The graph above is a graph of what function? (It's not a parabola)

Answer: 380 ft

Step-by-step explanation: To find the length in between, you simply subtract the numbers.

1,515 - 1,135 = 380

Therefore, the ladder needs to be extended 380 ft.

Answer: the initial value is 2 and the rate of change is 1.

The equation that can be used to solve for y, the length of the room is;

y² - 5y = 750

The formula for the area of a rectangle is;

Area = L * W

where;

L is length

W is width

The width of the room is 5 feet less than the length of the room. Thus;

Width = Length - 5

If length is y, then;

Width = y - 5

Area = y(y - 5)

y(y - 5) = 750

y² - 5y = 750

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Answer:

x = 3

Step-by-step explanation:

Let's check

3^4 + 7(3)^2 - 144 = 0

81 + 63 - 144 = 0

144 - 144 = 0

0 = 0

So, x = 3 is the correct answer.

79.1 mL is equal to 0.0791 litres with correct significant figures.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

79.1 mL is equal to 0.0791 litres. To convert millilitres to litres, we divide the number of millilitres by 1000:

79.1 mL / 1000 = 0.0791 liters

So, 79.1 mL is equal to 0.0791 litres with correct significant figures.

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The four basic right that were included in the first amendment are Freedom of speech , Freedom of religion , Freedom of press and Freedom of assembly .

The First Amendment of the U.S. Constitution guarantees the following four basic rights:

(i) Freedom of Speech: This includes the right to express oneself freely, whether through oral or written communication.

(ii) Freedom of Religion: This protects an individual's right to practice their own religion or to not have a religion at all, without government interference.

(iii) Freedom of the Press: This protects the right of the media to publish and report the news without government censorship or restraint.

(iv) Freedom of Assembly: This allows individuals to gather and associate with others, including the right to form and participate in organizations and protest movements.

The given question is incomplete , the complete question is

The First Amendment include four basic right or freedom. What are they ?

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The total differential to estimate the maximum error in the calculated volume of the cylinder is 200.96.

The base radius of a right circular cylinder are measured as 8 cm.

The height of a right circular cylinder are measured as 16 cm.

The possible error in measurement of as much as 0.2 cm each.

We have to calculate the maximum error in the calculated volume of the cylinder.

The formula of volume of cylinder is:

V = πr^2h

The value of dr = 0.2 and dh = 0.2. So;

dV(max) = ∂V/∂r dr + ∂V/∂dh dh

dV(max) = ∂(πr^2h)/∂r dr + ∂(πr^2h)/∂dh dh

On differentiating

dV(max) = 2πrh dr + πr^2 dh

r = 8 cm, π = 3.14 and h = 16 cm.

Now putting the value

dV(max) = 2×3.14×8×16×0.2 + 3.14×(8)^2×0.2

dV(max) = 160.768 + 40.192

dV(max) = 200.96

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Factoring out negative 1 from the expression -4-(5+3) is -1(12).

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

A) 7+(-6)

= 7-6

= 1

2) -4-(5+3)

= -4-8

= -12

= -1(12)

3) -9-1

= -10

= -1(10)

4) 8-(-6)

= 8+6

= 14

5) 3+(-4+8)

= 3+4

= 7

Therefore, factoring out negative 1 from the expression -4-(5+3) is -1(12).

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The expression x² + 6x + 9 / 4 ÷ 3x + 9 / 8 can be simplified as 2(x + 3) / x .

To simplify an expression means to write an equivalent expression which contains no similar terms. In other words, we have to reduce the expression to the simplest form.

Therefore,

x² + 6x + 9 / 4 ÷ 3x + 9 / 8

Let's convert the division sign to multiplication.

Therefore,

x² + 6x + 9 / 4 × 8 / 3x + 9

Let's factorise the numerators and the denominators expression

x² + 6x + 9 = (x +3)² = (x + 3)(x + 3)

3x + 9  = 3(x + 3)

Therefore,

(x + 3)(x + 3) / 4 × 8 / x(x + 3)

Hence,

(x + 3)(x + 3) / 4 × 8 / x(x + 3) = 2(x + 3) / x

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Answer:

(All given options are incorrect)

Correct answers: [tex]3^6[/tex] or [tex]9^3[/tex]

Step-by-step explanation:

There are several ways to write [tex]3\times3\times3\times3\times3\times3[/tex].

