suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. suppose that it takes 100 workers 6 weeks to build 4 miles of Highway. how long will it take a 160 workers to build 16 miles of Highway?___weeks

Given the polynomial:

You can factorize it as follow:

1. Rewrite the term with exponent 2 in this form:

2. Rewrite the x-term in this form:

3. Rewrite the expression:

4. Make three groups of two terms each using parentheses:

5. Identify the Greatest Common Factor (GCF) of each group (the largest factor that all the terms in the group have in common):

- For:

The Greatest Common Factor is:

- For:

The Greatest Common Factor is:

- And for:

It is:

6. Factor the GCF of each group out:

7. Notice that each expression is common in all the terms:

Then, you can factor it out:

8. In order to factor the Quadratic Polynomial in the second parentheses, you can find two numbers whose Sum is -8 and whose Product is 15. These are -3 and -5. Then, you get:

Hence, the answer is: Option D.

Explanation

Step 1

A square root of a number is a value that, when multiplied by itself, gives the number.

hence, we need to find a value(s) that when multiplied by itself gives 121,so

because

I hope this helps you

Answer:

3x

Explanation:

First, find the prime factorization of each of the terms:

Next, pick the term that is common in the three products:

The GCF of -3x, 6x, and 12x is 3x.

Let L and M represent two positive numbers.

Since one positive number is 5 times another number, we can make the statement:

Since the difference between those numbers is 148, we can write down:

Where we have chosen L-M instead of M-L since L is greater than M and both are positive numbers (by using M-L, the difference would be negative).

Substitute 5M for L in the second equation:

Solve for M:

Once knowing M, multiply by 5 to get L:

Therefore, those two numbers are 37 and 185.

The value of x = 42

Given : A right angled triangle with the below mentioned measures :

angles ∠ 1 = 28 °

∠ 2= 25° and the length is 600

To find : the value of x

Let us assume the rest of the length is y that is the side opposite of the angle will now be x + y

thus tan 28 ° = [tex]\frac{x+y}{600}[/tex]

tan 28 °= 0.53 thus the equation after cross multiplying becomes ;

0.53 × 600 = x + y

318 = x + y ------------------ equation 1

And tan 25° = [tex]\frac{y }{600}[/tex]

tan 25 ° = 0.46  

After cross multiplying we get : 0.46 × 600 = y

=> 276 = y

Substituting this value in equation 1 we get : 318 = x + 276

=> x = 318 - 276

=> x = 42

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The vowel is the Roster method representation of all lowercase English letters except 'y'.

={a, e, i, 0, u}

This is further explained below.

Generally, A set comprises elements or members that may be mathematical objects of any sort, including integers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical model for a collection of various things.

In conclusion, the Roster method representation of a set of all lowercase letters in the English alphabet except the letter 'y' is Vowel.

={a, e, i, 0, u}

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[tex]A^{-1} =\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]

[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]

Given matrix A:

[tex]\left[\begin{array}{ccc}5&-15&-44\\-1&2&6\\1&-3&-9\end{array}\right][/tex]

To find the inverse of the matrix we start by finding the determinant of the matrix.

|A| = 5(-18+18) + 15(9-6) - 44(3-2)

= 0 + 15(3) - 44 = 45 - 44 = 1

As the determinant 1 ≠ 0, hence the inverse of the matrix exists.

Now, we find the minors of each element of the matrix.

m₁₁ =  [tex]\left[\begin{array}{ccc}2&6\\-3&-9\end{array}\right][/tex]  = 0

m₁₂= [tex]\left[\begin{array}{ccc}-1&6\\1&-9\end{array}\right][/tex] = 3

m₁₃ =  [tex]\left[\begin{array}{ccc}-1&2\\1&-3\end{array}\right][/tex] = 1

m₂₁ = [tex]\left[\begin{array}{ccc}-15&-44\\-3&-9\end{array}\right][/tex] = 3

m₂₂ = [tex]\left[\begin{array}{ccc}5&-44\\1&-9\end{array}\right][/tex] = -1

m₂₃ = [tex]\left[\begin{array}{ccc}5&-15\\1&-3\end{array}\right][/tex] = 0

m₃₁ = [tex]\left[\begin{array}{ccc}-15&-44\\2&6\end{array}\right][/tex] = -2

m₃₂ = [tex]\left[\begin{array}{ccc}5&-44\\-1&6\end{array}\right][/tex] = -14

m₃₃ = [tex]\left[\begin{array}{ccc}5&-15\\-1&2\end{array}\right][/tex] = -5

The cofactor matrix can be obtained as:

