The sum of two numbers is 24. The difference of the numbers is 16. Find the numbers.

The asymptotes for the given functions can be identified by using limits and analyzing the graphs.

Function Analyzing the graph Graph (identify the asymptotes) lim f(x) = 3 Asymptote y=3 lim g(x) = 2 x-00 Asymptote y=2 lim g(x) = 0 X-3- Asymptote x=-3 lim f(x) = 0The given table below shows the different functions and their asymptotes. FunctionAsymptoteLim f(x) = 3y = 3Lim g(x) = 2x → ∞y = 2Lim g(x) = 0x → -3x = -3Lim f(x) = 0No asymptote exists for the limit of f(x) as it approaches zero (0).Analyzing the graph:An asymptote is a line that a curve approaches but never touches. We can use limits to determine where vertical or horizontal asymptotes exist by looking at the limits of a function as it approaches a certain value or infinity. The asymptotes can also be identified by observing the graph. When we approach an asymptote, the function approaches a specific value, which is the equation of the asymptote.

Know more about asymptotes here:

https://brainly.com/question/32038756

#SPJ11

The solution of the sum of the numbers will be 5.

To make the addition easier, we can first simplify the fractions by finding a common denominator. The smallest common multiple of 2, 3, and 4 is 12. We can rewrite the fractions with this denominator:

7/4 = (7/4) x (3/3) = 21/12

1/2 = (1/2) x (6/6) = 6/12

5/3 = (5/3) x (4/4) = 20/12

1/3 = (1/3) x (4/4) = 4/12

1/4 = (1/4) x (3/3) = 3/12

1/2 = (1/2) x (6/6) = 6/12

Now we can add the fractions together:

21/12 + 6/12 + 20/12 + 4/12 + 3/12 + 6/12

Combining like terms, we get:

60/12 = 5

So the sum of the original fractions is equal to 5.

To know more about summation follow

https://brainly.com/question/542712

#SPJ1

Answer:

Rule (where m is months, and t is total saved): 200 + 30m = t

After 12 months: $560

Step-by-step explanation:

So, we start with $200, and we save $30 each month. Let's call 'month' M.

And we can just use t to stand for total

The arithmetic rule would be: 200 + 30m = t

Alrighty, let's plug in 12 for our m value

200 + 30(12) = t

200 + 360 = t

t = $560

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 5 and (a, b) = (2, - 7), thus

y - (- 7) = - 5(x - 2) , that is

y + 7 = - 5(x - 2) → B

Answer;

We can have the equation as;

where 3 is k which is the proportionality constant

Explanation;

Firstly, we need to understand the relation of being directly proportional

When two variables are proportional, the relationship between them is of the nature;

where K is the proportionality constant

We can have k as 3, and that means we have the relationship as;

So, from the question, x is ? and y = -6; we can have x calculated as;

The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).

Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.

So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.

To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.

The given expression is ;

∛a²

The rational exponent is calculated as follows;

∛a² = \((a)^{\frac{2}{3}\)

Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)

Learn more about rational exponents here: brainly.com/question/30603002

#SPJ1

The complete question is below:

Find the equivalent expression of the rational exponent ∛a². does anyone know it

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

Learn more about tickets here:

https://brainly.com/question/25333829

#SPJ1

Answer: pretty sure it’s 52.63

Step-by-step explanation:

Answer:

1000/19

Step-by-step explanation:

\(\frac{10}{19}\) x \(\frac{100}{1}\) = 1000/19

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

Learn more about index notation here:

https://brainly.com/question/10339517

#SPJ1

Answer:

-6

Step-by-step explanation:

2n can be the smallest integer, and 2n + 18 will be the largest integer.

The sum of this, divided by two, will result in the average/mean.

(2n + 2n + 18)/2 = 3

Multiply each side by 2:

(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2

2n + 2n + 18  =  6

Combine the like terms:

4n + 18 = 6

Subtract 18 from both sides:

4n + 18 - 18 = 6 - 18

4n = -12

Divide each side by 4:

4n/4 = -12/4

n = -3

Since we decided to go by 2n:

2n = 2(-3) = -6

The area of the enclosure is approximately 128.6 acres

To find the area of the trapezoid ABCD, we first need to find the lengths of its parallel sides. Let's use the fact that the angles of a quadrilateral add up to 360 degrees:

Angle ABC = 124 degrees

Angle BCD = 85 degrees

Angle CDA = 96 degrees

Angle DAB = 360 - 124 - 85 - 96 = 55 degrees

Now we can use the tangent function to find the lengths of the sides:

tan(2 degrees) = (height of AB) / (distance between Anna and Benito)

