Which set represents the domain of the function

Answer:

It would take 10 years for the given sum of money be doubled at the given simple interest rate.

Step-by-step explanation:

A 10% interest would be added to the the principal amount after each year. So  the interest would reach 100% i.e. equal to the principal amount in 10 years.

Answer:

Step-by-step explanation:

-y + 5x = 0

   -5x      -5x

-y = -5x

/ (divide by) -1

y = 5x

or

y = 5/1x

Use rise/run (rise over run)

rise five space and move over one starting at the origin because the y-intercept is 0.

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

Learn more about circle here

brainly.com/question/11878555

#SPJ4

The distance between points L(-5, 8/5) and M(5, 2/5) is approximately 10.16 units when rounded to the nearest hundredth.

To find the distance between two points in a coordinate plane, we can use the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Here, (x₁, y₁) represents the coordinates of point L and (x₂, y₂) represents the coordinates of point M. Plugging in the values, we get:

d = √[(5 - (-5))² + (2/5 - 8/5)²]

 = √[10² + (-6/5)²]

 = √[100 + 36/25]

 = √[(2500 + 36)/25]

 = √[2536/25]

 ≈ √101.44

 ≈ 10.16

Hence, the distance between points L and M is approximately 10.16 units.

Learn more about coordinate plane here: brainly.com/question/13611766

#SPJ11

Answer:

Andre is right. Steps and explanation below.

Step-by-step explanation:

total people = number of elementary students + adult teachers

                    = 280 + 40

                    =  320 people total

First type bus can hold 50 people

Second type can hold 56 people

if 3 for each types of buses are brought :

3 * 50 + 3 * 56 = 318 people.

Yes, this means Andre is right and can hold more 2 people extra.

Answer:

total people = number of elementary students + adult teachers

                   = 280 + 40

                   =  320 people total

First type bus can hold 50 people

Second type can hold 56 people

if 3 for each types of buses are brought :

3 * 50 + 3 * 56 = 318 people.

Yes, this means Andre is right and can hold more 2 people extra.

Step-by-step explanation:

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

y=3x+13; y=7x+17

Step: Solve y = 3x + 13 for y:

y=3x+13

Step: Substitute 3x + 13 for y in y = 7x + 17 :

y=7x+17

3x+13= 7x+17

3x+13+-7x=7x+17+-7x (Add -7x to both sides)

-4x+13=17

-4x+13+-13=17+-13 (Add -13 to both sides)

-4x=4

-4x/-4 = 4/-4 (Divide both sides by -4)

x=-1

Step: Substitute -1 for x in y=3x+13:

y=3x+13

y=(3)(-1)+13

y=10(simplify both sides of the equation)

Answer:

x= -1 and y= 10

(Hope this helped!)

The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The local gym is offering this new promotion:

An enrollment fee of $40 and a monthly fee of $30.

Let m be the total number of months

Total monthly fee = 30m

Total cost(including the enrollment fee of $40) = 40 + 30m

Let the total cost is c:

c = 40 + 30m

If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.

Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

Answer:

a) 18.84 cm

b) 28.26 cm²

Step-by-step explanation:

We Know

Each pancake is a circle with a diameter of 6 centimeters.

a)  Calculate the circumference of each pancake.

Circumference of circle = d · π

d = 6 cm

We Take

6 · 3.14 = 18.84 cm

So, the circumference of each pancake is 18.84 cm.

b) Calculate the area of each pancake.

Area of circle = r² · π

r = 1/2 · d

r = 1/2 · 6 = 3 cm

We Take

3² · 3.14 = 28.26 cm²

So, the area of each pancake is 28.26 cm².

Answer:

P = -1

Step-by-step explanation:

3(2p-1)-2(3p+4)=11p

Distribute:

6p-3-6p-8=11p

Combine like terms:

-11 = 11p

Solve for p by dividing by 11:

-11/11 = 11p/11

Simplify:

-1 = p

Step-by-step explanation:

6p - 3 - 6p - 8 = 11p

-11 = 11p

p = -1

Giving me brainiest will be appreciated

The projected balance of cash at the end of August is $38,000. The correct option is D.

To calculate the projected balance of cash at the end of August, we need to consider the cash balance at the beginning of the month, cash collections, and cash payments for August.

