(Algebraic and graphical modelling)

please hellpp

For n≥2, the corresponding recursive function is f (1) =3f(n)=f(n1) +5.

In mathematics, a function is a rule that pairs each element from the domain with exactly one from the range or codomain of two sets.

In a recursive function, the output value at a certain input value is defined as a function of the output value at the previous input value. In this instance, we may use the definition to derive the recursive function from the explicit function:

f (n) = 5n - 2 f (n) = 5n - 3 f (n) = 5(2) - 8 f (n) = 5(3) - 13

The right response is: A. When n=2, f(1) = 2f(n)= f(n1) + 5.

As a result, the recursive function can be written as: f (1) =3f(n)=f(n1) +5 for n2.

Thus, for n≥2, the analogous recursive function is f (1) =3f(n)=f(n1) +5.

To know more about the functions, visit:

https://brainly.com/question/11624077

#SPJ1

The given quantity 240 g can be divided as 100 g, 60 g, and 80 g such that the quantities are in the ratio 5: 3: 4.

A ratio is a comparison between two or more quantities that are measured in the same units.

It is often expressed as a fraction or a colon and is used to describe the relative size or amount of one quantity compared to another.

Here we have 240g

We need to divide 240 g into a 5: 3: 4 ratio

Let 5x, 3x, and 4x be the divided parts

=> 5x + 3x + 4x = 240 g

=> 12x = 240 g

=> x = 20 g  

Now calculate the divided parts as follows

5x = 5(20 g) = 100 g

3x = 3(20 g) = 60 g

4x = 4(20 g) = 80 g

Therefore,

The given quantity 240 g can be divided as 100 g, 60 g, and 80 g such that the quantities are in the ratio 5: 3: 4.  

Learn more about Ratios at

https://brainly.com/question/728076

#SPJ1

Answer: 38.465 feet

Step-by-step explanation: The diameter (7 feet) divided by 2, equals 3.5. multiply 3.5 squared (12.25 feet) by pi (3.14) equals your answer of 38.465 feet.

Answer:

R is (-10,4) S is (-1,7) T is (-1,-2) U is (-10,-2)

After 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet

The depth of the water variations via- 3/ 4 foot each hour, this means that the depth decreases by employing 3/4 foot every hour.

Still, also after one hour of draining, the intensity of the water might be

If the primary depth of the water was five bases.

5-(3/4) = 41/4 ft

After hours, the depth might be

-(3/4) = 31/2 fr

After three hours

-(3/4) = 23/4 ft

After 4 hours

-(3/4) = 2 ft

After five hours

2-(3/4) = 11/4 bases

Thus, after 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet

Learn more about Formula of depth Calculation:-

https://brainly.in/question/11742804

#SPJ4

The length of y for the triangle is 27.8 in

The sine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

w/sinW = x/sinX = y/sinY

where w, x and y are the lengths and W, X and Y are the angles

Given: w = 55 inches,   m∠W = 162° and m∠X= 9°

m∠Y = 180 - 162 - 9 =  9° (angle sum in a triangle)

Using the formula:

w/sinW = y/sinY

55/sin162° = y/sin9°

y = (55*sin9°)/sin162°

y = 27.8 in

Learn more about sine rule on:

brainly.com/question/3240813

#SPJ1

Answer:

First, subtract 10x on both sides so you get

12=10x-2

Then add 2 odd both sides

14=10x

Then divide both sides by 10

14/10= 10X/10

So you get x=1.4

The simplified form of [tex](4x-3)(-5x^(2)+2x-4)[/tex] is: [tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

To multiply and simplify the given expression [tex](4x-3)(-5x^(2)+2x-4)[/tex], we can use the distributive property. This means we will multiply each term in the first parentheses by each term in the second parentheses and then combine like terms.

First, we will distribute the 4x to each term in the second parentheses:
[tex]4x * (-5x^(2)) = -20x^(3)4x * (2x) = 8x^(2)4x * (-4) = -16x[/tex]

Next, we will distribute the -3 to each term in the second parentheses:
[tex]-3 * (-5x^(2)) = 15x^(2)-3 * (2x) = -6x-3 * (-4) = 12[/tex]

Now we will combine all of the terms:
[tex]-20x^(3) + 8x^(2) - 16x + 15x^(2) - 6x + 12[/tex]

Finally, we will combine like terms:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

So the simplified expression is:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

To know more about simplest form refer here:

https://brainly.com/question/290068

#SPJ11

Answer:

Step-by-step explanation:

Decreasing.

