Fully factorise the following expression in a suitable factor form x^2+6x+8

The analysis of the number of runners, can be presented as follows;

a. The sequence is a geometric sequence

b. r(3) = 72, which indicates that the number of runners after the third week is 72

c. r(6)/r(5) = (2/3)

d. The recursive rule for r(w) is that the number of  runners in a week is (2/3) × The number of passengers in the previous week

A sequence is an ordered list of items.

The number of passengers currently in the  running club = 243

The amount by which the  number reduces each week =  2/3 the number in the previous week.

a. Therefore, the number of passengers each week can be presented as follows;

First week = 243

Second week = (2/3)  × 243 =  162

Third week = (2/3)³ ×  243

Therefore, the number  of runners in the nth week is; an= (2/3)ⁿ × 243, which is a geometric sequence

b. The number of runners in the wth week, r(w) =  2/3)^w × 243,

Therefore; r(3)  = (2/3)³ × 243  = 72

The meaning of the value is that the number of runners in the third  week, r(3) =  72 runners

c. r(6))/(r(5)) can be obtained as follows;

r(6) = (2/3)^6 × 243

r(5) = (2/3)^5 × 243

r(6)/r(5) = ((2/3)^6 × 243)/( (2/3)^5 × 243) = (2/3)

d. The recursive formula can be obtained as follows;

The number of passengers in a specified week =  (2/3) × The number of passengers in the previous week

r(w + 1) = (2/3)^w  ×  243

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[tex](\sqrt[9]{7} = 7^{1/9}[/tex]  is true about the value of n in polynomial.

What is a polynomial, simply put?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

                                     A polynomial function is a function that can be expressed in the form of a polynomial. The definition can be derived from the definition of a polynomial equation. A polynomial is generally represented as P(x). The highest power of the variable of P(x) is known as its degree.

 the value of n is 1/9 because  ([tex](\sqrt[9]{7} )^{9}[/tex]  = 7¹

          and ( [tex](7^{1/9})^{9}[/tex]  = 7¹

                [tex](\sqrt[9]{7} = 7^{1/9}[/tex]

 is correct option .

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Answer:

what am i suppose to answer !!!!

Answer:

he has 180 left

Step-by-step explanation:

because 224-44=180

Answer:

$6981

Step-by-step explanation:

If you put $6981 in a deposit and your interest rate is 8.5% monthly it will give you $2,019.62 which then means your total will be $9,000.62

Hope this helped :) please mark as brainlyist

With the infοrmatiοn prοvided, the sοlutiοn is 2x + y = 9.

A mathematical equatiοn, including such 6 x 4 = 12 x 2, states that twο numbers οr values are equivalent. a meaningful nοun. An equatiοn is used when twο οr even mοre factοrs must be cοnsidered jοintly in οrder tο understand οr explain the whοle situatiοn.

Given:

Slοpe οr gradient οf line = -2

The lοcatiοn where the line passes = (1,7)

Equatiοn οf a line thrοugh (h,k) with a slοpe οf m:

(y - k) = (x -h) m

Equatiοn οf a line thrοugh (1,7) with a slοpe οf (-2): -

⇒ (y - 7) = (x - 1)(-2)

⇒ y - 7 = - 2x + 2

⇒ y = -2x + 2 + 7

⇒ y = -2x + 9

οr

⇒2x + y = 9

Verificatiοn οf respοnse:

We may check οur respοnse by substituting (1,7) in the fοrmula 2x+y=9.

⟹ LHS = (2×1)+7

⟹ LHS = 2+7

⟹ LHS = 9

Therefοre , LHS = RHS.

Alsο, yοu can use the equatiοn tο determine the gradient οr slοpe and cοnfirm yοur sοlutiοn.

⟹ Slοpe is equal tο -(cοefficient οf x)/ (cοefficient οf y)

⟹ Slοpe = - 2 /1

⟹ slοpe = -2

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Answer:

322 ft^2

Step-by-step explanation:

((a+c)*v )/2 35+11 *14 /2

Answer:

onomatopoeia

Step-by-step explanation:

Answer:

Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.

Step-by-step explanation:

We can use the ratio of 4:3:2 to find the total number of parts:

4 + 3 + 2 = 9

This means that the money will be divided into 9 equal parts, and Ayanda will get 4 parts, Zipho will get 3 parts, and Palesa will get 2 parts.

To find the value of one part, we divide the total amount by 9:

45,360 / 9 = 5,040

Therefore, one part is worth R5,040.

Now we can find the amount of money each person will receive by multiplying their respective parts by the value of one part:

Ayanda: 4 parts × R5,040/part = R20,160

Zipho: 3 parts × R5,040/part = R15,120

Palesa: 2 parts × R5,040/part = R10,080

Therefore, Ayanda will receive R20,160, Zipho will receive R15,120, and Palesa will receive R10,080.

