PLEASE HELP ASAP THERE ARE 3 QUESTIONS!!!!!! CORRECT ANSWER GETS BRAINLLEST!!! WORTH 100 POINTS. PLEASE HELP!!!!!!!!!!!!!!!!!!!!

All these antiderivatives are equivalent as they are different ways of solving the same problem and differ only by a constant value.

What is an antiderivative?

An antiderivative, also known as a primitive function or indefinite integral, is the reverse operation of taking a derivative. In other words, if the derivative of a function f(x) is g(x), then f(x) is said to be an antiderivative of g(x).

The antiderivative of sin(x)cos(x) can be found using the product-to-sum identities:

(sin(x)cos(x))' = (sin(x)cos(x))'
                      = (1/2)(cos(2x) - sin(2x)) + C

Another way to find the antiderivative of sin(x)cos(x) is to use the chain rule:
(sin(x)cos(x))' = (sin(x))'cos(x) + sin(x)(cos(x))'
                     = -sin(x)cos(x) + cos(x)sin(x) + C

A third way is to use integration by parts, where we take u = sin(x) and dv = cos(x)dx. This gives us:
(sin(x)cos(x))' = sin(x)cos(x) - ∫cos(x)sin(x)dx + C

Another way is to use the substitution method, where we set u = cos(x) and du = -sin(x)dx. This gives us:
(sin(x)cos(x))' = sin(x)cos(x) + ∫-sin(x)cos(x)du + C

Lastly, we can use the trigonometric identity method where we use sin(2x) = 2sin(x)cos(x) and integrate.
This gives us: (sin(x)cos(x))' = (1/2)sin(2x) + C

Hence, All these antiderivatives are equivalent as they are different ways of solving the same problem and differ only by a constant value.

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The correct option for the given congruence of triangle is:

ΔGTA ≅ ΔQME.

Consider the order in the given triangles: ΔGTA and ΔQME:

GT = QM

TA = ME

AG = EQ

Thus,

ΔGTA ≅ ΔQME

By using the side side side (SSS) congruence.

Therefore, the correct option for the given congruence of triangle is:

ΔGTA ≅ ΔQME.

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The correct number of question is 11.

Th area of parallelogram with vertices (-3, 0), b(-1, 7), c(9, 6), and d(7, -1) is 46.5 square units.

The vertices of a parallelogram are a (-3, 0), b(-1, 7), c(9, 6), and d(7, -1).

Area of triangle abc= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\-1&7&1\\9&6&1\end{array}\right][/tex]

=1/2[-3(7-6)-1(-6-63)]

= 1/2[-3(1)-1(-66)]

=1/2[63]

=63/2 sq. units

Area of triangle acd= [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}-3&0&1\\9&6&1\\7&-1&1\end{array}\right][/tex]

=1/2[-3(6+1)-1(-9-42)]

= 1/2[-3(7)-1(-51)]

=1/2[-21 + 51]

=1/2[30]

=15

Area of parallelogram abcd = Area of triangle abc + Area of triangle acd

= 63/2 + 15

= (63 + 30)/2

= 46.5 sq units.

Therefore, the area of the parallelogram is 46.5 sq. units.

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Answer:

correct answer is 72

Step-by-step explanation:

The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:

1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)

2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).

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The probability of the sum of the two recorded numbers being less than 4 is [tex]\frac{3}{4}[/tex].

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.

This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.

1) both numbers are 1 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} = \frac{1}{16}[/tex])

2) one number is 1 and the other is 2 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} =[/tex] [tex]\frac{1}{16}[/tex])

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The number of 2-button special moves possible with the controller is 42 combinations.

For the given query:

The number of total buttons : 4 + 3 = 7

Number of digits two be formed 2-button special moves.

So,

First place cane be filled with all 7 numbers.

Second place can be filled with remaining 6 numbers.

Thus,

= 7 x 6

= 42 combinations.

Thus, the number of 2-button special moves possible with the controller is 42 combinations.

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Answer: 12

Step-by-step explanation:

For the equation to have infinitely many solutions, it must be an identity.