This is because the as you increase the X value and solve for Y, the Y value decreases.

For example:

[tex]x=1 \\y=2(\frac{1}{3} )^1\\y=\frac{2}{3} =0.667\\\\x=2\\y=2(\frac{1}{3} )^1\\y=\frac{2}{9}=0.222\\\\x=3\\y=2(\frac{1}{3} )^3\\y=\frac{2}{27}=0.074[/tex]

Answer:

Below

Step-by-step explanation:

9/5  X   4/1  X  1/6   =  ( 9 x 4 x 1)  / (5 x 1 x 6) = 36/30  = 1 6/30 = 1  1/5

Answer:

1 1/5

Step-by-step explanation:

By applying simplification and factoring concepts, it can be concluded that:

1. (-5x⁻³ y⁻⁵) (3x⁵ y⁻⁵) = -15x² / y¹⁰

3. 20x² – 12x – 14 = 2(10x² - 6x - 7)

5. 2x(x - 1) + 3(x - 1) = (x - 1)(2x + 3)

6. 12x² – 15x + 8x – 10 = (3x + 2)(4x - 5)

7. 3x² – 13x – 10 = (3x + 2)(x - 5)

Simplification is the process of rewriting an expression in a simpler or easier-to-understand form, while still maintaining the same values.

Factoring means to factor a number means to break it up into numbers that can be multiplied together to get the original number.

Q1: Simplifying (-5x⁻³ y⁻⁵) (3x⁵ y⁻⁵)

Multiplying the number and applying rule (-x) = x, we get:

= -15x⁻³ · x⁵ · y⁻⁵· y⁻⁵

Apply rule xᵃxᵇ = xᵃ⁺ᵇ, we get:

= -15x²· y⁻¹⁰

Apply rule x⁻ᵃ = 1/xᵃ, we get:

= -15x² / y¹⁰

Q3: Factoring 20x² – 12x – 14

Divide each term by 2, and we get:

= 2(10x² - 6x - 7)


Q5: Factoring 2x(x - 1) + 3(x - 1)

Factoring out common term (x - 1), we get:

= (x - 1)(2x + 3)

Q6: Factoring 12x² – 15x + 8x – 10

Factoring out 4x from 12x² + 8x, we get:

= 4x(3x + 2)

Factoring out -5 from – 15x – 10, we get:

= -5(3x + 2)

Now the full expression becomes:

= 4x(3x + 2) - 5(3x + 2)

Factoring out common term (3x + 2), we get:

= (3x + 2)(4x - 5)

Q7: Factoring 3x² – 13x – 10

Break expression into groups:

= 3x² + 2x – 15x – 10

Factoring out x from 3x² + 2x, we get:

= x(3x + 2)

Factoring out -5 from – 15x – 10, we get:

= -5(3x + 2)

Now the full expression becomes:

= x(3x + 2) - 5(3x + 2)

Factoring out common term (3x + 2), we get:

= (3x + 2)(x - 5)

To learn more about simplification and factoring, click here: https://brainly.com/question/9276424

#SPJ11

The volume of the cylinder is 126π cubic meters.

Volume is the measure of the space occupied by a three-dimensional object. It is typically expressed in cubic units.

The radius of the cylinder is half of the diameter, so the radius is 3 meters. The formula for the volume of a cylinder is

V = πr²h,

where r is the radius and h is the height. Substituting the given values, we get V = π(3)²(14) = 126π cubic meters.

Therefore, the volume of the cylinder is 126π cubic meters.

To learn more about Volume from the given link

https://brainly.com/question/463363

#SPJ1

A dilation with a scale factor of 8:7 creates an image that is eight times larger than the original.

A scale factor is a numerical value which is used to multiply or divide a given measurement. It is used to compare the sizes of two different objects, or to enlarge or reduce the size of an object. The scale factor can be used to calculate the area, perimeter, and volume of an object. For example, if an object is enlarged by a scale factor of 2, its area will increase by a factor of 4. Similarly, if an object is reduced by a scale factor of 0.5, its area will be reduced by a factor of 0.25.

This means that all of the points in the original image are moved away from the center of the dilation by a factor of eight. This creates an image that is eight times wider and seven times taller than the original. This type of dilation is also known as an enlargement. By enlarging the image, it is possible to see more detail and make the image easier to see. Additionally, it may also be possible to see features that were previously too small to be seen.

To know more about scale factor click-
https://brainly.com/question/2826496
#SPJ1

The expression [tex]20.x^25y^3+4x[/tex] is a polynomial of degree 25 and it is a binomial.

