Which system of linear inequalities is graphed?
x ≤ -2
y≤ -x-3

x< -3
y< -x-2

x<-2
y≤ -x+2\

x< -2
y≤-x -2

The dimensions of the poster with the smallest area are; 27.75 cm x 27.75 cm

Let "x" and "y" denote the length and the width of the poster.

We are told that the margin of a poster are 4 cm and the side margins are 4 cm.

The length of the print = x - 2(4) = x - 8

The width of the print = y - 2(4) = y - 8

The area of the print = length * width = (x - 8)(y - 8)

The area of the print is given as 390 square inches. Thus;

(x - 8)(y - 8) = 390

Making y the subject gives;

y = (390/(x - 8)) + 8

The area of the poster is; A = xy

Thus;

A = x[(390/(x - 8)) + 8]

A =  (390x/(x - 8)) + 8x

Minimizing the area gives;

A' = 8 - (3120/(x - 8)²)

Equating to zero gives;

8 - (3120/(x - 8)²) = 0

8(x - 8)² = 3120

(x - 8)² = 3120/8

(x - 8)² = 390

x = 27.75 cm

y = (390/(27.75 - 8)) + 8

y = 27.75 cm

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Answer:

y = -x or y= -2x+3 will work

For an average intake of 2200 calories per day, the number of acres of land owned is 2.03

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

C(x) = 270 ln(x + 1) + 1900

Also from the question, we have

Average intake of calories = 2200 inches

This means that

C(x) = 2200

So, we have the following equation

270 ln(x + 1) + 1900 = 2200

Subtract 1900 from both sides

270 ln(x + 1) = 300

Divide 270 from both sides

ln(x + 1) = 1.11

Take the exponent of both sides

x + 1 = 3.03

So, we have

x = 2.03

Hence, the number of acres is 2.03

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Answer: It will take Stephanie 20 minutes to run 2 miles.

Step-by-step explanation:

Since 3 miles is equal to 30 minutes, let us find the number of minutes run per mile

divide 30 by 3

10-It takes 10 minutes to run 1 mile

multiply 10 by the number of miles, which is 2

2x10=20

20 minutes

The measure for the exterior angle to the angle X of the triangle XYZ is 112.55°

In any triangle, an exterior angle is equal the sum of its two opposite interior angles is equals.

For the triangle XYZ, the exterior angle to the angle X is equal to the sum of the two opposite interior angles Y and Z

angle Y = 38.25° and angle Z = 74.3°

exterior angle to X = 38.25° + 74.3°

exterior angle to X = 112.55°

This implies that the angle X = 180° - 112.55° = 67.45°

and 67.45° + 38.25° + 74.3° = 180° which is true for the sum of interior angles of a triangle.

Thus, exterior angle to the angle X that is derived to be 112.55° is true for the triangle XYZ.

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Answer:

112.55

Step-by-step explanation:

i got it right

a) Probability that the calls  last between 3.8 and 4.5 minutes is;

0.3413

b)  The probability that calls last more than 4.5 minutes is;

0.1587

c) Probability that the calls  last between 4.5 and 5.5 minutes is;

0.1511

d) Probability that the calls  last between 4.5 and 5.5 minutes is; 0.6607

The formula for z-score is;

z = (x' - μ)/σ

a) Probability that the calls  last between 3.8 and 4.5 minutes is;

P(3.8 < x' < 4.5)

z1 = (3.8 - 3.8)/0.7

z1 = 0

z2 = (4.5 - 3.8)/0.7

z2 = 1

The p-value between the two z-scores is; p-value = 0.3413

b)  The probability that calls last more than 4.5 minutes is;

P(x' > 4.5)

z =  (4.5 - 3.8)/0.7

z = 1

P(x > Z) = 0.1587

c) Probability that the calls  last between 4.5 and 5.5 minutes is;

P(4.5 < x' < 5.5)

z1 = (5.5 - 3.8)/0.7

z1 = 2.43

z2 = (4.5 - 3.8)/0.7

z2 = 1

The p-value between the two z-scores is; p-value = 0.1511

d) Probability that the calls  last between 4.5 and 5.5 minutes is;

P(3.5 < x' < 5.5)

z1 = (3.5 - 3.8)/0.7

z1 = -0.43

z2 = (5.5 - 3.8)/0.7

z2 = 2.53

The p-value between the two z-scores is; p-value = 0.6607

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Answer:

Definition of an isosceles triangle

Answer:

[tex]\frac{1}{4}s^2[/tex]

Step-by-step explanation:

Use the formula for the area of a square and divide the result by 4.