[tex]3(5+x)+kx+8=7(2x+3)+(x+2)\\\\15+3x+kx+8=14x+21+x+2\\\\x(k+3)+23=15x+23\\\\\implies k+3=15 \implies k=12[/tex]

a function that transforms the parent root function with a horizontal compression by a factor of 5 and a downward shift of 10 units is: [tex]f(x) = \sqrt[n]{5x} -10[/tex]

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Parent root function is given by:

[tex]f(x) = \sqrt[n]{x}[/tex]

According to rules-

Combining these 2 transformation gives us the function: [tex]f(x) = \sqrt[n]{5x} -10[/tex]

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Answer:

Step-by-step explanation:

We are given that,

The surveyor is located 340 meters from one entrance at an angle of 58°.

The surveyor is located 193 meters from one entrance at an angle of 21°.

Let the length of the tunnel = x meters

Using the Law of Cosines,

[tex]x^{2} =(340)^{2}+(193)^{2}-(2)(340)(193)cos(21+58)\\x^{2} =115600+37249-131240cos(79)\\x^{2} =115600+37249-25041.77255\\x^{2} =127807.2274\\x=\sqrt{127807.2274} \\x=357.50 meters\\[/tex]

Answer:

See below

Step-by-step explanation:

Better description of what you want.

D)

3 - 2(s - 1) = 13 + 6s  Distribute the -2

3 -2s + 2 = 13 + 6s  Combine like terms

5 - 2s = 13 + 6s  Add 2s to both sides

5 - 2s + 2s = 13 + 6s + 2s

5 = 13 + 8s  Subtract 13 from both sides

5 - 13 = 13 - 13 + 8s

-8 = 8s  Divide both sides by 8

[tex]\frac{-8}{8}[/tex] = [tex]\frac{8s}{8}[/tex]

-1 = s

E)

2(n + 9) = -6 (2n-5) + 8  Distribute the 2 nd the -6

2n + 18 = -12n + 30 + 8  Combine like terms

2n + 18 = -12n + 38  Add 12n to both sides

2n + 12n + 18 = -12n + 12n + 38

14n + 18 = 38  Subtract 18 from both sides

14n + 18 - 18 = 38 - 18

14n = 20  Divide both sides by 14

[tex]\frac{14n}{14}[/tex] = [tex]\frac{20}{14}[/tex]

n = [tex]\frac{20}{14}[/tex]  Divide the numerator and denominator by 2 to simplify

n = [tex]\frac{10}{7}[/tex]

F)

5(4k -3) -5k = 10 +2(3k + 1)  Distribute the 5 and the 2

20k -15 - 5k = 10 +6k +2  Combine like terms

15k - 15 = 12 + 6k  Subtract 6k from both sides

15k - 6k - 15 = 12 + 6k -6k

9k -15 = 12  Add 15 to both sides

9k - 15 + 15 = 12 + 15

9k = 27  Divide both sides by 9

[tex]\frac{9k}{9}[/tex] = [tex]\frac{27}{9}[/tex]

k = 3

This is a piecewise defined function. For input values of x between -4 and 3 (exclusive), the function is defined as f(x) = x + 4. For input values of x between 3 and 6 (exclusive), the function is defined as f(x) = 2x - 1.

In the given time interval [0,7]:

(a) the maximum speed is 1096.63 units at t = 7 and

(b) the minimum speed is 0.91 units at time t = ln2/4.

Parametric equations of the curve

x(t) = [tex]e^t + e^{-t}[/tex]

y(t) = [tex]e^{-t}[/tex]

so, dx/dt = [tex]e^t - e^{-t}[/tex]

dy/dt = [tex]-e^{-t}[/tex]

So, speed: v(t) = [tex]\sqrt{(dx/dt)^2 + (dy/dt)^2}[/tex] = [tex]\sqrt{(e^t-e^{-t})^2 + (-e^{-t})^2}[/tex]

When v(t) is maximized or minimized, evidently v² is also maximized or minimized because speed is a positive quantity.

or (speed)² = v² = [tex](e^t-e^{-t})^2 + (-e^{-t})^2[/tex] = [tex](e^{2t} + 2e^{-2t} -2)[/tex]

Now, to get the maxima or minima of a curve we have to derivate function

d/dt(v²) = 0 or d/dt[tex](e^{2t} + 2 e^{-2t} -2)[/tex]

or [tex]2e^{2t} -4 e^{-2t} = 0[/tex] or [tex]e^{2t} = 2 e^{-2t}[/tex]

taking logs on both sides

4t lne = ln2 or 4t = ln2 or t = ln2/4

so, the only critical point is t = ln2/4 ∈ [0,7]

To calculate the maxima/minima of v, we will find functional values at the critical point and boundary values of the given interval [0,7].