(height of AB) = (distance between Anna and Benito) × tan(2 degrees)

(distance between Anna and Benito) = (713 - 690) / tan(2 degrees) ≈ 18490.3 ft

(height of AB) ≈ 429.4 ft

Similarly, we can find the height of CD:

tan(3 degrees) = (height of AD) / (distance between Anna and Deon)

(height of AD) = (distance between Anna and Deon) × tan(3 degrees)

(distance between Anna and Deon) = (725 - 690) / tan(3 degrees) ≈ 8639.5 ft

(height of AD) ≈ 459.6 ft

Now we can use the trapezoid area formula:

Area = (height of AB + height of CD) × (sum of the parallel sides) / 2

Area = (429.4 + 459.6) × ((18490.3 + 8639.5) / 2) / 5280 ≈ 128.6 acres

Learn more about area here

brainly.com/question/21025771

#SPJ4

Answer:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Step-by-step explanation:

There are an even number of negative factors, so the product is positive:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Answer:

Solutions given:

opposite side [0pp]=x

hypotenuse [Hypo]=7

angle A=36°

Now

relationship between opposite side and hypotenuse is given by Sin angle

Sin A=\( \frac{oppo}{hypo} \)

Sin 36=\( \frac{x}{7} \)

x=Sin36*7

x=4.11

So second one x=4.1 is your answer

Expected Value (EV) is the expected outcome of a random variable in a particular trial.

The expected value of going for 1 or 2 when a football team scores a touchdown to pull within 8 points is as follows:

Going for 1: The expected value of going for 1 is calculated by using the probabilities of scoring 1 or 0 and multiplying it by the number of points earned for each outcome.

Let's assume that the probability of scoring 1 is p and the probability of scoring 0 is 1-p.

Therefore, the expected value of going for 1 can be calculated as follows:EV of going for 1 = p × 1 + (1-p) × 0 = p

The probability of making a 1-point conversion is around 94 percent, while the probability of failing is around 6 percent, or 0.06.

Hence, the expected value of going for 1 is: EV of going for 1 = 0.94 x 1 + 0.06 x 0 = 0.94 or 0.94.

Going for 2: Let's assume that the probability of scoring 2 is p and the probability of scoring 0 is 1-p.

Therefore, the expected value of going for 2 can be calculated as follows:EV of going for 2 = p × 2 + (1-p) × 0 = 2p

The probability of converting a 2-point conversion is around 47%, or 0.47, while the probability of failing is around 53%, or 0.53.

Therefore, the expected value of going for 2 is: EV of going for 2 = 0.47 x 2 + 0.53 x 0 = 0.94 or 0.94.

Given the answers to the previous two questions, if the trailing team scores a touchdown to pull within 8 points, they should go for 2 points. The expected value of going for 2 is 0.94, which is greater than the expected value of going for 1, which is 0.94.

Therefore, going for 2 points gives the team the highest expected value of points.

To know more about expected outcome, visit:

https://brainly.com/question/30189648

#SPJ11

Answer:

Step-by-step explanation:

4 + 0.666.. = 0.75

the 6's repeat

Answer:

The exponential form has two parts: base and exponent

Answer:

Step-by-step explanation:

C and E look good Dani

Answer:

a = - 4

Step-by-step explanation:

Assuming you require to find the value of a

Given (x + h) is a factor of f(x) then f(- h) = 0

Here f(x) = x³ + ax² - 29x + 12 and h = - 4 , then

(- 4)³ + a(- 4)² - 29(- 4) + 12 = 0

- 64 + 16a + 116 + 12 = 0

16a + 64 = 0 ( subtract 64 from both sides )

16a = - 64 ( divide both sides by 16 )

a = - 4

The factor of an equation means that the factor value must give the equation zero.

If x + 4 is a factor of the equation  x³ + ax² - 29x + 12

The value of a is -4.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

x³ + ax² - 29x + 12 ______(1)

We need to find the value of a when x + 4 is a factor of equation (1).

If x + 4 is a factor then the x³ + ax² - 29x + 12 must be zero when x + 4 = 0.

This means,

x + 4 = 0

x = -4

Substituting x = -4 in (1) we must get zero.

Now,

x³ + ax² - 29x + 12 at x = -4.

(-4)³ + a(-4)² - 29x(-4) + 12 = 0

-64 + 16a + 116 + 12 = 0

16a + 64 =

16a = -64

a = -4

Thus,

The value of a when x+ 4 is a factor of x³ + ax² - 29x + 12 is -4.

