which of thw following equations has roots x=-1, x=-2, and x=3i, and passes through the point (0,36)?

Which Of Thw Following Equations Has Roots X=-1, X=-2, And X=3i, And Passes Through The Point (0,36)?

Answers

Answer 1

Answer:

  C.  f(x) = 2x⁴ +6x³ +22x² +54x +36

Step-by-step explanation:

You can use Descartes' rule of signs and the y-intercept to help you select the correct answer.

Y-intercept

The given point (0, 36) is the y-intercept of the function. This tells you 36 is the constant in the polynomial, eliminating choices A and B.

Rule of signs

Descartes' rule of signs tells you the number of positive real roots will be less than or equal to the number of sign changes in the coefficients when the function is written in standard form. The number of negative real roots will be the number of sign changes after the signs of odd-degree terms are reversed.

Given roots

The given real roots are both negative. There are zero positive real roots, so all of the signs of the coefficients in the function must be the same (no changes). This eliminates choice D, and tells you C is the correct answer.

  f(x) = 2x⁴ +6x³ +22x² +54x +36


Related Questions

Baseball And Calculus

Answers

Answer:

Calculus in baseball. In baseball, calculus can be used to optimize the pitcher’s throw to achieve maximum efficiency. Also, calculus can be used to calculate the projectile motion of baseball’s trajectory and to predict if runners can make it to the next base on time given their running speed and the speed of a hit ball.

Step-by-step explanation:

Can someone tell me what number on the number line is greater than -9 for an inequality?

Answers

Answer: Any number that is to the right of it, hence greater/bigger.

-8,-7,-6,-5.....

Step-by-step explanation:

Example: If you have -8 vs -9 vs -10 dollars, You have more with -8 vs -9 or -10.

Hence anything to the right of a give number on the number line is greater.

Also, think of the opposite with negatives.

For example with positive numbers, the larger the number the greater, but with negative numbers its the other way around, the smaller the number the greater.

The graph below shows how much money Isaac earns by washing cars. 1. Explain if the graph above displays a proportional relationship, including evidence to support your reasoning. 2. Explain what the coordinate shown on the line represents given the problem context provided. ​

Answers

1. The graph will represent a proportional relationship if these two following statements are correct.

The intercept is of zero.The slope of the line is constant.

2. The coordinate (x,y) represents the amount of money y earned for washing x cars.

What is a proportional relationship?

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

Input x: number of cars washed.Output y: amount of money earned.

Hence the coordinate (x,y) represents the amount of money y earned for washing x cars.

Missing Information

The problem is incomplete, hence the answer is given in general terms using concepts of proportional relationships.

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You start with $575 in your bank account and deposit $60 each month. Write a linear or exponential equation

Answers

Answer:

A linear equation can be used to represent the situation where a fixed amount is added to the original balance each month. The equation would have the form:

y = mx + b

where x is the number of months, y is the balance in the bank account, m is the monthly deposit amount, and b is the initial balance. In this case, we have:

y = 60x + 575

This equation can be read as: "The balance in the bank account (y) is equal to 60 dollars (m) added to the account each month (x), plus the initial balance of 575 dollars (b)."

An exponential equation can also be used to represent the situation where the balance in the bank account increases by a fixed percent each month, it would be:

y = a(1+r)^x

Where a is the initial amount, r is the interest rate and x is the number of months.

Step-by-step explanation:

A triangle has angle measures 23° and 35°. What is the measure of the third angle?

Answers

Answer:

122°

Step-by-step explanation:

All triangles have a total of 180°.

Angle 1 will be X

Angle 2 will be Y

Angle 3 will be z

180 - (x + y) = z

1. Find the present value of $5000 to be received in 2 years if the money can be invested at 12%
interest rate compounded continuously.(1 Point)
$6272
O $6365.75
$6356.25

Answers

The present value of $5000 to be received in 2 years at a 12% interest rate compounded continuously is $6356.25. This can be calculated by using the formula PV = FV/(1 + r)^t, where PV is the present value, FV is the future value, r is the interest rate, and t is the time period. Therefore, PV = 5000/(1 + 0.12)^2 = $6356.25.

Answer:

C) $6356.25

------------------------------

Use the continuous compound equation:

A = Pe^(rt), where A  - future value, P - present value, r - annual interest rate, t - number of years

Substitute and calculate:

A = 5000*e^(0.12*2) = 6356.25 (rounded)

The matching choice is C.

