Factor higher degree polynomials

(x^2 - 4) (x^2 + 6x + 9)

The type of rule that can be used to find any number of terms in sequence without knowing the previous term is called the Explicit rule formula.

The formula that determines the sequence's nth term is the explicit rule of an arithmetic sequence.

Using explicit formulae, one can compute any term in a series without first determining the value of the terms that came before it.

Therefore, we can conclude that the type of rule that can be used to find any number of terms in sequence without knowing the previous term is called the Explicit rule formula.

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Answer:

  $0.49 per soda

Step-by-step explanation:

The cost per soda is found by dividing the cost by the number of sodas.

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  $5.86/(12 sodas) = $0.48833.../soda ≈ $0.49/soda

The unit rate is $0.49 per soda.

The time it will take the ride to reach the floor is  77.29 seconds

These are equations that has a leading  degree of 2.

Given the function that represents the height of the roller coaster

h(t) = –0.086t^2 + 6t + 50,

At the ground level, h = 0

Substitute

h(t) = –0.086t^2 + 6t + 50,

–0.086t^2 + 6t + 50 = 0

0.086t^2 - 6t - 50 = 0

Factorize

On factorizing, the time it will take the ride to reach the floor is  77.29 seconds

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Answer:

D)  t = 77.29 seconds

Step-by-step explanation:

The height of the rollercoaster at ground level is zero.

Therefore, to find how long it will take riders to pass over the hill and reach ground level, set h = 0 and solve for t.

Set the equation equal to zero:

[tex]-0.086t^2 + 6t + 50=0[/tex]

Solve the equation using the quadratic formula.  

The quadratic formula is a formula that can be used to find the solutions of any quadratic equation, which is an equation of the form ax²+bx+c=0, where a, b, and c are constants and x is the variable.

[tex]\boxed{x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}}[/tex]

In this case:

Substitute these values into the quadratic formula and solve for t:

[tex]t=\dfrac{-6 \pm \sqrt{6^2-4(-0.086)(50)}}{2(-0.086)}[/tex]

[tex]t=\dfrac{-6 \pm \sqrt{36+17.2}}{-0.172}[/tex]

[tex]t=\dfrac{6 \pm \sqrt{53.2}}{0.172}[/tex]

[tex]t=-7.52228495..., \;\; 77.2897268...[/tex]

As time is positive only, t = 77.29 seconds (2 decimal places).

The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6

The solution sets on the number line are given as:

x = {-8, -4}

Calculate the average of the solutions

Mean = (-8 - 4)/2

Mean = -6

Calculate the difference of the solutions divided by 2

Difference  = (-4 + 8)/2

Difference = 2

The absolute value equation is the represented as:

|Difference - x | = Mean

Substitute known values

|2 - x| = -6

Hence, the absolute value equation is |2 - x| = -6

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Answer:

|b+6|=2

Step-by-step explanation:

Option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

As we know, a convex heptagon is a polygon with seven sides, seven internal angles, and seven vertices, which means that a convex heptagon has seven sides.

A convex heptagon is a polygon that has 7 sides. No angles go inside of the shape.

Thus, option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.

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Answer: the first option

Step-by-step explanation:

The equation that represents the profit function is P(x) = 5x - 260

The given parameters are:

C(x) = 3x^2 - x + 200 --- cost function

R(x) = 3x^2 + 4x - 60 --- revenue function

The profit function is calculated as:

P(x) =R(x) - C(x)

This gives

P(x) = 3x^2 + 4x - 60 - 3x^2 + x - 200

Evaluate the like terms

P(x) = 5x - 260

Hence, the equation that represents the profit function is P(x) = 5x - 260

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All else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal (finance charge) over a year.

A credit card finance charge is the fee associated with using credit.

Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.

                   Card A         Credit B

APR              22%               25%

Annual fee  $40                $0

To calculate the balance required, the required equation is

= 22%x + $40 = 25%x

Where x = required balance

Thus,

= 0.22x + $40 = 0.25x

= $40 = 0.03x (0.25x - 0.22x)

= 0.03x = $40

x = $40/0.03

x = $1,333.33

Credit card A has an APR of 22% and an annual fee of $40, while credit card B has an APR of 25% and no annual fee.

Thus, all else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal over the course of a year.

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Answer:

the answer is [9÷3+6]×

Step-by-step explanation:

the Answer is [9÷3+6]×3 =25

Point D would be translated to the point (0, 5).

Translation is an aspect of geometry that moves plane shapes from one point to another along the cartesian coordinates without changing the form in which the shape exists.