The true statements are:-

( 1 ) The square root of a positive number cannot be negative.

( 2 ) √49 = 7 because 7(7) = 49.

( 3 ) √25 = 5 because 5²= 25.

Algebra is one of the many branches of mathematics. Algebra, in broad terms, is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a thread that runs through almost all of mathematics.

The right statements are:-

( 1 )The square root of a positive number cannot be negative.

Example, √100 = 10

(2) √49 = √ ( 7 x 7 ) = 7

(3) √25 = √ ( 5 x 5 ) = 5

Hence, the correct statements are options A, D and E.

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The domain and the solution of the equation log₄²(1+x²)=0.25  are x = ±1

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

log₄²(1+x²)=0.25

In this case, the domain of the expression and the solution are the same

So, we start by taking the square root of both sides

log₄(1+x²) = 0.5

Next, we apply the change of base law of logarithm

So, we have

1 + x² = 4⁰°⁵

Evaluate the exponent

1 + x² = 2

Evaluate the like terms

x² = 1

Take the square root of both sides

x = ±1

Hence, the domain and the solution are x = ±1

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The equation of the polynomial on the given graph is: C. f(x) = x³ + 2x² - 5x - 6

On the graph we can see a polynomial, let's analyze some key features so we can identify it. First, we can see that when x = 0 (at the y-axis) the graph intercepts the axis at y = -6. So the constant term is -6.

Then we can discard the first and fourth options. The remaining options are:f(x) = x³ - 2x² - 5x - 6f(x) = x³ + 2x² - 5x - 6

Also on the graph, you can notice that when x = -1 the function becomes zero, so let's evaluate these two options in x = -1

The first one gives:f(-1) =  (-1)³ - 2*(-1)² - 5*-1 - 6f(-1) = -1 - 2 + 5  -6 = -4

So this option is not correct. The other function gives:f(x) = (-1)³ + 2*(-1)² - 5*(-1) - 6     = -1 + 2 + 5  -6 = 0

So we conclude that the correct option is the third one.f(x) = x³ + 2x² - 5x - 6

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The equation is n(n+1) = n + n+1 +29. The two consecutive integers are 6, 7 or -5, -4

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Given that: the product of two consecutive integers is 29 more than their sum.

Let the first integer and second  integer be n and n+1 respectively

We can write the equation as:

n(n+1) = n + n+1 +29

n² + n = 2n + 30

n² + n - 2n - 30 = 0

n² + - n - 30 = 0

(n - 6) (n + 5) = 0

n - 6 = 0 or n + 5 = 0

n = 6 or n = -5

Thus, n+1 = 7 or n+1 = -4

Therefore, the two  integers are 6, 7 or -5, -4

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The statements true is :

The standard equation of a circle is expressed as:

x²+y²+2gx+2fy+C = 0

Centre is (-g, -f)

radius = √g²+f²-C

Given a circle whose equation is x²+y² - 2x- 8 = 0

Get the center of the circle

2gx = -2x

2g = -2

g = -1

Similarly, 2fy = 0

f = 0

Centre = (-(-1), 0) = (1, 0)

This shows that the center of the circle lies on the x-axis

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

The radius of the circle is 3 units.

For the circle x² + y² = 9, the radius is expressed as:

r² = 9

r = 3 units

Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.

A = [tex]\left[\begin{array}{ccc}9&5\\1&6\\\end{array}\right][/tex],  B =[tex]\left[\begin{array}{ccc}1&6\\3&-1\\\end{array}\right][/tex]

3A = [tex]\left[\begin{array}{ccc}27&15\\3&18\\\end{array}\right][/tex]

2B = [tex]\left[\begin{array}{ccc}2&12\\6&-2\\\end{array}\right][/tex]

3A + 2B = [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

Hence, the addition of the matrix 3A + 2B is [tex]\left[\begin{array}{ccc}29&27\\9&16\\\end{array}\right][/tex]

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Using division and multiplication, the values of the operation are 5/4, 203/6, 1/3 and 32/21 respectively

Division of numbers is the process of breaking down a number into definite proportions of value. In dividing a number, we are reducing it's size by a specific factor. The number to be divided is the dividend. The number by which we divide is the divisor.

In the question given, we have several division operations to carry out.

A) 5/11 ÷ 4/11

Since this are fractions, when we take the inverse of one of the values, we change the sign to multiplication.

