Which equation can be used to solve the problem

The statements are:

y=e" and y = ln x are inverses.

This is false. The inverse of y = e^x is y = ln x, and the inverse of y = ln x is y = e^x. So, the two functions y = e^x and y = ln x are inverses of each other, but y = e^x and y = e^ln x are not.

In een In(x) = log. (x)

This is false. The statement should be: e^ln(x) = x, which is true by the definition of logarithms.

ln e = 1

This is true. The natural logarithm of e is 1.

In (x) = log10 (x)

This is false. The statement should be: log10(x) = log(x) / log(10).

In e = 10

This is false. The natural logarithm of e is 1.

In(e) and en both equal x.

This is false. In(e) = 1, and e^n = x does not necessarily imply that In(e) = x.

Answer:

192

Step-by-step explanation:

2x9=18

18x12=192

Answer:

well in 9.5 40 you have to multiply which is 40 times 9.5h

Breakeven's time is 31.7 years.

The loan term is only 25 years, so it is not a wise decision.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

To determine if the purchase of negative points is a wise decision, we first need to calculate Millie's monthly payment with and without the negative points.

Without negative points:

Principal = $600,000

Interest rate = 3.49%

Loan term = 25 years or 300 months

Now,

Monthly Payment = $2,967.27

With negative points:

Millie needs to purchase 2 negative points to cover the bank's closing cost. Each negative point will increase her APR by 0.125%, so the new interest rate will be:

New interest rate.

= 3.49% + (2 x 0.125%)

= 3.49/100 + (2 x 0.125/100)

= 3.74%

Monthly Payment = $2,998.84

The breakeven time.

This is the amount of time it takes for the cost of the negative points to be offset by the savings in monthly payments.

The total cost of the negative points.

We see that,

Each negative point costs 1% of the principal.

Cost of negative points,

= 2 x $6,000

= $12,000

The breakeven time.

Monthly savings.

= $2,967.27 - $2,998.84

= -$31.57

i.e

The value is negative because the new monthly payment is higher.

So,

Breakeven time.

= $12,000 ÷ -$31.57

= 380.2 months

This is,

1 year = 12 months

so,

31.7 years

Thus,

Breakeven's time is 31.7 years.

The loan term is only 25 years, so it does not make sense to purchase the negative points.

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Answer:

³/₂

Step-by-step explanation:

1.5 = ¹⁵/₁₀

= ³/₂

The total cost of the trip is a function of the velocity v is:

Cost (v) = 500v + 400/v

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Distance = 500 km

Velocity = v km/h

Now,

Velocity = Distance /Time

Time = distance/velocity

= 500 / v

The total cost of the trip.

Cost = fuel cost per hour x time + other costs per hour x time

= v² x 500/v + 400 x 500/v

= 500 v + 400/v

Thus,

The total cost of the trip is a function of the velocity v is:

Cost (v) = 500v + 400/v

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The complete question.

The cost of fuel per hour that a train spends on its journey is v^2 pesos, where v is the velocity in kilometers per hour. Note that the cost depends on the square of the velocity.

Other costs, including labor, are $400 per hour.

Express the total cost of a 500-kilometer trip as a function of the velocity v.

Answer:

Step-by-step explanation:

So if they sell approximately 376 pizzas the first shift and then the same amount for the second, all you have to do is add 376 by 367 or multiply by 2 because adding the same number twice is like multiplying the number by 2.

Answer: 564

Step-by-step explanation: From 10-2 they sell 376 pizzas. So, in 4 hours they sell 376 pizzas, and they sell 94 pizzas per hour, because 376/4 is 94. So from 5-7, 2 hours, they should sell 94 times 2 pizzas, which is 188 pizzas. So 188+376 is 564.

Answer: 4

Step-by-step explanation:

1+1=2 but  if it is 2+2 then it would = 4

The answer is C. 1/10 of a centimeter.

