Four years after paying $2700 for shares in a startup company, you sell the shares for $1300 (at a loss).

[tex] { 3 }^{ - 1} \times {3}^{x + 1} - { 3}^{x - 2} + {3}^{ - 2} \times { 3}^{x + 3} = 35 \\ {3}^{ - 1 + x + 1} - {3}^{x - 2} + {3}^{ - 2 + x + 3} = 35 \\ {3}^{x} - {3}^{x - 2} + { 3}^{ - 2 + 3 + x} = 35 \\ { 3 }^{x} - {3}^{x - 2} + {3}^{x + 1} = 35 \\ {3}^{x} - {3}^{x} \times {3}^{ - 2} + {3}^{x} \times {3}^{1} = 35 \\ {3}^{x} (1 - {3}^{ - 2} + 3) = 35 \\ {3}^{x} (3 + 1 - \frac{1}{9}) = 35 \\ \\ {3}^{x} (4 - \frac{1}{9} ) = 35 \\ {3}^{x} ( \frac{35}{9} ) = 35 \\ \frac{ {3}^{x}( \frac{35}{ 9 } )}{ \frac{35}{9} } = 35 \div ( \frac{35}{9} ) \\ {3}^{x} = 9 \\ {3}^{x} = { 3 }^{2} \\ x = 2[/tex]

ATTACHED IS THE SOLUTION.

I USED THE LAWS OF EXPONENTS.

GOODLUCK.

Answer: 10%

Step-by-step explanation:

2 out of 20 people are willing to pay a maximum of 4.01 to 5 which is 0.10 which equals 10%

The overall percentage reduction in the price of the radio is 40%.

Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentages is %.

Let's assume that that initial price of the radio is 100.

Price of the radio after the 20% decline in price = (1 - 0.2) x 100

0.8 x 100 = 80

Price of the radio after the 25% decline in price = (1 - 0.25) x 80

0.75 x 80 = 60

The percentage decline in price = (initial price / final price) - 1

(60 / 100) - 1 = 0.4 = 40%

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Answer: -33

Step-by-step explanation: I guess he had like debt to pay lol but he would've had to have -33 dollars and added $84 to get a total of $51

Hello

we are given a function and asked to find the reminder when it is divided by a binomial

According to the remainder theorem, f(a) would be the remainder from dividing f(x) by x -a

but our f(x) is given as

From the calculation above, the answer to this question is 31

Not true, true, true, true, true, true, true, not true, true, true

See explanation below

From the diagram, we noticed a change in lengths when all four vertex was dragged.

This means the 4 sides will not always be the same (congruent).

Not always true: The four sides are congruent

From both diagrams. we found the opposite sides are the same (congruent)

Always true: The opposite sides are congruent

Since they opposite sides arecongruent, this also means the opposite sides are parallel

Always true: opposite sides are parallel

All four angles from both diagrams are equal (congruent)

Always true: all four angles are congruent

SInce all four angles areequal, then the angles opposite each other will also be equal.

Always true: opposite angles are congruent

The diagonals of both shapes bisect each other. Hence, they are congruent.

Always true: Diagonals are congruent

Always true: diagonals bisect each other

Diagonals of a square (the shapethat has all sides equal ) intersect at a right right angle.

Diagonals of a rectangle ( the shape with opposite sides equal) don ot intersect at right angle.

Not always true: Diagonals intersect at a right angle

The interior angles were split by the two diagonals in both shapes.

Always true: Diagonals bisect interior angles

The sum of angles in a quadrilateral is equal to 360°

Both shapes are quadrilaterals. Hence, the sumof their angles is 360°.

Always true: sum of all angles equal 360°

Answer:

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

Vertex form of quadratic equation:

Convert the given expression into vertex form by completing the square:

Answer:

[tex]f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To find the vertex form of the given function, complete the square.

Given function:

[tex]f(x)=x^2+x+1[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=x^2+x+\left(\dfrac{1}{2}\right)^2+1-\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+1-\dfrac{1}{4}[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}[/tex]

Factor the perfect square trinomial formed by the first three terms:

[tex]\implies f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Question on Compound Interest.

The formula below can be used to calculate the compound interest;

Where A= ? , P =$2000, r =2.5% and n = 10 years

Substituting these values into the formula above, we get

Note that: Amount = Principal + Interest, though not needed in this question.

Thus, the correct answer is $2560.17

The z-score values for the given quantile are found.

For the given question;

The given normal quantile plot are-

-1.28, -0.52, 0.00, 0.52, 1.28

The corresponding z-score taken from the positive and negative z table are-

The z-score values for the given quantile are found.

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We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.

Angles that are on the fourth quadrant have a negative sine and a positive cosine.

We can start with the cot():

We can relate the cosine with the tangent as:

We can now calculate the sine of the angle as:

We can now calculate the sec() and csc() as:

Answer:

sin() = -3/5

cos() = 4/5

cot() = -4/3

sec() = 5/4

csc() = -5/3

The Solution.

The correct answer is y = 0.34x - 0.9 (option A ).

Step 1:

First, we shall determine the slope of the line by picking two coordinates from the table.

Answer:

  zero

Step-by-step explanation:

You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.

Average velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...

  Vave = (change in position)/time = 0/time = 0

Her average velocity is zero.

