the shorter leg of a right triangle is 8 less than the hypotenuse. the longer leg is one less than the hypotenuse. find the perimeter

The polynomial is:

f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)

Let's assume the leading coefficient is A, we know that the degree is 4, the y-intercept is 40, and we have the roots (-5, 4, 1, 1)

Then the polynomial is:

f(x) = A*(x + 5)*(x - 4)*(x - 1)*(x - 1)

Now we use the fact that the y-intercept is 40, so we have:

f(0) = 40 = A*(0 + 5)*(0 - 4)*(0 - 1)*(0 - 1)

        40 = A*-20

        40/-20 = A = -2

Then the polynomial is:

f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)

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The ounces of raisins and peanuts needed for different numbers of serving are :

for 4 serving = 8 raisins and 12 peanuts

for 12 serving = 24 raisins and 36 peanuts

According to the question we have been given that in one number of serving the ratio of number of ounces of raisins to the number of ounces of peanuts is given as :

                               ratio = 2 : 3

We need to find ounces of raisins and peanuts needed for different numbers of serving.

For 4 serving,

              Raisins = 4*2 = 8

              Peanuts = 4*3 = 12

and we see that their ratio = 8/12 = 2/3

For 12 serving,

               Raisins = 12*2 = 24

              Peanuts = 12*3 = 36

and we see that their ratio = 24/36 = 2/3

Hence the ounces of raisins and peanuts needed for different numbers of serving are :

for 4 serving = 8 raisins and 12 peanuts

for 12 serving = 24 raisins and 36 peanuts

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Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Now, firstly refer to the image attached.

Since each large square is one whole, we've been provided with two complete squares, where 4 filled rows and 3 empty rows make up the last entire square row.

According to the third square, the answer is 2.43, i.e., the answer is 2.43 after you multiply to find which of 0.27 and 9 truly equals it, by basic algebra.

The figure is therefore represented by the multiplication equation.

⇒ 0.27 × 9 = 2.43

Hence, Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.

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The given number is a real number.

A real number is a value of a continuous quantity that can be used to indicate a distance along a line in mathematics.

We are given the following in the question:

{natural​ numbers, whole​ numbers, integers, rational​ numbers, real numbers}

π / 108

We have to tell the type of number that describes the given fraction.

Evaluating the value, we have,

0.0290888208666...........

This is not a natural number or a whole number. This is not a rational number.

Since is an irrational number, thus quotient of an irrational number and a rational number is an irrational number.

Thus, it is a real number.

The complete question is given below:-

Choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number. StartFraction pi Over 108 EndFraction.

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AT 25 SQUARE FEET OF FLOORING

CHOOSE WOODY'S HARDWOOD FLOORING

Typically, the price of engineered hardwood flooring is $6 to $10 per square foot, plus $1.75 to $2.20 per square foot for installation. High-quality hardwood flooring typically costs between $6 and $13 per square foot from customers. Your home renovation project could be very stressful. Expectations, timeframes, budgets, and the cost of flooring contractors all need to be harmonized.

There will always be a time when you want to give up on the renovation project. For some reason, finding someone to install your flooring is usually the first step.

1 - 8s + 150 = 6s + 200

      2s = 50

         s= 25 sq.feet

2 - 120 * 8 + 150 = 1110

      120 * 6 + 200 = 920

1110 > 920

so choose woody's hardwood flooring.

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4=8/3

I hope this helps, I think thin is the right answer

Answer:

Step-by-step explanation:

solution of 1/3x=21 is greater than 21.

A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.

Solving the linear equation

x/3 = 21

multiplying  by  3 on  both  sides

x/3 * 3 = 21 * 3

x = 63

→63>21,

that is, solution of the linear equation is greater than 21.

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This shows that she covered 0.4 miles in 10mins

Speed is defined as the rate of change of distance.

If it takes 24 minutes for jana to walk one mile, the rate of Jana is expressed as;

Rate= 24/1 mile

Rate = 24min/mile

In order to determine the distance she walk in 10 minutes, we will have;

Distance in 10min = 10/24

Distance in 10 min = 0.4 miles

This shows that she covered 0.4 miles in 10mins

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Answer:

x = 5

Step-by-step explanation:

Mode: The most frequently occurring data value.

Median: The middle value when all data values are placed in order of size.

Mean: The sum of all data values divided by the total number of data values.

As the mode is the most frequently occurring data value, x must be 3, 4, 5 or 8.

If the mode is 3 or 4, then the data set will be {3, 3, 4, 5, 8} or {3, 4, 4, 5, 8}.  Therefore, the median would be 4.

If the mode is 5 or 8, then the data set will be {3, 4, 5, 5, 8} or {3, 4, 5, 8, 8}.  Therefore, the median would be 5.

Therefore, the median is 4 or 5.

