RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.

RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.
Because the height cannot be negative, and the ramp is _ feet tall, the relevant range is {y | 0 ≤ y ≤ __ }. The graph is symmetric in the line x = _ This means that the height from a distance of 0 to _ feet away from one side of the ramp is the same as the height from a distance of _ to _ feet away from one side of the ramp.

Answer:

He plans to kayak a total of 6.4 miles. Damon kayaks at an average speed of 1.6 miles per hour. How many hours will it take Damon to kayak the 6.4 miles? It will take Damon 4 ‾ hours to kayak 6.4 miles.

[tex]{3 }^{p} = \frac{1}{9} [/tex]

[tex]{3 }^{p} = 9 {}^{ - 1} [/tex]

[tex]{3 }^{p} = (3 {}^{2} ) {}^{ - 1} [/tex]

[tex]{3 }^{p} = 3 {}^{} {}^{ - 2} [/tex]

[tex]p = - 2[/tex]

Answer:

125, 216, 343, 512

Step-by-step explanation:

The next number in the sequence 1, 8, 27, 64 is 125.

This sequence follows the pattern of starting with the number 1, then finding the cube of each subsequent integer (the cube of a number is found by multiplying the number by itself twice, so the cube of 2 is 222=8). Therefore, the next number in the sequence would be 555=125.

The value of 8 cube 512

As we know the cube of a number is the value that are obtained when a number is multiplied by itself three times.

If n be any real valued number then the cube of p is the product of number n  three times.

i.e., n × n × n

The cube of number is represented by the third power (exponent = 3) of that number.

For above the cube of number 'n' is represented by n³

Here we need to find the cube of number 8.

From definition of cube of number,

8³ = 8 × 8 × 8

8³ = 64× 8

8³ = 512

Thus the cube of number 8 = 512

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Point B on line AB, which is tangent to circle O, has a length of 12 units. The circle is intersected by the line AO from point A to the circle's centre at point C, and the line segment AC has a length of 8 units.

If you know the circumference C, you can calculate the radius of a circle using the formula r = C / (2 * ). If you know a circle's diameter, d, you can calculate its radius using the formula r = d / 2. The line AB crosses the circle at the precise locations P and Q. Here, the line AB is known as the secant of the circle.

Due to the fact that the endpoints of the line segment P Q are on the circle's circumference, it is known as the circle's chord.The two-headed arrow over AB designates a line that passes through points A and B. The name of a line that crosses two distinct points A and B is written as "line AB" or as.

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Step-by-step explanation:

remember,

x^-n = 1/x^n

any negative exponent of 1.3 means we have to consider it as 1/1.3 with the positive exponent.

so, if the given temperature (x) is negative, 1.3 has a positive exponent and gets bigger and bigger the lower (smaller) x gets.

if the given temperature (x) is positive, 1.3 has a negative exponent and gets smaller and smaller the higher (bigger) x gets.

the domain is the interval or set of all valid x-values.

there is no need for any restriction for x.

so, the domain is all real numbers.

the question is : up to what temperature will there be heating ?

at 5°C ? yes, sure.

at 10°C ? yes, sure.

at 15°C ? some people still need heating.

at 20°C ? most likely not.

but f(20) = $0.042094266... ≈ $0.04

so, still a tiny little bit of heating is happening for the function, but in reality most likely not at all.

the information about such a limit is missing in the question. so, again no limit for x.

f(-8) means that x = -8.

f(-8) = 8(1.3)^--8 = 8(1.3)⁸ = 8×8.15730721 =

= 65.25845768

when the low outside temperature is -8°C, it would cost $65.26 to heat the building.

I don't know the answer options to the last part, but the interpretation certainly is in the context of the problem.

According to the given statement In the given case- The  correct answer the predicted sales for different prices is 180.

Income = 34x

To break even, the company needs to sell 6 bracelets.

Given: C=4x+180 is the price (in dollars) of beads needed to make bracelets.

x is the quantity of bracelets.

The cost of each bracelet is $34.

To Locate:

A. Construct an equation that relates the revenue R to the quantity of bracelets.  

B. How many bracelets must be sold for the company to turn a profit?

Given that the bracelet costs $34,

Let's say x bracelets are sold.

Revenue formula: Price * Quantity

Income = 34x

The revenue R in terms of the quantity of bracelets is equal to 34x.

How many bracelets must be sold for the company to turn a profit

⇒4x+180

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The perimeter of the given polygon is about 16.4 units.

We want to find the perimeter of the polygon whose vertices are (-3, 2), (2, 2) and (-1, -3).

The perimeter will be equal to the sum of the distances between the vertices, and remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

d = √( (x₂ - x₁)² + (y₂ - y₁)²)

The distances are:

between (-3, 2) and (2, 2)

d = √( (-3 - 2)² + (2 - 2)²) = 5

between (-1, -3) and (2, 2)

d = √( (-1 - 2)² + (-3 - 2)²)

d = √( 9 + 25) = 6

between (-1, -3) and (-3, 2)

d = √( (-1 + 3)² + (-3 - 2)²)

d = √29 = 5.4

Then the perimeter is:

5.4 + 6 + 5 = 16.4

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Using simultaneous equations, the cost of one slice of pizza bought by Max's dad at the concession stand is $1.75.

