has a positive slope.

The line with no slope will be line b because the line is a horizontal line.

Therefore, the line with no slope will be a horizontal line the correct option is line b.

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Answer:

C. Line C

Step-by-step explanation:

Edge 2023

Answer:

Your answer is 17.5 hours

Step-by-step explanation:

Simply multiply 2.5 and 7 to get your answer.

You have to multiply the number of hours by the number of days to get the correct product or answer.

The following are the equations which matches the given word problems:

a. Skate rental charges an additional $3 :

y = x+3

b. Jeff is 3 years less than Tony's age:

y=x-3

c. Marie buys balloons for a party that are $3.00 each:

y = 3x

Given, we have the word problems:

a. Skate rental charges an additional $3 :

here, based on the fixed charge, additional charge is taken as $3.

let the total charge be represented as y and

x represent the fixed charge,

hence the equation we get is:

y = x+3

b. Jeff is 3 years less than Tony's age.

let y represent the age of Jeff

and x represent the age of Tony.

hence we frame the equation as:

y = x - 3

c. Marie buys balloons for a party that are $3.00 each:

let the cost of the balloon be represented as y

and x represent the number of balloons Marie wants to buy for $3 each.

hence the equation we frame is:

y = 3x

Hence we get the required equations.

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The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.

In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.

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May, 4,000

The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.

With the help of binomial distribution we can conclude our answer.

acc to our question-

The confidence interval can be found out using,

Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).

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Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

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Answer:

y=6x+2

Step-by-step explanation:

y=mx+c

8=6(1)+c

8=6+c

c=2

y=6x+2

The maximum height covered is 32m and the time taken to reach maximum height is 1.25 seconds

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change = change in y / change in x. Rates of change can be positive or negative.

h(t) = -16[tex]t^{2}[/tex] +40t + 7

at maximum height the rate of change of h(t) with respect to t is zero.

so [tex]\frac{dh(t)}{dt}[/tex] = 0

but  [tex]\frac{dh(t)}{dt}[/tex] =  -32t + 40

so,

-32t + 40 = 0

32t = 40

t = 40/32

t = 1.25

to find h(t), we substitute t = 1.25 into the equation above

h(t) = -16[tex](1.25)^{2}[/tex] + 40(1.25) + 7

h(t) = 32m

In conclusion, the maximum height reached is 32m and the time taken to reach maximum height is 1.25 seconds

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The domain is { x ∈ R | x ≠ -2 }.

The range is { y ∈ R | x ≠ -8 }.

What are the domain and range of a function?

The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.

A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)

Find domain:

Set the denominator equal to zero and solve for x.

x+2=0

x=-2

This means, domain is set of all real numbers except x=2.

Set builder notation: { x ∈ R | x ≠ -2 }. R= real numbers

Find range:

Replace f(x) by y in the given equation and solve for x.

[tex]y=\frac{x^2-4x-12}{x+2}[/tex]

Write the factors of the numerator

[tex]y=\frac{(x+2)(x-6)}{x+2}[/tex]

common terms x+2 cancel out

y=x-6

x=y+6

substitute x=-2

-2=y+6

y= -8

This means range is the set of all real numbers except y= -8.

Set builder notation: { y ∈ R | y ≠ -8 }. R= real numbers

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After simplification, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.

In the given question we have to solve the given expression.

The given expression is (-7 + i)(-3 + 6i).

Using the distributive property to solve the given expression.

a(b+c)=ab+ac

Now simplifying the expression.

(-7 + i)(-3 + 6i) = -7(-3 + 6i) + i(-3 + 6i)

(-7 + i)(-3 + 6i) = (-7)*(-3) + (-7)*(6i) + (-3)i + (6i)i

(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6i^2

As we know that i^2 = -1. So

(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6(-1)

(-7 + i)(-3 + 6i) = 21 - 42i - 3i - 6

Simplifying

(-7 + i)(-3 + 6i) = 15 - 45i

Hence, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.

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Answer:

x = 10

Step-by-step explanation:

48 = x + 8 + 2x + x

    48 = 4x + 8

   -8           -8

40 = 4x

divide both sides by 4

10 = x or x =10

The point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

What is equation of line ?