A polynomial is an expression made up of variables and coefficients, combined using addition, subtraction, and multiplication, with no division by a variable. In this expression, we have two terms, [tex]20.x^25y^3[/tex] and 4x, which are combined using addition.

Since the degree of a term is the sum of the exponents of its variables, the degree of the first term is 25 (the sum of the exponents of x and y), and the degree of the second term is 1 (the exponent of x). Since this is a polynomial with only two terms, it is a binomial.

Learn more about polynomial https://brainly.com/question/4142886

#SPJ11

The length of the arc XYZ is 59.3 inches .

The radius of the circle is 10 inches. The central angle that subtend the arc is 340 degrees.

Therefore, the length of the arc xyz can be found as follows:

length of an arc = ∅/ 360 × 2πr

where

length of an arc(xyz) = 340 / 360 × 2 × 3.14 × 10

length of an arc(xyz) = 21352 / 360

length of an arc(xyz) = 59.3111111111

length of an arc(xyz) = 59.3inches

Learn more on arc length here: https://brainly.com/question/16237232

#SPJ1

Based on the given information, the cost of a pound of pistachios and a pound of cashews is $7.875 and $5.50, respectively.

To find the cost of a pound of pistachios and the cost of a pound of cashews, we can use a system of equations.

Let's let P represent the cost of a pound of pistachios and C represent the cost of a pound of cashews.

Then we can write two equations based on the information given:

4P + 1C = 37

3P + 3C = 48

Now we can use the elimination method to solve for one of the variables.

Let's multiply the first equation by -3 to eliminate the P variable:

-12P - 3C = -111

3P + 3C = 48

Adding these two equations together gives us:

-8P + 0C = -63

Simplifying gives us:

P = 63/8

This means that the cost for a pound of pistachios is $63/8 or $7.875.

Substitute the value of P to any of the two equations so we can have the value of C.

4(63/8) + 1C = 37

C = 11/2 = 5.5

Therefore, the cost of a pound of pistachios is $7.875 while the cost of a pound of cashews is $5.50.

Learn more about system of equation here: https://brainly.com/question/25976025.

#SPJ11

To model the path of the rock, we can use a quadratic equation of the form y = ax^2 + bx + c, where y is the height of the rock, x is the distance from the catapult, and a, b, and c are constants.
We can use the given information to find the values of a, b, and c.

First, we know that the rock launches out of the catapult at a height of 0 feet, so when x = 0, y = 0. This means that c = 0.
Next, we know that the rock reaches its maximum height of 50 feet when it is 75 feet away from the catapult, so when x = 75, y = 50. We can plug these values into the equation and simplify:
50 = a(75)^2 + b(75) + 0
50 = 5625a + 75b

Finally, we know that the rock hits the wall 8 feet from the top when it is 120 feet away from the catapult, so when
x = 120, y = 40 - 8 = 32. We can plug these values into the equation and simplify:
32 = a(120)^2 + b(120) + 0
32 = 14400a + 120b
We now have a system of two equations with two unknowns:
5625a + 75b = 50
14400a + 120b = 32

We can use substitution or elimination to solve for a and b. Using elimination, we can multiply the first equation by -1.6 to eliminate the b term:
-9000a - 120b = -80
14400a + 120b = 32
Adding the two equations together gives:
5400a = -48
Solving for a gives:
a = -48/5400 = -0.00888888889

We can then plug this value of a back into one of the original equations to solve for b:
5625(-0.00888888889) + 75b = 50
-50 + 75b = 50
75b = 100
b = 100/75 = 1.33333333333

So the equation that models the path of the rock is:
y = -0.00888888889x^2 + 1.33333333333x + 0
Or, rounding to three decimal places:
y = -0.009x^2 + 1.333x

To know more about quadratic equation refer here:

https://brainly.com/question/30098550

#SPJ11

Answer:

Let's first simplify the left-hand side and right-hand side of the inequality:

2 - 5(x + 1) = 2 - 5x - 5 = -5x - 3 3(x - 1) - 24 = 3x - 27

So the inequality becomes:

-5x - 3 ≥ 3x - 27

Now we can solve for x:

-5x - 3 ≥ 3x - 27 -8x ≥ -24 x ≤ 3

The solution set is all x-values less than or equal to 3. We can express this in interval notation as:

(-∞, 3]

The solution set in interval notation is (-∞, 4].

