yossi used to have a square garage with 364ft of floor space. recently built an addition to it. The garage is still a​ square, but now it has​ 50% more floor space. What was the length of one side of the garage​ originally? What is the length of one side of the garage​ now? What was the percent increase in the length of one​ side?

The required polynomial function is x^4 + 8x³ + 22x² + 24x + 9

In this question,

We have been given  the zeros of a polynomial and the degree of a polynomial.

We need to find the polynomial of degree 4 and has zeros x = -3, -1

If a polynomial function f(x) has zeros x = -3, x = -1, then it has factors

(x + 3), (x + 1).

If these were its only factors, then polynomial would be a quadratic.

This means, both the zeros must be of multiplicity 2.

So, the roots of the polynomial must be of the form f(x) = (x + 3)²(x + 1)²

f(x) = (x + 3)²(x + 1)²

f(x) = (x² + 6x + 9)(x² + 2x + 1)

f(x) = x^4 + 8x³ + 22x² + 24x + 9

Therefore, the required polynomial function is x^4 + 8x³ + 22x² + 24x + 9

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The solution set in interval notation [7, ∝)

The compound inequality is given as:

x+8 ≥ 9 and 2x − 6 ≥ 8

Take the like terms

x ≥ 9 - 8 and 2x ≥ 8 + 6

Evaluate the like terms

x ≥ 1 and 2x ≥ 14

Divide by 2

x ≥ 1 and x ≥ 7

The solution set of x ≥ 7 is greater than x ≥ 1

So, we have

x ≥ 7

In interval notation, it is [7, ∝)

Hence, the solution set in interval notation [7, ∝)

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Last week, Ella worked 16 hours after school and 8 hours before school using the concept of algebraic equations.

The equality of two mathematical expressions is demonstrated by a mathematical statement called an equation.

Algebraic equations in mathematics frequently have one or more variables.

Given: Ella makes $11.25 per hour before school and $11.75 per hour after.

Total earnings of Ella from = $278

Let x be the number of hours Ella worked before school.

Let y be the number of hours Ella worked after school.

11.25x + 11.75y = 278

Given that she works twice as long after school, it follows that

y = 2x

Substituting in the equation, we get

11.25x + 11.75(2x) = 278

11.25x + 23.5x = 278

34.75x = 278

x = 8

Similarly, y= 2x

y = 16

Ella accordingly worked 16 hours after school and 8 hours before school.

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Answer: $25

Step-by-step explanation:

t = t-shirts

3t + 15 = 90

3t = 75

t = 25

Answer:

about 4.89% is the percentage of population under 20 in Japan 2018

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

Mean = Sum of all observations/Number of observations

Mean = (12 + 34 + 45 + 50 + 24)/5

Mean = 165/5 = 33

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus

median = middle value i.e. 4.

suppose Given data:

0, 40, 60, 70, 75, 80, 85, 95, 95, 100

a)Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9

                           = 700/9

                         = 77.777

Median without '0' = 80

Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70

Median with '0' = 80

b)standard deviation= 18.121673811445. (without '0')

standard deviation with 0 = 28.982753492379

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The value of the given expression is 16. The correct option is the fourth option 16

From the question, we are to find the value of the given expression

The given expression is

|-8| + 4(-5 + 9) ÷ 2

Simplifying by applying PEMDAS

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

Simplifying

|-8| + 4(-5 + 9) ÷ 2

8 + 4(4) ÷ 2

8 + 16 ÷ 2

8 + 8

= 16

Hence, the evaluation of the expression is 16

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Answer:By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) The shape of the data remains the same

(b) The mean and median are increased by $1,000

(c) The standard deviation and interquartile range remain the same

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

Therefore, following an increase of $1,000, we have;

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, , are increased by $1,000, the median salary, , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

(c) The standard deviation, σ, is given by ;

Where;

n = The number of teaches;

Given that, we have both a salary, , and the mean, , increased by $1,000, we can write;

Therefore;

; The standard deviation stays the same

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

The interquartile range stays the same

Step-by-step explanation:

Answer:5/3

Step-by-step explanation:

first u need to change is mixed fraction in to normal fraction

3 1/3-5

3 1/3 means 3*3+1 =10

therefor 10/3-5

u need to find the lcm or the common for the two factor (3 and 1 )

the lcm is 3

so 10-5/3 =5/3

Answer:

I took the time to graph the image onto the image that you had used, I hope this helps! <3

Step-by-step explanation:

Dilating by 1/2, is a contraction, it makes the pre-image smaller than the image.

I stitched a photo of the solution.

Answer:

Step-by-step explanation:

(2/1)(2/9) = (-4/5m)

4/9 = (-4/5m)

(-5/4)4/9 = ((-4/5)(-5/4))m  cancel out common factor on both sides

       -5/9 = M  or M = -5/9  use symmetric property of equality either one is fine for answer.

The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

Polynomial is an expression that involves the operations of addition, subtraction, multiplication of variables.

Given the polynomial:

3x² + 4x - 4

Factorizing the polynomial gives:

= 3x² + 6x - 2x  - 4

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

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

The factors of the polynomial 3x² + 4x - 4 are (3x - 2) and (x + 2)

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The total capacity will be 8 2/5 liters.

From the information, the bottles wee filled with 6/5 liters each.