Given that the cash balance on July 31 was $32,000.00, we start with this amount.

Cash collections for August are $52,000.00, which means this amount is added to the cash balance.

Next, we consider cash payments for August, which include purchases of direct materials and operating expenses. The total cash payments for August are $20,000 (purchases of direct materials) + $26,000 (operating expenses) = $46,000.00. This amount is subtracted from the cash balance.

Finally, we calculate the projected balance of cash at the end of August by adding the cash collections and subtracting the cash payments from the beginning cash balance:

Projected cash balance at the end of August = Beginning cash balance + Cash collections - Cash payments

= $32,000 + $52,000 - $46,000

= $38,000

Therefore, correct option is D.

To learn more about balance click on,

https://brainly.com/question/32973850

#SPJ4

Complete question is:

Berman Company is preparing its budget for the third quarter. Cash balance on July 31 was $32,000.00. Assume there is no minimum balance of cash required and no borrowing is undertaken. Additional budgeted data are provided here:

                                         July           Aug             Sep

Cash collections       $51,000.00 $52,000.00 $50,000.00

Cash payments

Purchases of direct materials     23,000     20,000        24,000

Operating expenses       32,000      26,000    22,000

Capital expenditures      7,000       9,000      13,000

Calculate the projected balance of cash at the end of August.

A. $23000

B. $29000

C. $107000

OD. $38000

Answer:

28

Step-by-step explanation:

According to the question,

2 helmets and 1 football cost $80, while 1 helmet and 2 football cost $76

Let x represent cost of football and let y equal cost of helmet.

Write the system of equations,

\(x +2 y = 80\)

\(2x + y = 76\)

Eliminate the x variable by multiplying the top equation by -2

\( - 2x - 4y = - 160\)

\(2x + y = 76\)

Add both equations.

\( - 3y = - 84\)

\(y = 28\)

So one helmet cost $28

Answer:

3.935 x 10^5.

Step-by-step explanation:

There are five digits after the first 3 so  it will be 10^5.

The answer is 3.935 x 10^5.

393500 equals 3.935×10⁵

If we write xⁿ then we mean to say that x is multiplied n times.

The exponent of a number says how many times the number is multiplied by itself.

393500=3.935×100,000=3.935×10⁵

Hence, 393500=3.935×10⁵

Learn more about exponents here- https://brainly.com/question/5497425?referrer=searchResults

#SPJ2

The value of correct option for maps ΔABC to a triangle that is similar, but not congruent, to ΔABC are,

⇒  dilation with scale factor 2 about the origin

We have to given that;

To find correct option for maps ΔABC to a triangle that is similar, but not congruent, to ΔABC

Since, We know that;

For any translation the condition of congruency is not change.

But for any type of dilation condition of congruency for triangles are change.

Thus, The value of correct option for maps ΔABC to a triangle that is similar, but not congruent, to ΔABC are,

⇒  dilation with scale factor 2 about the origin

Learn more about the transformation visit:

https://brainly.com/question/30097107

#SPJ1

Answer:

150

Step-by-step explanation:

1216-1066 is 150, simple subtraction

Answer:

150

Step-by-step explanation:

1216 - 1066= 150

All you do is subtract the bigger year from the smaller one

Thus 1216 - 1066 is 150

HOPE THIS HELPED

Answer: Given two points on a line, we can write an equation for that line by finding the slope between those points, then solving for the y-intercept in the slope-intercept equation y=mx+b.

Step-by-step explanation:

please need brainliest

The polygons are similar.

This is because dividing the corresponding sides forms the same ratio, as shown by the three equations below

35/28 = 1.25

25/20 = 1.25

(15.5)/(12.4) = 1.25

So the larger figure on the right has side lengths that are 1.25 times larger compared to the corresponding sides of the figure on the left.

You'll need to flip the figure on the left so that the side labeled "20" is along the top, and the "28" is along the bottom.

After this flip happens, also note that the angle arc markings match up. The bottom pairs of angles of each figure are shown with a single arc, while the top angles are shown as double arcs. This helps visually show which angles pair up and are congruent to one another.

Because we have similar proportions as discussed earlier, and congruent pairs of angles like this, this shows the two figures are similar quadrilaterals. The one on the right is simply an enlarged scaled up copy of the figure on the left.