Simultaneous equations are two or more equations solved concurrently or simultaneously.

Simultaneous equations are also called a system of equations.

                       Bottles     Slices of     Total

                     of Water       Pizza        Cost

1st purchase     5                8            $20.25

2nd purchase    1                3              $6.50

Let the cost of bottles of water = b and the cost of slices of pizza = p

Equation 1: 5b + 8p = 20.25

Equation 2: b + 3p = 6.50

Multiply Equation 2 by 5:

Equation 3: 5b + 15p = 32.50

Subtract Equation 1 from Equation 3:

5b + 15p = 32.50

-

5b + 8p = 20.25

7p = 12.25

p = 1.75

The cost of one slice of pizza (p) = $1.75

Check:

b + 3p = 6.50

b + 3(1.75) = 6.50

b + 5.25 = 6.50

b = 1.25

= $1.25

Thus, the cost of one slice of pizza is $1.75.

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Answer:

  y = 900(0.91^t)

Step-by-step explanation:

You want a function that describes the value of a $900 sound system that decreases in value by 9% per year.

When the amount of change is proportional to the amount, the amount is described by an exponential function:

  y = ab^x

where 'a' is the initial value, and 'b' is the "growth factor."

Here, the change is expressed as a "growth rate" of -9% per year. The growth factor is 1 added to the growth rate:

  b = 1 +(-9%) = 1 -0.09 = 0.91

The initial value is given as ...

  a = 900

So the function you want is ...

  y = 900(0.91^t)

__

Additional comment

The independent variable in this case is time, and the problem statement tells you to use 't' to represent it. The decay rate is given as a percentage per year, so the units of t will be years.

Negative numbers doesn't have real square roots since a square is either positive or 0.

Negative Square Roots Simplifying an expression involving the square root of a negative quantity is done by simplifying the quantity as if it was positive, and placing an i in front as a coefficient.

for example:-

The square root of -9 is 3i. But if you are talking about real numbers, then there would be no solution.

Square root

The square root of a number is defined as the value, which gives the number when it is multiplied by itself.

The √ symbol that is used to denote square root or nth roots.

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The product of two sets is the set of ordered pair of elements from each set.

We know that the set is nothing but the collection of well-defined objects or elements or numbers.

The elements of sets are written in the curly brackets, seperated by comma.

A set is represented by a capital letter symbol.

For example., the set of natural numbers is denoted by N.

N = {1, 2, 3, 4, . . .}

As we know the Cartesian Product of sets M and N is defined as the set of all ordered pairs (x, y) such that x belongs to set M and y belongs to set N.

It is denoted as M × N = {(x,y) | x ∈ M and y ∈ N}

For example, consider a set P = {1, 2}

and set M = {3, 4, 5},

From the definition of the Cartesian Product of P and M,

P × M = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}

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We can see here that the expression that represents the total change in Anaya's account on Monday is: (- $10.5) x 3.

Note that Anaya sees 3 entries for Monday, each for - $10.50.

An expression is a combination of variables, operators, and/or values that can be evaluated to a single value. Expressions can be used in various programming languages or mathematical contexts to perform operations and make calculations. For example, in a programming language, an expression may be used in an assignment statement to assign a value to a variable, or it may be used in a control flow statement to determine which code block to execute.

We see here that since Anaya actually saw 3 entries that read -$10.50, it then means the expression as seen is above.

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We know that the average price of a gallon of milk in 2000 was $2.78 and that it increased by about $0.11 per year. To find the years in which the price of a gallon of milk is between $3 and $4, we can use the following inequality:

2.78 + 0.11y < x < 4

Where x is the price of a gallon of milk in a given year y, and y represents the number of years since 2000.

The inequality can also be written as:

2.78 + 0.11y < x < 4

That can be simplified as

y > (3-2.78) / 0.11 = (0.22) / 0.11 = 2

y < (4-2.78) / 0.11 = (1.22) / 0.11 = 11

So, the years in which the price of a gallon of milk is between $3 and $4 are y > 2 and y < 11

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K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin().

To find the length of the side next to the angle, you can also divide the length by tan().

Let the hypotenuse be AC=x

Now given AB=Kx

In △ABC

sin45 ∘ = AC / AB

1/2 = kx/x

K= 1/2

K is therefore equal to 1/2 since in the right-angled triangle, one angle is 45 and the perpendicular is 10 cm.

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12 rows had been completed before Elena started working.

What is meant by rows ?

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The Equation is biquadratic , the four solutions of the equation  x⁴ - 5x² - 14 = 0 are  x = +√7 , x = -√7 ,  x = +√2i and x = -√2i   .