Therefore, the capacity will be:

= Number of drums × Quantity

= 7 × 6/5

= 42/5..

= 8 2/5 liters.

Therefore, the total capacity will be 8 2/5 liters.

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Answer:

1026.9

Step-by-step explanation:

Use a calculator!

Answer:

1026.9

Step-by-step explanation:

Line the two numbers up, and start adding from the tenths place and carry numbers if needed. This could also be done with a calculator or online.

The value of KM is equal to 5.

A line segment is a section of a straight line that is enclosed by two clearly defined endpoints and contains every point on the line located within.

Consider a point L on a line segment KM such that:

We have the values,

KL = 3x ;

LM = 2

Now, we know,

KL + LM = KM

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

Now, KM = x + 4                                                                         ---------(2)

Equating the equations (1) and (2),

We get,

3x + 2 = x + 4

Now, subtract 2 from each side of the equation.

3x + 2 - 2 = x + 4 - 2

3x = x + 2

Subtracting x from each side of the equation.

3x - x = x + 2 - x

2x = 2

Dividing each side of the equation by 2.

( 2x / 2 ) = ( 2 / 2)

x = 1

Therefore,

KM = x + 4

KM = 1 + 4

KM = 5

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The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

3a(15 + 3 - 3²) + 7a(8/4)

Simplifying the exponents:

3a(15 + 3 - 9) + 7a(8/4)

Simplifying the terms in the bracket:

3a(9) + 7a(2)

Opening the parenthesis:

27a + 14a

Adding:

= 41a

The simplification of the expression 3a(15 + 3 - 3²) + 7a(8/4) gives 41a

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Answer:

okay!

Step-by-step explanation:

3x5=15+4=19 so I think 10 5 5 10 hope it he,ped I tried!

Answer: The answer is  6x^4-4x

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

v = √(2e / m)

B lost the election by 15,840 votes.

Since A got 132000+12% of 132000 votes=147840 votes.

The mean of the set of numbers is 4362.92

The median is 4164.5

The mode is 0.

It should be noted that the mean is the average sat of numbers. The addition of the numbers is 52355 and there are 12 numbers.

The mean will be:

= 51355 / 12

= 4362.92

The median is the number in the middle. This will be:

= (3838 + 4491)/2

= 4164.5

The mode is 0 since the observations were only once.

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Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given the data in the question;

To determine the with of the rectangular prism, plug the given values into the formula above and solve for w.

V = w × h × l

528 ft³ = w × 11ft × 6ft

528 ft³ = w × 66ft²

Reorder the equation and divide both sides by 66ft²

w × 66ft = 528 ft³

( w × 66ft )/66ft² = 528 ft³ / 66ft²

w = 528 ft³ / 66ft²

w = 8ft

Given the volume, length and height, the width of the rectangular prism rounded to the nearest foot is 8ft.

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we conclude that the equation x + 10 = 5 has only one solution, which is x = -5

Here we have the linear equation:

x + 10 = 5

In general, linear equations have only one solution, but let's solve this to see how many solutions it has.

If we subtract 10 in both sides of the linear equation, we will get:

x + 10 - 10 = 5 - 10

x = -5

So there is a single solution, which is x = -5.

Then we conclude that the equation below has only one solution.

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The solution of the equation 12x + 31 = 15 is x = -4/3

In this question we have been given an equation.

12x + 31 = 15

We need to find the solution of the given equation.

12x + 31 = 15

12x + 31 - 31 = 15 - 31                 ..............(Subtract 31 from each side)

12x = -16

x = -16/12                                   .............(Divide each side by 12)

x = -4/3

Therefore, the solution of the equation 12x + 31 = 15 is x = -4/3

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Answer:

5 x 10^-5

2.5 x 10^-3

0.02

0.0016

Step-by-step explanation:

A) The amount that the retailer should charge for each candle in order to maximize its profit is; $27

B) The domain of the function is; x ≥ 120

The range of the function is; P(x) ≥ 3645

A) Let the total sales be represented by P(x).

Let the number of candles sold be x.

Now, since the retailer  120 jar candles at $30 per candle and estimated that or each $2 decrease in price, they will sell 10 additional candles.. Thus;

P(x) = (30 - 2 * (x - 120)/10)x

P(x) = 30x - x²/5 + 24x

P(x) = - x²/5 + 54x

Using -b/2a, we can get the number of candles that maximizes profit as;

-54/(2 * -1/5) = 135 candles

Plugging 135 for x into the P(x) equation gives;

P(135) = $27

B) The domain of the function is; x ≥ 120

The range of the function is; 135 * 27 = 3645

P(x) ≥ 3645

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The number of miles that he walked is 4.5 miles. Then the number of laps that your friend walks will be 3 laps.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A 9/10 miles long walkway around the lake. In the morning you walk three laps around the lake, and in the evening you walk two. On a 1 1/2 mile track, your companion walks the same overall distance as you do.

The number of miles that you walked will be

⇒ 9/10 x (3 + 2)

⇒ 9 x 5 / 10

⇒ 4.5 miles

Then the number of laps that your walk will be

⇒ 4.5 / (1 1/2)

⇒ 4.5 / (3/2)

⇒ 4.5 x 2 / 3

⇒ 3 laps

The number of laps that your friend walks will be 3 laps.

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