To solve the inequality 2 − 5(x + 1) ≥ 3(x − 1) − 24 and write the solution set in interval notation, we need to follow these steps:

Distribute the -5 and 3 on the left and right sides of the inequality, respectively:
2 - 5x - 5 ≥ 3x - 3 - 24

Simplify both sides of the inequality by combining like terms:
-3x - 3 ≥ 3x - 27

Add 3x to both sides of the inequality to isolate the variable on one side:
-3 ≥ 6x - 27

Add 27 to both sides of the inequality:
24 ≥ 6x

Divide both sides of the inequality by 6 to solve for x:
4 ≥ x

Write the solution set in interval notation. Since the inequality is "greater than or equal to," we use a closed bracket for the lower bound and an open bracket for the upper bound:
(-∞, 4]

Therefore, the solution set in interval notation is (-∞, 4].

Learn more about interval notation

brainly.com/question/29531272

#SPJ11

The equation of line is y = -4x - 3 and the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 5 )

Let the second point be Q ( -1 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 5 ) / ( -1 - ( -2 ) )

On simplifying , we get

Slope m = ( -4 ) / 1

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = -4 ( x - ( -2 ) )

y - 5 = -4 ( x + 2 )

y - 5 = -4x - 8

Adding 5 on both sides , we get

y = -4x - 3

Hence , the equation of line is y = -4x - 3

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ9

The composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

Given functions are \( f(x)=6x−5 \) and \( g(x)=x^2−6x+3 \). Let's find the composition of functions below:\((f\circ g)(x)\)First, we need to substitute \( g(x) \) in place of \( x \) in \( f(x) \). Hence,\( (f\circ g)(x) = f(g(x)) \)\( f(g(x)) = 6g(x) - 5 \)Substitute \( g(x) \) in the above equation,\( (f\circ g)(x) = 6(x^2-6x+3) - 5 \)\( (f\circ g)(x) = 6x^2 - 36x + 13 \)\((g\circ f)(x)\)First, we need to substitute \( f(x) \) in place of \( x \) in \( g(x) \). Hence,\( (g\circ f)(x) = g(f(x)) \)We are given that \( f(x)=6x−5 \) , substitute this in the above equation,\( (g\circ f)(x) = g(6x-5) \)Substitute this in the function \( g(x) \),\( (g\circ f)(x) = (6x-5)^2 - 6(6x-5) + 3 \)\( (g\circ f)(x) = 36x^2 - 72x + 29 \)Hence, the composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).

Learn more about Composition

brainly.com/question/13808296

#SPJ11

The amount of water each beaker would hold is x/8

From the question, we have the following parameters that can be used in our computation:

Number of beakers = 8

Represent the size with x

So, we have the following quotient expression

Size of each beaker = x/Number of beakers

Substitute the known values in the above equation, so, we have the following representation

Size of each beaker = x/8

Hence, the amount is x/8

Read more about proportions at

https://brainly.com/question/16828793

#SPJ1

John owes his mom R1041.6 after 2 years

To find out how much John owes his mom after 2 years, we need to calculate the interest on the loan. The formula for calculating interest is I = Prt, where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.

In this case, the principal is R840, the annual interest rate is 12% (or 0.12), and the time is 2 years. Plugging these values into the formula, we get:

I = (R840)(0.12)(2) = R201.6

So the interest on the loan is R201.6.

To find out the total amount John owes his mom, we need to add the interest to the principal:

Total amount owed = Principal + Interest = R840 + R201.6 = R1041.6

Therefore, John owes his mom R1041.6 after 2 years.

For more such questions on Interest calculation.

https://brainly.com/question/29011216#

#SPJ11

The cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

In mathematics, an equatiοn is a statement that asserts the equality οf twο expressiοns, typically separated by an equals sign (=). The expressiοns οn either side οf the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) οf the equatiοn.

Let's use variables tο represent the cοst οf each item. Let c be the cοst οf a candle and l be the cοst οf a licοrice stick, and let y be the cοst οf a candy.

Frοm the given infοrmatiοn, we can set up twο equatiοns tο represent the tοtal cοst fοr each persοn:

2c + l = 3.25 (Equatiοn 1)

y + 4l = 2.50 (Equatiοn 2)

We can then sοlve fοr each variable by using algebraic manipulatiοn.