Answer:

HI: 57.4 cm; KM: 0.4 mil

Step-by-step explanation:

Question 17:

ΔGHI is a right-angled triangle

where:

Side GI = Hypotenuse

α = 55°

With respect to 55° angle:

Side HI = Adjacent side

∴Trigonometric function used: Cosα (CAH)

Cos55° = [tex]\frac{Side HI}{100cm}[/tex]

Cross-multiplication is applied:

Side HI = (Cos55°)×(100 cm)

Side HI = 57.4 cm (Rounded to 3 significant figures)

Question 18:

ΔKLM is a right-angled triangle

where:

Side KL = Hypotenuse

β = 27°

With respect to 27° angle:

Side KM = Opposite side

∴Trigonometric function used: Sinβ (SOH)

Sin27° = [tex]\frac{Side KM}{0.8 mil}[/tex]

Cross-multiplication is applied:

Side KM = (Sin27°)×(0.8 mil)

Side KM = 0.4 cm (Rounded to 1 decimal places)

Answer:

35

Step-by-step explanation:

DUDE JUST PLUG IN THE NUMBER.

[tex]x^4 -3x^3 + x -3\\(-2)^4 - 3(-2)^3 + (-2) -3\\16 + 24 -2 - 3\\35[/tex]

Part (a)

The error happens on the 2nd step.

The student multiplied both sides by the LCD (x+3)(x-3) to clear out the fractions, but forgot about the first "1" at the very left.

=================================================

Part (b)

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\(x+3)(x-3)*1 - (x+3)(x-3)*\frac{2}{x+3} = (x+3)(x-3)*\frac{x+1}{x-3}\\\\(x+3)(x-3) - 2(x-3) = (x+1)(x+3)\\\\x^2-9 - 2x+6 = x^2+4x+3\\\\x^2-2x-3 = x^2+4x+3\\\\x^2-2x-3-x^2-4x-3=0\\\\-6x-6=0\\\\-6x=6\\\\x = 6/(-6)\\\\x = -1[/tex]

Check:

[tex]1 - \frac{2}{x+3} = \frac{x+1}{x-3}\\\\1 - \frac{2}{-1+3} = \frac{-1+1}{-1-3}\\\\1 - \frac{2}{2} = \frac{0}{-4}\\\\1 - 1 = 0\\\\0 = 0\\\\[/tex]

The answer is fully confirmed.

You can use a graphing tool like GeoGebra to visually confirm the answer.

No, a matrix does not have to be symmetric to be orthogonally diagonalizable. Orthogonal diagonalization is a property of square matrices that can be used to simplify calculations and solve certain types of problems.

A square matrix A is orthogonally diagonalizable if there exists an orthogonal matrix P and a diagonal matrix D such that A = PDP^T, where D contains the eigenvalues of A and P contains the corresponding eigenvectors.

A symmetric matrix is always orthogonally diagonalizable, meaning that there exists an orthogonal matrix P such that A = PDP^T, where D is a diagonal matrix containing the eigenvalues of A. However, not all matrices are symmetric and still can be orthogonally diagonalizable.

For a non-symmetric matrix, the eigenvectors and eigenvalues may not have certain symmetrical properties that make orthogonal diagonalization straightforward, but it is still possible to diagonalize the matrix. In such cases, we can use other techniques, such as the Schur decomposition, to obtain a similar diagonal form.

In summary, a matrix does not have to be symmetric to be orthogonally diagonalizable, but symmetric matrices are always orthogonally diagonalizable. Other techniques may be used for diagonalizing non-symmetric matrices.

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Answer:

Step-by-step explanation:

Transcribed image text: Situation: Find the age of the bird skeleton to the nearest A geologist in South America discovers a bird skeleton that contains 74% of its original amount of C-14. Enter the correct answer. N-Noekt No-inital amount of C.14 (at time t 0) N amount of C-14 at time t k 0.000 t time, in years.

Answer:

2,295 cm2

Step-by-step explanation:

Answer:

  (b)  2295 cm²

Step-by-step explanation:

You want the area of icing on a cake 13 cm high and 17 cm in radius.

The area of the top is ...

  A = πr²

The area of the side is ...

  A = 2πrh

Then the total area of icing on the cake is ...

