A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go, and it steadily rose 3 feet per second.

Answer:

The function f(x)= 16-4x forms an arithmetic sequence when x=1,2,3,...

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same.

The function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

When x = 1, f(x) = 16 - 4(1) = 12

when x = 2, f(x) = 16 - 4(2) = 8

when x = 3, f(x) = 16 - 4(3) = 4

As you can see, the difference between any two consecutive terms is 4, which is the same for all terms, therefore the function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

On the other hand, the function f(x) = 8 (2)^x increases exponentially, so the values obtained would be not part of an arithmetic sequence. The function f(x) = x^2/5 has no common difference between the consecutive terms, so it is not an arithmetic sequence. The function f(x) = 4/x -2 is not an arithmetic sequence either, due to the division of 4 by x and the subtraction of 2.

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This is the simplified form of the expression.

2x^2 + 4x - 9y^2 - 4y

Simplifying:

3x^2 + 2y^2 - x^2 + 4x - 5y^2 - 4y

The process of simplifying an expression involves combining like terms and eliminating any unnecessary terms. In the given expression, we have multiple terms that have the same variable and exponent, these are called like terms. Like terms can be combined by adding or subtracting their coefficients.

In this case, we have 3x^2 and -x^2, the x^2 terms have the same exponent and variable so they can be added together by combining their coefficients (3-1) = 2x^2.

3x^2 - x^2 + 4x - 5y^2 - 4y + 2y^2

Similarly, we have -5y^2 and 2y^2, the y^2 terms have the same exponent and variable so they can be added together by combining their coefficients (-5+2) = -3y^2.

The x terms and y terms are separated and not interacting with each other, so we can't combine them. Finally, we have -4y and 4x, they are not like terms and can't be combined.

So, we have 2x^2 + 4x - 3y^2 - 4y as the simplified form of the expression.

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Answer: 5 tables

Step-by-step explanation:30/6=5

You would need 5 hexagonal tables

The slope of the line y = 1/2 x - 3 is equal to 1/2.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would use an online graphing calculator to plot the given equation in slope-intercept form. By critically observing the graph (see attachment), we can logically deduce that the y-intercept is equal to -3 while the slope's line is equal to 1/2.

In conclusion, the linear function does not represent a proportional relationship because the line didn't pass through the origin (0, 0).

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Answer:

[tex]y=-3x-3[/tex]

Step-by-step explanation:

[tex]y+15=-3(x-4) \\ \\ y+15=-3x+12 \\ \\ y=-3x-3[/tex]

Answer:

C) 2hours and 3 minutes

Step-by-step explanation:

rate x number of people x time =  1 job

Rate:

[tex]\frac{1}{18(100)}[/tex]   To get 1 job done, it takes 18 people and 100 minutes  (1 hours + 40 minutes is 60 + 40 or 100 minutes

[tex]\frac{1}{18(100)}[/tex] x 12 x time = 1

[tex]\frac{12}{1800}[/tex] t = 1   Multiply both sides by [tex]\frac{1800}{12}[/tex]

t = [tex]\frac{1800}{12}[/tex] = 150

The time is 150 minutes, which is the same as 2 hours and 30 minutes.

The value of the sequence aₙ₊₁ is -5.5

The definition of the sequence is given as

8.0, 6.5, 5.0, 3.5, . . .

The above definitions imply that we simply subtract 1.5 from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ₊₁ = aₙ - 1.5

From the question, we have

aₙ = -4.0

Substitute the known values in the above equation, so, we have the following representation

aₙ₊₁ = -4.0 - 1.5

Evaluate

aₙ₊₁ = -5.5

Hence, the value of aₙ₊₁ is -5.5

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Reason:

The equation is t = 1.5p

The input p leads to the output t.

The domain only cares about the input. It's the set of allowed inputs. Since p refers to a number of something, we can only work with whole numbers {0,1,2,3,4,...} which is why Bonnie is correct.

Unfortunately Buffy is incorrect because something like p = 2.7 isn't allowed in the domain. It's a real number, but not a whole number. It doesn't make sense to have a fractional or decimal amount of pens.

An equation that shows the best estimate for the quotient include the following: D. 140 ÷ 7 = 20.

Jake is not correct because 192.5 is not close to the estimate. The decimal point belongs after the 9.

In Mathematics, a quotient simply refers to a mathematical expression that is typically used for the representation of the division of a number by another number.

