(+7) (–4) Write each multiplication expression as a repeated addition.

The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

The function in this problem is defined as follows:

f(x) = (x + 2)/(x - 3).

Using the notation y = f(x), it is given as follows:

y = (x + 2)/(x - 3).

To obtain the inverse, the first step is exchanging the variables x and y, as follows:

x = (y + 2)/(y - 3).

Now the variable y must be isolated to obtain the inverse function, as follows:

xy - 3x = y + 2

xy - y = 3x + 2

y(x - 1) = 3x + 2

y = (3x + 2)/(x - 1).

Hence the inverse function is given by:

[tex]f^{-1}(x) = \frac{3x + 2}{x - 1}[/tex]

Meaning that the fourth option is correct.

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There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.

A vector quantity is average velocity. The change in position and otherwise displacement (x) divided by that of the time intervals (t) during which the displacement happens is the definition of average velocity. The average velocity may be either positive or negative depending on the displacement's direction.

The distance covered by the rubber ducks = 1600 miles.

The duration needed to cover this distance = 10 months.

The average ocean speed, according to definition, is

v = (1600 miles)/(10 months)

Now,

1 mile = 1609 m

10 months = (10 months)*(30 days/month) *(24 hours/day)

                 = 7200 hours (approx.)

                 = 7200*3600

                 = 2.592 x 10⁷ s

So that,

ν = [tex]\frac{(1600 \mathrm{~m}) *\left(1609 \frac{\mathrm{m}}{\mathrm{mi}}\right)}{(10 \mathrm{months}) *\left(2.592 \times 10^7 \frac{\mathrm{g}}{10 \mathrm{mon} t h}\right)}[/tex]

   = 0.0993 m/s

Also,

ν = 1600/7200

  = 0.222 mi/h

There is an approximate average velocity. 0.1 m/s, or 0.222 m/h.

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I understand that the question you are looking for is:

A severe storm on January 10, 1992, caused a cargo ship near the Aleutian Islands to spill 29,000 rubber ducks and other bath toys into the ocean. Ten months later hundreds of rubber ducks began to appear along the shoreline near Sitka, Alaska, roughly 1600 miles away.

What was the approximate average speed of the ocean current that carried the ducks to shore in m/s and in mi/h? (Rubber ducks from the same spill began to appear on the coast of Maine in July 2003.)

[tex]f + b = m \\ f + b - f = m - f \\ b = m - f[/tex]

Answer:

Step-by-step explanation:

56/89

Answer:135

Step-by-step explanation:6075/45=135 hope this helps

Answer:

135

Step-by-step explanation:

Let x be the number of sessions.

Create an equation.

45x=6075

Divide 45 from both sides.

x=135

135 practice sessions.

Hope this helps! :)

The probability of scoring exactly four out of the given six shots is 0.311, calculated using the concept of binomial distribution in probability theory.

What is a Binomial Distribution?

Binomial Distribution in probability theory is defined as getting x number of successes on repetition of trial n times, the formula for binomial distribution is C(n,r) × (p)x × (q)n - r, where p denotes the probability of success and q denotes the probability of failure.

Calculation of the probability of scoring exactly four shots out of six

Let p denote the probability of success and q denote the probability of failure, which is equal to 1 - p.

Using Binomial Distribution, we get,

P(x = r) = C(n,x) × (p)x × (q)n - x

Taking r = 4,

P(x = 4) = C(6,4) × (0.6)4 × (0.4)2

= 6! / (4! 2!) × (0.6)4 × 0.16

= 0.31104

~ 0.311

Hence, the required probability using binomial distribution is 0.311.

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The properties used, in order, are:

We start by writing the linear equation:

3*(x + 2) = 4x + 1

The first step is using the distributive property to distribute the left product.

3x + 6 = 4x + 1

Then we use the addition property of equality to subtract 4x in both sides, we will get:

-x + 6 = 1

And we use it again to subtract 6 in both sides:

-x = 1 - 6 = -5

Finally, we multiply both sides by -1 (multiplication property of the equality)

x = 5

That is the solution of the linear equation.