  πr² +2πrh = πr(r +2h)

  = 3.14(17 cm)(17 cm + 2·13 cm) = 2295.34 cm²

The area of icing needed for the cake is about 2295 cm².

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When sales are under $15,000, the current job pays less than the new offer. The new job offer is therefore favoured for sales below $15,000.

a)   Wc = 2000+.07S

b)  Wn =2300+.05S

c)  When the totals are similar, the sales level at which she would not care

   2000 + .07S = 2300 + .05S

   subtract .05S from both sides

    2000 +.02S = 2300

   subtract 2000 from both sides

    .02S = 300

   divide both sides by .02

   S = 300/.02 = 15000

Sales of $15,000 equate to identical pay.

If we apply the same calculation, substituting less than for the = sign... The result of our equation is

2000 + .07S < 2300 + .05S

S < 15000

The present employment pays less than the new offer when sales are under $15,000. Therefore, the new job offer is preferred for sales below $15,000.

check:  Let S = 10,000

Wc = 2000+.07(10000) = $2700

Wn = 2300 + .05(10000) = $2800

As can be seen, at sales of $10,000 the new job earns more.

The complete question is:

A salesperson receives a monthly salary $2000 plus commission of 7% of sales. she is offered a new job at $2300 per month plus commission of 5% os sales.

a) write a linear equation for her current wage W in terms of her monthly sales S.

b)write a linear equation for her monthly wage W of the job offer in terms of her monthly sales S.

c) what level of sales will make her indifferent between the two jobs? Which scheme is preferred when sales are below this level?

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The statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.

It is a branch of mathematics that deals with the occurrence of a random event.

Students are more likely to own exactly 2 devices than any other number is

true because the number of students own exactly 2 devices is greater than the other categories.

Less than half as many students own 3 or more devices as compared to students who own 1 device is true because 18 students own 1 device, the half of them is 9, and the number of students own 3 or more devices is 7 which is less than 9.

About 10 more students own 1 device than own 3 or more devices is true because the difference between students own 1 device and those own 3 or more devices = 18 - 7 = 11 which is about 10 more.

Hence, the statements, Students are more likely to own exactly 2 devices than any other number, Less than half as many students own 3 or more devices as compared to students who own 1 device and About 10 more students own 1 device than own 3 or more devices are true.

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Parabola A and parabola B are similar in that they are both vertically oriented parabolas with the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix, which means they have different equations and open in different directions.

Both parabola A and parabola B are examples of vertically oriented parabolas that have the x-axis as their axis of symmetry. However, they differ in their vertex, focus, and directrix.

Parabola A has its vertex at (0, 0) and its focus at (0, 4). The directrix is the line y = -4, which is a horizontal line 4 units below the vertex. This means that any point on parabola A is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.

Parabola B has its vertex at (0, 0) and its focus at (0, -6). The directrix is the line y = 6, which is a horizontal line 6 units above the vertex. This means that any point on parabola B is equidistant to the vertex and the focus, and the distance between any point on the parabola and the directrix is equal to the distance between the point and the focus.

In terms of their equations, the equation of parabola A is y^2 = 16x, while the equation of parabola B is y^2 = -24x. Notice that parabola B has a negative coefficient of x, which means it opens to the left instead of the right like parabola A.

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Circle A and circle A' have the same circumference and the radii of circle A and circle A' have the same lengths. Therefore, options A and B are the correct answers.

Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.

Given that, circle A' is the result of rotating circle A by 180° about point P.

When we rotate any object its shape and size does not change, only its position changes.

Therefore, options A and B are the correct answers.

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Answer: 1,422

Step-by-step explanation:

The measure of the angle B in the triangle is 51.34 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.

The angle of a right triangle can be found using trigonometric ratios as follows:

tan B = opposite / adjacent

tan B = 25 / 20

B = tan⁻¹ 5 / 4

B = tan⁻¹ 1.25

B = 51.3401917459

Therefore,

B = 51.34 degrees

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Answer:

1) 7995.9 feet

2) 12 degrees

Step-by-step explanation:

1)

We can start by drawing a diagram of the situation. Let's label the height of the tower as "h", the distance from the airplane to the tower as "d", and the angle of depression as 56°.