The first is as a power of 3. An exponent represents the number of times a number is multiplied by itself. This would be written as [tex]3^6[/tex].

The second is as a power of 9. Combining each pair of [tex]3\times3[/tex] gives:

[tex]9\times9\times9[/tex]  which is equal to [tex]9^3[/tex].

None of the given options are correct for  [tex]3\times3\times3\times3\times3\times3[/tex]. Please double check that your question and answer options are written correctly. Correct answer options would be [tex]3^6[/tex] or [tex]9^3[/tex].

Answer:

The expression that represents the verbal phrase "One-fourth times a number n, minus thirty" is (1/4)n - 30.

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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The zeros of the polynomial p(x)=(4x−5)(4x + 5) are x = 5/4 and x = -5/4

We know that the zeros of a polynomial are the points where the polynomial becomes zero.

To find the zeros of polynomial P(x), equation the polynomial to zero P(x) = 0 and find the solutions of the equation P(x) = 0

Here, the polynomial is p(x)=(4x-5)(4x + 5)

To find the zeros of polynomial p(x) we equate p(x) to zero.

We get,

p(x) = 0

(4x - 5)(4x + 5) = 0

We solve above equation for x.

⇒ (4x - 5)(4x + 5) = 0

⇒ (4x - 5) = 0   OR   (4x + 5) = 0

⇒ 4x = 5         OR       4x = -5

⇒ x = 5/4      OR     x = -5/4

Therefore, x = 5/4 and x = -5/4 are zeros of p(x)

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The rule for the pattern is to add 6 to each number.

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Answer:

x^3 = 1000

Step-by-step explanation:

The price per square foot of the house is $51.18.

The price per square foot of the house is determined by taking the total price of the house, $348,000, and dividing it by the total square footage of the house, 25' x 68' and we get $51.18.

For example- The total square footage is 1700, so when divided into the total cost, $348,000, the price per square foot of the house is $204.71. This means that for every square foot of the house, the buyer paid $204.71. The total cost of the house is a combination of the price per square foot in addition to any additional fees, such as taxes and closing costs.

When purchasing a home, it is important to know the price per square foot as this can help to determine the value of the home.

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Answer:

c.  $60

Step-by-step explanation:

Go along the x-axis until you get to 8, then go straight up until you hit the line, now go straight over to the left until you hit the y-axis.  Your horizontal line will hit the y-axis at y=$60.

Answer:

D. sign chart; zeros

Step-by-step explanation:

To fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes

A number system is defined as a system of writing to express numbers.

The term that completes the sentence and makes it grammatically and conceptually correct is "sign chart; zeros".

To fill out a function's sign chart; zeros and after each of the function's zeros, you will need to use test numbers before and after the zero to determine the sign of the function on each interval.

Hence, to fill out a function's sign chart, you will need to use test numbers before and after each of the function's zeros and asymtopes

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Z would ultimately have a value of 2, since 5 minus 7 equals 2.

x = 5; y = 7; z = x - y z = 5; y z = 7; z = 2;Consequently, z's final value is 2.

Given that x is 5 and y is 7, the final value of z would be 2. These two numbers are divided by two, giving the answer 2. Subtraction is the action of comparing two integers to determine their differences. In this instance, since x and y differ by 2, the ultimate value of z is also 2. The solution is 2, which can alternatively be written as 5 - 7 = 2. In this case, the ultimate value of z is 2, since the difference between x and y is 2, which can be found using the useful mathematical technique of subtraction.

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Oliver is farther from the station.

Let's call the initial distance from the station for Oliver and Roel as d1 and d2, respectively. The Law of Cosines states:

d1^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(30°)

d2^2 = 3^2 + 4^2 - 2 * 3 * 4 * cos(40°)

By solving the above equations, we can determine the distances d1 and d2. The hiker who is farther from the station will have the larger value of d1 or d2.

