Select the correct answer.
What is the factored form of 1,458x3 − 2?

A.
2(9x − 1)(81x2 + 9x + 1)
B.
2(9x + 1)(81x2 − 9x + 1)
C.
(9x − 2)(81x2 + 18x + 4)
D.
(9x + 2)(81x2 − 18x + 4)

When population grows exponentially with a proportionality constant, k , this population will take 4.620 time to double.

If the population is growing exponentially, the rate of population change is directly proportional to its current size. So assume that the total population at some point in time t is y.

Next, write the differential equation subject to the condition that it increases in proportion to its magnitude. We can get rid of the proportional sign by introducing a constant of proportionality. We then isolate and integrate the variables of the differential equation thus formed and use the initial values to find the value of the constant of proportionality. We have , a population grows exponentially.

The proportionality constant, k = 15% = 0.15

The exponential growth function is y = y₀ eᵏᵗ

where y₀ --> initial population or at t = 0

k --> proportionality constant

t --> time

y --> is value of y at any t

let there be population y₀ at t = 0 . Then, we have to calculate how much time take the population to double.

2 yo = yo e⁰·¹⁵ᵗ

=> 2 = e⁰·¹⁵ᵗ

Introducing natural logarithms on both sides of above equation,

=> ln (2) = ln ( e⁰·¹⁵ᵗ )

=> ln (2) = 0.15t ( since ln e = 1)

=> t = ln(2)/1.5 = 4.620

Hence, required time is 4.620.

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x = 2

Step-by-step explanation:

\(\begin{aligned}\rm 4x - 6&= 2\\\rm 4x &= 2 + 6\\\rm 4x&= 8\\\rm x &=\frac{8}{4}\\\bf x&=\underline{\underline{\bf 2}}\end{aligned}\)

Solution :

let's check if x = 2 is solution of 4x - 6 = 2

by plugging the value of x as 2 in the given equation :

here, L.H.S = R.H.S

so, the above statement is true.

Answer:

Smaller Trapezoid: 12

Bigger Paralleogram: 24

Bigger Triangle: 22/40

Smaller Triangle : 2.75/ 5

Step-by-step explanation:

cross multiplication

Bigger Paralleogram: 9 x 16= 144 / 6= 24

Bigger Triangle: 5 x 22= 110 / 2.75 = 40

hope this helps

Answer:

Use colon method

Step-by-step explanation:

So it is more easy

Answer:

area of semicircle only = 113.43 mm²

total area = 185.43 mm²

Step-by-step explanation:

(8.5²)(π)(0.5) = 113.43 mm²

(12)(12)(.5) = 72 mm²

72 + 113.43 = 185.43 mm²

Answer:

185.43 mm²

Step-by-step explanation:

Answer:

17%

Step-by-step explanation:

1/3 is the rate of change (slope) given the set of data points below

To find the rate of change (slope) given the set of data points, we can use the formula for slope:

slope = (change in y) / (change in x)

Using the given points:

Point 1: (10, 19)

Point 2: (4, 17)

Point 3: (-2, 15)

Point 4: (-8, 13)

We can calculate the slope between each pair of points:

Slope between Point 1 and Point 2:

slope = (17 - 19) / (4 - 10) = -2 / -6 = 1/3

Slope between Point 2 and Point 3:

slope = (15 - 17) / (-2 - 4) = -2 / -6 = 1/3

Slope between Point 3 and Point 4:

slope = (13 - 15) / (-8 - (-2)) = -2 / -6 = 1/3

The rate of change (slope) between these points is consistent and equal to 1/3.

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Answer:

6.4

Step-by-step explanation:

The question requires us to prove the following using the characteristic function method:

(A ∪ B) \ C = (A \ C) ∪ (B \ C), where A, B, and C are subsets of X. We use the characteristic function method, which assigns 1 to an element in the subset and 0 to an element not in the subset, and then performs algebraic operations on the characteristic functions.

Let's define the characteristic functions of the sets A, B, and C: χ_A, χ_B, and χ_C, respectively, and X be the universal set.

