Find a formula for the described function. A rectangle has perimeter 8 m. Express the area A of the rectangle as a function of the length, L, of one of its sides. State the domain of A

Answer:

[tex]\boxed{x^2 - x - 6}[/tex]

Step-by-step explanation:

If a is the root of a polynomial then x-a is a factor of that polynomial

Since - 2 is a root, x -(-2) = x + 2 is a factor

Since 3 is a root, x - 3 is a factor

Multiplying the factors of a polynomial gives you the polynomial equation

So the polynomial equation is

[tex](x + 2)(x-3)[/tex]

Apply FOIL method:
[tex](x + 2)(x-3) \\\\= x\cdot x+ x\left(-3\right)+2x+2\left(-3\right)\\\\= x^2 -3x + 2x -6\\\\x^2 - x - 6\\\\Answer: \boxed{x^2 - x - 6}[/tex]

The graph shows that the x-values increase as the y-values increase, which is consistent with the inequality x+4y ≤ 15. The y-values are all greater than or equal to 0, which is consistent with the inequality y ≥ 0.

Inequality is the unequal distribution of resources or opportunities among different individuals, groups, or social classes. It is a situation in which some individuals or groups have significantly more resources or opportunities than other individuals or groups. Inequality can be seen in terms of income, wealth, social class, access to education and health care, political power, or other factors. Inequality can be caused by systemic oppression and discrimination, or by the unequal distribution of resources within a society. It can have a negative impact on the ability of individuals and groups to meet their basic needs and achieve their full potential.

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Answer:

  DE = 9

Step-by-step explanation:

Given quadrilateral DEFG with DG≅EF, ∠FDG≅∠DFE, and markings EF=(6x+4), DG=(4x+8), and FG=(4x+1), you want the measure of DE.

The given congruences mean that the figure DEFG is a parallelogram. Opposite sides are the same length.

  EF = DG

  6x +4 = 4x +8

  2x = 4 . . . . . . . . subtract (4x+4)

  x = 2 . . . . . . . . divide by 2

Now, we can find FG.

  FG = 4x+1 = 4(2) +1 = 9

Opposite side DE is the same length:

  DE = 9

__

Additional comment

You can prove ΔEFD ≅ ΔGDF using SAS. Then CPCTC tells you corresponding parts of the triangles are congruent: DE≅FG.

The simplified form of the univariate monomial expression as requested in the task content is; 1.6 y⁴.

It follows from the task content that the simplified form of the univariate monomial expression is to be determined.

Since the given expression is;

32 y⁶ / 20 y²

The expression can be simplified as follows;

( 32 / 20 ) • y⁶ / y²

= 8/5 • y⁴

= 1.6 y⁴.

On this note, it can be inferred that the simplified form of the expression is; 1.6 y⁴.

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Answer:

maximum value = 2

Step-by-step explanation:

the maximum value of the function is the y- coordinate of its vertex

given a quadratic function in standard form

y = ax² + bx + c (a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = - x² + 2x + 1 ← is in standard form

with a = - 1 and b = 2 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{2}{-2}[/tex] = 1

to find the y- coordinate of the vertex, substitute x = 1 into y

y = - 1² + 2(1) + 1 = - 1 + 2 + 1 = 2

then maximum value of the function is 2

The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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Answer:

Step-by-step explanation:

Answer:

14 inches is to 56 miles

Step-by-step explanation:

First, let's convert the question into an "equation"

1in : 4mi as xin:56mi

Since we need to multiply 4mi by 14 to 56mi, we will multiply 1in by 14 to find the value of x. 1 * 14 = 14. So, x must be equal to 14 and 1 inch is to 4 miles as 14 inches is to 56 miles.

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It is given to us in the question that we have a proportion of 1 inch is to 4 miles.

The proportion we need to solve is, 1 : 4 :: x : 56  as given in the question.

To solve this,

If 1 inch is equal to 4 miles, that means 4 miles is equal to 1/4 inch.

i.e. 1x = 4y; where x is inches and y is miles

1y = 1x/4....................(i)

Similarly, from the above-given proportion, we see that

x = 56y;

Taking the value of y from (i),

x = 56 * (1/4)

= 14

So the proportion becomes,

1 inch : 4 miles :: 14 inch : 56 miles

Hence, it can be determined that 1 inch is to 4 miles as 14 inches is to 56 miles.