Answer:

The correct answers are below, if you want a more in depth explanation let me know and I will provide

Step-by-step explanation:

- The Diver surfaced 3 min before the Watcher

- When the noticed was received, the Diver was 20 ft deeper than the watcher

- 3 Min after receiving the notice, the diver and the watcher are at the same depth

Answer:

y = 3x+3

Step-by-step explanation:

The rate of change, or slope, in this case, is 3, as we can either count the increase in y-values or perform the Δy/Δx (slope equation: [tex]\frac{9-3\\}{2-0}[/tex])to yield three, meaning that the (3x) in this equation would be the slope. Since the y-intercept is the constant in the equation and the y-intercept is always when x=0 (when the graph crosses the y-axis) on the XY plane, we can just subtract 3 from the x=1 coordinate, meaning that the y-intercept/x=0 coordinate would be (0, 3), leaving 3 as the constant.

Therefore,

the equation is y = 3x+3.

Answer:

6:20 - 2:4 (simplified)

Step-by-step explanation:

20 total slips

6 red slips

Kali needs to work between 10 to 22 hours to earn an income between 200 and 400

Flat fee earned by Kali = 50

Earning per hour of Kali = 15.75

Required income is between 200 and 400

Inequality: Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Inequality represents the equation:

200<=15.75x + 50<=400

200<= 15.75x + 50

150<= 15.75x

x = 9.52

So, she needs to work a minimum of 10 hours

15.75x+50<=400

15.75x <=350

x <= 22.22

So, she can work a maximum of 22 hours

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ANSWER:

Option c

STEP-BY-STEP EXPLANATION:

The function given in the statement is the following:

If D(h) = 383, we substitute and solve for h, just like this:

Therefore, the correct answer is option c.

The solution of the given system of equation will have infinite many solutions.

In the above question, the following equations are given

4x + 6y = 24

2x + 3y = 8

Now, we need to find the number of solutions that this system of equation will have

We know that,

a1 x + b1 y = c1

a2 x + b2 y = c2

is the general system of equation, and

[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex] then unique solution, or

[tex]\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}[/tex] then there will be infinite solutions or,

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] then there will be no solution

Now, we'll check for the given system of equations

a1 = 4, b1 = 6 , c1 = 24

a2 = 2, b2 = 3 , c2 = 8

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] = 2 = 2 [tex]\neq[/tex] 3

As this condition satisfies the third condition, the solution of the given system of equation will have infinite many solutions.

Now as we multiply the first equation 4x + 6=24 by 3 we get we have 12x+18y=72, the system will still have same solutions as only the equations are multiplied by a constant k = 3 which does not affect the solution.

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We can see that if we rotate P 90° counterclockwise it would be located in the first quadrant. So it can be A or B. But A forms a 90° with the position of point P. So, the answer is A.

Given the Subtraction:

You can identify that the denominators are different, then, you need to follow these steps in order to find the Difference (the result of the Subtraction):

1. Find the Least Common Denominator (LCD):

- Decompose the denominators into their Prime Factors:

- Multiply the common and non-common factors with the largest exponents:

2. Divide the LCD by each original denominator and multiply the Quotient by the corresponding numerator:

3. Subtract the whole number parts and then subtract the fractions. You get:

Hence, the answer is:

x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

The domain of f(x)=ln(cosx) =  x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

Given function,

            f(x)=ln(cosx)

When cos(x) is positive, the domain is.

(cos(x)) > 0

since,

cos0 = 1

cos π/2 = 0

cos π = -1

cos 3π/2 = 0

cos 2π = 1

cos 3π/2 = 0

The values of cos(x) are then between -1 and 1.

That is domain of  f(x)=ln(cos x)

= cos x ∈ (0;1] -> x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

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Answer:

1. 6 units

2. 13 units

3. 5 units

Step-by-step explanation:

Based on the sequence given of 3,5,8,12,17, it would be incorrect to say that the sequence is arithmetic. The sequence is not arithmetic.

In an arithmetic sequence, one would find that the number that separates each of the figures in the sequence is the same. In other words, the common difference between each figure is the same.

For instance, 2, 5, 8, 11, 14 has the common difference of 3 so this is an arithmetic sequence.

The sequence given of 3,5,8,12,17 is not arithmetic because the difference between each number is not common and instead increases.

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we have that the figure of a rectangle and a triangle. So the area of this figure is:

so the answer is 68 in^2

Answer: A relation is just a relationship between x and y-coordinates. It maps inputs to outputs. A function is just a special kind of relation: any input has exactly one output.

Step-by-step explanation:

Answer:A rate of change is a rate that describes how one quantity changes in relation to another quantity. Constant rate is also called as uniform rate which involves something travelling at fixed and steady pace or else moving at some average speed. For example, A car travels 3 hours.

Step-by-step explanation:

Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).

To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.

For point A and B with coordinates:

For points (2, 3) and (5,8)

For the points (-7, 5) and (-12, 8)

• Two lines are said to be ,parallel, ,if their gradients are the same.

• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.

Product of the two gradients

Since the product of the gradients is -1, the two lines are said to be perpendicular.

The correct option is D

To solve this problem, we will use the formula for compound interest:

Where:

• Pₙ = principal amount after N years,

• P₀ = initial principal amount,

• r = interest ratio in decimals,

• k = compound periods per year.

From the statement, we know that:

• N = 3.4 years,

• P₀ = $56,000,

• Pₙ = P₀ + interest = $56,000 + $1,400 = $57,400,

• r = ?,

• k = 4 (the interest is compounded quarterly.

Replacing these values in the formula above, we get:

The annual interest must be 0.73%.

For any given angle in a right triangle that is not the 90° angle its sine is given by the quotient between its opposite side and the hypotenuse. For triangle ABC the hypotenuse is BC and the opposite side to theta is AB. Then the sine of this angle is given by the following equation:

Then the answer is the third option, 4/5.