Frοm Equatiοn 1, we can isοlate l by subtracting 2c frοm bοth sides:

l = 3.25 - 2c

We can substitute this expressiοn fοr l intο Equatiοn 2, and sοlve fοr y:

y + 4(3.25 - 2c) = 2.50

y + 13 - 8c = 2.50

y = 2.50 - 13 + 8c

y = 8c - 10.5

Nοw we can substitute the expressiοn fοr y and the expressiοn fοr l intο a single equatiοn tο sοlve fοr c:

2c + (8c - 10.5) = 3.25 + 2.5

10c - 10.5 = 5.75

10c = 16.25

c = 1.625

Sο a candle cοsts $1.625. We can use this value tο find the cοst οf a licοrice stick:

l = 3.25 - 2c

l = 3.25 - 2(1.625)

l = 0.975

Sο a licοrice stick cοsts $0.975. Finally, we can find the cοst οf a candy using the expressiοn we fοund earlier:

y = 8c - 10.5

y = 8(1.625) - 10.5

y = 2.5

Sο a candy cοsts $2.50.

Therefοre, the cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

To learn more about the equations, visit:

https://brainly.com/question/22688504

#SPJ1

Answer:

Step-by-step explanation:

Sorry, i can't heip you

As a result, there is a 6% sales tax.

Percentages is a relative figure used to represent hundredths of a quantity. Because one percent (symbolised as 1%) represents one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Percentile is a related topic in mathematics.

The difference in sales tax is the price of the snowboarder with tax versus the price of the snowboarder without tax.

Sales tax therefore equals $848 - $800 = $48.

We need to multiply the result by 100 to get the sales percentage of tax, which we can then divide by the price of the snowboard before taxes.

Sales tax percentage = (Sales tax / Cost without tax) x 100

= ($48 / $800) x 100

= 0.06 x 100

= 6%

To know more about Percentage visit:

https://brainly.com/question/29306119

#SPJ1

The final answer are 7 fractions of the form (1)/(n), where n is an integer from 2 up to and including 20, that are equivalent to terminating decimals.

Geoff is investigating fractions of the form (1)/(n), where n is an integer from 2 up to and including 20. To find out how many of these fractions are equivalent to terminating decimals, we need to understand what makes a fraction equivalent to a terminating decimal.

A fraction is equivalent to a terminating decimal if the denominator (the bottom number) is a power of 10 (10, 100, 1000, etc.), or if it can be reduced to a fraction with a denominator that is a power of 10. In other words, the denominator must only have factors of 2 and/or 5.

So, we need to find out how many of the numbers from 2 to 20 have only factors of 2 and/or 5.

These numbers are:

- 2 (2^1)
- 4 (2^2)
- 5 (5^1)
- 8 (2^3)
- 10 (2^1 * 5^1)
- 16 (2^4)
- 20 (2^2 * 5^1)

Therefore, there are 7 fractions of the form (1)/(n), where n is an integer from 2 up to and including 20, that are equivalent to terminating decimals.

To know more about investigation fractions refer here:

https://brainly.com/question/5707608#

#SPJ11

When the point (1, 3) is substituted in the equation y = ax, then 'a' i,e slope of the line is 3

If a line passes through the origin, its equation can be written in the form y = mx, where m is the slope of the line.

The slope of a line passing through the origin is the ratio of the change in y to the change in x between any two points on the line.

Here we have  

A line passes through the origin, the equation is in the form y = ax

Given that y = ax passes throgh (1, 3)

So substitute x = 1 and y = 3

=> 3 = a(1)

=> a = 3/1

=> a = 3  

Therefore,

When the point (1, 3) is substituted in the equation y = ax, then 'a' i,e slope of the line is 3.  

Learn more about Equation of lines at

https://brainly.com/question/28476898

#SPJ1

No, the point (1,4) is not a solution of the set of linear inequalities y > 5x + 1 and y ≥ (1/2)x - 1 since the point does not satisfy both inequalities.

To determine if a point is a solution, we can substitute the x and y values of the point into the inequalities and see if they are true.

For the first inequality, y > 5x + 1:
4 > 5(1) + 1
4 > 6
This is not true, since 4 is not greater than 6. So the point (1,4) is not a solution for the first inequality.

For the second inequality, y ≥ (1/2)x - 1:
4 ≥ (1/2)(1) - 1
4 ≥ 0.5 - 1

4 ≥ -0.5

This is true, since 4 is greater than -0.5.

But since the point does not satisfy both inequalities, it is not a solution for the set of linear inequalities.

Learn more about linear inequalities here: https://brainly.com/question/11897796.

#SPJ11

Answer:

Step-by-step explanation:

ISSA PARADE INSIDE MY CITY YEAHHHHH