[tex]\boxed{\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]

If x = 4, the mean would be:

[tex]\sf \implies mean=\dfrac{3+4+5+8+4}{5}=\dfrac{24}{5}=4.8[/tex]

If x = 5, the mean would be:

[tex]\sf \implies =\dfrac{3+4+5+8+5}{5}=\dfrac{25}{5}=5[/tex]

Therefore, the only value of x that allows the mean, median and mode to all have the same value is x = 5.

Equation that best models the situation is where c = 11

Living plants are used in phytoremediation technologies to purify contaminated soil, air, and water. According to the definition, it involves "the use of green plants, associated microbes, suitable soil amendments, and agronomic techniques to either contain, remove, or render dangerous environmental toxins harmless." The word is a combination of the Greek words phyto (plant) and remedium (remedy) (restoring balance). Despite being appealing due to its low cost, phytoremediation hasn't been shown to significantly address any environmental issues, at least not to the point where contaminated space has been returned. A cost-effective plant-based method of environmental cleanup called phytoremediation is being proposed. It makes use of plants' capacity to concentrate elements and chemicals from the environment and to detoxify different contaminants. The ability of certain plants, known as hyperaccumulators, to bioaccumulate substances is what causes the concentrating effect. The impact of cleanup is very different. Organic contaminants, which can be destroyed, are typically the main targets for phytoremediation while toxic heavy metals cannot. Several field tests supported the viability of employing plants to clean up the environment.

Let the number of crops needed to remove pollution = c

Since one crop can remove 15 mg of pollution per square meter.

Then, "c" number of crops may remove "15 C" mg of pollutant per square meter.

Now, the total amount of pollution per sq. meter Equals 170 mg

Additionally, it is necessary to reduce pollution to 5 mg per square meter.

Consequently, the equation for the scenario is given by,

Pollutants 'c' crops can remove from the total amount of pollution equal the amount of pollution required, or 170-15c=5.

Upon solving the equation, we get, c= 11.

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The solution of the linear equation:

-x/3 + 4 = 20

Is x = -48

Here we have the linear equation:

-x/3 + 4 = 20

And we want to solve it for x. Which means that we need to isolate x in one of the sides of the linear equation.

Remember that we can perform the same operation in both sides of the equation, so we start by subtracting 4 in both sides, then we get:

-x/3 + 4 - 4 = 20 - 4

-x/3 = 16

Now we can multiply both sides of the equation by -3, then we get:

-3*(-x/3)=  -3*16

x = -48

The solution of the linear equation is x = -48

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The length of the ladder to the nearest tenth of a foot as evaluated by trigonometric ratios is; 12.2ft.

Since the base of the ladder as indicated in the task content is 10 feet away from the bottom of a building's wall, it follows that the set-up in discuss is analogues to a right triangle whose adjacent is 10ft;

Therefore, the length of the ladder which is the hypothenuse can be evaluated as follows;

cos 35° = 10/L

L = 10/cos 35

L = 12.2ft.

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If she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188

For given question,

a basketball player makes approximately 69% of free throws.

So, the probability of success (p) = 0.69

the probability of failure (q) = 0.31

She plays in a game in which she shoots 7 free throws.

So, n = 7

We need to find the probability that she will make all 7.

Using Binomial probability Distribution,

For x = 7,

[tex]P(x = 7) =~ ^7C_7\times (0.67)^7\times (0.31)^{7-7}\\\\P(x=7)= 1\times 0.0606\times 0.31\\\\P(x=7)=0.0188[/tex]

Therefore,  if she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188

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The possible denominators are {3, 9, 11, 33, 99}.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given that a and b are digits, not both nine and not both zero, and the repeating decimal.

⇒ 100x = ab⋅abababab

⇒ x = 0.abababab

Subtract the above equation from 100x = ab⋅abababab,

So  99x = ab

The denominator of this fraction will always be a divisor of 99 when represented in the lowest term = 3⋅3⋅11    

According to this, we have the options in the set. {1, 3, 9, 11, 33, 99}.  

Since a and b both are not both 9 and not both zero the denominator 1 cannot be possible.

Hence, the possible denominators are {3, 9, 11, 33, 99}.

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Answer:

5

Step-by-step explanation:

rs + 14s

(6)(1/4) + 14(1/4)

[tex]\frac{6}{4}[/tex] + [tex]\frac{14}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5

Answer:

5

Step-by-step explanation:

rs + 14s

r = 6

s = 1/4

= 6*1/4 + 14*1/4

= 6/4 + 14/4

= (6+14) / 4

= 20/4

= 5

1.  The elements of the set are {m, I, s, p}

The elements of the set are the letters in Mississippi. Elements cannot repeat themselves.. So the elements of this set would be {m, I, s, p} since all the other letters are just repetitions.

2. Set of months in a year are

{January,February,March,April,May,June,July,August,September,October,November,December}

3. Verbal Descriptions: It is a verbal description of the set is an English sentence to specify a law that allows us to decide the category of objects to be addressed and to determine whether it is in the set for any particular object.

Since, 3, 6  and 9 are divisible by 3 also less than 10.

4.  Verbal description of the set {a,e,i,o,u} is vowels

In English these five alphabets{a,e,i,o,u} are known as vowels .

since the given set contains only vowels.