  C (top of tower)

               /|

              / |

             /  |h

            /   |

           /θ   |

    A_____/_____|

        d   B

In this diagram, point A represents the airplane, point B represents the base of the tower, and point C represents the top of the tower. The angle θ is the angle of depression from the airplane to the top of the tower.

We can use trigonometry to solve for the distance "d" from the airplane to the tower. In particular, we know that:

tan(θ) = h / d

We can rearrange this equation to solve for "d":

d = h / tan(θ)

Substituting the values we know, we get:

d = 320 / tan(56°)

Using a calculator, we can evaluate this to get:

d ≈ 215.8 feet

However, the airplane is flying at an altitude of 7,450 feet, so we need to add this to the height of the tower to get the total distance from the airplane to the ground:

total distance = d + 320 + 7,450

Plugging in the value we found for "d", we get:

total distance ≈ 7995.8 feet

Rounding to the nearest tenth, we get:

total distance ≈ 7995.8 ≈ 7995.9 feet

2)

We can use the tangent function to find the angle of depression. Let theta be the angle of depression. Then:

tan(theta) = (275 / 1324)

We can solve for theta by taking the inverse tangent (or arctan) of both sides:

theta = arctan(275 / 1324)

Using a calculator, we find:

theta ≈ 11.92 degrees

Rounding to the nearest whole number, we get:

The angle of depression is approximately 12 degrees.

Interval of increase and decrease refers to a period of time in which a quantity rises or falls. For example, a stock market index may have an interval of increase and decrease over a certain period, such as a month or a year.

Interval of increase and decrease is a term used to describe a period during which a certain quantity either increases or decreases. This phenomenon is commonly seen in financial markets, such as the stock market, where indices may go up and down over a certain period of time. This interval of increase and decrease can be measured using different measures such as time, percentage growth, and movement. This interval helps investors and analysts to determine how the stock market is performing and if there are any changes in the market. It also helps them to predict future trends and make better investment decisions. During this interval, it is important to monitor the stock market and any changes that may occur. This helps to ensure that investments are made with the best possible outcome.

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Answer:

0: 4

1: 2

2: 0

3: -2

Step-by-step explanation:

To find out the values of 0, 1, 2 and 3 we have to substitute these numbers into the place of x

0...

y = -2(0) + 4 = 4

1...

y = -2(1) + 4 = 2

2...

y = -2(2) + 4 = 0

3...

y = -2(3) + 4 = -2

TIP:

We can see that there is a pattern of decreasing of 2 so to keep finding the following values we just have to keep subtracting 2. For any question like this, if we see a pattern to make it easier and quicker all we have to do is follow the pattern!

Hope this helps, have a lovely day! :)

To find the value of f(-1), we simply need to substitute -1 for x in the function f(x) = 2x - 1 and evaluate:

f(-1) = 2(-1) - 1

= -2 - 1

= -3

Therefore, the value of f(-1) is -3.

Answer:

f=2x-1/x

Step-by-step explanation:

I hope this helps :) <3

The total amount of money Tegan paid for tax last year from her income of £48,300 is £4,830

Tegan's income last year before tax = £48,300

Tegan's earnings is upto £43,000 and in excess of £48,300 - £43,000

= £5,300

Assume, Tegan's tax rate is 10% since her excess is not up to £11,000

Tegan's tax = 10% of £48,300

= 0.10 × 48,300

= £4,830

Ultimately, Tegan paid a total amount of £4,830 as tax last year.

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Answer:

To solve this problem, we need to start by setting up an equation. The equation should express the fact that the result of the two operations on the fractions is both 4 and 5/4.

We can do this by writing:

4x/(x-2) = 4

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

Solving for x, we get x=16. Therefore, the fraction we are looking for is 4/14, since 4 times 16 divided by 16 minus 2 equals 4 and 5 times 16 divided by 2 times 16 minus 2 equals 5/4.