At t = 0 : v(0) = [tex]\sqrt{e^0 + 2e^0 - 2} = \sqrt{1+2-2}[/tex] = 1

At t = ln2/4: v(ln2/4) = [tex]\sqrt{e^{2ln2/4} + 2e^{-2ln2/4} - 2} = \sqrt{2\sqrt{2} -2 }[/tex] = 0.91

At t = 7: v(7) = [tex]\sqrt{e^{14} + 2e^{-14} - 2}[/tex] = 1096.63

Therefore, in the given time interval [0,7]: (a) the maximum speed is 1096.63 units at t = 7 and (b) the minimum speed is 0.91 units at time t = ln2/4.

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The experimental probability of a cube tossed 60 times, landing on a number greater than 4 is the option;

18 over 60

A probability is the fraction or proportion of the times an event will occur when an experiment or task is repeated. It is the measure of the liklyhood an event will occur

Probability compares the number of times an event occurs to the number of times all possible event outcomes occurs.

The formula for the experimental probability is presented as follows;

[tex]Probability = \frac{The \ sum \ of \ the \ times \ the \ event \ takes \ place}{The \ sum \ of \ the \ trials}[/tex]

The number of times the outcome from tossing the coin is greater than 4 obtained by adding the frequencies when for the outcomes of 5 and 6 are;

Number of outcomes greater than 4 = 10 + 8 = 18

The sum of all trials = 12 + 13 + 11 + 6 + 10 + 8 = 80

Therefore, the experimental probability = 18/60

The correct option is; 18 over 60

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Answer: B: 18/60 (18 over 60)

Step-by-step explanation:

The distance between base of ladder and the building should be

4.4 meter.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC² = AB² + BC²

Given,

Height of the window from the ground AB = 9 meter

Length of the ladder AC = 10 meter

Distance between base of ladder and building BC = ?

By Pythagorean theorem,

In the right ΔABC

AC² = AB² + BC²

10² = 9² + BC²

BC² = 10² - 9²

BC² = 100 - 81

BC² = 19

BC = √19

BC = 4.359 meter

BC = 4.4 meter

Hence, base of ladder should be 4.4 meter away from the building.

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Square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Net of a square pyramid consist of triangles and square.

The net of a pentagonal prism consists of two pentagons and five rectangles.

The net of a triangular prism consists of nine triangles

The net of a triangular pyramid consists of four triangles

Hence, square pyramid has triangles and square, pentagonal prism has two pentagons and five rectangles,  triangular prism has nine triangles and  triangular pyramid has triangles

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The simples radical form in which the line divides quadilateral is 4 + √ 5

Congruent quadrilaterals are quadrilaterals that have the same size and shape. They have corresponding sides and angles that are equal in measure. In other words, if one quadrilateral can be superimposed on another, they are congruent.

y  =  x/2

This line will  intersect the square at x values  -a  and a

So....the associated y values are:

y =  (-a)/2  =  -a/2     and   (a)/2  

So....the perimeter of one of the quadrilaterals is

=> 2a  +  [(a) -  (-a/2)] + [(a) - a/2 ]  + √  [ ( a - (-a)) ^2 + ( a/2 - (-a/2)^2]  =

=> 2a  + 3a/2  + a/2  + √  [ 4a^2  + a^2 ]  

4a  +  a√ 5  

dividing the above equation by a  produces  = 4  + √ 5

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Complete question:

The square with vertices (-a, -a), (a, -a), (-a, a), (a, a) is cut by the line y = x/2 into congruent quadrilaterals. The perimeter of one of these congruent quadrilaterals divided by a equals what? Express your answer in simplified radical form.