Using the definition of characteristic functions, we can say that for any element x in X,

\(χ_(A∪B)(x) = χ_A(x) + χ_B(x) - χ_A(x) * χ_B(x),\)

and,

\(χ_(A-B)(x) = χ_A(x) * (1 - χ_B(x)).\)

Now, we can expand the left side of the equation we are supposed to prove:

\((A ∪ B) - C = (A ∪ B) * (1 - χ_C(x))\)

⇒ \(χ_((A∪B)-C)(x) = χ_A(x) * (1 - χ_C(x)) + χ_B(x) * (1 - χ_C(x))\)

⇒ \(χ_((A∪B)-C)(x) = χ_A(x) - χ_A(x) * χ_C(x) + χ_B(x) - χ_B(x) * χ_C(x).\)

Next, we can expand the right side of the equation:

\((A - C) ∪ (B - C) = (A - C) + (B - C)\)

⇒\(χ_((A-C)∪(B-C))(x) = χ_A(x) * (1 - χ_C(x)) + χ_B(x) * (1 - χ_C(x))\)

⇒\(χ_((A-C)∪(B-C))(x) = χ_A(x) - χ_A(x) * χ_C(x) + χ_B(x) - χ_B(x) * χ_C(x).\)

Since both sides of the equation are equal, the proof is complete. Therefore, we have proved that \((A ∪ B) \ C = (A \ C) ∪ (B \ C)\) using the characteristic function method.

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Answer:

d = - 50

Step-by-step explanation:

common difference is

50 - 100 = 0 - 50 = - 50 - 0 = - 50

a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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Answer:

What do you need help with?

Step-by-step explanation:

The boy can have 9 dimes, 0 nickels, and 8 pennies.

We have,

a boy finds $1.05 in dimes, nickels, and pennies.

Let's assume that the boy has x number of dimes, y number of nickels, and z number of pennies.

We know that the total value of these coins is $1.05, and there are 17 coins in total.

Now, let's convert the values into cents.

We have 10 cents for each dime, 5 cents for each nickel, and 1 cent for each penny.

Therefore, the equation we can set up is:

10x + 5y + z = 105

(since $1.05 is equal to 105 cents)

We also know that the total number of coins is 17, so:

x + y + z = 17

Now, we have a system of equations.

Let's solve it using a method called substitution.

From the second equation, we can express z in terms of x and y:

z = 17 - x - y

Substituting this value of z into the first equation, we get:

10x + 5y + (17 - x - y) = 105

Simplifying this equation, we get:

9x + 4y = 88

Now we have a new equation to work with.

We can rearrange it to solve for x:

x = (88 - 4y) / 9

To find the possible values for x and y, we can try different values of y and calculate the corresponding values for x.

Since the number of coins cannot be negative, we can start by setting y to 0 and calculate x:

x = (88 - 4(0)) / 9

x = 88 / 9

x ≈ 9.78

Since the number of coins must be a whole number, we can round x down to the nearest whole number, which gives us x = 9.

Now, let's substitute this value of x back into our second equation:

9 + y + z = 17

Simplifying this equation, we get:

y + z = 8

We can now try different values of y and calculate the corresponding values of z that satisfy this equation.

Let's start with y = 0:

0 + z = 8

z = 8

So, one possible solution is x = 9, y = 0, and z = 8.

This means the boy can have 9 dimes, 0 nickels, and 8 pennies.

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After forming a system of equations according to the given information

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

Given that,

The boy finds a total of $1.05 in dimes, nickels, and pennies.

There are 17 coins in total.

Number of pennies  = 5

Let "d" represent the number of dimes.

Let "n" represent the number of nickels.

Let "p" represent the number of pennies = 5

We know that,

1 $ = 100 cent

1 cent = 0.01$

According to the given information:

The system of equations be:

0.10d + 0.05n + 0.01 x 5 = 1.05   ......(i)

d + n + 2 = 17 .....(ii)

Proceeding with equation (i):

After simplifying:

0.10d + 0.05n = 1

Multiply 10 both sides

10d + 5n = 10  ....(iii)

Proceeding with equation (i):

After simplifying:

d + n = 15  .

Multiply 5 on both sides,

5d + 5n = 75 ....(iv)

Subtract (iii) from (iv):

5d = 65

d = 13

So, there are 13 dimes.

Now substitute this value of d into (iv),

n = 2

So, there are 2 nickels.

Hence.

We find that the boy can have  5 pennies, 13 dimes, and 2 nickles.

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The complete question is attached below:

A boy finds $1.05 in dimes, nickels, and pennies.

Dimes are 10 cents coins, Nickle is 5 cents coins and pennies are 1 cent coins. If there are 17 coins and the number of pennies is 5 in all.

How many coins of each type can he have?

Answer:

Step-by-step explanation:

Answer: 94 square millimeters

Step-by-step explanation:

The best way to solve this would be by separating it into three separate shapes.

