Select the correct answer.
What is the solution to the equation 41xl - 8 = -8?
O A.
O B.
O C.
O D. No solutions exist.
X=0
X = -16
x = -4 or x = 4

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:

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.

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.

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 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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The change in wavelength of the radio signal is 100m.

The change in wavelength of the radio can be calculated using the velocity of the given radio signal.

[tex]c = v \lambda\\[/tex]

Let's substitute the values and solve.

But then, we have to convert the velocity from km to m

[tex]1km = 1000m\\3000km = x\\x = 3000000m[/tex]

we solve the wavelength here by

[tex]c = \lambda v\\3.0*10^8 = \lambda * 3.0^6\\\lambda = \frac{3.0*10^8}{3.0*10^6} \\\lambda = 1.0*10^2m\\\lambda = 100m[/tex]

The wavelength of the radio signal is 100m.

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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.

[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.

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 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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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;

The required inequality is k > 8.48. Option A is correct.

Given that,
To determine the equivalent expression to the k / -1.6 > -5.3

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
As per the given condition, we have to simplify the given expression to get the equivalent expression,
k / -1.6 > -5.3
k > -1.6 (-5.3)
k > 8.48.

Thus, the required inequality is k > 8.48. Option A is correct.

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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

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

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.

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.

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

"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

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.

The complete question is written below.

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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?

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

Then, the quadratic expression can be expressed as

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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10 less than the product of 4 and a number is the same as:

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.

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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The equation contains two unknown variables. They are usually x and y. The ordered pair would be written as (x, y). To determine if the ordered pair is a solution of the equation, we would substitute the value of x into the equation. If the resulting value of y is the same as the one in the ordered pair, then the ordered pair is a solution to a given equation

The value of r = -9 is a solution, and r = -11 is not a solution.

We are given a quadratic equation.

r² + 11r + 28 = 10

We need to verify whether r = -9 and r = -11 are the solutions of the above quadratic equation or not.

We will first simplify the quadratic equation.

r² + 11r + 28 = 10

r² + 11r + 28 - 10 = 0

r² + 11r + 18 = 0

Now, we will draw the graph of the equation :

y = r² + 11r + 18

Now, we will see the roots of the equation.

We will see the x-coordinates of the intersection points of the graph and the x-axis.

The graph is attached below.

We can see that the roots of the equation are r = -9 and r = -2.

So, r = -9 is a solution, and r = -11 is not a solution.

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