Based on Jake's calculations, we can logically deduce that he forgot to place the decimal point in the following expression;

142.45 ÷ 7.4 = 1,925

Next, we would determine the maximum value of this quotient;

142.45 ÷ 7.4 = 140/7

142.45 ÷ 7.4 = 20

Therefore, the whole number part for the given decimal number would be nineteen (19) and as such, the decimal point must be placed immediately after 9 as follows;

142.45 ÷ 7.4 = 19.25

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Answer: D. x+2/x^3+2

Step-by-step explanation:

x2+x−2/x3−x2+2x−2

x2+x−2/x3−x2+2x−2

(x−1)(x+2)/(x−1)(x2+2)

x+2/x2+2

The total amount paid for the car is $13,200.00.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Convert the interest rate to decimal

Rate r = 3.5%

Rate r = 3.5/100

Rate r = 0.035

Plug the given values into the above formula and solve for accrued amount A.

A = P( 1 + rt )

A = $12,000( 1 + (0.035 × 3) )

A = $12,000( 1 + 0.105 )

A = $12,000( 1.105 )

A = $13,200.00

Therefore, the accrued amount is $13,200.00.

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Answer:

.5

Step-by-step explanation:

2.5/5

Answer:1/2 of a time

Step-by-step explanation:

The perimeter of an equilateral triangle with sides (11x - 2) will be;

⇒ (33x - 6)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The side of equilateral triangle = (11x - 2)

Now,

Since, The side of equilateral triangle = (11x - 2)

We know that,

⇒ The perimeter of equilateral triangle = 3 × Side

Thus, We get;

⇒ The perimeter of equilateral triangle = 3 × Side

                                                             = 3 × (11x - 2)

                                                             = (33x - 6)

Thus, The perimeter of equilateral triangle = (33x - 6)

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Probability that a randomly selected point falls in the white area is; 84.1%

The formula for area of a circle is;

A = πr²

where r is radius.

Thus;

A_circle = π * 4² = 50.265 cm²

Now, formula for area of triangle is;

A_tria = ¹/₂ * base * height

A_tria = ¹/₂ * 4 * 4 = 8 cm²

Thus;

Area of white portion = 50.265 cm² - 8 cm²

Area of white portion = 42.265  cm²

Thus;

Probability that a randomly selected point falls in the white area is;

P(White area) = 42.265/50.265 = 0.8408

= 84.1%

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The statement is false because adding a vector to a set of vectors can increase its span, but the new span is not necessarily the same as the original span.

The statement is false. To prove this, consider three vectors u1, u2 and u3 that span R3, and a vector u4 that is not a linear combination of

u1, u2 and u3.

The span of

{u1, u2, u3, u4}

will be a subset of the span of

{u1, u2, u3}.

This means that the span of

{u1, u2, u3, u4}

will contain all the vectors that the span of {u1, u2, u3} contains, plus the vector u4. However, it does not necessarily mean that the span of

{u1, u2, u3, u4} will be the same as the span of {u1, u2, u3},

as there may be other vectors that are in the span of

{u1, u2, u3, u4}

but not in the span of {u1, u2, u3}. Hence, the statement is false.

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The complete question is

Determine if the statement is true or false, and justify your answer. If (u1, u2, u3) spans R3, then so does (u1, u2, uz, u). O False. Consider u4 =0 True, the span of a set of vectors can only increase (with respect to set containment) when adding a vector to the set. O True, since the span of {ul, u2, u3, u4} is a subset of the span of {u1, u2, us), O False. Consider u4 = 0. The span of {u1, u2, u3, u4} is a subset of the span of {u1, u2, us}, but the span of {u1, u2, u3, u4} is not the same as the span of {u1, u2, us}.

The most common method for finding complex roots of polynomials is the use of the Durand-Kerner Method. This method is based on the Newton-Raphson Method and takes advantage of the fact that complex numbers can be represented by a pair of real numbers.

1. Initialize a set of initial guesses for the roots of the polynomial.

2. Calculate the value of the polynomial at each of the initial guesses.

3. Calculate the derivative of the polynomial at each of the initial guesses.4. Calculate the new root value by subtracting the value of the polynomial at the current guess divided by the derivative of the polynomial at the current guess.

5. Repeat steps 3 and 4 until the values of the roots converge.

6. The final set of roots is the answer.

The most common method for finding complex roots of polynomials is the use of the Durand-Kerner Method. This method is based on the Newton-Raphson Method and takes advantage of the fact that complex numbers can be represented by a pair of real numbers.

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Answer: 14.9 feet

Step-by-step explanation:

To find the distance above the ground that the top of the ladder touches the wall, we can use the Pythagorean Theorem.

We can set up the equation as follows:

a^2 + b^2 = c^2

Where c is the length of the ladder (15 feet), a is the distance above the ground that the top of the ladder touches the wall, and b is the distance that the bottom of the ladder is from the wall (2 feet).