The identity Sin(α)/Tan(α) = Cos(α) is valid

Trigonometry is study of triangles. All trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. Three major of them are as follows :-

Sine Function:

sin(θ) = Opposite / Hypotenuse

Cosine Function:

cos(θ) = Adjacent / Hypotenuse

Tangent Function:

tan(θ) = Opposite / Adjacent

Lets prove this identity by proceeding with the LHS

= Sin(α)/Tan(α)

= Sin(α)/ (Sin(α)/Cos(α)) (Tan(α) = Sin(α)/Cos(α))

= Sin(α)xCos(α) / Sin(α)

= Cos(α)

Hence verified

Learn more about Trigonometric Ratios here :

https://brainly.com/question/13776214

#SPJ4

Answer:

2p²-5p+3 is the final answer as they aren't any like terms to collect in order to simply the solution further.

Step-by-step explanation:

Wishing you a splendiferous day,

stay salty...

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

Answer:

D, E

Step-by-step explanation:

D. all angles do not have to be congruent

E. diagonals do not have to be congruent

Option D is incorrect 100%

Option E should be incorrect aswell.

The probability of getting exactly 0 heads is, 0.031.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

A fair coin is tossed 5 times.

So, the the total number of possibilities are,

\(2^5= 32\)

We have to find the probability of getting exactly 0 heads.

The only possible set of flips that yields 0 heads is {T, T, T, T, T}.

So,

The probability is, \(\frac{1}{32}=0.03125\)

Probability ≈ 0.031

Hence, the probability of getting exactly 0 heads is, 0.031.

To know more about probability, click on the link

https://brainly.com/question/24756209

#SPJ4

Miss Kito would need to invest approximately $11,309 initially to have at least $15,000 after 5 years, rounded to the nearest whole dollar.

To calculate the initial investment needed for continuous compounding, we can use the formula:

A = P × \(e^{rt}\)

Where:

A = the final amount (desired amount) = $15,000

P = the initial investment (unknown)

e = the mathematical constant approximately equal to 2.71828

r = the interest rate = 6% = 0.06 (in decimal form)

t = the time period in years = 5 years

We want to solve for P, so we rearrange the formula:

P = A / \(e^{rt}\)

Substituting the given values into the formula, we have:

P = $15,000 / \(e^{0.06(5)}\)

Using a calculator, we can evaluate the expression:

P ≈ $11,308.65

Therefore, Miss Kito would need to invest approximately $11,309 initially to have at least $15,000 after 5 years, rounded to the nearest whole dollar.

To know more about invest click here :

https://brainly.com/question/33875859

#SPJ4

The complete question is :

Inspired by her entrepreneurial success, Miss Kito decides to invest some of her money in an account gaining 6% interest compounded continuously. She ultimately would like to purchase a $15000 car. How much would she have to invest initially to have the necessary money in 5 years? Round your answer to the nearest whole dollar that will ensure that she has at least $15000 after 5 years

By using the Cauchy-Riemann equations on a real-valued function, it can be proven that the function f(z) is constant in the domain D. This is important for understanding analytic functions in complex analysis.

To prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D, let a function f be analytic everywhere in a domain D. We know that a real-valued function is said to be a function whose values lie on the real line. In the case of the complex plane, a function whose values lie on the real line is real-valued.

The Cauchy-Riemann equations, which define the necessary conditions for a function f(z) to be analytic in a domain, say that the imaginary component of f(z) is determined by its real component.

To be more precise, if f(z) is real-valued for all z in D, then we can say that:u(x, y) = f(z),v(x, y) = 0

By definition, the Cauchy-Riemann equations can be stated as:

∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x

Taking the first equation, we get:

∂u/∂x = ∂v/∂y => ∂v/∂y = 0

Since v is equal to 0 for all values of x and y, the above equation reduces to ∂u/∂x = 0, which implies u is constant with respect to x.

Similarly, taking the second equation, we get:

∂u/∂y = -∂v/∂x => ∂u/∂y = 0

Since u is equal to a constant for all values of x and y, the above equation reduces to ∂v/∂y = 0, which implies v is constant with respect to y. Since u and v are both constant with respect to their respective variables, u + iv = f(z) is a constant with respect to z throughout the domain D. Thus, we have proved that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D.