The Biquadratic equation is given as :  x⁴ - 5x² - 14 = 0 ;

to change the given equation to a quadratic equation ,

we substitute x⁴ = y² and x² = y .....equation(1)

the quadratic equation becomes as :  y² - 5y - 14 = 0;

Now, we observe that to factor this expression, we find the two number whose product is 14 and whose difference is 5, such numbers are 7 and 2.

that means ⇒  y² - 5y - 14 = (y - 7)(y + 2);

from equation(1) ,

we get ; ⇒  x⁴ - 5x² - 14 = (x² - 7)(x² + 2) = 0;

Solving the two factors ,

we get ;

⇒ x² - 7 = 0 ⇒ x² = 7 ⇒  x = +√7 and x = -√7 ;  and

⇒ x² + 2 = 0  ⇒ x² = -2 ⇒  x = +√2i and x = -√2i .

Therefore , the given equation has two Real Solutions and two Complex Solutions .

The given question is incomplete , the complete question is

What are the solutions of the equation  x⁴ - 5x² - 14 = 0   ?

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Multiplication fact is 4 x 4

Division fact is 16 ÷ 4

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

       16

4   4    4   4

This means,

Multiplication facts = 4 x 4 = 16

Division facts = 16 ÷ 4 = 4

Thus,

The multiplication and division facts are:

4 x 4 and 16 ÷ 4.

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Amount paid by each student = Rs.45765 / 150 = Rs.305

The school contributed an extra 1.7%. for the payment order on top of the registration fee of Rs. 45000.

To find the total amount paid by the school, we need to calculate the additional amount and add it to the registration fee:

Additional amount = (1.7/100) * 45000 = Rs. 765

Total amount paid by the school = registration fee + additional amount = 45000 + 765 = Rs.45765

To find the amount paid by each student, we need to divide the total amount paid by the school by the number of students:

Amount paid by each student = total amount paid by the school/number of students

Amount paid by each student = Rs.45765 / 150 = Rs.305

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The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)

The list of options represents the given parameter

All ordered pairs are relations but not all ordered pair are functions

For an ordered pair to be a function, the following must be true:

The y values on the ordered pair must have  different x values

Using the above as a guide,

This means that the ordered pair in option (b) represents a function

Hence, the ordered pair that is a function is (b)

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9)The value of x is 26 degrees

10)The value of x is 13 degrees

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Vertical angles are equal

2x+1=53

=> 2x=53-1 = 52

x=52/2 = 26 degrees

similarly,

5x+1=66

=> 5x=66-1 = 65

=> x=65/5 = 13 degrees

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According to estimates, there were 7,060,268,214 people on Earth as of August 16, 2012. Rounding to the nearest hundred million, 7,060,268,214 equals 7,100,000,000.

Find the digit that is 100,000,000 places away first. The next step is to check if the number that comes after the hundred million place is 5 or higher. Next, multiply the result by 100 million to the nearest billion. 200,000,000 is the reply. 4,000,000 or 5,000,000 may be the million closest to you.

Take a glance at the number in the right-hand column, the hundred thousands, to determine the nearest million. 5 appears in the column for "hundred thousands." It is standard practise to round up numbers that are five or more. This means that you should look at the digit in the ten thousand spot to round numbers out to the nearest hundred thousand. 1,000,000 is added as a rounding error.

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Trial Balance as of December 31, 20X1:

Account Debit Credit

Cash: 179,000

Equipment: 69,000

Accounts Receivable: 11,100

Accounts Payable: 69,000

Supplies: 35,000

Scott Hamilton, Capital: 179,000

Fee Income: 29,200

Telephone Expense: 590

Scott Hamilton, Drawing: 3,900

Salaries Expense: 9,900

Total: 368,190 368,190

Income Statement for the month ended December 31, 20X1:

Revenue: 29,200

Expenses:

Equipment: 69,000

Supplies: 35,000

Telephone Expense: 590

Salaries Expense: 9,900

Total Expenses: 114,490

Net Income: (85,290)

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Answer:its b

Step-by-step explanation:yall dume

Answer: 25 degrees

Step-by-step explanation:

2x + 10 + 30 = 90

2x = 50

x = 25 degrees

Answer:

I am so glad you were able to do it! Congrats on 100%

Step-by-step explanation:

That's great you got 100%!!!

A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

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The linear equation perpendicular to the line y = 1/2x - 4 is:

y = -2x + 25

A general linear equation can be written as:

y = m*x + b

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

And two lines are perpendicular if the product between the slopes is -1, then if we want to find a line perpendicular to:

y = 1/2x - 4

Then the slope m must be sch that:

m*(1/2) = -1

m = -2

Then the line is like:

y = -2*x + b

And we know that this passes through (10, 5), replacing these values:

5 = -2*10 + b

5 = -20 + b

5 + 20 = b

25 = b

So the linear equation is:

y = -2x + 25

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The log₂(7) is irrational, because if we assume that it is rational, we can reach a contradiction.

Assume that log₂(7) is rational. This means that it can be written as the ratio of two integers, a/b, where a and b are integers and b is not equal to zero.

Then, using the definition of a logarithm, we have: 2^(a/b) = 7

Multiply both sides by b, we have: 2^a = 7b

Now we have a problem, because 7b is not necessarily a power of 2. This means that our assumption that log₂(7) is rational leads to a contradiction, and therefore log₂(7) must be irrational.

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