Learn more about solutions of equations here:

https://brainly.com/question/545403

#SPJ2

The fourth vertex's coordinates are as follows: ( 2.1, -3.6)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, let the missing coordinates be (a,b).

Let's now utilize the midpoint formula to locate the erroneous coordinate.

Let the reference point be (-2.3, 3.6) A.

Let point B be (2.3, 2.2).

(2.1, 2.2) Let C be the point.

The center of AC should be at BD.

Step 1: Locating the AC's midpoint

Middle pint of AC:

(-2.3 + 2.1/2), (-3.6 + 2.2/2)

(0.2/2), (1.4/2)

(-0.1, -0.7)

Let's equate the midpoints in step two.

The BD mid-point:

(a + -2.3/2), (b + 2.2/2) =  (-0.1, -0.7)

(a + -2.3/2) = -0.1

(a -2.3/2) = -0.1*2

a = -0.2+2.3

a = 2.1

(b + 2.2/2) = -0.7

b + 2.2 = -0.7*2

b + 2.2 = -1.4

b = -1.4 -2.2

b = -3.6

Therefore, the fourth vertex's coordinates are as follows: ( 2.1, -3.6)

Know more about coordinates here:

https://brainly.com/question/29362355

#SPJ1

Complete question:

Freddy drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Answer:

x=1 y=10

Step-by-step explanation:

5x+y=15

2x+y=12

y=12-2x

5x+12-2x=15

3x=3

x=1  

5+y=15

y=10

Answer:

59+b or b+59

Step-by-step explanation:

If b is Beth, then 59+b is Andy.

The number of books Andy has is b+59 or 59+b

To determine if the degree of the function is odd or even we need to look at the extrema of the graph. If both points to the same side, it is, if X goes to positive infinity or to negative infinity, to both direction Y of the graph is going to the same direction, it means that the degree os even. Otherwise, when the extrema are pointing in different directions, it means the degree is odd.

In the present graph, the degree is odd, because the graph has different directions for each extrema.

To determine the signal to the leading coeficient, we check the direction Y is going to increasing values of X. If Y goes positive, the leading coeficient is positive, if it is negative, the leading coeficiente is negative.

In the present graph, the leading coeficient is positive, because for increasing values of X we have increasi

An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. The conic's shape is fixed because the equation also contains a constant.

An ellipse is described by this equation. It is a conic section because it has two variables, x and y, that are squared and multiplied together. A constant in the equation, 4x2 + 3xy + 5y2 - x - y = 0, shows that the conic's shape is fixed.  The equation is neither a parabola nor a hyperbola because it lacks any x or y terms. The equation therefore describes an ellipse. An oval-shaped closed curve known as an ellipse is produced when a plane and a cone intersect. The foci, or the two places at which the ellipse is symmetric, serve as its two defining points. The standard form of an ellipse, which is centred at the origin and contains the equation A(x2) + B(xy) + C(y2) + D(x) + E(y) + F = 0, is described by the equation provided. In this case, the constants are A=4, B=3, C=5, D=1, and E=1, and F=0. The major axis to minor axis ratio in the equation is 4:5, describing a moderately flattened ellipse. The equation can be used to determine the ellipse's area, circumference, and other parameters because it is symmetrical.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The Greek mathematicians started using the symbol pi (π) for as long as 4000 years in mathematical world.

A Short History of Pi

Even if we counted the number of seconds in those 4000 years and round the value of pi (π) to so many places, we would still only be estimating the true value of pi. Pi has been known for over 4000 years. Below is a quick summary of the discovery of.

By multiplying the radius of a circle by three, the ancient Babylonians determined its area, yielding the number pi = three. About 1900–1680 BC Babylonian tablets show a value of 3.125 for, which is a more accurate estimate.

The Rhind Papyrus, which dates to around 1650 BC, sheds light on ancient Egyptian mathematics. The calculation used by the Egyptians to determine a circle's area yielded a result that was around 3.1605 for.

Learn more about Symbol Pi (π):

https://brainly.com/question/16277677

#SPJ4

Answer:

D. Reflection across the y-axis

Step-by-step explanation:

In the points (-5, -3) and (5, -3), first, notice that the y-coordinates are the same. However, the x-coordinates are positive and negative, meaning one will be on the left side of the y-axis and one will be on the right side of the y-axis, bringing us to answer D. Graph proof is also attached.