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Answer:

third option

Step-by-step explanation:

Instead of having a constant rate of change, the third option does not as it goes up by 1 then 3 then 5

Answer:

Yes.

(2, 23) is a solution for the equation y = 9x + 5

Step-by-step explanation:

(2, 23) means that for an x value of 2, the y value should be 23

The equation is y = 9x + 5

Substitute x = 2 on the right side

y = 9(2) + 5 = 18 + 5 = 23

Since this matches the given value of y =23, we can conclude that

(2, 23) is a solution for y = 9x + 5

The y - intercept of the function f(x) = (3x + 4)⁴(x - 5)⁵ is (0, -800,000)

When an equation's graph crosses the y-axis, that location is known as the y-intercept. When x = 0, it is y's value.

A linear equation's constant term serves as a representation for the y-intercept. The y-intercept of the equation y = 2x + 3 is 3, for instance. This indicates that the coordinate plane point (0, 3) is at y = 3 when x = 0.

y= mx + b, where m is the slope and b is the y-intercept, is another way to express a linear equation.

For instance, the equation y = -2x + 5 can be written as y = -2x + 5, and since the y-intercept is 5, the point (0, 5) is on the graph of the equation.

The y-intercept of an equation, or the value of y when x = 0, is the point at which the graph of the equation crosses the y-axis. It can be represented by b in the slope-intercept form of a linear equation as well as by the constant term in the equation.

In the function given;

f(x) = (3x + 4)⁴(x - 5)⁵

Substitute the value of 0 for x and solve to find the y - intercept.

f(0) = (3(0) + 4)⁴(0 - 5)⁵

f(0) = -800000

The value of y - intercept(s) is (0, -800000)

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The y-intercept of the function f(x) = (3x + 4)^4(x - 5)^5 is given as follows:

-800,000.

The function for this problem is defined as follows:

f(x) = (3x + 4)^4(x - 5)^5

Graphically, the y-intercept of a function represents the value of y assumed by the function when the graph of the function crosses the y-axis.

Hence, algebraically, the y-intercept of a function is given by the numeric value of the function when the input x assumes a value of zero.

The numeric value of the function at x = 0 is calculated replacing the two instances of x in the function by zero, hence the y-intercept of the function is defined as follows:

f(0) = (3(0) + 4)^4(0 - 5)^5

f(0) = 4^4 x (-5)^5

f(0) = -800,000.

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Answer:

A 10

Step-by-step explanation:

a proportional relationship is defined as

y = kx

k is the constant of proportionality, because it is constant for this function for any value of x.

it is usually called the slope of the line or rate of change.

these are special lines : lines that go through the origin (0, 0).

and for these lines people often call k the constant of proportionality.

as we can see right in the given equation, this constant of proportionality is 10.

Answer:

$101.75

Step-by-step explanation:

You work 4 hours in the morning from 8-12 and 5 hours and 15 minutes in the afternoon from 12:45 to 5:30 (a.k.a. 17:30)

15 minutes is a quarter of an hour.  1/4 = 0.25

4 + 5.25 = 9.25

You worked for 9.25 hours

Multiply that by $11 per hour.

9.25 · 11 = 101.75

You make $101.75 on Monday.

Answer:

D. 2r2 + 23r > 645

Step-by-step explanation:

The equation "2r^2 + 23r > 645" represents the situation because it states that the number of spaces in the parking lot, represented by the left-hand side of the equation (2r^2 + 23r), is greater than the maximum number of spaces that the parking lot can hold (645). This is consistent with the information given in the problem, which states that the parking lot has been expanded and can now hold more spaces.

The other equations given (A, B, C) do not accurately represent the situation because they do not take into account the expansion of the parking lot and the addition of new rows and spaces.

Answer:

(9b-4c)(9b+4c)

Step-by-step explanation:

81b^2-16c^2

Using the the difference of square formula: a^2-b^2=(a-b)(a+b)

(9b-4c)(9b+4c)

The coordinates of the square are 2.8

A square is a polygon whose all sides are equal.  the if the sides are equal, the coordinates of the vertices are also equal to each other.