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Answer:

[tex]15 \frac{1}{6}=15.167\:\:\sf(nearest\:thousandth)[/tex]

Step-by-step explanation:

[tex]15 \frac{1}{6}=15+\dfrac{1}{6}[/tex]

Convert ¹/₆ into a decimal by using long division:

[tex]\large \begin{array}{r}0.1\:6\:6\phantom{..}\\6{\overline{\smash{\big)}\,1. 0 \:0\: 0\: \phantom{.}}}\\{-~\phantom{(}\underline{0.6\:0\phantom{-)}}\\0.4\:0\:\:\phantom{))}\\-~\phantom{()}\underline{0.3\:6\:\:\phantom{))}}\\0.0\:4\:0\:\:\phantom{}\\-~\phantom{()}\underline{0.0\:3\:6\:\:\phantom{}}\\0.0\:0\:4\:\:\phantom{}\\\end{array}[/tex]

Therefore, ¹/₆ = 0.166666.....

[tex]\begin{aligned}\implies 15 \frac{1}{6} & =15+\dfrac{1}{6}\\\\& = 15 + 0.166666...\\\\& = 15.166666...\\\\& = 15.167\:\:\sf(nearest\:thousandth)\end{aligned}[/tex]

The total area under the normal curve is 1.

Why is there a standard deviation?

the total area under the normal curve is 1.

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Answer:

42 plants

might be easier to find how many plants are planted in 1 hour then multiply that by 6. In this case, 7 plants will be planted within an hour. So, multiply 7 x 6 to get 42.

Answer:

[tex]10\frac{11}{20}[/tex]

Step-by-step explanation:

[tex]5\frac{1}{2} + 3\frac{4}{5} + 1\frac{1}{4}[/tex]

1.Find the LCM(Least Common Multiple).

That would be 20.

2.Multiply so all denominators are equal.

[tex]5\frac{10}{20} + 3\frac{16}{20} + 1\frac{5}{20}[/tex]

3. Add

[tex]9\frac{31}{20}[/tex]

4. Simplify

[tex]10\frac{11}{20}[/tex]

Check to discover if an issue even exists before attempting to address it. not just to you, but also to those it will effect. You may create the criteria to compare and evaluate the potential remedies by developing an understanding of what makes this a problem in the first place.

Before programming starts, evaluation enables us to think through a problem's solution, ensure that it satisfies the original design requirements, yields the right answer, and is appropriate for the task at hand.

Three methods can be used to evaluate your problem-solving skills: asking for examples of times you've previously solved an issue; posing you with potential scenarios and asking you to reply; and observing how you use your problem-solving abilities in various exams and activities.

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Based on the triangle sum theorem:

20° + (y - 10)° + 4y° = 180

y = 34

The triangle sum theorem states that if we add up all the three interior angles in a triangle, the sum we would get would be equal to 180 degrees.

Given the following are interior angles of a triangle:

Based on the triangle sum theorem, we have the following equation:

20° + (y - 10)° + 4y° = 180

Solve for y

20 + y - 10 + 4y = 180

10 + 5y = 180

5y = 180 - 10

5y = 170

5y/5 = 170/5

y = 34

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Answer:

25

Step-by-step explanation:

j(k + 2)

5(3 + 2)

5(5)

25

Answer:

Hello,

answer : 259269764699508231

Step-by-step explanation:

We must use permutations with repetitions

Answer:

option C: 69

Step-by-step explanation:

We are to find approximately how many pink flowers are predicted to bloom on a shrub with 40 red flowers. The equation given is: y = 1.73x + 0.0924 and we see that red flowers are on the x-axis and pink flowers are on the y-axis.

Since we know there are 40 red flowers and red flowers are on the x-axis, x = 40. Plug into the equation:

y = 1.73x + 0.0924 where x = 40

y = 1.73(40) + 0.0924

y = 69.2  + 0.0924

y = 69.2924

best answer is C. 69.

The factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

(w - 4) will be the height

(w + 10) will be the length

Given,

The length of the enclosure for the pancake tortoise will be greater than the height, that is: l > h

The volume of enclosure = w³ + 6w² - 40w

Where w is the width.

Now, factorize the expression:

w³ + 6w² - 40w = 0

10 - 4 = 6

10 × (-4) = -40

Therefore, the factors of the expression  w³ + 6w² - 40w = 0 is (w - 4) and (w + 10)

Here, we know that length is greater than height.

So, (w - 4) will be the height and (w + 10) will be the length.