Create a rectangle ABCD on a coordinate plane that meets the following conditions:

1. all four points are in different quadrants
2. point A is in Quadrant Il with coordinates (-a, b)
3. the distance from point A to point B is 3a
4. the distance from point A to point D is 4b
5. neither axis is a line of symmetry in the rectangle

Answers

Therefore , the solution of the given problem of expression comes out to be 794.0481.

Describe expression.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

Here,

3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Given : 5 +

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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On solving the provided question, we can say that a rectangle ABCD on a coordinate plane, point A is in Quadrant Il with coordinates (-a, b), the distance from point A to point B is 3a

What is rectangle?

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

a rectangle ABCD on a coordinate plane,

point A is in Quadrant Il with coordinates (-a, b).

the distance from point A to point B is 3a

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Angela ran for 45 mins, her pace was 9 mph. How far did she run (in miles)?

Answers

Angela ran for 6.75 miles

Round the angle measure to the nearest hundredth of a degree

Answers

The measure of the angle is 30.00 degrees

How to find sin⁻¹(0.5)?

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is concerned with the measurement of angles and the calculation of sines, cosines, and tangents of those angles.

These ratios are known as trigonometric functions and they are used to relate the ratios of the sides of a right triangle to the angles opposite or adjacent to the right angle.

Since sin 30° = 0.5

Thus, sin⁻¹(0.5) = 30.00 degrees

Note: Angle 30° is one of the special angles and trigonometric are very easy recall.

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Please helpppp
solve the inequality

Answers

Answer:

A) [tex]x>-2[/tex]

Step-by-step explanation:

[tex]x+4>-x \\ \\ 2x+4>0 \\ \\ 2x>-4 \\ \\ x>-2[/tex]

Use a trigonometric ratio to solve for y. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?

Answers

Using Trigonometric identities, the value of y = 11.49.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.

These are identities that, geometrically speaking, involve certain functions of one or more angles.

They are not to be confused with triangle identities, which are identities that may involve angles but may also involve side lengths or other lengths of a triangle.

Using Trigonometric Identities,

Cos θ = Base / Hypotenuse

Cos 29 = 10 / y

0.87 = 10 / y

y = 10 / 0.87

y = 11.49

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Is △pmr similar to △smn? if so, which postulate or theorem proves these two triangles are similar? responses ​△pmr​ ​is similar to ​△smn​ ​ by the ​​​ ​ssa similarity theorem​. ​, triangle p m r, ​, , ​, , is similar to , ​, , , triangle s m n, ​, , ​, , , by the , ​, ​, , ​, , ​, s s a similarity theorem, ​, , . ​△pmr​ ​is similar to ​△smn​ ​by the ​​ ​sas similarity theorem​. ​, , triangle p m r, ​, , ​, , is similar to , ​, , , triangle s m n, ​, , ​, , by the , ​, ​, , , ​, s a s theorem, ​, . ​△pmr​ ​is similar to ​ ​ ​△smn​ ​by the​ ​sss similarity theorem​​. ​, triangle p m r, ​, , ​, , is similar to , ​, , ​, , ​, triangle s m n, ​, , ​, , by the, ​, , , , ​, s s s similarity theorem, ​, ​, . ​△pmr​ ​is not similar to△smn​​. ​, , triangle p m r, ​, , ​, , is not similar to, , , , triangle s m n, ​, , ​, . a triangle with vertices p m r. segment s n is inside the triangle. point s is on side p m. point n is on side m r. p s is equal to 8 feet. s m is equal to 14 feet. m n is equal to 21 feet. n r is equal to 12 feet.

Answers

Right angles, isosceles triangles, acute angles, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.

Describe the triangles.

The term "trigon" is frequently (though not usually) used to refer to a triangle, a 3-sided polygon. Every triangle consists of a set of three angles and three sides, of which some might be the same. Three points and three sides make up a triangle, which is a polygon. The three angles of the triangle sum up to 180 degrees. With three sides & three vertices, triangles are a specific type of polygon in geometry. The two-dimensional figure displayed here has three straight sides. A triangle is a type of 3-sided polygon.

Here ,

are a number of triangles.

Triangular Scalene. a triangle that doesn't have adjacent sides.

a triangle where each of a three angles is far less than 90° degrees is referred to as a sharp triangle.

Straight triangle a triangular including one angle that extends beyond 90 degrees.

Isosceles, right, and equilateral triangles are examples of triangles.

Right angles, isosceles triangles, acute triangular, obtuse triangles, scalene triangles, and equilateral triangles are some of the several types of triangles.