First, solve the Big Rectangle:

Area of Big Rectangle = Length * Width

Area of Big Rectangle = 6 mm * 9mm

Area of Big Rectangle = 54 mm^2

Next solve the Small Rectangle:

Area of Small Rectangle = Length * Width

Area of Small Rectangle = 3mm * 4mm

Area of Small Rectangle = 12 mm^2

Next solve the Triangle:

Area of Triangle = 1/2 * Base * Height

Area of Triangle = 1/2 * 8 mm * 7 mm

Area of Triangle = 28 mm^2

Lastly, Add them all up:

54 mm^2 + 12mm^2 + 28mm^2

Total = 94 mm^2

Hope this helps!

As per the congruency theorem, the two triangles are congruent.

Congruency theorem:

Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."

Given,

Here we need to prove that  congruency theorem can be used to prove that △wut ≅ △vtu.

Let us consider triangles WUT and VTU.

And in these triangles:

=> WU≅VT

And in those one, ∠T≅∠U,

Therefore, m∠T = m∠U = 90°

Here the side TU is common.

Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.

Then the side TU is common leg and sides WU and VT are hypotenuses.

Therefore, the HL theorem states: if the hypotenuse (WU) and one leg  (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.

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Answer: HL

Step-by-step explanation:

No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer: length = 28.80 feet

Width = 19.20 feet

Step-by-step explanation:

Scale used = 1 inch:2.4 feet

Length or scale drawing = 12 inches

Width of scale drawing = 8 inches

Length of actual flag = (12 × 2.4 feet) = 28.80 feet

Width of actual flag = (8 × 2.4 feet) = 19.20 feet.

Answer:Answer: length = 28.80 feet

Width = 19.20 feet

Step-by-step explanation

Scale used = 1 inch:2.4 feet

Length or scale drawing = 12 inches

Width of scale drawing = 8 inches

Length of actual flag = (12 × 2.4 feet) = 28.80 feet

Width of actual flag = (8 × 2.4 feet) = 19.20 feet.

The required equation of a line is y = 9/5 (4x - 12)

Given-

The point from which the line passes through is (3,2)

The slope of the given line m is -4/5.

Equation of the line

The linear equation of a line can be represented by a set of points on a graph using the equation of the line.

The standard form of the line passing through the point x₁, y₁

The slope m is given by,

m = (y - y₁) / (x - x₁)

Put the values of points and slope in the above equation, we get,

-4/5 = (y - 2) / (x - 3)

-4/5(x - 3) = y -2

-4x/5 + 12/5 = y - 2

-1/5 (4x - 12) + 2 = y

y = 9/5 (4x - 12)

The linear equation of a line can be represented by a set of points on a graph using the equation of the line. The following equation depicts a line that crosses (3, 2) and has a slope of -4/5: y = 9/5 (4x - 12)

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The actual length of the living area is 134.4 feet if the length in the scale drawing is 16.8 in the scale.

To determine the actual length of the living space from a scale drawing, we need to use the scale factor, which is the ratio of the length in the drawing to the actual length. If the length in the scale drawing is 16.8 inches and the scale is given as a ratio of 1 inch in the drawing to 8 feet in actual size, we can set up a proportion:

1 inch (drawing) / 8 feet (actual)

= 16.8 inches (drawing) / x (actual)

We can cross-multiply and simplify to find x's value:

1 inch × x = 8 feet × 16.8 inches

x = (8 feet × 16.8 inches) / 1 inch

x = 134.4 feet.

Therefore, the actual length of the living space is 134.4 feet.

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We want to see how many solutions has an equation given some restrictions on the vectors of the equation.

We have 3 vectors in R2.

v₁, v₂, and v₃.

Where we know that v₁ and v₂ are parallel. And two vectors are parallel if one is a scalar times the other.

Then we can write:

v₂ = c*v₁

Where c is a real number.

Then our system:

x*v₁ + y*v₂ = v₃

Can be rewriten to:

x*v₁ + y*c*v₁ = v₃

(x + y*c)*v₁ = v₃

Assuming x, y, and c are real numbers, this only has a solution if v₁ is also parallel to v₃, because as you can see, the equation says that v₃ is a scallar times v₁.

Geometrically, this means that if we sum two parallel vectors, we will get a vector that is parallel to the two that we added.

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Answer:

It is Inaccurate: The angles in the order listed do not correspond. I just took the test

Answer:

Inaccurate. The angles in the order listed do not correspond.

Step-by-step explanation:

I am doing the test rn and I think this is the right answer

Sofia's favorite bag of chips were on sale for $5 for two bags. If she wanted to buy seven bags, the cost would be $17.50.

To calculate this, we need to use the formula for finding the total cost of a given number of items: Total Cost = Number of Items x Cost Per Item.In this case, we need to find the total cost of seven bags, so the equation looks like this: Total Cost = 7 x $5.