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The vertex is (3,16) and the quadratic equation in vertex form is [tex]f(x)=(x-3)^{2}+16\\[/tex].

Any equation in algebra that can be put into standard form is called a quadratic equation (from the Latin quadratus, which means "square").

As well as being referred to as the roots or zeros of the expression on the left-hand side of the equation, the values of x that satisfy it are known as solutions of the equation. There are only two possible answers to a quadratic equation. A double root is said to exist if there is only one solution. In the case where all of the coefficients are real values, there are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or all three of the aforementioned options. If complex roots are taken into account, then a quadratic equation will always have two roots, with a double root counting as one. An equivalent equation  can be created from a quadratic equation.

Calculations:

[tex]f(x)=x^{2} -6x+25\\ = x^{2} -2.x.3+(3^{2} )-(3^{2} )+25\\=(x-3)^{2} -9+25\\=(x-3)^{2}+16\\[/tex]

Comparing this from the vertex, y=[tex]a[/tex][tex](h-x)^{2} +k\\[/tex]

h=3 and k=16

Hence, vertex is (3,16).

[tex]f(x)=(x-3)^{2}+16\\[/tex]

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Answer:

7x

Step-by-step explanation:

Answer:

34-5=29

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

hope it helps and have a nice day! :)

Answer:

Z = ky/x where y=12, x=-12 and z=-6

-6= k(12)/-12

-k = - 6

K = 6

The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

Given: height of helicopter = 300√3 feet from the ground.

To find: Distance between zoo and library.

Finding:

(Refer to the image attached.)

Let the distance from the plane to the zoo and library be d1 and d2 respectively.

Then, with the help of concepts of applications of trigonometry,

[tex]tan(60) = \frac{300\sqrt{3}}{d1}[/tex]

=> [tex]\sqrt{3}=\frac{300\sqrt{3}}{d1}[/tex]

=> d1 = 300 feet

[tex]tan(30) = \frac{300\sqrt{3}}{d2}[/tex]

=> [tex]\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}[/tex]

=> d2 = 300 (3) = 900 feet

The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.

Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

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The difference between depths in January and July is equal to: D. 16 feet.

An absolute value function can be defined as a type of function that consist of an algebraic expression, which placed within absolute value symbols

In order to determine the difference between depths, we would calculate the magnitude of the depth for each of the month.

For January, we have:

January depth = 20 - 6

January depth = 14 feet.

For July, we have:

July depth = 20 - 22

July depth = -2 feet.

Now, we can calculate the difference between depths in January and July:

Difference = 14 - (-2)

Difference = 14 + 2

Difference = 16 feet.

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Answer:

Graph the solution to this inequality on the number line.

0.3(x − 4) > -0.3

Step-by-step explanation:

The time required to work at temperature of75degree celsius is 56.25 minutes

If a machine starts working in 45 minutes at the temperature of 60degree celsius, the amount of time worked at a temperature of 1 degree is expressed as:

Unit rate = 45/60

Unit rate = 0.75degrees celsius/minute

Determine the time it required to work at temperature of 75degree celsius

Time required = 0.75 * 75

Time required = 56.25 minutes

Hence the time required to work at temperature of75degree celsius is 56.25 minutes

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The reasonable Domain and Range for the situation.

Given that

To find

So, according to the question

We have,

So, we can say that

          Total charges = 8 (total number of peoples in a party)

Let's assume

                                 Total charges = y , and

Total number of peoples in a party =  x

Then, we get a equation of this problem,

                y = 8x ------------(1)

So, the domain of this equation will be greater then and equal to 64. and range will be greater then and equal to 8 and less then and equal to 40.

Answer:

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Step-by-step explanation:

so, we have a kite here.

a kite is a quadrilateral, that is totally symmetric along one of its diagonals.

the sum of all internal angles of a quadrilateral is always 360°.

remember, the sum of all angles around one point on one side of a line is always 180°.

a full circle airways represents 360°.

the inner angle at 140° is

180 - 140 = 40°

the inner angle at 250° is

360 - 250 = 110°

the inner angles at x and its opposing corner are equal (due to the symmetry) and are in sum with the other 2 inner angles 360°.

so, we have for the inner angles

360 = 110 + 40 + 2×xinner

210 = 2×xinner

the inner angle of x = 105°.

x (the outer angle of the inner angle of x) is

x = 360 - 105 = 255°