A seamstress has three colours of ribbon; the red is 126cm, the blue is 196cm and the green
is 378cm long. She wants to cut them up so they are all the same length, with no ribbon
wasted. What is the greatest length, in cm, that she can make the ribbons?

y varies directly as x, y = 7 when x = 21. Determine x when y = 5.

Step 1

Let

y varies directly as x, it is y depends on x, in math terms

f(x)=y

y = 7 when x = 21

f(21)=7

Determine x when y = 5. f(?)=5

Step 2

there is a proportion, this must be equal, make a rule of three to find the value

so

x y

so , when y=5, x=15

we have the function

Find out the first derivative of the given function

Equate to zero the first derivative

The values of x are

x=0 and x=1

we have the intervals

(-infinite,0) (0,1) (1,infinite)

Interval (-infinite,0) -----> f'(x) is positive

interval (0,1) ---------> f'(x) is negative

interval (1,infinite) -----> f'(x) is positive

that means

x=0 is a local maximum

x=1 is a local minimum

Find out the y-coordinates of the extreme values

For x=0 -----> substitute in the function f(x) ---------> f(x)=0

For x=1 ------> substitute in the function f(x) ------> f(x)=-0.5

therefore

The extreme values are

-2 decimal 3/% because if you divide the principal in half its 1% of 3

Given the functions:

We will find: f(x) • g(x)

So, we will find the product of the functions

We will use the distributive property to get the result of the multiplications

So,

so, the answer will be:

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]

[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]

how much will it be in interest alone?

well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned

[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]

State A have 42 counties and State B have 40 counties.

Define Linear equation

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant

Let,

x = The number of counties of state B

x + 2 = The number of counties of State A

It's given, The sum of counties of state A and state B is 82

so, the equation become is linear.

The linear equation will be,

x + (x + 2) = 82

solve for x,

2x + 2 = 82

2x = 82 - 2

2x = 80

x = 80/2

x = 40  (counties of State B)

put the value in x in x + 2,

40 + 2 = 42 (counties of State A)

Therefore, State A have 42 counties and State B have 40 counties.

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Number 4

The meaning of the symbols are

> means greater than

< means less than

For the first statement, 30 is greater than 10. It is true

For the second statement, 30 is less than 10. It is not true

For the third statement, 10 is greater than 30. It is not true

For the fourth statement, 10 is less than 30. It is true

Mass=79gram

Volume=10ml

density=Mass/Volume

The equation for number of books collected by Robert is given as;

n= 14 d + 21

where d is the number of days he spent collecting .

Answer A. represents the number of books per day that are collected

THe length of each cube is inreasing by 1. This means that the increment is in arithmetic sequence.

The formula for determining the nth term of an aritmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first tem of the sequence

Common difference, d represents the difference between consecutive terms

Given that a = 3, d = 1

Tn = 2 + (n - 1)1

Tn = 2 + n - 1

Tn = 1 + n

For the 18th term, n = 18

T18 = 1 + 18 = 19

The number of boxes in the square for the 19th term is

19 * 19 = 361

Answer:

f(x) = 1(x - 4.5)² - 6.25

Step-by-step explanation:

Hello!

Let's find the Vertex Form of the quadratic by Completing the Square.

The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².

To find b², we need to divide -9 by 2 and square it.

Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).

Convert this back to function form:

The equation is f(x) = 1(x - 4.5)² - 6.25.

A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?​

Let

x -----> number of boys

y -----> total number of children

we have that

x=11 -----> given

y=21 ----> given

therefore

The fraction of the class that is made up of boys is equal to

x/y

substitute

The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x

Given,

The cost of a convention center to host an event = $300 + $45 per person attending

Number of attendees = x

We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.

Here,

Total cost for the event = Fixed cost + cost per person attending x number of person

Total cost = 300 + 45 × x

Total cost = 300 + 45x

Now,

The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x

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a quadratic function has any root when replacing that number the equation is equal to zero

so

now solve the multiplication

Sidney will use 57 cups of soda for 19 cups of ice cream.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

The ratio of cups of ice cream to cups of soda.