We can solve this equation by multiplying the two numbers together. 7 multiplied by 5 equals 35. However, the question is asking us to find the total cost of seven bags, which is $17.50. To convert the answer from 35 to 17.50, we need to divide 35 by two: 35 divided by 2 equals 17.50.

Therefore, the cost of seven bags of Sofia's favorite chips would be $17.50.

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The payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

For Project A: Initial Investment: $875,000, Sale of old equipment: $30,000, Incremental Revenues: $380,000, Incremental Cash Costs: $175,000, Major overhaul at the end of 3 years: $80,000, Initial working capital: $60,000

Equipment life: 6 years, Salvage value at the end of 6 years: $0

For Project B: Initial Investment: $875,000

Equipment life: 6 years: Salvage value at the end of 6 years: $90,000, Revenues: Year 1: $150,000

Year 2: $250,000

Year 3 to 6: $450,000, Cash costs: Year 1: $125,000, Year 2: $175,000, Year 3 to 6: $210,000, Hurdle rate: 8%

The requested analysis has to be done using Net Present Value (NPV), Profitability Index (PI), Payback Period (PBP), and Internal Rate of Return (IRR) calculations.

Formula view for each of the measures is given below: Net Present Value (NPV) calculation: Negative cash flows have to be entered with a negative sign and positive cash flows with a positive sign.

We have to use the NPV formula as given below: NPV = PV of cash inflows - PV of cash outflows

where, PV = Present Value of Cash Flow, i = The time period, n = The total number of time periods, r = Discount rate (hurdle rate)

Profitability Index (PI) calculation: Profitability Index is the ratio of present value of cash inflows to the present value of cash outflows.

The formula for PI is as follows: Profitability Index = PV of Cash Inflows / PV of Cash Outflows

Payback Period (PBP) calculation: Payback Period is the time period required to recover the initial investment. The formula for Payback Period is as follows: Payback Period = Initial Investment / Annual Cash Inflows

Internal Rate of Return (IRR) calculation: IRR is the discount rate at which the present value of cash inflows equals the present value of cash outflows. The IRR formula is as follows: NPV = 0 = PV of cash inflows - PV of cash outflows

Summing up the above-mentioned formulas, the calculations for Project A and Project B are shown below:

Calculations for Project A: Calculations for Project B:

Evaluation and brief explanation of relative benefits:

For Project A: Net Present Value (NPV)

= $34,328.70 > 0

Profitability Index (PI) = 1.039 > 1,

Payback Period (PBP) = 3.87 years < 6 years

Internal Rate of Return (IRR) = 13.03% > 8%

For Project B: Net Present Value (NPV)

= $191,738.43 > 0

Profitability Index (PI) = 1.22 > 1

Payback Period (PBP) = 2.84 years

< 6 years

Internal Rate of Return (IRR) = 18.28%

> 8%

The NPV and PI are positive for both projects, which means that they are expected to be profitable.

However, the payback period is less than the life of the project only for Project B. Also, the IRR is higher than the hurdle rate for both projects, but it is higher for Project B.

Hence, Project B is more preferable than Project A.

Project A and Project B are not identical because of their different cash flow patterns.

Project A has higher cash outflows in the initial years, which reduces the NPV and PI.

Also, the payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

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Answer:

Domain= neg infinite, pos infinite

range= neg infinite, 4

mass (m) = 5.4g

Volume (V) = 2 cm^3

To find the density (p), we have to apply the next formula:

p= m/v

Replacing:

p´= 5.4/2 = 2.7 g/cm^3

Answer:

60 degrees

Step-by-step explanation:

Using the 172 degrees and calculating it's distance from the angle, i conclude that it's 60

9514 1404 393

Answer:

  (b)  60

Step-by-step explanation:

The external angle is half the difference of the two subtended arcs.

  x° = (172° -52°)/2 = 120°/2

  x° = 60°

The value of x is 60.

Step-by-step explanation:Step-by-step explanation:

For Sienna to be able to take the square root of both sides while solving a quadratic equation, she must have an expression with square on at least, the side that contains the variable she is trying to determine. Equation of the form:

(x + a) ² = b

'a' and 'b' could be any number, -1, 0, 1/3, -5/6, anything really.

So, she can take square roots of both sides then, like this

√(x + a)² = √b

x + a = ±√b

x = -a ± √b

Square roots always cancel out squares, and the '±' is because a square is satisfies by both + and -, 3² = 9, and (-3)² = 9.

It is the nature of the problem being solved that determines if we take just one or both of these answers.