In this case, it can be seen that d1 > d2, meaning Oliver is farther from the station than Roel.

This is because the angle of 30° is larger than the angle of 40°, so the cosine of 30° is smaller than the cosine of 40°.

Therefore, Oliver is farther from the station.

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Answer:

f(x) = -4[tex]x[/tex] - 2 or y = -4[tex]x[/tex] - 2

Step-by-step explanation:

In this question, you should use the graph to write the function/equation in slope intercept form.

y = mx + b where m is the slope and b is the y intercept

To calculate the slope, you can use rise/run between any two points. I will use the points (-2, 6) and (0, -2). In these points, the "rise" would be -8 as that is the number of units they are away from each other vertically. It is negative because the line obviously has a negative slow as it is travelling from up to down. The run in this case would be 2 as that is the distance the two points are away from each other horizontally.

Then, substitute.

[tex]\frac{-8}{2}[/tex] = -4, so m = -4

Now we will find the b value.

B is the y-intercept, or what the y value of the coordinate of the point that the line touches the y-axis. The coordinate is (0, -2). Therefore, the b value is 2.

This is a false conclusion. Just because Marcelino did not win the game 2 days ago or yesterday, it does not necessarily mean he will win the game today. There could be many other factors at play that determine the outcome of the game.

This statement is referring to a hypothetical game and the outcome of it, but the conclusion that Marcelino will win today is not logically deduced from the information given (that Marcelino did not win 2 days ago or yesterday). The outcome of a game can be influenced by many factors such as the skill level of the players, the strategies used, and luck. Simply not winning in the past does not guarantee a win in the future.

This statement is not related to mathematics. It is a logical conclusion based on the given information about a hypothetical game, but the conclusion does not follow logically from the information provided.

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2³ × 3 × 5² is the prime factorization of the composite number 600.

Composite numbers are whole numbers that can be divided evenly by numbers other than 1 or themselves. For example, 4 is a composite number because it can be divided evenly by 1, 2, and 4. Other examples of composite numbers are 6, 8, 9, 10, 12, 14, 15, and so on.A composite number is a positive integer that has more than two divisors. It is the product of two or more prime numbers. Examples of composite numbers include 4, 6, 8, 9, 10, 12, 14, 15, 16 and so on.

2³ × 3 × 5² = 2 × 2 × 2 × 3 × 5 × 5

= 600

Thus, 2³ × 3 × 5² is the prime factorization of the composite number 600.

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A variable is an alphabet or phrase used to represent an unknown quantity, unknown value, or unknown number in mathematics.

The values of one or more independent variables determine the values of a single dependent variable in a mathematical connection known as a function. Function denotes a relationship between two variables where one influences expression the other (s).

Here,

Given :

=> 50 assembly kit  be y

and => 20 profit be x

Thus,

Equation is = > 50y + 20y = 15

In mathematics, a variable is an alphabet or phrase that denotes an unknowable quantity, unknowable value, or unknowable number. In the case of algebraic expressions or algebra, the variables are employed specifically.

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).

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Answer:

  (a) {6, 8, 10} cm

  (b) {12, 35, 37} cm

  (d) {10, 24, 26} cm

Step-by-step explanation:

You want to know which of the given sets of dimensions could be those of a right triangle.

A set of side lengths will form a right triangle if they satisfy the Pythagorean theorem:

  a² +b² = c²

  6² +8² = 36 +64 = 100 = 10² . . . . . {6, 8, 10} forms a right triangle

  12² +35² = 144 +1225 = 1369 = 37² . . . . . {12, 35, 37} forms a right triangle

  4 + 6 = 10 . . . . . {4, 6, 10} doesn't even form a triangle

  10² +24² = 100 +576 = 676 = 26² . . . . . {10, 24, 26} forms a right triangle

__

Additional comment

For three side lengths to form a triangle, the sum of the two short sides needs to be longer than the longest side. (This is the triangle inequality.)

Lengths 4, 6, 10 do not meet that requirement.