The initial weight of the toy before removing the spare parts was found to be 440gm since the weight after 25% removal was given as 330gm

The final weight of the toy after removal of spare parts is given as 330g

Percentage weight removed in the form of spare parts from the toy= 25%

Let us consider the initial weight to be x

The equation becomes,

x – 0.25x = 330, since 25% is removed from the original weight of the toy to give us the final weight of 330gm

0.75x= 330

x = 330/0.75

x = (330*100)/75

x = 440

Therefore, initial weight of the toy was found to be 440g

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A formula is used to find a Center of a circle with a (h, k) center and a radius of r has the equation:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A circle is a collection of all points in a plane that are uniformly distanced from a fixed point. The radius of a circle is the difference between the center and any point itself along the perimeter.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. The equation for a circle with a (h, k) center and a radius of r is:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

This is the equation's standard form. So, if we know the radius and center coordinates of a circle, we can rapidly determine its equation.

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There are two ways to fence the garden in 3 areas with some equal sections.

2/5, 2/5, 1/5 and 3/5, 1/5, 1/5.

Fraction definition

A fraction depicts a segment or component of the whole. It represents the equal parts that make up the whole. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that are taken.

Given The garden is divided into 5 equal pieces, each of which is 1/5 of the total garden size.

By arranging some equal parts together, she will fence the garden into three sections. There are two ways to do this.

(1/5 +1/5) = 2/5

(1/5 +1/5) = 2/5

1/5

these are the 3 areas 2/5, 2/5, 1/5.

and

(1/5 +1/5 + 1/5) = 3/5

1/5, 1/5

these are 3 areas =  3/5, 1/5, 1/5.

Hence there are only two ways to fence the garden into three areas by grouping some equal sections.

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On solving the provided question, we can say that the probability of both = 4/9*1/3 or 4/27

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

18 marbles  = 8 are blue and 6 are red .

probability  a blue marble = 8/18 = 4/9.

probability of getting a red marble i=6/18 = 1/3.

probability of both = 4/9*1/3 or 4/27

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The value of x in the simplest radical form is 6.633

What is value ?

Value in mathematics can refer to a number of concepts that are closely related. Any specific mathematical object can be a mathematical value in general. In elementary mathematics, this is typically a number, such as a real number like or an integer like 42.

The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. For illustration, let's look at the number 45.

The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.

cos Ф = adjacent / hypotenuse

cos 45° = √22 / x

x = √22 / cos 45°

  = (√22* √2 )

  = √44

  = 6.633

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Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 chocolate for $10 by setting up and solving a system of equations.

The question is asking how much of each kind of chocolate Jim can buy for $10. To solve this, you can set up a system of equations.

Let x = pounds of kind 1, and y = pounds of kind 2

x + y = 5 (total pounds of chocolate)

1.8x + 2.3y = 10 (cost of chocolate)

Solving the system of equations, you get x = 3.75 pounds of kind 1 and y = 1.25 pounds of kind 2. Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 for $10.

1.8x + 2.3y = 10

1.8x = 10 - 2.3y

x = (10 - 2.3y)/1.8

x + y = 5

x = 5 - y

(10 - 2.3y)/1.8 = 5 - y

10 - 2.3y = (1.8)(5 - y)

10 - 2.3y = 9 - 1.8y

1.2y = 10 - 9

1.2y = 1

y = 1/1.2

y = 0.833 (rounded to 1.25)

x = 5 - y

x = 5 - 0.833

x = 4.167 (rounded to 3.75)

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Answer:

so the square root is x so when you point the square root at the rwaterfall you waill have your

Step-by-step explanation:

the drone would need to be 1.4 miles away from your to be the opposite value. pou pou pou pou pou pou pou pou pou pou pou pou ufo p

Step-by-step explanation:

A random sample variance is when a subset of individuals from a population is chosen using a random selection method, such as a random number generator, to ensure that each individual has an equal chance of being chosen.

A random sample is a type of sampling method used to select individuals from a population to form a sample. To generate a random sample, a list of all the individuals in the population must first be created. Each individual should be numbered consecutively. A random number generator, such as a computer or calculator, can then be used to generate a list of random numbers between 1 and the total number of individuals in the population. The individuals who correspond to the numbers generated by the random number generator form the sample. This ensures that each individual in the population has an equal chance of being chosen for the sample.

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No , it is not possible to draw a triangle with the given side length of 4cm , 3cm , and 7cm as sum of two sides ( 4cm + 3cm ) is not greater than the third side ( 7cm).

As given in the question,

Measure of the required triangle are given as follow:

Measure of Side length 1 = 4cm

Measure of Side length 2= 3cm

Measure of Side length 3 = 7cm

To draw a triangle following condition need to be satisfied:

Sum of the measure of two side length is always greater than the measure of the third side length.