The statement (D) "If f(c) is differentiable on its domain, then it is also continuous on its domain" must be true.

(A) The statement "Continuous functions are differentiable wherever they are defined" is false. While it is true that differentiable functions are continuous, the converse is not always true. There exist continuous functions that are not differentiable at certain points, such as functions with sharp corners or cusps.

(C) The statement "If f() is differentiable on the interval (0,0), then it must be differentiable everywhere" is false. Differentiability on a specific interval does not imply differentiability everywhere. A function can be differentiable on a particular interval but not differentiable at isolated points or on other intervals.

(D) The statement "If f(c) is differentiable on its domain, then it is also continuous on its domain" is true. Differentiability implies continuity. If a function is differentiable at a point, it must also be continuous at that point. Therefore, if f(c) is differentiable on its domain, it must also be continuous on its domain.

(B) The statement "The product of two differentiable functions is not always differentiable" is false. The product of two differentiable functions is always differentiable. This is known as the product rule in calculus, which states that if two functions are differentiable, then their product is also differentiable.

Learn more about differentiable  here:

https://brainly.com/question/24898810

#SPJ11

The rate at which water is being pumped into the tank is approximately 314.16 cm^3/min.

Let's consider the volume of water in the tank as a function of time. Let V(t) be the volume of water in the tank at time t, and let h(t) be the height of the water in the tank at time t.

At any time t, the volume of water in the tank can be calculated using the formula for the volume of a cone

V(t) = (1/3) × π × r^2 × h(t)

where r is the radius of the circular base of the tank, which varies with height. We can express r in terms of h using similar triangle

r/h = 2/6

r = h/3

Substituting this expression for r into the formula for V(t), we get

V(t) = (1/3) × π × (h/3)^2 × h = π × h^3 / 27

The problem tells us that water is leaking out of the tank at a rate of 7,000 cm^3/min. This means that the rate of change of V with respect to time (dV/dt) is -7,000 cm^3/min.

We are also given that water is being pumped into the tank at a constant rate. Let P be the rate (in cm^3/min) at which water is being pumped into the tank. Then the rate of change of V with respect to time is also given by dV/dt = P.

We know that when the height of the water is 2 m, the water level is rising at a rate of 20 cm/min. This means that dh/dt = 20 cm/min when h = 2 m.

We can relate dh/dt and dV/dt using the formula for the volume of a cone

V = π × h^3 / 27

Differentiating both sides with respect to time, we get

dV/dt = (π/9) × h^2 × dh/dt

Substituting the values we know, we get

-7,000 = P = (π/9) × (2)^2 × 20

Solving for P, we get

P = 100π ≈ 314.16 cm^3/min

Learn more about volume here

brainly.com/question/13659182

#SPJ4

The radius of the cylinder is 2.26 ft

The cylinder has a volume of 400 cubic feet

The height of the cylinder is 25 feet

The radius of the cylinder can be calculated as follows

radius= √ v/πh

= √ 400/(3.142)(25)

√ 400/ 78.55

= √ 5.09

= 2.26

Hence the radius of the cylinder is 2.26 ft

Read more on radius here

https://brainly.com/question/3715323

#SPJ1

a) Using the Euclidean algorithm, we can find gcd (707,413) as follows:707 = 1 · 413 + 294413 = 1 · 294 + 119294 = 2 · 119 + 562119 = 2 · 56 + 71356 = 4 · 71 + 12 71 = 5 · 12 + 11 12 = 1 · 11 + 1

Thus, gcd (707,413) = 1.

We can find the coefficients s and t that solve the equation 707s + 413t

= 1 as follows:1 = 12 - 11 = 12 - (71 - 5 · 12) = 6 · 12 - 71 = 6 · (119 - 2 · 56) - 71

= - 12 · 56 + 6 · 119 - 71

= - 12 · 56 + 6 · (294 - 2 · 119) - 71 = 18 · 119 - 12 · 294 - 71

= 18 · 119 - 12 · (413 - 294) - 71 = 30 · 119 - 12 · 413 - 71

= 30 · (707 - 1 · 413) - 12 · 413 - 71 = 30 · 707 - 42 · 413 - 71

Thus, s = 30, t = -42. So we have found that 707(30) + 413(−42) = 1.

b) Since 707s + 413t = 1 and 9 does not divide 1, the equation 707x + 413y = 9 has no integer solutions. Therefore, we can conclude that there are no such integers x and y.

To know more about Euclidean visit :

https://brainly.com/question/3589540

#SPJ11