You may notice that the long sides of these triangles differ in length by 2 units. The short side is twice the square root of their average. This relation will hold for any right triangles having long sides that differ by 2.

  {6, 8, 10}  ⇒  6 = 2·√9

  {12, 35, 37}  ⇒  12 = 2·√36

  {10, 24, 26}  ⇒  10 = 2·√25

Along the same lines, if the longest sides differ by 1, the short side is the square root of their sum.

The required interval for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
From the graph, the portion of the function below the axis shows the f(x) ≤ 0.
So the interval where f(x) ≤ 0, from the graph, is given as,
(-∞, -2) and (2, 7)

Thus, the required intervals for which the function is f(x) ≤ 0 are (-∞, -2) and (2, 7).

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Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.

Statistical information made up of categorical variables—data that have been divided into categories—is known as categorical data. A set of grouped data is one of example. More specifically, countable qualitative data or quantitative data clustered within predetermined intervals could be used to create category data. The information is condensed into a probability table. However, the word "categorical data," which is used to describe data sets, is used when discussing data analysis. It should be noted that although the data set includes some categorical variables, it may also include non-categorical variables.

Categorical data is a collection of information that is divided into groups. I.e, if an organization or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical. This data is called categorical because it may be grouped according to the variables present in the biodata such as sex, state of residence, etc.

A. Hair color Categorical data is a type of data that can be stored into groups or categories with the aid of names.

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There are approximately 368,739,406 possible hexadecimal strings of length 9 with exactly three a’s, no b’s and two 7’s.

Hexadecimal is a numbering system that uses 16 symbols (0-9 and A-F) instead of the standard 10 symbols in decimal.

A hexadecimal string of length 9 with exactly three a’s, no b’s and two 7’s can be represented as

=> XaXaXaX7X7,

where X can be any of the hexadecimal symbols other than a and 7.

To calculate the number of possible combinations, we need to calculate the number of possible values for X.

In total, there are 16 possible hexadecimal symbols, but we need to subtract 3 (a’s) and 2 (7’s) to find the number of possible values for X.

So, the number of possible values for X is

=> 16-3-2 = 11.

With 9 positions to fill and 11 possible values for X, the total number of combinations is 11⁹, which is approximately 368,739,406.

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An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.

Given that,

h(7)=329 and h(11)=553

Linear function, y = [tex]mx + c[/tex]

Let, h = y and [tex]x =x[/tex]

A function whose graph is a straight line and which is represented by an equation of the form y = mx + c where a and b are constants, m does not equal zero, and x is any real number.

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

So,

[tex]h(x)[/tex] = [tex]mx + c[/tex]

When,

[tex]x[/tex] = 7 , [tex]h(x)[/tex] = 329

( [tex]x_{1}[/tex] , [tex]h(x_{1} )[/tex] ) = ( 7 , 329 )      (Equation-1)

When,

[tex]x[/tex] = 11 , [tex]h(x)[/tex] = 553

( [tex]x_{2}[/tex] , [tex]h(x_{2} )[/tex] ) = ( 11 , 553 )         (Equation-2)

Linear function,

[tex]\frac{h(x)-h(x_{1} )}{x-x_{1} }[/tex] = [tex]\frac{h(x_{2} )-h(x_{1} )}{x_{2} -x_{1} }[/tex]

We can substitute equation -1 and 2

[tex]\frac{h(x)-329}{x-7}[/tex] = [tex]\frac{553-329}{11-7}[/tex]

[tex]\frac{h(x)-329}{x-7}[/tex] = 224/4

[tex]\frac{h(x)-329}{x-7}[/tex] = 56

[tex]h(x)[/tex] - 329 = 56 ( [tex]x-7[/tex] )

[tex]h(x)[/tex] - 329 = 56[tex]x[/tex] - 392

[tex]h(x)[/tex] = 56[tex]x[/tex] - 392 + 329

[tex]h(x)[/tex] = 56[tex]x[/tex] - 63

Therefore,

An equation for a linear function is, [tex]h(x)[/tex] = 56[tex]x[/tex] - 63 where h(7)=329 and h(11)=553.

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