Here for a given triangle ,

4cm + 3cm

= 7cm

= measure of the side length 3

It does not satisfied the required property to draw a triangle.

Therefore, it is not possible to draw a triangle with given measurements as ( 4cm + 3cm ) is not greater than the third side.

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Triangle ΔABC is comparable to triangle ΔABC, which was formed after ABC's dilatation. The appropriate answers are The characteristics of dilations show that angles ∠B =∠ B'.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the flanks of the hook, that converge at the vertex of both the angle, which is located in the centre. Two rays may combine to form an angle in the plane in which they are positioned. Two planes colliding results in an angle as well. We refer to them as dihedral angles.

Here,

Assuming that A (0, -3), C (0, 5), and B are the triangle's vertices (6, 3)

Set point P to be (0, 0)

There is;

A' = 3/2 * (0,-3) = (0,-9/2) = (0,-4.5) (0,-4.5)

C' = 3/2 * (0,5) = (0, 15/2) = (0,7.5) (0,7.5)

B' = 3/2 * (6,6/3) = (9 , 9/2) = (9,4.5) (9,4.5)

Therefore, on a scale, the image of ABC is bigger than that of the image of A'B'C.

The proportion of the adjacent angles of ABC is given by a factor of 1.5.

since and "A'B'C" are both equal, the angle made by section BC and

BA,

AB/sin(C) = AC/sin(B)

AB/sin(C) = A'C'/A'B' = sin(B)/sin (C)

This means that

sin(B)/sin(C) = sin(B')/sin(C').

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The complete question is "A. Dilate triangle ABC using center p and scale factor 3/2.

B. What do properties of dilations tell you about B'? (please answer B)"

There are a total of 9 women and 6 men on the council, for a total of 15 council members.

If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:

So the total number of ways to choose 2 people of the same gender is 3+15 = 18.

The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105

So the probability of choosing 2 people of the same gender is 18/105 = 6/35

So, the probability that these chairpersons are the same gender is 6/35.

Answer:

12B + 8L ≤ 140

Step-by-step explanation:

B = number of hours babysitting.

L = number of hours landscaping.

Harper must earn no less that $140, so the amount Harper must eqrn is greater than or equal to 140.

Amount earned from babysitting at $12/hour = 12B

Amount earned from landscaping at $8/hour = 8L

Total amount earned = 12B + 8L

Inequality:

12B + 8L ≤ 140

The numbers that are potential roots of the function given above are:
Option B-D. That is -  ±1, ±2, and ±12.

It is correct to state that in mathematics, a root of an equation is a value that, when substituted into the equation, makes the equation true.

To obtain the potential roots of the expression p(x) = x⁴ + 22x² - 16x - 12:

Note that from the rational root theorem, all the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

Thus, according to the polynomial above,  we know that

Factors of 1 are ±1.

Thus, according to the theorem of rational root, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function from the options listed are: are ±1, ±2, and ±12.

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Full Question:

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² - 16x - 12?

± 5
±1

±2

±12

±17

So, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate

To find out how many days it takes for all 24 gallons of water to leak out of the pool, we need to determine the rate at which the water is leaking and use that to calculate the total time it takes for the pool to empty.

We know that the pool initially has 24 gallons of water and that it is leaking out at a rate of 2 gallons every 3 days. This means that the pool loses 2/3 of a gallon of water per day.

To find out how many days it will take for the pool to empty, we can divide the total amount of water in the pool by the rate at which it's leaking out.

24 gallons / (2/3 gallons/day) = 24*3/2 = 36 days

Therefore, it would take 36 days for all 24 gallons of water to leak out of the pool at this rate.

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As stated in the problem, the equation can be modeled by the equation:

[tex]y=0.35x[/tex]

The problem also defines the meaning of these variables:

y = bounce height in feet

x = release height in feet

Now, the question asks "If the ball is released from a height of 70 feet, what is the height the ball will achieve after the first bounce?"

From this question, we know that we want to solve for bounce height (y). We are also given the release height (x) of 70. Plug this value into the equation we were given at the start.

[tex]y=0.35(70)[/tex]

Now, just multiply the two values together:

[tex]y=24.5[/tex]

Therefore, we now know that the ball achieved a bounce height of 24.5 ft on the first bounce!