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Are complex numbers the same as real numbers?

Answers

Although every complex number is a real number, not all complex numbers are real numbers.

What connection exists between real numbers and complex numbers?On the number line, the real numbers can be plotted.The number line cannot be used to plot the complex numbers.The symbol designates it.Complex numbers make up all real numbers.Real numbers are not all complex numbers.Although every complex number is a real number, not all complex numbers are real numbers. The symbol Z C Z in mathbb C ZC denotes the collection of all complex numbers.If a number can be expressed as a+bi using the real integers a, b, it is complicated. So, certainly, a complex number can be both real and totally fictitious.

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The prism below has dimensions of 2 feet (ft.), 3 feet (ft.), and 8 inches (in.).

What is the volume of the prism in cubic inches?

Answers

The volume of the prism in cubic inches is 6912 inch³.

What is Volume?

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Volume of Cuboid = length x width x height

Given:

length =  3 feet = 36 inch

width = 8 inch

height = 2 feet = 24 inch

So, Volume of cubic prism

= length x width x height

= 36 x 8 x 24

= 6912 inch³

Hence, the volume is 6912 inch³

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Which are two solutions for the given equation 3x 4y 7?

Answers

The solutions of the given equation  are given below:

(i) 3x+4y =7

(ii) x=6y

(iii) x+πy =4

(iv) x-y =4

All these equations are having infinitely many solution.

Infinitely Many solution:

An equation can have an infinite number of solutions if certain conditions are met. If the lines are coincident and have the same y-intercept, the system of equations has infinitely many solutions. If two lines have the same y-intercept and slope, they are really on the same line.

(i) Given :

3x + 4y = 7                        --------------------------- (1)

On putting x = 0 in equation 1

3x + 4y = 7

⇒ 3 × 0 + 4y = 7

⇒ 0 + 4y = 7

⇒ 4y = 7

⇒ y = 7/4

Therefore, ( 0, 7/4) is a solution of given equation.

On putting y = 0 in equation 1

3x + 4 × 0 = 7

⇒ 3x + 0 = 7

⇒ 3x = 7

⇒ x = 7/3

Thus, (7/3, 0) is a solution of given equation.

Hence, 2 out of the infinitely many solutions of the given equation are(0,7/4), (7/3,0).

 

(ii) x = 6y

Let x = 0

⇒ x = 6y

⇒ 0 = 6y

⇒ y = 0/6

⇒ y = 0

(0,0) is the solution.

Let x = 1

⇒ x = 6y

⇒ 1 = 6y

⇒ y = 1/6

(1,1/6) is the solution.

Hence, 2 out of the infinitely many solutions of the given equation are (0,0), (1,1/6).

(iii) x + πy = 4

let x = 0

⇒ x + πy = 4

⇒ 0 +  πy = 4

⇒ πy = 4

⇒ y = 4/π

(0, 4/π) is the solution.

Let y = 0

⇒ x + πy = 4

⇒ x + 0(y) = 4

⇒ x  + 0 = 4

⇒ x = 4

(4, 0) is the solution.

Hence, 4 out of the infinitely many solutions of the given equation are (0, 4/π), (4, 0).

(iv) x - y = 4

Let x = 0

⇒ x - y = 4

⇒ 0 - y = 4

⇒ -y = 4

⇒ y = - 4

(0,- 4) is the solution.

Let x = 1

⇒ x - y = 4

⇒ 1 - y = 4

⇒ -y = 4 - 1

⇒ -y = 3

⇒ y = - 3

(1,- 3) is the solution.

Hence, 4 out of the infinitely many solutions of the given equation are(0,- 4), (1,- 3).

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What is equation easy?

Answers

A mathematical equation can be defined in a variety of ways.

Equation that is linear.A quadratic equation.Cubic Formula.Define the term equation?

A mathematical equation can be defined in a variety of ways. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Equation that is linear.

There could be multiple variables in a linear equation. If a variable's highest power is always 1, an equation is said to be linear. A one-degree equation is another name for it.

A quadratic equation.

A second-order equation is this one. At least one of the variables in quadratic equations needs to be raised to exponent 2.

Cubic Formula.

Third-order equation.There should be at least one variable raised to exponent 3 in cubic equations.

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Why 5 Is it possible to construct a triangle with lengths of its sides as 4 cm 3 cm and 7 cm give reason for your answer?

Answers

With sides that are 4 cm, 3 cm, and 7 cm long, a triangle cannot be built. Because the sum of the other two sides does not exceed that of the third side.