To know more about the Cauchy-Riemann equation: https://brainly.com/question/30385079

#SPJ11

y = -\(\frac{5}{3}\)x+5  equation has an X intercept of 3 and a y intercept of 5 .

  The point on a line where it crosses an axis is referred to as the "intercept." The slope of the line passes through a point called an intercept on the y-axis.

The equation for a line, which is written as y = mx+c, which stands for slope and y-intercept, respectively, reflects this.

The two main intercepts are X-intercept and Y-intercept. Where the line crosses the x and y axes, respectively, is where the line's x-intercept and y-intercept are situated.

In this case, you are given both intercepts.

Plot a line from the third x-axis point.

On the y-axis, place the coordinates y = 5.

The necessary line is a straight line that passes through these two places is

y = -\(\frac{5}{3}\)x+5

For more such questions on Intercept :

brainly.com/question/14180189

#SPJ4

Answer: NO

Step-by-step explanation:

The line that separates the two part is a dashed line which means that the point on the lines are not in the solution

EXTRA: ONLY IF IT IS A SOLID LINE, THE POINTS WILL BE A SOLUTION

(-2,0) is on the dashed line, so it is not a solution

The charges of the polyatomic ions listed:

- Hydroxide: OH⁻ (charge of -1)

- Carbonate: CO₃²⁻ (charge of -2)

- Sulfate: SO₄²⁻ (charge of -2)

- Ammonium: NH₄⁺ (charge of +1)

- Nitrate: NO₃⁻ (charge of -1)

Polyatomic ions are charged groups of atoms that behave as a single unit and carry a net electrical charge. These ions are made up of two or more atoms covalently bonded together, but they have an overall charge due to the loss or gain of one or more electrons.

Polyatomic ions are often formed from non-metal elements that share electrons in covalent bonds, and they can have either a positive or negative charge depending on the number of electrons they gain or lose. Some examples of polyatomic ions include hydroxide (OH⁻), ammonium (NH₄⁺), carbonate (CO₃²⁻), and sulfate (SO₄²⁻).

learn more about Polyatomic ions: https://brainly.com/question/30348555

#SPJ1

Max reaches the y-axis in roughly 11.932 seconds, covering the necessary distance based on the given information about his movement and the time delay compared to John.

To find the time it takes for Max to reach the y-axis, we can use the information provided about John's movement and the fact that Max passes through the same point on the x-axis but 2 seconds later.

Let's analyze John's movement first:

John starts at (0, -6) and heads towards (10, 5) in 10 seconds. We can calculate John's velocity by dividing the change in y-coordinate by the change in time:

Velocity of John = (5 - (-6)) / 10 = 11 / 10 = 1.1 units per second.

Since Max passes through the same point on the x-axis, the x-coordinate of that point will be the same for both of them. Let's call it x_0.

Now, let's consider Max's movement:

Max starts at (9, -14) and reaches the same point on the x-axis 2 seconds after John. Since Max moves in a straight line, we can calculate Max's velocity as well:

Velocity of Max = (x_0 - 9) / (10 + 2) = (x_0 - 9) / 12.

Since both John and Max are moving at constant speeds, their velocities remain the same throughout their movements.

We can equate their velocities:

1.1 = (x_0 - 9) / 12.

Now, let's solve this equation to find the value of x_0:

1.1 * 12 = x_0 - 9,

13.2 = x_0 - 9,

x_0 = 22.2.

Therefore, the point where both John and Max pass through on the x-axis is (22.2, 0).

To find the time it takes for Max to reach the y-axis, we can calculate the distance between Max's starting point (9, -14) and the point (22.2, 0):

Distance =

=\(\sqrt{(22.2 - 9)^2 + (0 - (-14)} ^2)\\ =\sqrt{(174.84 + 196) } \\= \sqrt{(370.84)} \\ =19.24 units.\)

Since Max's velocity is given by (x_0 - 9) / 12, we can set up the equation to find the time (t) it takes for Max to cover the distance of 19.24 units:

t = 19.24 / [(x_0 - 9) / 12] = 19.24 * 12 / (22.2 - 9) ≈ 11.932.

Therefore, it takes Max approximately 11.932 seconds to reach the y-axis.

For more question on distance visit:

https://brainly.com/question/30395212

#SPJ8