[tex]\left[\begin{array}{ccc}0&3&1\\3&-1&0\\-2&-14&-5\end{array}\right][/tex]

Now the adjoint of matrix A (written as adj A) by taking the transpose of the cofactor matrix of A is,

[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]

To determine the inverse of a square matrix A, we use the formula:

A⁻¹ = adj(A) / |A|

Therefore, the inverse of the given matrix is:

A⁻¹ = 1/1 [tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]

It is given, Ax = b

and b = [tex]\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]

Let x be [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex]

Putting values in Ax = b equation,

[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right]\left[\begin{array}{ccc}a\\b\\c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}-3b-2c\\-3a-b+14c\\a-5c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]

Equating the three equations with the respective values,

So, -3b - 2c = -2

-3a -b + 14c = -2

a - 5c = -2 ⇒ a+2/5 = c

Solving the above equations we obtain the values of a,b, and c as 108, -14, and 22.

So, the matrix x is

[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]

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[tex]\stackrel{a}{4\sqrt{7}}~~ - ~~\stackrel{b}{9}i ~~ \begin{cases} r=\sqrt{a^2 + b^2}\\\\ \theta =\tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{(4\sqrt{7})^2 + 9^2}\implies r=\sqrt{16(7)+81}\implies r=\sqrt{193} \\\\\\ \theta =\tan^{-1}\left( \cfrac{9}{4\sqrt{7}} \right)\implies \theta \approx 40.38^o \\\\[-0.35em] ~\dotfill\\\\ z~~ = ~~\sqrt{193}( ~~ \cos(319.62^o)~~ + ~~i\sin(319.62^o) ~~ )\qquad \textit{\LARGE IV Quadrant}[/tex]

let's take a quick look at the (a , bi) pair, "a" is positive whilst "b" is negative, that means the IV Quadrant, now let's keep in mind that tan⁻¹(x) has a range that lies on the I and IV Quadrants, so, if you check in your calculator for tan⁻¹(x) for those values, you'll notice it gives the one in the I Quadrant, namely 40.38°, however our coordinate pair is on the IV Quadrant, so we need its twin.

Make sure your calculator is in Degree mode.

1) As the number of meals is integer, 5, 8, 11, and so on

2) Then we have a discrete relationship between the numbers of meals.

Answer:

7/16

Step-by-step explanation:

Convert "mixed numbers" into "improper fractions":

1 1/6 = 7/6

2 2/3 = 8/3

1 1/6 divided by 2 2/3 = 7/6 divided by 8/3

Apply the KFC rule:

1) Keep the first

7/6

2) Flip the second

8/3 becomes 3/8

3) Change the sign

7/6 multiplied by 3/8

7/6 × 3/8

= 7×3 / 6×8

= 21/48

= 7/16

the expression has a value closest to 1 is √37 - √26 (option C)

Explanation:

To determine the expression, we need to solve each of the options.

a) 7π/√10 = 7(3.14) /√10 = 21.98/3.1623

= 6.95

b) √75 - √74 = 8.66 - 8.60

= 0.06

c) √37 - √26 = 6.083 - 5.099

= 0.984

d) (3√5 - √20)/√2 = (6.708 - 4.472)/1.414 = 2.236/1.414

= 1.58

√37 - √26 = 0.984 is closest to 1

From the above, the expression has a value closest to 1 is √37 - √26 (option C)

The area of the moulding is;

Here, we want to get the area of the moulding

From the question, we are told that the 80% of the frame is a glass photo

What this mean is that 20% of the picture frame will be that of the moulding

Mathematically, by calculating 20% of the area of the frame, we get the area of the moulding

As we can see that the frame is a rectangular shape, the area is the product of its length and its width

We have this as;

The area of the moulding is 20% of this which is the same as one-fifth or 1/5

we have this as;

ANSWER:

a. 280 cm^3

b. 343 cm

STEP-BY-STEP EXPLANATION:

The formula for the volume of the rectangular prism is as follows:

We replace for each case:

a.

b.

c.