5. Yes (1,3,5) is the subset of odd integers.

The set of odd integers is the superset containing elements :-

Let A = { 1 , 3 , 5 , 7 , 9 ,..... ,( 2n + 1 ) }

And,

B = { 1 , 3 , 5 }

B is a subset of A because all elements of B lie in A .

6. Yes (a,b,c) is the subset of letters of the alphabet.

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The midpoint of the line segment with the endpoints is (2.4, -1)

The endpoints are given as:

(3.2,2.5) and (1.6,-4.5)

The midpoint of the line segment with the endpoints is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (3.2 + 1.6, 2.5 - 4.5)

Evaluate the sum

So, we have:

Midpoint = 0.5 * (4.8, -2)

Evaluate the products

So, we have:

Midpoint = (2.4, -1)

Hence, the midpoint of the line segment with the endpoints is (2.4, -1)

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Answer:

22.2%

Step-by-step explanation:

Total number of people at the recreation center=81

Number of people swimming=18

=18/81 x 100

=22.22222

Round of to the nearest tenth

=22.2%

The statement ''The average age of the students in a statistics class is 20 years'' describes descriptive statistics.

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Answer:

$167.50

Step-by-step explanation:

Since the state pays 40% of the health insurance, Maggie will have to pay 100 - 40 = 60% of the insurance amount annually

60% = 0.6 decimal

So Maggie pays 0.6 x 6700 = $4,020

Maggie is paid semi-monthly ie 2 paychecks a month

In a year, there are 12 months so Maggie receives 24 paychecks annually

The total insurance amount of 4020 is split over 24 paychecks

So each paycheck deduction will be 4020/24 = $167.50

The absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

According to the question.

We have solutions of a absolute value equation.

As we knoaw that, the non-negative value of a real number x without regard to its sign is known as its absolute value or modulus equation  in mathematics and is indicated by the symbol |x|.

To find the absolute value equation whose solution are x = -10 and x = -5 we need to add some previous steps, which make the equation an absolute value equation.

|(x+10)(x+5)|=0,

x=-10 and x=-5

Hence, the absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.

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Answer:

A) 4

Step-by-step explanation:

First note that m cannot exceed 10 otherwise 100-m² will be negative and √(100-m²) will not be a real number much less an integer

Enumerate all values of m from 0 through 10, find the square, subtract from 100 and see if the result is a perfect square.- we take the square root and see if it is an integer value. The table below details everything. m and n are integers on in 4 cases m = 0, 6, 8 or 10.

Hence the answer is 4 solutions

m   m²    100-m²    √(100-m²)        

0 0 100        10

1 1 99

2 4 96         9.797958971

3 9 91         9.539392014

4 16 84         9.16515139

5 25 75         8.660254038

6 36 64         8

7 49 51         7.141428429

8 64 36         6

9 81 19        4.358898944

10 100 0        0

Answer:

0

Step-by-step explanation:

Answer:

-24r⁵ + 4r⁴ + 18r³ - 22r².

Step-by-step explanation:

-2r² (12r³ − 2r² − 9r + 11)

= -24r⁵ + 4r⁴ + 18r³ - 22r²

Answer:

Step-by-step explanation: Refer to attachment.

To minimize their royal costs to $200, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.

Ratios are numerical relationships between variables that show how much each variable is contained in another.

Ratios are stated in fractions, percentages, or decimals.

Total songs to include in the song = 20

The ratio of Donovan and Beatles = 5:1.5

The number of Donovan songs to include = 15 (20/6.5 x 5)

The number of Beatles songs to include = 5 (20/6.5 x 1.5)

Royalty cost per Donovan song = $11

Royalty cost per Beatles song = $7

Total royalty costs for Donovan and Beatles song = $200 ($11 x 15 + $7 x 5)

Thus, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.

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Aji and Sunshine want to make a CD of songs from the 1960s to donate to their school library to be broadcast during school picnics. Sunshine's parents were big fans of the 60s singer Donovan, and they named her after his song "Sunshine Superman." Aji's folks were devotees of the Beatles. Aji and Sunshine want their CD to consist entirely of songs by Donovan and the Beatles. Because Sunshine is named after a Donovan song, she wants to include at least as many Donovan songs as Beatles songs. Aji agrees. In return, Sunshine agrees to include at least five Beatles songs. 5 1.5 To provide enough variety to make the mix interesting, they decide to include at least 20 songs altogether.

Answer:

Step-by-step explanation:

The collection of current NFL players is well defined and is a set

Step-by-step explanation:

For a collection to be termed as a set, it is necessary that it has distinct objects that are defined.

For example, a set of first 10 natural numbers is

A= [1,2,3,4,5,6,7,8,9,10]

It is well defined and therefore called as set which has first 10 natural numbers as its elements.

Same is the case with the collection of current NFL players.

The collection contains defined number of players. Therefore, this collection is called a set.

The members of the collection or team will be known as the elements of the set.

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