Answer:

6,000 Video Games

Step-by-step explanation:

To find out how many video games Cloey sold on Sunday, we need to add the number of video games she sold on Friday and Saturday and then subtract that total from the total number of video games she sold over the three days:

Total number of video games sold on Friday and Saturday = 3,878 + 8,999 = 12,877

Total number of video games sold over the three days = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday)

We know that the total number of video games sold over the three days is the sum of the number sold on Friday and Saturday plus the number sold on Sunday. We can rearrange this equation to solve for the number sold on Sunday:

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Substituting in the values we know, we get:

Number sold on Sunday = (number sold on Friday) + (number sold on Saturday) + (number sold on Sunday) - (number sold on Friday) - (number sold on Saturday)

Number sold on Sunday = Total number sold over three days - Number sold on Friday and Saturday

Number sold on Sunday = (3,878 + 8,999 + X) - 12,877

Number sold on Sunday = X - 0

Simplifying this expression, we get:

Number sold on Sunday = 6,000

Therefore, Cloey sold 6,000 video games on Sunday.

The equations that represent a linear functions are:

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

The list of options

As a general rule

Linear functions are functions with a degree of 1

Using the above as a guide, we have the following equations with a degree of 1:

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Answer:

True

Step-by-step explanation:

(2 + 3) + 5 = 2 + (3 + 5)

5+5=2+8

10=10

this statement is true

Answer:

77 ft long.

Step-by-step explanation:

Explanations are clearer in the photo I sent. These are actual photos I have had screen shot. Since, I even commented saying answer "50" is wrong and now this is the proof of a real answer.

The total amount of water in buckets that contain more than one quart is 39 gallons.

Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.

According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.

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The total amount of water in buckets that contain more than one quart is 39 gallons.

Amount is a noun that refers to a quantity or number of something. It can also be used to refer to a sum of money. Amount is commonly used in mathematics, banking, and accounting to represent a specific quantity or monetary figure. Amounts are often expressed as a whole number, fraction, or decimal. Amounts can be expressed in various ways, such as in dollars, euros, pounds, or other forms of currency. Amount is also used to describe the size or extent of something, such as an amount of time or effort.

According to the line plot, buckets with numbers 1, 2, 3, 4, 6, 8, 12, 14, 15, and 17 all contain more than one quart of water, for a total of 39 gallons. Bucket 5 has one quart exactly, and the other buckets contain less than one quart.

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None of the given options match this result, so the answer is none of the above.

What is ratio ?

A ratio is a quantitative comparison of two or more quantities or values, expressed as the quotient of one divided by the other. It is usually represented in the form of a fraction, using a colon, or by the word "to". For example, if there are 6 boys and 4 girls in a class, the ratio of boys to girls can be represented as 6:4, or 6/4, or 6 to 4. Ratios are often used to compare the relative sizes or amounts of two or more things, such as ingredients in a recipe, parts in a machine, or components in a financial statement.

The rate for a ratio of the two different quantities is the number of one quantity for each unit of the other quantity. In this case, the rate is the number of puppies per litter.

Mallory had 13 puppies in 2 litters, so the rate is:

13 puppies / 2 litters = 6.5 puppies per litter

None of the given options match this result, so the answer is none of the above.

Therefore, none of the given options match this result, so the answer is none of the above.

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Answer:

Let's call the length of the rectangular room "L" and the width "W". We know that the area (A) of the room is 80 square feet, so:

A = L x W

We also know that the perimeter (P) of the room is 36 feet. The formula for the perimeter of a rectangle is:

P = 2L + 2W

We can use the fact that P = 36 to solve for one of the variables in terms of the other. Solving for W, we get:

W = (36 - 2L) / 2

Now we can substitute this expression for W into the formula for the area:

A = L x ((36 - 2L) / 2)

Simplifying, we get:

80 = (L x (36 - 2L)) / 2

Multiplying both sides by 2, we get:

160 = L x (36 - 2L)

Expanding the right side, we get:

160 = 36L - 2L^2

Rearranging and simplifying, we get a quadratic equation:

2L^2 - 36L + 160 = 0

We can solve this quadratic equation using the quadratic formula:

L = [36 ± sqrt(36^2 - 4(2)(160))] / (2(2))

Simplifying, we get:

L = [36 ± sqrt(576)] / 4

L = [36 ± 24] / 4

L = 15 or L = 5

Since the length cannot be smaller than the width, we can disregard the solution L = 5. Therefore, the length of the rectangular room is 15 feet, and the width can be found using the formula we derived earlier:

W = (36 - 2L) / 2 = (36 - 2(15)) / 2 = 3

So the length of the room is 15 feet and the width is 3 feet.

The variable cost for x doughnuts produced is 0.25x.

What is variable cost?

Costs that vary according on how much of an item or service a company produces are known as variable costs.