The statement makes sense. This is because A 200 percentage increase in price corresponds to a price that is 300% of the original price

You can express a fraction of something using percentages. A change in something can be described using percentages. As an illustration, the price of milk increased by 5% last month.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.

A figure or ratio stated as a fraction of 100 is called a percentage. The % sign is frequently used to indicate it. In this case, 200% of something implies that it will give 300% of the initial amount.

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The price of tuition has tripled since my parents went to school thats a 200% increase in price corresponds to a price that is 300% of the original price. Does this makes sense?

we have the system of equations

y=3x+4 ----> equation 1

y=ax+b ----> equation 2

Remember that

The only condition for the system, to have only one solution is that the slopes of both lines are different

so

The values for a are all real numbers except for a=3

The values for b are all real numbers

Therefore

A solution could be

The solution is (0,4)

The inner core is solid because the inner core consists of a lot of pressure and high temperatures. This is true.

The pressure surrounding the inner core, as well as the planet's atmosphere, keeps the iron from melting. The iron atoms cannot migrate into a liquid form due to the pressure and density, which are simply too high.

Temperature is a measure of how hot or cold something is, more particularly the average kinetic energy of the particles in an object, which is a sort of energy related with motion. Temperature is a measure of how hot or cold something is represented in terms of one of several scales, including Fahrenheit and Celsius.

Because the inner core is under intense pressure and is extremely hot, it is solid. And the stuff becomes denser as pressure and temperature increase. Therefore, the inner core's high heat and pressure are what are solidifying it since the denser the stuff is, the more solidified it becomes.

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The inner core is solid because the inner core consists of a lot of pressure and high temperatures. And the more pressure and high temperatures the more dense the substance gets. True or false?

We can calculate the slope as:

From this, we have: (FIRST ANSWER)

The length of the non-parallel sides can be measured as:

From this, we have: (SECOND ANSWER)

From the figure in the beginning and the values we found, this is a Rhombus.

The equation with infinitely many solutions are 3(x – 1) = 3x – 3  and 2x + 2 = 2(x + 1) .

An infinite solution has both sides equal to each other.

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

Therefore, the equation with infinitely many solution are as follows:

D.

3(x – 1) = 3x – 3

open the brackets on the left side of the equation

3x - 3 = 3x - 3

E.

2x + 2 = 2(x + 1)

open the brackets on the right side of the equation

2x + 2 = 2x + 2

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To calculate the area of a circle you have to use the following formula:

Where

A is the area

π is the number pi, for this exercise you have to use up to its two first decimal values: 3.14

r is the radius.

The radius of a circle is half its diameter, so the radius of the circular garden will be

Next, you can calculate the area of the circular garden as follows:

The area of the circle is 50.24yd²

The role of financial accounting standard setting in the United States is to establish and improve financial accounting and reporting standards to provide useful information to those who need it.

The Financial Accounting Standard is a term to refer to an institution established in 1973 that was created with the objective of establishing financial reporting and accounting standards for public and private companies and non-profit organizations.

The main role of this institution is to create accounting standards focused on public companies. This process of creating accounting standards is focused on promoting financial information in the financial field for different institutions and people interested in investing.

