Which expression is equivalent to 30 ÷ (3 + x)

A. (3 + x) ÷ 30
B. 30 ÷ (x +3)
C (3÷30) + x
D 30 ÷ 3 + 30 ÷ x​

1Wht2

2The3

3Frick4

4Is5

5that6

The name of the shape in the figure is a hexagon.

A polygon is often a plane figure in geometry that is enclosed by a closed chain made up of a finite number of straight-line segments that end in a loop. The spots where two of these segments meet are referred to as the polygon's vertices (plural: vertices) or corners. These segments are known as its edges or sides.

Given a shape,

the shape is a polygon,

to name a polygon first count the number of sides of the figure,

as we count there are 6 sides for the shape,

There are some specific names for the shapes according to their number of sides, like

Number of Sides Name          

3                      Triangle                    

4                 Quadrilateral

5                    Pentagon

6                     Hexagon

The name for the shape is Hexagon.

Hence the name of the figure is Hexagon.

Learn more about polygons;

https://brainly.com/question/24464711

#SPJ2

A) The equation for a line that passes through the points (8, 2) and (6, 10) is:

y = -4*x + 34

B) line that has a slope of -2 and that passes through the point (-3, 5)

y = -2*x - 1

A) First we want to find the equation for a line that passes through the points (8, 2) and (6, 10).

Remember that a general linaer equation is of the form:

y = m*x + s

Where m is the slope and s is the y-intercept.

If the line passes through (a, b) and (c, d), then the slope is given by:

m = (d - b)/(c - a)

Then in this case, the slope is:

m  =(2 - 10)/(8 - 6) = -8/2 = -4

Replacing that we get:

y = -4*x + s

To find the value of s we use the fact that the line passes through (8, 2), this means that:

2 = -4*8 + s

2 + 32 = s

34 = s

The linear equation is:

y = -4*x + 34

B) Now we want to find a line that has a slope of -2 and that passes through the point (-3, 5)

Here we already know the slope, so we can write:

y = -2*x + s

Again, to find the value of s, we replace the values in the point in the linear equation:

5 = -2*-3 + s

5 = 6 + s

5 - 6 = s = -1

We conclude that this linear equation is:

y = -2*x - 1

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

It is the first answer

Step-by-step explanation:

Because you are multiplying which also means (product of something).

The variable is up against an upper limit. in a maximization problem, a binding less than or equal to (≤)

constraint indicates that the variable associated with the constraint has reached or is at its upper limit. It implies that the variable cannot increase further without violating the constraint.

This constraint acts as a restriction that limits the potential values the variable can take in the optimization problem.

When a constraint is binding, it means that the optimal solution to the problem is achieved when the constraint is satisfied with equality. In the context of a maximization problem,

if a variable is up against an upper limit and the constraint is binding, it suggests that the variable is already maximizing its value within the given constraint.

In contrast, if the constraint is not binding, it means that the variable has not reached its upper limit and has the potential to increase further while still satisfying the constraint. In such cases, the variable can be increased to improve the objective function value and optimize the problem further.

It's important to note that the shadow price, also known as the dual value or marginal value, represents the rate of change of the objective function with respect to a constraint. It indicates the sensitivity of the objective function to changes in the constraint.

The sign of the shadow price is not determined by the direction of the constraint (≤ or ≥), but rather by the problem formulation and the specific constraints and variables involved.

To know more about variable click here

brainly.com/question/2466865

#SPJ11

Inequalities with absolute value need to be set up differently to solve based on whether it is an "and" situation or an "or" situation.

When dealing with an "and" situation, we use a compound inequality and solve two separate inequalities. For an "or" situation, we set up two separate inequalities and solve them independently.

The approach differs because the absolute value can result in both positive and negative solutions, which must be considered when determining the valid range of solutions.

When encountering an "and" situation in absolute value inequalities, we use a compound inequality to account for both the positive and negative solutions. For example, if we have |x - 3| ≤ 5 and need to find the valid range for x, we set up two separate inequalities: x - 3 ≤ 5 and -(x - 3) ≤ 5. Solving each inequality separately yields the range of valid solutions for x.

On the other hand, when dealing with an "or" situation, we set up two separate inequalities to handle the positive and negative solutions independently. For instance, if we have |x + 2| > 3 and need to find the valid range for x, we set up the inequalities: x + 2 > 3 and -(x + 2) > 3. Solving each inequality separately provides the distinct ranges of valid solutions for x in the given scenario.