Analysis:

Point D is at (0,0) if it is translated up from 0,0 the point D moves 5 units along the y-axis while x axis remain same. So that the new point of D becomes (0,5)

In conclusion, the point D will land at point (0,5)

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Answer: 1.5 or 1 1/2

Step-by-step explanation:

He payed $1.50 for each candy bar

Answer:

Step-by-step explanation:

Answer:

there are 20 while numbers between 32 and 96

Step-by-step explanation:

hope it helps and give me a brainliest

The number of whole numbers that come between 32 and 96 will be 64.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The number of whole numbers that come between 32 and 96 is given as,

⇒ 96 - 32

⇒ 64

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Answer:

a)  30 square units

b)  36 square units

c)  18 square units

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Base = 10

Height = 6

⇒ Area = 1/2 × base × height

            = 1/2 × 10 × 6

            = 30 units²

⇒ Area = 1/2 × base × height

            = 1/2 × 12 × 6

            = 36 units²

⇒ Area = 1/2 × base × height

            = 1/2 × 6 × 6

            = 18 units²

Answer:

O the amount of plant food used each day

Step-by-step explanation:

O the initial amount of plant food the length of time it takes for Ryan to use all the plant food is the y-intercept therefore wrong.

O the length of time it takes for the height of the plant to reach 72 centimeters​

Answer:

the function is only increasing.

Step-by-step explanation:

Answer:

a) 1/5 bucket = 1 gallon

b) 8.4 buckets = 1 barrel

c) 5376 fl oz per barrel

Step-by-step explanation:

a) From the given information, 1 bucket = 5 gallons. This means 1/5 of a bucket is 1 gallon.

b) From the given information, 8.4 buckets = 1 barrel. This seems to be in the form that the question is asking for. If the question was asking how many barrels were in a bucket the answer would be 1/8.4 barrels = 1 bucket.

c) From the previously determined conversion factors, we can take ounces to barrels by converting barrels down to gallons.

1/8.4 barrels = 1 bucket; 1/5 bucket = 1 gallon; 1 gallon = 128 fluid ounces

We need to set up a series of fractions that use these factors:

[tex]\frac{128 fl oz}{1 gallon}*\frac{1 gallon}{1/5 buckets}*\frac{1 bucket}{1/8.4 barrels}[/tex]

These fractions can be simplified to [tex]\frac{128 fl oz}{1 gallon}*\frac{5 gallon}{1 bucket}*\frac{8.4 buckets}{1 barrel}[/tex]

Multiply the fractions: 5376 fl oz per barrel

(Note that the units cancel out in the fractions so that only fluid ounces per barrel are left.)

Answer:

Table D

Step-by-step explanation:

I have all of the tables listed below and the correct one circled! I used to tutor my cousin about this topic!

I hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!

Have a great day!

:)

The 4th table in the option is the correct one.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars.

The given equation is y = 6x + 50

Put x = 0

y = 50

Put x = 5

y = 80

Put x = 10

y = 110

Put x = 15

y = 140

Creating the table,

                 x                                                                 y

                 0                                                                50

                 5                                                                80

                 10                                                               110

                 15                                                               140

Hence, we get the table.

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The number of books she would have completed in one day will be 2 books.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

Emily completed reading 24/3 books in 32/4 days

Emily completed 8 books in 4 days. The number of the books will be calculated by using the expression below:-

4 days = 8 books

1 day = 8 / 4 = 2 books

Therefore the number of books she would have completed in one day will be 2 books.

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Answer:

m<A = 120

m<BCD = 120

m<DEC = 30

m<BFE = 90

Step-by-step explanation:

m<A is 120 cause all internal angles equal 720 added together in hexagons. 720 ÷ 6 = 120

m<BCD is 120 cause regular hexagons have eqaul angles

m<DEC is 0 cause total of the angle of triangle of triangle EDC is 180 where m<D = 120 which leaves m<E + m<C = 60 since they are equal we can combine them to m<E • 2 = 60. Divide and we get 30

m<BFE =  90 cause m<AFB = 30 and m<AFE = 120 subtract 120 and 30 to get 90

Answer:

x=5    y=3      z=5

Step-by-step explanation:

The coefficient is the number in front of the variable

Answer:

Step-by-step explanation:

The coefficient in an expression is the multiplier of a designated part of a term of the expression.

__

The given expression is

  5z -2 +6x +3y

It consists of four (4) terms, added together. One term is a constant, -2. The others each have a single variable that is multiplied by a constant. When we ask for the coefficient of the variable, we are asking for the value of that constant multiplier.