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Answer:

x  =  7

y  =  3

z (max)  =  4950/3  =  1650

Step-by-step explanation:

Let call  

x numbers of church goup and

y numbers of Union Local

Then  

First contraint

2*x + 2*y ≤ 20

Second one

1*x + 3*y ≤ 16

Objective Function

z = 150*x + 200*y

Then the system is

z = 150*x + 200*y To maximize

Subject to:

2*x + 2*y ≤ 20

1*x + 3*y ≤ 16

x ≥ 0 y ≥ 0

We will solve by using the Simplex method

z - 150 *x - 200*y = 0

2*x + 2*y + s₁ = 20  

1*x + 3*y + 0s₁ + s₂ = 16

First Table

z           x          y          s₁           s₂          Cte

1        -150    -200       0            0     =      0

0          2         2           1            0     =    20

0          1          3          0            1      =     16

First iteration:

Column pivot   ( y column ) row pivot (third row) pivot 3

Second table

z           x                y          s₁           s₂                Cte

1       -250/3           0          0         200/3    =    3200/3

0      - 4/3               0          -1           2/3       =    -20/3

0         1/3               1            0           1/3       =    -20/3

Second iteration:

Column pivot  ( x column ) row pivot  (second row)  pivot  -4/3

Third table

z           x                y          s₁           s₂                Cte

1            0               0      750/12    700/6    =   4950/3

0            1                0        3/4          -1/2     =    7

0            0                1         -1/4          1/2     =  9/3

Step-by-step explanation:

The value of the function (g•f )(x) is 8x-3.

Given the functions are:

g(x) = 4x+5

f(X) = 2x-2

we are asked to determine (g•f )(x) = ?

⇒ g(x) = 4x+5

⇒ f(x)  = 2x-2

⇒  (g•f )(x), substitute the value for f(x)

⇒ g(f(x))

⇒ g(2x-2)

now put the value g(2x-2) in g(x)

⇒ g(2x-2) = 4x+5

⇒ g(2x-2) = 4(2x-2) + 5

⇒ g(2x-2) = 8x - 8 + 5

⇒ g(2x-2) = 8x - 3

Hence we get the value of  (g•f )(x) as 8x-3

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we can factor this quadratic expression finding the zeros, as follows:

Then, the quadratic expression can be expressed as

Answer:

X = 3

Step-by-step explanation:

To solve this you want to first make the X variable alone by itself by moving it to the left or right it doesn't really matter, for this I moved it to the left making the new equation

-x = -1 - 2

I then make the 2 a negative using the order of operations and a negative adding a negative makes -3 making the following

-x = -3

then I change the signs making it

x = 3

Debt can be defined as a sum of money that is owed or due.

Debt creates financial risk and instability by:

a) spreading economic pain and hardship to the country's citizens and to other countries.

b) causing Financial losses, market turmoil, and sharp slowdowns in trade and economic growth are some of the ways countries can feel the effects of a debt crisis in other countries.

c)Creating a heavy debt load that you can’t pay off, your credit score will start to go down resulting in a bad credit score and report.

d) leading to stress by limiting your ability to enjoy life. This can result in various health issues.

Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, differentiating it from an immediate purchase. It can lead to financial risk and instability for both individuals and the state at large.

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The function that we want to get is:

t(h) = √(-h + 500)/4

And the height is 250 ft after 3.95 seconds.

Here we have the height function defined as:

h(t) = 500 - 16t²

And we want to write t as a function of h, so we just need to isolate the variable t.

h - 500 = -16*t²

(-h + 500)/16 = t²

√((-h + 500)/16) = t

√(-h + 500)/4 = t

This is the function that defines h as a function of t. Notice that we only care for the positive solution of the square root.

The time at which the height is 250ft is given by:

√(-250 + 500)/4 = t

√(250)/4 = 3.95

So the height after 3.95 seconds is 250ft.

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To solve this

QUESTION

Eight men can do a piece of work in 12

days. How long will 6 men take to do the

same work if they work at the same rate?

SOLUTION

Let X be thr time taken for 6 men to work at the same rate

Looking at the question, it is an indirect proportion

because as the number of men increases, the time taken to do the work decreases

So therefore;

8 men = 6 men

X days = 12 days

cross-multiply

6 x X = 12 x 8

6X = 96

divide both-sidde of the equation by 6

6X/6 = 96/6

X = 16 days

Therefore, it takes 16 days for 6 men men to do the work at the same rate.

"A number is 11 more than another number" can be expressed as

"Twice the sum of the two numbers is 42" can be expressed as

So, these two equations for a system. Let's combine them to find y in the first place

Then, we find x