The length of the diagonal of the square is gotten by the use of the formula for distance between two points

d = √(y₂-y₁)²+(x₂-x₁)²

distance = √(6-2)²+(-2-2)²

distance = √4²+-4²

Distance = √16+16

distance = √32 = 5.7 units

This implies that the sides of the square = 5.7/2 = 2.8

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Answer:

if it is bracket than see explanation

darw a table with

x 3 5 -4

y 0 2 -7

taking x as 3 so

y= (3-1)-2

= 0

so like this do by 5 also and -4 too

and after solving plot in in the graph

Answer:

1, 2, 7, 14

Step-by-step explanation:

its all of those

The diameter of the wheel of the truck is 3.33 feet.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

The distance around the wheel of a truck is 10.45 feet.

Let the diameter of the wheel = d feet.

Circumference of the wheel

= Distance around the wheel,

πd = 10.45 feet.

d = (10.45/π) feet.

Here, we take the π = 3.14.

So,

d = 3.326

d = 3.33

Therefore, the diameter is 3.33 feet.

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On solving the provided question we can say that 1,000,000 nanometers =  1 millimeter; 1e-6 millimeter = nanometers

A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.

1,000,000 nanometers =  1 millimeter

1e-6 millimeter = nanometers

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A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec

Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.

Ans as h = -5t2+30t+10

at t=0, H = 10, which is height of the building from the ground

at t= 2 sec

h= -5.4+30.2+10

= -20+60 +10 = 50 m

For max height dh/dt = 0

-10t+30 = 0

t=3 sec

Therefore, the Distance from ground = 10 + height after 3 sec

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The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation as 4y+16x=28 or y+4x=7

putting (1,3) in the equation we get 3+4×1=7

Similarly we can find the ordered pair as (2, -1) , (3,-5) , (4,-9)

Hence, The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)

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Answer:

1267 people

Step-by-step explanation:

The area of the 10 feet by 10 feet square is 100 square feet. If 20 people fit comfortably in this area, we can use this information to estimate the number of people in a larger area.

Since we know that 20 people fit in 100 square feet, we can calculate how many people would fit in a larger area by multiplying the number of square feet by 20.

A 1 mile section of a parade route is approximately 5280 feet long and 12 feet deep (on one side of the street). Therefore, the area that the crowd is occupying is approximately 5280*12 = 63,360 square feet.

So, the number of people that would fit in this area would be approximately:

63,360 square feet * 20 people/100 square feet = 1267.2 people.

So we can estimate that 1267 people will comfortably fit in a 1 mile section of a parade route that is 12 feet deep on one side of the street.

Answer:

389 people

Step-by-step explanation:

Step 1 we convert 1500 inches to feet

There are 45 pounds are needed for 6045 square​ feet.

What is pounds?

The United Kingdom and nine of its associated territories use the sterling as their currency. The pound is the primary unit of sterling, and the term "pound" is also frequently used to refer to the British pound or the pound sterling in international contexts.

Given:

3 pounds of grass seed cover 403 square​ feet.

We have to find the how many pounds are needed for 6045 square​ feet.

As 3 pounds of grass seed cover 403 square​ feet.

⇒ 403/3 = 134.33

⇒  1 pound of grass seed cover 134.33 square feet.

Let x pounds needed for 6045 square feet.

⇒ x = 6045 / 134.33 = 45

Hence, there are 45 pounds are needed for 6045 square​ feet.

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The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of  

The formula for the area of a rectangle is the product of length and wide. This is written mathematically as

= length * wideness

In the problem the rectangular array made by Casey has a the following dimensions

length = 1167 units

wide = 7 units

Area of rectangle = length * wideness

substituting the values

Area of rectangle = 1167 * 7

Area of rectangle = 8169 square units

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Answer:

The annual percentage yield (APY) is the effective annual rate of return on an investment, taking into account the effects of compounding. To calculate the APY, we can use the formula:

APY = (1 + (APR / n))^n - 1

Where APR is the annual percentage rate (the stated interest rate), and n is the number of times the interest is compounded per year.

In this case, the APR is 4.86% and the interest is compounded daily, so n = 365 (the number of days in a year).

APY = (1 + (0.0486 / 365))^365 - 1

Plugging in the numbers, we get:

APY = (1 + 0.000132876712328767123)^365 - 1

APY ≈ 4.87%

So, the annual percentage yield is 4.87%

Answer: 9n-7

Step-by-step explanation:

9n-7 because there are no like terms

Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

Given :

=> B = 8

=> S = 40

Tangent :

=> Angle ∠A = 40/9

For tangent ∠B:

=> Angle ∠B = 41/9

Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

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Answer:

Step-by-step explanation:

y2-y2/x2-x1