Suppose you have a rectangular flower bed whose area is 24ft^2 . The shortest side is (x-4) feet and the longest side is (2x) feet. Find the length of the shortest side.

The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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Find time needed to drive 200 miles:

50 miles = 1 hour

1 mile = 1/50 hour

200 miles = 1/50 x 200 = 4 hours

Find time of arrival:

7:00am + 4 hours = 11am

Answer: She will arrive at 11am

Answer:

The woman will arrive at New York City at 11 am.

Step-by-step explanation:

At an average speed of 50 miles per hour, it will take the woman 4 hours to reach New York City. If she leaves at 7 am, she will arrive at 11 am. Here's the math:

200 miles / 50 miles per hour = <<200/50=4>>4 hours

7 am + 4 hours = 11 am

So the woman will arrive at New York City at 11 am.

Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.

What are algebraic expressions?

Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.

Examples of algebraic expressions include:

2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)

A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.

A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.

A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.

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Answer:

Impossible

Step-by-step explanation:

Answer:

1/7778

Step-by-step explanation:

We multiply each event

1/6 x 1/6 x 1/6 x 1/6 x 1/6 =

1/36 x 1/36 x 1/6

= 1/7776

Answer:

C. 1

Step-by-step explanation:

I calculated it logically

Step-by-step explanation:

The correct choice is C

C.1

Answer:

≈ 2.76%

Step-by-step explanation:

Price increase

297.9 - 289.7 = 8

% increase

8/289.7 * 100 = 2.7614773904%

≈ 2.76%

Answer:

84/60

Step-by-step explanation:

1 hour is 60 minutes so 84 minutes /60 gives how much it is in hours

From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0

and solution of these equations are x = -1/2 and y= 15/2

An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.

we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.

From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a  and detect two location of point (1, 6) and (6, 1) for line b.

As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)

hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)

                                                 y-6 = 3(x-5)

                                               y-6 = 3x -15

                                             y-3x -9 = 0

In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)

                                                       y-6 = -1(x-1)

                                                     y-6 = -x+1

                                                   x+ y -7 =0

 now, we get two equations, -3x+ y -9 =0

                                                  x+ y -  7 =0

Solving these two equations by addition method, we get x= -1/2 and y = 15/2

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Answer:

The probability is 0.7449

Step-by-step explanation:

Given

[tex]n = 12[/tex] ---- total

[tex]r = 5[/tex] --- selection

[tex]Genre =\{Rap(4), Country (5), Heavy\ metal (3)\}[/tex]

Required

Probability of buying at least 1 of each genre

First, we calculate the total possible selection.

To select 5 CDs from a total of 12, we use:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

[tex]^{12}C_5 = \frac{12!}{(12 - 5)!5!}[/tex]

[tex]^{12}C_5 = \frac{12!}{7!5!}[/tex]

Expand

[tex]^{12}C_5 = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{12*11*10*9*8}{5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{95040}{120}[/tex]

[tex]^{12}C_5 = 792[/tex]

So, the total selection is:

[tex]Total = 792[/tex]

To select at least 1 from each genre, there are 6 possible scenarios.

And they are:

[tex]\begin{array}{ccc}{Heavy\ Metal (3)} & {Rap (4)} & {Country(5)} & {3} & {1} & {1} & 2 & {1} & {2} & {2} & {2} & {1}& {1} & {2} & {2}& {1} & {3} & {1}& {1} & {1} & {3} \ \end{array}[/tex]

The possible selections for the given scenario is:

[tex]Possible = ^3C_3* ^4C_1 * ^5C_1 +^3C_2* ^4C_1 * ^5C_2 +^3C_2* ^4C_2 * ^5C_1 +^3C_1* ^4C_2 * ^5C_2 +^3C_1* ^4C_3 * ^5C_1 +^3C_1* ^4C_1 * ^5C_3[/tex]

Using a calculator, we have:

[tex]Possible = 1*4*5 +3*4*10 +3*6*5 +3*6*10+3*4*5+3*4*10[/tex]

[tex]Possible= 20 +120 +90 +180+60+120[/tex]

[tex]Possible = 590[/tex]

The probability is then calculated using:

[tex]Pr = \frac{Possible}{Total}[/tex]

[tex]Pr = \frac{590}{792}[/tex]

[tex]Pr = 0.7449[/tex]

The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.