Substituting these values and solving for a, we get:

a^2 + 2^2 = 15^2

a^2 + 4 = 225

a^2 = 221

a = sqrt(221)

Rounding to the nearest tenth, we get a = 14.866 feet. This is the distance above the ground that the top of the ladder touches the wall.

Therefore, X = 14.9 feet.

Answer:

14.9

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {2}^{2} + {b}^{2} = {15}^{2} \\ 4 + {b}^{2} = 225 \\ 4 - 4 + {b}^{2} = 225 - 4 \\ {b}^{2} = 221 \\ \sqrt{ {b}^{2} } = \sqrt{221} \\ b = 14.866 \\ b = 14.9[/tex]

Answer:

0 slice of pizza

Step-by-step explanation:

Total no of slice is 12

Dwayne ate half (6 slice) and

Mark ate half (6 slice)

12 -6 -6 = 0

Given that there were 12 slices of pizza, if Dwayne ate half (6 slices) and Mark ate a quarter (3 slices) for example, there would be 3 slices left. However, the question doesn't specify how much pizza Mark ate.

This question involves a concept in Mathematics known as fractions. Dwayne and Mark ordered a pepperoni pizza that was cut into 12 slices. If Dwayne ate half of the pizza, he ate 12/2 slices, which equals 6 slices. Since the question does not specify how much pizza Mark ate, we cannot provide the exact number of slices left. However, if for example, Mark ate 1/4 of the pizza, he would have eaten 12/4 slices, which equals 3 slices. Therefore, the number of slices that were left after both of them finished eating, in this example, would be 12 - (6+3) = 3 slices remaining.

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The unknown value of the given expression is 750.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Let x represents the square.

And y and z represent the triangle and star, respectively.

So, from the diagram we have,

x + 3y + z = 51   ....(1)

12x + 5z = 234   .....(2)

8x -6x + 3x = 60

That means,

x = 12

So, from the equation (2),

144 + 5z = 234

z = 18

Then y = 7.

Now, the required diagram in the equation form,

z(y+z-x) + x(y + z + z) = n

Substituting, the value of x, y and z,

n = 234 + 516

n = 750

Therefore, the unknown value is 750.

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Answer:

D. x > -2 and x ≤ 1

Step-by-step explanation:

-5 < 4x + 3 ≤ 7

-8 < 4x ≤ 4

-2 < x ≤ 1

x > -2 and x ≤ 1

It is found that there is a 0.493 = 49.3% probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty.

Formula for Binomial probability distribution:

[tex]P(X=x)=C_{n}_,_x_.p^x.(1-p)^{n-x}[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

It is given that 21% of customers purchase extended warranty, hence p=0.21.

The probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty is the probability that none of the first three buy, which is P(X = 0) when n = 3, hence:

[tex]P(X=x)=C_{n}_,_x_.p^x.(1-p)^{n-x}\\P(X=x)=C_{3}_,_0_.(0.21)^0.(0.79)^{3}\\=0.49[/tex]

0.493 = 49.3% probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty.

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Using the vertical angles theorem, the equation created is: 3x - 3 = 2x + 13

The value of x = 16.

To solve the problem given, use the vertical angles theorem to create an equation then find the value of x.

(3x - 3)° and (2x + 13)° are vertical angles, therefore, based on the vertical angles theorem, the equation created is:

3x - 3 = 2x + 13

Combine like terms:

3x - 2x = 3 + 13

x = 16

The value of x is: 16.

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By solving a linear equation, we will see that lines are parallel only if x = 15.

Ok, so we know that:

Notice that angle 2 is on the third quadrant of the intersection at the top, and angle 4 is on the second quadrant of the intersection below.

The two lines will be parallel only if these two angles are supplementary, this means that the measures add up to 180°.

Then we need to solve this linear equation:

2x + 10 + 4x + 80 = 180

Now we can solve that for x.

2x + 4x + 10 + 80 = 180

6x + 90 = 180

6x = 180 - 90

6x = 90

x = 90/6 = 15

So the lines A and B are parallel if and only if x = 15.

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The value of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm. This can be solved using the concept of mathematical operators.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation:

Operands: Operands are the numbers that an operation uses. The terms that are given to the operands vary according to the kind of operation.

Operator: An operator is the symbol that denotes a math operation, such as: division, addition, subtraction, and multiplication.

Given that,

length of wooden plank AB is 252 cm

divides it into four parts by inserting the points C, D and E

parts of plank are AC, CD, DE, EB

CD = 3AC,

DE = 2CD, and

DE = 2(3AC)

DE = 6AC

EB = 4AC

AB = AC + CD + DE + EB

substitute the values we get,

AB = AC + 3AC + 6AC + 4AC

252 = 14AC

AC = 252/14 = 18cm

CD = 3AC = 3(18) = 54 cm

DE = 6AC = 6(18) = 108 cm

EB = 4AC = 4(18) = 72 cm

Hence length of each part is AC = 18 cm, CD = 54 cm, DE = 108 cm, and

EB = 72 cm.