The term containing x is 6x. The multiplier of x in that term is 6, so we say ...

  the coefficient of x is 6.

The term containing y is 3y. The multiplier of y in that term is 3, so we say ...

  the coefficient of y is 3.

The term containing z is 5z. The multiplier of z in that term is 5, so we say ...

  the coefficient of z is 5.

__

In an expression such as πr²h, different parts of the expression will have different coefficients. If we ask for the coefficient of the expression, we are generally asking for the constant: π. (The Greek letter pi is the symbol used to represent the irrational constant ratio between the circumference and diameter of a circle. Is is about 3.1415926535....)

If we ask for the coefficient of h, we are asking for the product (πr²) that multiplies h in this expression. Similarly, the coefficient of r² is (πh). Note that we have specified a "designated part" of the expression for which we want the coefficient. This is important when we are solving equations.

__

The commutative property of multiplication means that parts of a product can be written in any order. That is, 5·z is the same product as z·5. When the constant and variable parts of the expression can be unambiguously identified, the order does not matter. In some cases, a constant coefficient may come in several parts: 3z·5·2 has a z-coefficient of 30, for example.

See below for a case where there may be some ambiguity.

__

In the expression r², the constant 2 that comes after the variable, written as a superscript, is called an "exponent," not a coefficient. Often on Brainly, and sometimes in curriculum materials, you will see this written as r2, because superscripts do not get properly rendered. If you're writing this in plain text, the form r^2 is preferred.

Answer:

2.5 kilometers

Step-by-step explanation:

One kilometer is 1000 meters

To convert from metres to kilometers, we divide by 1000

2500 ÷ 1000 = 2.5km

Step-by-step explanation:

t = 20n + 15

t = 80

80 = 20n + 15

65 = 20n

n = 65/20 = 13/4 = 3.25 hours

Answer:

Area: 113cm²

Circumference: 37.7cm

Step-by-step explanation:

to find area use the formula πr², π being Pi (3.14) and r being radius

radius = 6cm (half the diameter)

3.14 × 6² = 113.04cm²

to find the circumference use the formula πd

diameter = 12cm

3.14 × 12 = 37.68

Answer:

2,3,7,2,5

Step-by-step explanation:

When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.

42 is equal to 6 and 7 and 6 is 2 times 3

2,3,7 is prime

10 is 2 times 5

2 and 5 is prime

Answer:

420 = 2² × 3 × 5 × 7

Step-by-step explanation:

The first few prime numbers are:  2, 3, 5, 7, 11, 13, 17, ...

To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:

⇒ 420 ÷ 2 = 210

As 210 is not a prime number, we need to divide again.  Let's try dividing by 2 again:

⇒ 210 ÷ 2 = 105

As 105 is not a prime number, we need to divide again.  105 is not divisible by 2, so let's try dividing it by the next prime number, 3:

⇒ 105 ÷ 3 = 35

As 35 is not a prime number, we need to divide again.  35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:

⇒ 35 ÷ 5 = 7

As 7 is a prime number, we can stop.

Therefore, 420 is the product of all the prime numbers we found together with the final one:

⇒ 420 = 2 × 2 × 3 × 5 × 7

As 2 appears twice, we can write this using exponents:

⇒ 420 = 2² × 3 × 5 × 7

The translation of line AB to line A'B' is valid and the translation rule is (x,y) ⇒ (x - 7, y - 3)

The graph that completes the question is added as an attachment

From the graph, we have:

A = (3,9) and B = (5,6)

A' = (-4,6) and B' = (-2,3)

Subtract the x and y coordinates of A' from A and B' from B.

So, we have:

AA' = (3 + 4, 9 - 6)

AA' = (7, 3)

BB' = (5 + 2, 6 - 3)

BB' = (7, 3)

See that:

AA' = BB' = (7, 3)

This means that the line AB is translated 7 units left and 3 units down

The translation above means:

(x,y) ⇒ (x - 7, y - 3)

Recall that:

A = (3,9) and B = (5,6)

So, we have:

A' = (3 - 7, 9 - 3)

A' = (-4, 6)

Also, we have:

B' = (5 - 7, 6 - 3)

B' = (-2, 3)

Hence, the translation is valid

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Answer:

she will need 728 pounds to buy 28 cans but she only has 10 pounds so she doesn't even have enough for 1 can of soda

Answer:

C.) The variable x represents the independent variable

Step-by-step explanation:

The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.

A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.

B.) is incorrect because "x" is the input.

D.) is incorrect because "x" is the input.