5/11 * 11 / 4

This becomes 5/4

B) 29 ÷ 6 / 7

We can also do the same thing we did above by simply taking the inverse of the divisor and then change the sign to multiplication.

29 × 7 / 6 = 203/6

C) 5/9 ÷ 1 2/3

We have to first convert the mixed fraction into an improper fraction and the take the inverse of it and multiply.

5/9 ÷ 5/3

5/9 × 3/5 = 3/ 9 = 1/3

D) 5 3/5 ÷ 3 1/2

We also change the mixed fraction into improper fraction and then take inverse before multiplying.

16/3 ÷ 7/2

16/3 × 2/ 7 = 32/21

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Since the normal distribution is symmetric, the response is 50%.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.

As per the given information in the question,

According to the Empirical Rule, if a random variable is regularly distributed:

One standard deviation from the mean is found for 68% of the measurements.

The mean is within two standard deviations for 95% of the measurements.

99.7% of the measurements are found within three standard deviations of the mean.

Additionally, because of the symmetry of the normal distribution, 50% of the measurements fall below the mean, and 50% fall above.

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The trigonometric equation is 5sin²x + 3sinx - 1 = 0.

What is a trigonometric equation?

A trigonometric equation is one that incorporates a variable-based trigonometric function. One illustration of a trigonometric equation is sin x + 2 = 1. This equation or one that is more complicated, such as sin2 x - 2 cos x - 2 = 0, can be used in the equations.

Here, we have

Given: (5/2)cos2x - 1/2 = 3sinx

We know that

cos2x = 1 - 2sin²x

Then our equation become

(5/2) (1 - 2sin²x) - 1/2 = 3sinx

5/2 - 5sin²x - 1/2 = 3sinx

2 - 5sin²x = 3sinx

-5sin²x + 2 - 3sinx = 0

5sin²x + 3sinx - 1 = 0

Hence, the trigonometric equation is 5sin²x + 3sinx - 1 = 0.

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Answer:

17 dollars

Step-by-step explanation:

100 - 15 = 85

85 percent of 20 = 17

The total cost of all the remaining tickets for the show will be equal to $1564.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

Total tickets left = 46

Price of each ticket = $34

Then, the price of 46 tickets will be,

46 × 34

= $1564

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For a parallelogram, g° = 36° and f° = 144°. and for pentagon, a° = 108° and h° = 36°.

What is a measurement of an angle?

Angles are measured in degrees (°) using a protractor. A protractor is a measuring device that is used to calculate or draw angles in terms of degrees.

In the first figure, adjacent angles of a parallelogram are supplementary.

so

         f° + 36° = 180°

Solving this we get f° = 144°

Opposite angles of the parallelogram are equal

so g° = 36°

Now in figure 2,

A regular pentagon has all the interior angles of 108°.

a° = 105°

and exterior angles of 72°

So we can find h°

72° + 72° + h = 180°

h = 180° - 144°

h = 36°

Hence, for a parallelogram, g° = 36° and f° = 144°. and for pentagon, a° = 108° and h° = 36°.

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Dana Jones have amount after 7 years is $1560.97.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given: Dana Jones invests $ 1100 at 5% interest compounded continuously for 7 years.

We have to find the amount after 7 years.

Consider, the formula

A = Pe^rt

where,

A is the amount after t years

P is the invested amount

r is the interest rate

t is the number of years

Plug P = 1100, r = 5% = 0.05, and t = 7 in the above equation.

[tex]A = 1100e^0^.^0^5^(^7^)\\A= 1560.9743\\A = 1560.97[/tex]

Hence, Dana Jones have amount after 7 years is $1560.97.

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The given sequence  48, 12, 3, .... written in the explicit formula is as follows:

aₙ = 48·(1/4)^(n-1)

The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-complex function's number zeroes and sums over prime powers.

An arithmetic sequence has the explicit formula aₙ = a + (n - 1)d, and each term of the sequence may be computed without knowing the values of the previous terms.

The nth term of arithmetic, geometric, or harmonic series is usually the explicit formula.

So, the sequence we have is as follows:

48, 12, 3, ....

The common ratio of the terms is 1/4, and the first term is 48.

