Work out an expression for the nth term of the quadratic sequence
2, 17, 40, 71
Give your answer in the form
an^2 + bn + c
where a, b and c are constants.
I

Answer: The teacher will receive 96 pencils

Step-by-step explanation:

1.) You take the amount of packs she ordered and multiply it with the amount pencils in each pack. (12x8)

The domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

From the graph, vertex is (h, k)=(0, 4) and (x, y)=(2, 0)

Here, y= a(x - h)² + k

0=a(2-0)+4

-4=2a

a=2

Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get

y=2(x-0)²+4

y=2x²+4

So, f(x)=2x²+4

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: [4,∞),{y|y≥4}

Now,

(a) f(-3)= 2(-3)²+4=18

(b) f(2)= 2(2)²+4=12

(c) f(0)= 2(0)²+4=4

(d) f(3)= 2(3)²+4=18

Therefore, the domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

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Answer:

third law of motion

Step-by-step explanation:

i learned this in the beginning of seventh grade !

Answer:

the 2nd law of motion is the answer. Because as the ball continues to move another force must be applied for the ball to stop in motion.

The domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

Now, According to the question:

What are the domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

Y = 4x²

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (-∞, ∞)

Set-Builder Notation:  {x | x ∈ R}

The range is the set of all valid y values: [0, ∞)

Set-Builder Notation: {y | y ≥ 0}

Hence, the domain and range of function Y = 4x² are:

Domain: (-∞, ∞) {x | x ∈ R}

Range: [0, ∞) {y | y ≥ 0}

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The complete question is this:

What is the domain of the function Y = 4x²

Answer:

he walked 56 more than rico

Jackie spends 15 minutes running every day.

Part A: The relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day can be represented by the following pair of linear equations:

Equation 1: x + y = 55 (This equation represents the total amount of time Jackie spends running and dancing every day, which is 55 minutes)

Equation 2: y = x + 25 (This equation represents the relationship between the number of minutes Jackie runs and the number of minutes she dances, which is that she dances 25 minutes longer than she runs)

Part B: To find out how much time Jackie spends running every day, we can substitute the second equation into the first equation:

x + (x + 25) = 55

2x + 25 = 55

2x = 30

x = 15

Therefore, Jackie spends 15 minutes running every day.

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Answer:

[tex]12 \sqrt{6} [/tex]

Step-by-step explanation:

If each side of the regular hexagon measures 8cm then the area of the given hexagon is 96√3 square centimeters. 96√3 simplified is 12√6.

Answer:

a) 15.375

B) at a minimum 65 dollars

Step-by-step explanation:

part one you multiply the pound by the price and get your answer and part 2 its a double digit number so you find the minimum

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here.

Given : Cosθ = -1/6

To find : Tanθ

Since cosθ is in second quadrant

Thus,

Cosθ = B/H

According to pythagoras theorem,

H²= B²+ P²

=> 6² = 1² + P²

=> 36-1 =P²

=>P= √35

So ,

value of Tanθ comes out to be

=> tanθ = - √35 /1

=>tanθ = - √35

Therefore , the solution to the given problem of trigonometry comes out to be tanθ = - √35 .

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Answer:

Sue travels for 3 hours and a half

Sue stays stationary for 2 hours and a half

Step-by-step explanation:

Everytime the curve climbs, it means Sue is travelling. Everytime the curve stays flat, it means Sue is stays stationary. It remains to count up the total for both categories, with one square being 30 minutes.

Sue spends 3.5 hours on travelling and 2.5 hours stationary.

It is a graph which shows how far an object has travelled in a given time.

It is graph of function which represents there is no change in the function value or the function value is constant.

"subtract old value from new value."

For given example,

Given distance-time graph represents a journey made by Sue.

Let 't' represents the travelling time and 's' represents the stationary time.

If we observe the graph,

from 2 pm to 3 pm Sue travelled 5 miles

⇒ t1 = 3 - 2

⇒ t1 = 1 hour

from 3.5 pm to 4 pm she travelled 10 miles

⇒ t2 = 4 - 3.5

⇒ t2 = 0.5 hour

from 5 pm to 6.5 pm she travelled 15 miles

⇒ t3 = 6.5 - 5

⇒ t3 = 1.5 hours

from 7.5 pm to 8 pm she travelled 5 miles

⇒ t4 = 8 - 7.5

⇒ t4 = 0.5 hour

So, the total travelling time would be,

⇒ t = t1 + t2 + t3 + t4

⇒ t = 1 + 0.5 + 1.5 + 0.5

⇒ t = 3.5 hours

Also, Sue spends stationary from 3 pm to 3.5 pm

⇒ s1 = 3.5 - 3

⇒ s1 = 0.5 hour

She spends stationary from 4 pm to 5  pm

⇒ s2 = 5 - 4

⇒ s2 = 1 hour

She spends stationary from 6.5 pm to 7.5 pm

⇒ s3 = 7.5 - 6.5

⇒ s3 = 1 hour

So, the total stationary time would be,

⇒ s = s1 + s2 + s3

⇒ s = 0.5 + 1 + 1

⇒ s = 2.5 hours

Therefore, Sue spends 3.5 hours on travelling and 2.5 hours stationary.

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Step-by-step explanation:

We are going to start by working out the interior angles so first of all to work out the interior angle we used the formula: num of sides - 2 * 180 for the sum of degrees in a shape.

Lets test this formula.