  A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

Here the given point ,

=> [tex](x_1,y_1)=(5,1)[/tex]

Slope m = [tex]\frac{1}{5}[/tex]

Here using equation formula

=> [tex]y-y_1 = m ( x- x_1)[/tex]

=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

Hence the point slope form of the equation is  y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)

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The function of the graph is f(x) = |x - 3| + 5

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

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the minimum point on the graph is located at the point (3, 5)

This means that

Vertex = (3, 5) i.e.  (h, k) = (3, 5)

Recall that the general form of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

On the graph, we have

(x, f(x)) = (2, 6)

So, we have

6 = a|2 - 3| + 5

This gives

a = 1

So, we have

f(x) = 1 * |x - 3| + 5

Evaluate

f(x) = |x - 3| + 5

Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5

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The values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.

According to the question,

We have the following information:

We have a ratio table where two rows from the beginning are given.

In these rows, we have 1:5 and 6:30.

Now, we can easily find that the number in the second column is found by multiplying 5 into the number in the first column.

Now, for the third row, we have the number in the second column,50:

x*5 = 50

x = 50/5

x = 10

Third row: 10 to 50

Fourth row:

Number in the first column = 11

11*5 = 55

11:55

Fifth row:

Number in the first column = 18

18*5 = 90

18:90

Hence, the values, 1:5, 6:30, 10:50, 11:55 and 18:90, will complete the given ratio table.

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The simplification of the fraction would be;

                   [tex]= \frac{350g}{1kg}[/tex]

                   [tex]= \frac{350g}{1000g}=\frac{7}{20}g= 0.35g[/tex]

What is fraction?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

In a simple fraction, both are integers.

A complex fraction has a fraction in the numerator or denominator.

In a proper fraction, the numerator is less than the denominator.

Explanation of the answer:

Given that :

350g/1kg

Firstly we convert kilogram into gram:

1 kg = 1000 g

The mass m in grams (g) is equal to the mass m in kilograms (kg) times 1000:

m(g) = m(kg) × 1000

So the given values are changes into:

[tex]\frac{350g}{1000g}\\[/tex]

[tex]= \frac{7g}{20g}[/tex](divide numerator and denominator by 50)

[tex]\\=0.35g[/tex]

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Answer: c/bd = a

Step-by-step explanation:

What we need to do is isolate a on one side of the equal side. Now, remember that multiplication and division cancel each other out, so if we divide b and d on the right side by b and d then we cancel those values and get a by itself. Now, we have to do this on the left side as well in order to keep the equation balanced. When we do this, we get c/bd = a. Keep working hard! You're doing great!

For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

As given in the question,

Given equation is equal to :

9 ( x - 4) - 5x = _ x - 30

Simplify Left hand side of the given equation we get,

9 ( x - 4) -5x

= 9x - 36 - 5x

Collect the like terms we have,

9x - 5x - 36

= 4x - 36

Now compare left hand side and right hand side to get no solution of the equation,

4x -36 = _x -30

Blank should be filled by 4

Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.

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Answer: 55.56%

Step-by-step explanation:

To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.

By studying the change of the y-intercept, we can see that the shift is of one unit upwards.

We know that the original y-intercept of the line is y = -1, then the line is of the form:

y = a*x - 1

Where a is the slope.

Now we apply a vertical shift of N units, this is written as:

y = a*x - 1 + N

And we know that the new y-intercept is 0, so:

y = a*0 - 1 + N = 0

y = -1 + N = 0

-1 + N = 0

N = 1

The shift is of 1 unit up.

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The required value of "b" is 7, where the equation is y = -3x + 7.

As per the given table, we take the two points (9, 1) and (3,7).

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -3, y₁ = 16

x₂ = 1, y₂ = 4

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute the values in the above equation,

y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))

y - 16 = (-12/4)(x+3)

y - 16 = -3(x+3)

y - 16 = -3x - 9

y = -3x - 9 + 16

y = -3x + 7  ....(i)

Compare the given equation y = mx + b with the above equation, and we get

b = 7

Therefore, the required value of "b" is 7.

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Answer: Ethiopia has a population growth rate above 2.5% and a life expectancy of 61 years old