The reason for this distinction lies in the absolute value's property of yielding both positive and negative solutions. By setting up separate inequalities for each case, we ensure that all possible valid solutions are considered and captured appropriately.

To learn more about range click here:

brainly.com/question/29204101

#SPJ11

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

To know more about demographics visit:

brainly.com/question/32805670

#SPJ11

Answer:

Angle Side Angle, aka ASA. The triangle LAP is congruent to triangle TAX

Step-by-step explanation:

Angle P and x are congruent, side AX and AP are congruent, and angle LAP and angle TAX are congruent because vertical angles are congruent.

#teamtrees #WAP (Water And Plant)

The area of the rooftop garden as required in the task content is; 272 ft².

It follows from the task content that the area of the rooftop garden is to be determined.

As evident in the attached image; the rooftop garden was modelled as a composite figure of a rectangle and a triangle.

Therefore, the area of the rooftop garden is the sum of areas of the rectangle and the triangle.

Where the heights of the triangle is; 20 - 12 = 8 ft.

Therefore, we have;

Area = { (1/2) × 8 × 8 } + { 12 × 20}

Area = 32 + 240

Area = 272 ft².

Ultimately, the required area of the rooftop garden is; 272 ft².

Read more on area of Triangles;

https://brainly.com/question/17335144

#SPJ1

The number of ways to select a subset of 1515 for a short list is,

⇒ ⁶⁶C₁₅

We have to give that,

A search committee is formed to find a new software engineer.

And, there are 66 applicants who applied for the position.

Hence, a number of ways to select a subset of 15 for a short list is,

⇒ ⁶⁶C₁₅

Simplify by using a combination formula,

⇒ 66! / 15! (66 - 15)!

⇒ 66! / 15! 51!

Therefore, The number of ways to select a subset of 1515 for a shortlist

⇒ ⁶⁶C₁₅

To learn more about the combination visit:

brainly.com/question/28065038

#SPJ4

The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

For more questions on Value.

https://brainly.com/question/843074

#SPJ8

By considering the IVP y = 1+ y² y(0) = 0:

a. The solution y(x) = tan(x) satisfies the given differential equation and initial condition for the IVP.

b. The solution's lack of definition for all x doesn't contradict the existence and uniqueness theorem, as it is defined and unique on the interval (-π/2, π/2) containing the initial point.

c. The validity of the solution is determined by its behavior within the specified interval, regardless of its behavior outside of that interval.

The IVP calculations steps are:

(a) Verifying that y(x) = tan(x) is the solution:

1. Substitute y(x) = tan(x) into the differential equation y' = 1 + y²:

  y' = sec²(x) = 1 + tan²(x) = 1 + y²

2. The differential equation is satisfied.

3. Substitute x = 0 into y(x) = tan(x):

  y(0) = tan(0) = 0

4. The initial condition is satisfied.

Therefore, y(x) = tan(x) is the solution to the IVP.

(b) Explaining why the solution not being defined for all -∞ < x < ∞ does not contradict the existence and uniqueness theorem:

The existence and uniqueness theorem (Theorem 2.3.1 of Trench) guarantees the existence and uniqueness of a solution on an interval containing the initial point. In this case, the initial condition y(0) = 0 implies that the solution exists and is unique on an interval that includes x = 0. The fact that y(x) = tan(x) is not defined for all x does not contradict the theorem as long as the solution is defined and unique on the interval containing the initial point.

(c) Finding the largest interval for which the solution exists and is unique:

1. The tangent function has vertical asymptotes at x = (n + 1/2)π, where n is an integer. These are points where the solution y(x) = tan(x) is not defined.

2. The largest interval for which the solution exists and is unique is determined by the presence of these vertical asymptotes. The solution is valid and unique on the interval (-π/2, π/2), which is the largest interval where the tangent function is defined and continuous.

Therefore, the largest interval for which the solution to the IVP y = 1 + y², y(0) = 0 exists and is unique is (-π/2, π/2).