Lets say we have a square it has 4 sides 4-2 = 2 *180 = 360 this is correct,meaning we can trust this formula.

Now lets put it to use.

Octagon has 8 sides - 2 = 6.

6 * 180 = 1080

Pentagon has 5 sides - 2 = 3

3 * 180 = 540

Another Pentagon 5 sides - 2 = 3

3 * 180 = 540

We have to find out a single angle because it is one side that joins to the other, also if it is a perfect fit then all the single angles must add up to 360.

1080/8 sides = 135 degrees

540 / 5 sides = 108 degrees

540 / 5 sides = 108 degrees

We add these up,

135 + 108 + 108 = 351 which cannot be a possible fit because we need 360 degrees.

Hope this helps

Answer:

c=8

c=100

Step-by-step explanation:

55

11 = 20% × y

11 = 20/100 × y

multiply both sides by 100 and divide both sides by 20

y = 11 x 100/20

y = 11 × 100 ÷ 20

y = 55

Answer:

5 degrees

Step-by-step explanation:

Corresponding angles in a transversal are congruent. This can be proved by using the alternate exterior angles theorem, which would make these two angles alternate interior angles. With this, we can form a new equation.

Solve Algebraically

5x+23=7x+13

5x+10=7x

10=7x-5x

10=2x

Answer:

y = -1

Step-by-step explanation:

In a sense this is a trick question.  Notice that the y-coordinates of these two points are the same:  -1.  That tells us that the line is a horizontal one with equation y = -1.  Nothing further to do here.

Answer:

Mean: 20

Median: 20

Mode: 20

Range: 20

Step-by-step explanation:

Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

Answer:

P = 12.50 + 1.25t

Step-by-step explanation:

To find an equation to represent the price of a pizza, we need to first figure out the original price of a pizze.
Since the price is 16.25 dollars, and there are 3 toppings, each of which cost 1.25, the original price would be:

16.25 - 3(1.25) = 12.50

Thus, we can represent the cost of a pizze with toppings as:
P = 12.50 + 1.25t, where P = Price and t = amount of toppings.

Hope this helps!

Answer:

1. MAD for Jada's data set = 1

Step-by-step explanation:

Mean Absolute Deviation = sum of the distances of each data value from the mean ÷ number of data value

Jada's data set is given as: 4, 4, 4, 6, 6 ,6

Mean = 5

✔️Find the distance between each data value form the mean

4 = |4 - 5| = 1

4 = |4 - 5| = 1

4 = |4 - 5| = 1

6 = |6 - 5| = 1

6 = |6 - 5| = 1

6 = |6 - 5| = 1

✔️Find the sum of the distances of each data value from the mean

1 + 1 + 1 + 1 + 1 + 1 = 6

✔️Find the MAD:

MAD = 6/6

MAD = 1

Using simple unitary method and with the total and per unit value provided, The answer is 8 boxes maximum can be bought.

The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.

The unitary method is a useful tool for solving problems involving units of measurement, it simplifies the problem and improves understanding of conversions. It also helps to develop critical thinking skills and is a useful tool for problem-solving in a variety of subjects.

each box costs  = 2.5

total money =20

maximum that can be bought = 20/2.5 =8

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The perimeter of rectangle could be  50.6 if a rectangle has an area of 7. 5 and One of the sides is 0. 3m in length.

What is Area of rectangle ?

area of rectangle could be the product of its sides that is length and breadth.

Given the area of rectangle is 7.5

one of its side, length = 0.3

let other side be x .

area = length*breadth

7.5 = 0.3 * x

x = 25

hence , other side could be 25.

perimeter of rectangle = 2 (length+breadth)

= 2 * (25+0.3)

= 2 * (25.3)

= 50.6

Hence, The perimeter of rectangle is 50.6

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Answer:

2,000(1.04)t

Step-by-step explanation:

To determine this answer, you would use the formula initial value (1 + interest) times the number of years. This would equal 2,000(1.04)t.

Answer:

Which expression represents the growth of an investment of $2,000 at 4% per year for a period of t years?

Step-by-step explanation:

Edge 2021

Answer:

the percentage is 62%

Step-by-step explanation:

Answer:

10 4/15

Step-by-step explanation:

(4+5)+(2/3+3/5)

9+(2/3+3/5)

9+19/15

9+1 4/15

10+4/15

10 4/15

Answer:

b^4

Step-by-step explanation:

you would just subtract the variables things

b^10-b^6

subtract 10-6 and keep the b

b^4 iis the answer we are learnng these in school right now

Answer:

b^10/b^6= b^4

Step-by-step explanation:

when dividing numbers with exponents, you have to subtract the numerator's exponent by the denominator's exponent to simplify the equation.

By plot in graph, we get Y=6 and x=-1 is perpendicular lines.

Parallel lines are lines in a plane that are always the same distance apart and never intersect. They are coplanar lines that do not intersect each other, and they have the same slope.

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, they are lines that are at a 90-degree angle to each other. The slope of perpendicular lines are opposite reciprocals of each other, meaning that if one line has a slope of m, the other line will have a slope of -1/m.

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On solving the provided question, we can say that the sum of the two expressions will be -4n + 6

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

let the two expression be

-4nand 6 and the sum will be -4n + 6

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Answer:

9.5

Step-by-step explanation:

delta math

Answer:

4 months

Step-by-step explanation:

y=179+40x.  Equation 1

y=31+77x.     Equation 2

179+40x=31+77x. Replace y from equation 1 and replace y of equation 2

148=37x

4=x