The rate of change of a function is the rate at which the output value changes per unit change in the input value.

The possible data and table obtained from a similar question on the website are presented as follows;

Student A

Number of minutes;         [tex]{}[/tex]1              2             3              4

Number of words read; 150        [tex]{}[/tex]300          450          600

Student B

y = 158·x

Where;

x = The time duration in minutes

y = The number of words read by the student

Student C

The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)

The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;

Reading rate for Student A = (300 - 150)/(2 - 1) = 150

The reading rate for Student A is 150 words per minute

The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute

The of the straight ling graph for the reading rate of Student C is found as follows;

Slope = (420 - 280)/(3 - 2) = 140

The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute

The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute

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Answer:

Step-by-step explanation:

That is not possible.

Answer:

Side BC: y = -2x + 10

Side AC: y = 2x + 4

Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.

Answer:

B.

Step-by-step explanation:

So we know right off the bat the angles ABE and CBD are congruent because of vertical angles.

Now we can look at the sides.

The ratio for 27:18 = 3:2

The ratio for 36:24 = 3:2

They check out.

That means that the answer is B. SAS

Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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The time to build the fence will be 10 hours.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.

The time to build the fence will be:

= 1 1/3 ÷ 1/6

= 5/3 × 6/1

= 30 / 3

= 10 hours.

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Answer:

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{9}{\sqrt{150}} = 1.2[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours

The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.

A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.

Here,

The common circle equation is,

( x - h )² + ( y - k ) ( y - k )

6² = r²

where the circle's radius is r and the center's coordinates are (h, k).

Part 1.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( -5 , 7 )

Consequently, the second choice is the right one.

Part 2.

Using the common circle equation, we obtain,

circle radius is six.

Consequently, the first choice is the right one.

Part 3.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( 2 , 3 )

Therefore False.

Part 1.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( -5 , 7 )

As a result, the second choice is the right one.

Part 2.

In comparison to the common circle equation, we obtain,

circle's diameter is six.

As a result, the first choice is right.

Part 3.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( 2 , 3 )

So, False.

Part 1.

Giving the distance between two points,

Distance between A(-5, 3) and B (5, 3), expressed as:

=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]

= >  [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]

=> 10

Thus, 3rd Option is correct.

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Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

Answer:

Parents' income

Step-by-step explanation:

The confounding variable also called the third or lurking variable is usually an unaccounted for variable or factor which may creep into our research, Hence, causing an association or relationship which does not actually exists between the two correlated variables. In the experiment abive, there is no really any actual relationship between increasing percentage of free lunch and less usage of bicycle helmets.

However, We may attribute the change in bicycle helmets used by the children to a swerve or change in the income of the parents of the students, being able to afford a bicycle helmet will depend in the income of the parent and this mightvhave caused the observed association between the variables.

Answer:

parents income

Step-by-step explanation:

The expression in the simplest form is -90p - 102

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

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

Then Rewrite in simplest terms:

9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

2 [ 9(-6p-4)+3(3p-5) ]

Solve the like terms;

2 [-54p - 36 + 9p - 15]

2 [-54p + 9p - 15 -  36]

2 x ( -45p - 51)

-90p - 102

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The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.

Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.

For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:

A² + B² + C² = 0

A² = -(B² + C²)

This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.

This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.

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Answer:

cool i think there are 4 questons

Step-by-step explanation:

Answer:

x^4 + 2x + 2

Step-by-step explanation:

Answer:

distributive property is your answer

the is answer is probably c

the answer makes sense