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The number that is both a multiple of 7 and 4 and is the smallest positive integer of the two is 28 .

A multiple in mathematics refers to the outcome of multiplying two numbers together.

This means that the multiples of 4 can therefore be found to be:

4, 8, 12, 26, 20, 24, 28, 32, 36, 40

The multiples of 7 would also be:

7 , 14 , 21 , 28 , 35 , 42 , 49

Given these list of multiples, the multiple that appears in both sets and is the smallest to appear is 28. This makes 28 the smallest positive integer that is a multiple of 7 and 4.

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Therefore , the solution of quadratic equation comes out to be the provided expression's factor is x-8.

Regression modeling for one-variable equations uses the polynomial result x = ax2 + b + c=0. Given that this polynomial has a second order, the First Thesis of Algebra states that there is only one solution. It is possible to find both simple and sophisticated solutions. Four variables make up a "quadratic formula," as the name suggests. This implies that there may only be one squared word. In the equation "ax2 + bx + c = 0," which is widely employed to solve arithmetic problems, the three mathematical variables a, b, and c are frequently used to depict the unknown variable "X."

Here,

x²+6x+16 is the algebraic expression provided.

The following identity can be used to factorize this:

(x+a)(x+b)=x²+(a+b)x+ab

We must therefore first identify the elements of 16.

8×2=4×4=16

That is obvious as 8-2=6.

So, as indicated, we divided the statement.

=>x²+2x−8x−16

=>x(x+2)−8(x+2)

=>(x+2)(x−8)

In light of this, the provided expression's factor is x-8.

Therefore , the solution of quadratic equation comes out to be the provided expression's factor is x-8.

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Answer:

The ratio of paper bags to hard bags is 6:2, which can also be written as 6/2 = 3/1. This means that for every 3 units of paper bags, there is 1 unit of hand bags.

If there are 192 bags in total, and the ratio of paper bags to hard bags is 3:1, then there must be 3 + 1 = 4 parts in total. We can find the number of bags in each part by dividing the total number of bags by the number of parts: 192 bags / 4 parts = 48 bags/part.

Since there are 3 parts of paper bags for every 1 part of hard bags, there must be 3 * 48 bags/part = 144 paper bags. Answer: {144}.

Step-by-step explanation:

The best approximation of the area of a circle with a radius of 5 ft is 75.4 ft².

Area is a quantity that expresses the size of a two-dimensional figure or shape, or planar lamina, in the plane. It can be thought of as the amount of surface that the shape covers. Calculating the area of a shape or surface can be an important step in many mathematical problems. There are several methods for calculating area, including the use of geometric formulas and equations, as well as using tools such as a ruler or calculator.

This is calculated using the formula A=πr², where π is 3.14 and the radius is 5 ft. Thus, A=3.14 x 5² = 75.4 ft².

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The measures of the missing angles for m<1, m<2, m<3, m<4, and m<5 are 35°, 145°, 55°, 125°, and 55°, respectively.

[tex]$m \angle 1=$[/tex] 35°

[tex]$m \angle 2=$[/tex] 180° - 35° = 145°

[tex]$m \angle 3=$[/tex] 90° - 35° = 55°

[tex]$m \angle 4=$[/tex]180° - ∠5 = 180° - ∠3 = 180° - 55° = 125°

[tex]$m \angle 5=$[/tex]∠3 = 55°

When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The law of sines states that the ratio of a triangle's side length to the sine of its opposing angle is constant. Given enough data, it is possible to use the law of sines to determine the unknown angles and sides of a triangle. The law of sines states that the ratio of a triangle's side length to the sine of its opposing angle is constant.

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To determine the value of an expression, substitution entails substituting numbers for letters.

In an algebraic statement, substitution refers to substituting the variables' (variables') letters with their numerical values. After that, we may calculate the expression's overall value.

To determine the value of an expression, substitution entails substituting numbers for letters.

Steps for the Replacement Method

x plus 3x equal to 32

4x equal to 32

xequal to 8

Therefore, the answer is -8.

The complete question is:

System of equations using substitution.

y=3x

x+y=-32

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The required solution of the given equation is x = y = -8.

The replacement strategy is the arithmetical technique to tackle synchronous straight conditions. As the word says, in this strategy, the worth of one variable from one condition is subbed in the other condition.

We have,

x = y

And 3x + y = -32

Then

3x + x = -32

4x = -32x

x = -8 = y

Thus, solution of equation x = y = -8.

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