Learn more about  IVP visit

brainly.com/question/33188858

#SPJ11

Answer:

51 seats

Step-by-step explanation:

96 = 2 buses minus six seats

96 = 2x -6

102 = 2x

102/2 = x

51 seats

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

Answer:

D = 8

Step-by-step explanation:

3 down 2 to the right

Answer:

just needed to answer a question

Step-by-step explanation:

just think about what sounds like it goes together

Answer:

3/4x-2

Step-by-step explanation:

3−4=8

∴3=4+8

∴4=3−8

∴=14(3−8)=34−2

Answer + Step By Step:

The simplest form is \(\frac{11}{2}\) .

fraction, In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that,

−2(−1 1/4)

Multiplying the numerator with numerator and denominator with denominator. According to integer multiplication of two negative terms is always positive.

= \(\frac{22}{4}\)

The simplest form =  \(\frac{11}{2}\)

Hence, The simplest form is \(\frac{11}{2}\) .

To learn more about fraction from the given link:

https://brainly.com/question/17220365

#SPJ9

Answer:

The inverse of 1/8 is 8.

Answer:

The population is 34,000. The sample is 2,000

Step-by-step explanation:

Population in statistics can be explained as the group or set of all elements which are of particular interest to a researcher or a study. In the scenario above, the research interest concerns customers who pay with a debit card, whose number amounts to 34,000, this value refers to the population. The sample is referred to as the subset of the population or larger sample, the sample from the study corresponds to number of debit card users who were selected at random to participate in the survey. This value is 2000.

If the first bus is boarded at a rate of 15 people per minute, the domain of the function is; (15 ≤ x ≤ 45)

We are told that;

Total number of Juniors at Smithers High School that are taking a class trip = 130

Number of buses taking each student to their destination = 3 buses

Capacity of each bus = 45 people

Now, if the function  f(x) describes the total number of people on the first

bus, where x is the number of minutes spent loading the bus.

Then since the maximum number of people on the first bus is 45, then it means that the domain of the function is;

(15 ≤ x ≤ 45)

Read more about Inequality Word Problems at; https://brainly.com/question/25275758

#SPJ1

Answer: (1,2)

Step-by-step explanation:

1)

x+y=3

y=-x+3

x | 0 | 3 |

y | 3 | 0 |

2)

3x+y=5

y=-3x+5

x | 0 | 2 |

y | 5 | -1 |

Answer:

15, 3, -1, -12

Step-by-step explanation:

15, 3, -1, -12

Answer:

First answer (15, 3, -1, -12)

Step-by-step explanation:

ez

North and end up at the starting point. The unique geographic properties of the North Pole allow you to travel one mile south, then one mile east, and then one mile north, and end up back at thepo starting point. This property is unique to the North Pole and cannot be found anywhere else on the planet.

The only place on earth where you can travel one mile south, then one mile east, and then one mile north and end up at the starting point is the North Pole. This is because at the North Pole, all directions are north, and so no matter which direction you travel, you will always be moving away from the equator and towards the North Pole. Additionally, since all longitudes converge at the North Pole, traveling one mile in any direction will not change your latitude or longitude, meaning that you will end up back at the North Pole after traveling one mile south, then one mile east, and then one mile north.

At the North Pole, there is no concept of east and west as all lines of longitude converge at the pole. Hence, traveling one mile east or west will bring you back to the same location. The same applies to traveling one mile north or south as all directions at the North Pole are north.

It's important to note that the North Pole is a remote and inhospitable environment, with temperatures that remain below freezing throughout the year. As a result, there are no permanent settlements at the North Pole, and accessing the area requires specialized equipment and training.

To learn more about North Pole :

https://brainly.com/question/16270877

#SPJ4

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

To know more about treat here

https://brainly.com/question/8876653

#SPJ1

The approximate shape of the sampling distribution of the sample mean in this scenario will be normal.

When a large sample (n ≥ 30) of observations is selected from a right-skewed population, the Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the underlying distribution of the population.

This is because as the sample size increases, the sample mean becomes more and more normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, the approximate shape of the sampling distribution of the sample mean in this scenario will be normal.

To know more about sampling distribution refer here:

https://brainly.com/question/31465269?#

SPJ11

Answer:

12/60 (1/5)

Step-by-step explanation:

9+15+24+12= 60 total

There are 12 purple.

12/60

12 / 12 = 1

60 / 12 = 5

please let me know if my math is correct, which it should be but just to make sure

Answer:

x = ± √ 22 − 3

Step-by-step explanation:

Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

For more references on division, click;

https://brainly.com/question/21416852

#SPJ1