3.5 cups ice cream = 10.5 cups of soda

Divide both sides by 3.5.

1 cup of ice cream = 3 cups of soda

Multiply 19 on both sides.

19 cup of ice cream = 57 cups of soda

Thus,

57 cups of soda.

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Answer:

2 and 3

Explanation:

Given the equation:

Now, observe the following:

Taking the indices:

She will need 12 flats and there will be 5 leftovers

From the question, we have

The number of flats is calculated as

So, we have the following equation

Number of flats = (Length)/Rate

So, we have

Number of flats = (77)/6

Evaluate

Number of flats = 12

This is calculated as

Leftover = Length - Number of flats * Rate

So, we have

Leftover = 77 - 12 * 6

Evaluate

Leftover = 5

Hence, the left over is 5

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Missing information in the question

The point of the problem is to remember the cosine relation. It says, in this case, that

Converting the last equation by the inverse function, we get

For the first decimal place (5) equals 5, and by the rounding rule to the nearest degree, we get 63. The answer is A.

okay so the answer is 9ft so option B

now we can take a look at how we arrived to that answer

do you know the formula for the volume?

Given the polynomial:

Let's factor the polynomial.

To factor, let's use the AC method.

Find a pair of numbers whose product is -18 and whose sum is 7.

We have the pair:

9 and -2

We have the factors:

(w + 9)(w - 2)

Therefore, the factored form of the polynomial is:

ANSWER:

For this problem we use the continuously compounded interest formula:

where M_0 is the initial amount, r is the interest rate per year and t is the number of years.

Substituting M_0=$3500, r=0.06, and t=2 we get:

Given the equation:

Let y = distance

Let x = time

- The distance from Denver when she began is given by x = 0, therefore:

Answer 1. 475 miles

- The change for each four hours, this is x = 4, so:

Answer 2. 235 miles

By solving the equations, we can conclude that the two numbers are 4 and 6.

So, the two numbers are:

The equation will be:

Now, solve this equation for 'x' as follows:

Now, 4x - 20:

Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.

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A pair of numbers that have a sum of 50

Let the number is x, so the other number is 50 - x

Let f(x) be the largest product so:

Simplify the expression :

Diffrentiate with respect to x

Now for to check for the f(x) is maximum for x = 25

Calculate the second derivative and put x = 25 is the f(x) is negative then the multiplication f(x) is maximum

Thus, the first number is 25

Second number is : 50 -x = 50-25 = 25

Numbers are 25, 25

Answer : 25 + 25 =50 (sum)

25 * 25 = 625 (maximum possible product)

We are given the following triangle:

We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":

Now, we multiply both sides by "sin107":

Solving the operations:

Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:

Adding the values:

Now, we subtract 155 from both sides:

Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:

Now, we multiply both sides by "sin(25)":

Solving the operations:

Now, we determine the area using the following formula:

Where:

Now, we determine the value of "s":

Solving the operation:

Now, we substitute the value in the formula for the area:

Solving the operations:

Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:

Now, we cross multiply:

Now, we divide both sides by 300ft^2:

Solving the operations:

Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.

we know that

the mass of Alison's Emperor Scorpio is

Answer:

a.35

Step-by-step explanation:

10 + 20/2 equals 20

20/2+5 equals 15

20+15 equals 35

As per given by the question,

There are given that function,

Now,

Find the value of f(g(3)).

Then,

There are given that,

And,

According to question, value of x is 3, that means g(3).

So,

Put the value of x in g(x).

Then,

Now,

For find the value f(g(3));

Put the value of g(3) in the above condition,

f(g(3)).

So,

Instead of x in f(x), put the g(3).

Then,

So, the value of f(g(x)) is 7.

Hence, the option first is correct.

For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.

Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".