The universal equation for a geometric sequence's n-th term is:
aₙ = a1·r^(n-1)

This is true when r = 1/4 and a1 = 48:

aₙ = 48·(1/4)^(n-1)

Therefore, the given sequence  48, 12, 3, .... written in the explicit formula is as follows:

aₙ = 48·(1/4)^(n-1)

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The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

The mathematical expressions that we used to find unknown numbers are called Linear Equations. These can be formed by variables and constant terms according to given conditions. Here we use variables like x, y, z, etc to represent unknown variables.

Here we have,

Music company A charges a $ 15 membership fee and a $ 0.75 for each downloaded song

Music company B charges $ 0.90 for each downloaded song without the membership fee

Given question

a. For what number of songs will both companies charge the same amount?  

Let for x songs both companies will charge the same amount

Cost to download x songs from Company A

=> 15 + 0.75x

Cost to download x songs from Company B

=>  0.90x

As we assumed both costs are the same

=> 15 + 0.75x = 0.90x

=> 0.90x - 0.75 = 15

=> 0.15x = 15

-> x = 100

Therefore,

The number of songs that both companies will charge the same amount is 100.

b) You anticipate that you will download 150 songs. Which company should you choose if you want to spend the least amount of money?  

Cost of 150 that charges company A =  15 + 150(0.75)  

= 15 + 150(0.75)  = 15 + 112.5 = 127.5  

Therefore,

Company A will charge $ 127.5 for 150 songs

Cost of 150 songs that charges company B = 150(0.90)

= $ 135  

Company B will charge $ 135 for 150 songs

Therefore,

Company B will charge $ 135 for 150 songs

Thus,

To pay the least amount of money we need to choose Company B.

Therefore,

The number of songs that both companies will charge the same amount is 100. And to pay the least amount of money we need to choose Company B.

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According to the combination technique,

A) 3 from A and 1 from B = 16320

B) 2 from A and 2 from B = 29070

C) All from A = 3060

D) 4 people regardless of department = 73815

E) at least 3 from department A = 19380

In math combination technique is used to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we have given that 4-person grievance committee is to be selected out of 2 how many ways can the following committees be selected

And we need to find the following

Here we know that  4-person grievance committee is to be selected out of 2 departments, A and B, with 18 and 20 people.

In this one we have to find the number ways can the following committees be selected.

A) While the first condition is to 3 from A and 1 from B

Here the term "and" means to multiply

Then it can be written as

=> (18 people choose 3) x (20 people choose 1)

=> (18C3)(20C1) = (816)(20) = 16320

B) And then the next condition is 2 from A and 2 from B

In this one is written as,

=> (18 people choose 2) x (20 people choose 2)

=> (18C2)(20C2) = (153)(190) = 29070

C) All from A

which is equal to the following,

=> 18 people choose 4 = 18C4 = 3060

D) Next, we have to do the calculation for 4 people regardless of department

=> 18+20 or 38 people choose 4 = 38C4 = 73815

E) Finally, at least 3 from department A.

'In other words, it can be written as choose 3 from department A and choose 1 from department B or  Choose 4 all from department A

Where "And" means to multiply and "or" means to add.

Therefore, the condition is written as,

=> [(18 people choose 3) times (20 people choose 1)] plus  (18 people choose 4)

=> (18C3)(20C1) + (18C4) = (816)(20) + 3060 = 19380

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As a result of it being so accessible, we became incredibly lax over the years.

The Complete Question.

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To produce the graph of y = (x+5)^2−2 from y=x , you should translate the graph left by 5 units, then downward by 2 units.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph. To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph. In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs.

Here,

Translate the graph left by 5 units, then downward by 2 units, to create the graph of y = (x+5)^2-2 starting from y=x.

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Answer:

0.4, 14%, 70%

Step-by-step explanation:

0.4= 0.4%

14= 14%

70= 70%

For both cases time needs to double the invested money is 7.7016 years

It is a mathematical expression define that interest can be compounded at any time even within any smallest period of time.

When annual interest rate is given in a data along with invested money, we can calculate the years required to get doubled money by using the formula A= Pe∧(rt)

A is the double money of the investment

P is the investment

r is the annual interest rate

t time in years

as per question A=2P, r=0.09

2P =Pe∧(0.09t)

2= e∧(0.09t)

㏑2=0.09t

t= 7.7016 years

hence, it takes 7.7016 years to get double money

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Answer:

its A

Step-by-step explanation:

cause 2.5 x 3 is 7.5 and 3500+7.5% is 3762.50

Answer:

79.25

Step-by-step explanation:

What is the quotient of 3,487 divided by 44?

3,487/44 = 79.25