The fixed cost for the company is $25,000, which is a constant amount that does not depend on the number of doughnuts produced. The variable cost, on the other hand, is the cost that varies with the number of doughnuts produced.

Since it costs $0.25 to produce each doughnut, the variable cost for x doughnuts can be calculated as 0.25x.

Therefore, the variable cost for x doughnuts produced is 0.25x.

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The total cost of the driver to fill the fuel is given by A = $ 251.72

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total cost of the driver to fill the fuel be A

Now , the value of A is

Let the total capacity of the fuel tank be = 28 Liters

Now , the driver fills half the tank

So , the amount of fuel to be filled = 28 / 2 = 14 Liters

Now , the cost of fuel per Liter = $ 17.98

And , the total cost of the driver to fill the fuel A = amount of fuel to be filled x cost of fuel per Liter

On simplifying the equation , we get

The total cost of the driver to fill the fuel A = 14 x $ 17.98

The total cost of the driver to fill the fuel A = $ 251.72

Hence , the equation is A = $ 251.72

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Answer:

the largest area that can be enclosed with 700 feet of fencing is 61,250 square feet

Step-by-step explanation:

Option C is correct, x=-1/12y² represents the equation of the parabola.

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane

The given curve represents a parabola

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

it's a sideway parabola (expressed as x=......) plus it does not have any x<0 as you can see in the graph,

so x must be always positive for every value of y

Hence, option C is correct, x=-1/12y² represents the equation of the parabola.

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Check the picture below.

Answer:

7pts=4.20332

i think

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the center and radius of the circle represented by the equation:

x^2 + y^2 - 8x - 20y + 52 = 0

We can start by completing the square for both x and y terms as follows:

(x^2 - 8x) + (y^2 - 20y) + 52 = 0

(x^2 - 8x + 16) + (y^2 - 20y + 100) + 52 = 16 + 100

(x - 4)^2 + (y - 10)^2 = 64

Thus, the equation can be rewritten in the standard form of the circle as:

(x - 4)^2 + (y - 10)^2 = 8^2

Therefore, the center of the circle is (4, 10), and its radius is 8 units.

Step-by-step explanation:

x² + y² - 8x - 20y + 52 = 0

the standard circle equation is

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle, and r is the radius.

now, we need to find the squared terms in the original equation.

x² and y² are clearly from the (x - h)² and (y - k)².

and then

(x - h)² = x² - 2hx + h²

-2hx = -8x

2h = 8

h = 4

(y - k)² = y² - 2ky + k²

-2ky = -20y

2k = 20

k = 10

h² + k² = 16 + 100 = 116

116 - r² = 52

r² = 64

r = 8

so, the center is (4, 10), the radius is 8.

Answer:

Step-by-step explanation:umm

All of the sections of a circle graph that each represent 1/8 of the entire circle include the following:

C. fruit.

D. yogurt.

In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Since there were 400 students surveyed, their preference can be calculated as follows:

Muffins = 70/400

Pretzels = 70/400

Fruit = 80/400 = 1/8

Yogurt = 80/400 = 1/8

Cheese and crackers = 80/400 = 1/5

Granola bars = 80/400 = 1/5.

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Answer:

8 yo

Step-by-step explanation:

A = age of Anthony

K = age of Kadeesha

Formulate equations based on the information given:

K = A + 1

A² + 2K = 82

Solve the simultaneous equations by substitution:

A² + 2(A + 1) = 82

A² + 2A + 2 = 82

A² + 2A - 80 = 0

(A + 10)(A - 8) = 0

A + 10 = 0 → A = -10

A - 8 = 0 → A = 8

Anthony can't be -10yo, so he is 8yo

Kadeesha is, therefore, 9yo

The values of are;

1. angle WXU = 104°

2. angle XUV = 109°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle.

The sum of opposite in angle Ina cyclic quadrilateral is 180°

angle v = 152/2 = 76°

therefore angle XWV = 180-(76) = 104°

angle XUV = 180-71 = 109°

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According to the information, the best measure to describes the typical length of time that a tent will stay inflated is mean (average).

To identify the option that corresponds to the best measure to describes the typical length of time that a tend te stay inflated we have to analyze data and then we have to select the best option. In this case the most adequated measure is mean because it allow is to establish the average of time that a tent stay inflated. According to the above, this is the mean of the time that a tent will stay inflated

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Answer:

Step-by-step explanation:

Let's assume that the normal air pressure in the Florida Keys before the hurricane is represented by the variable 'p'. The inequality that could be used to find 'p' based on the given information is:

p - 121 > n

This inequality states that the difference between the normal air pressure 'p' and the air pressure during the hurricane ('n') is greater than 121 millibars. By rearranging this inequality, we can solve for 'p':

p > n + 121

Therefore, the normal air pressure in the Florida Keys before the hurricane was greater than the air pressure during the hurricane plus 121 millibars.