A triangle is referred to as a three-sided polygon that has three vertices. The connection of the three sides ends to end at a single point forms the angle of the triangle. The sum of these angles adds up to 180 degrees.

The triangle's three sides are specified as being 4 cm, 3 cm, and 7 cm. Add the two sides together and see if the result exceeds the third side to determine whether these sides constitute a triangle.

Here, the sum of two sides 4 cm and 3 cm is calculated as,

A+B = 4+3

=7 cm

This sum is equal to the third side C = 7 cm.

Therefore,  [tex]A+B\ngtr C[/tex]. So, the given sides don't form a triangle.

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- To meet your sales quota at work, you need to average $125 per day. So far you have sold $150,
$175, $90, and $155. How much do you need to sell on the last day to meet your quota for this
week?

Answers

Hence he need to sell $55 on the last day to meet his quota for this

week.

What is average ?

average can be defined as the ratio of the sum of observations and total number of observations.

Given,

To meet your sales quota at work, you need to average $125 per day.

So far he  sold $150, $175, $90, and $155.

so ,

let last day he need to sell be x .

average = 150+175+90+155+x/ 5

125 = 570+x / 5

625 = 570 + x

x = 55

Hence he need to sell $55 on the last day to meet your quota for this

week.

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What are the 5 rules of factoring?

Answers

The five rules for factoring are taking the difference grouping the numbers, dividing, multiplying, taking the greatest common factor and by taking the LCM.

There are certain times when we encounters such kind of problems which includes the factoring of the components of the polynomial.

Ine Sach kind of cases there are several methods for factoring the components of the polynomial like taking the greatest common factor or finding the LCM of the components in order to make the polynomial more simplified.

Also we can take out the most common digit or the number from the whole polynomial which comes under the category of grouping.

Also we can use the method of taking the differences or like taking the division and multiplication of certain digit into the polynomials in order to do the factoring.

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Why is 21 a prime number?

Answers

Answer:

We do not consider 21 as a prime number, because it can be written as a product of two smaller natural numbers

Step-by-step explanation:

is 3(5a + 9) + 5a and 4(5a+6) equivalent

Answers

No, 3(5a + 9) + 5a and 4(5a+6) are not equivalent

What are equivalent expressions ?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

To know if 3(5a + 9) + 5a and 4(5a+6) are equivalent, we simplify both expressions and see if they will have result

simplifying 3(5a + 9) + 5a;

by opening the parentheses

15a+27+5a

collecting like terms

20a+27

simplifying 4(5a+6);

by opening the parentheses,

20a + 24

Therefore 20a + 27 is not thesame as 20a+24. This means 3(5a + 9) + 5a is not equal to 4(5a+6).

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Factorise the following.
2⁢x^2+7⁢x+3

Answers

Step-by-step explanation:

either x=-1/2

or x=-3

compare with ax²+bx+c=0

What is called longitude Class 6?

Answers

Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

How is longitude measured?

Distance from the primary meridian is measured in terms of longitude. Longitude lines, often known as meridians, are fictitious lines that divide the Earth. They sprint from pole to pole from north to south, but they gauge the distance in either an east or west direction. The units of longitude are degree, minute, and second.

The North and South Poles serve as the meeting points for imaginary lines that circle the globe vertically (up and down) and are used to calculate longitude. Meridians are the name for these lines. One arc degree of longitude equals one meridian. There are 360 degrees in an orbit around the Earth.

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Write an equation
in slope-intercept form of the line that passes through the points

Answers

The equation in slope-intercept form of the line that passes through the points is f(x) = 2x + 2

How to determine the linear function f with the given values.

From the question, we have the following parameters that can be used in our computation:

f(0) = 2 , f(-2) = -2

A linear equation can be represented as

f(x) = mx + c

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

m * 0 + c = 2

m * -2  + c = -2

Solving 0 * x + c = 2, we have

c = 2

So, we have

m * -2 + c = -2

This gives

-2 * m + 2 = -2

Evaluate the like terms in the above equation

So, we have the following representation

-2m = -4

Divide both sides of the equation by -2

So, we have

m = 2

Substitute the known values in the equation f(x) = mx + c, so, we have the following representation

f(x) = 2x + 2

Hence, the function is f(x) = 2x + 2

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Complete question

Write an equation in slope-intercept form of the line that passes through the points: f(0) = 2 and f(-2) = -2

Solve the following problem

Answers

Note that the area of the above triangle is given as: 42.

This is solved using the SOH CAH TOA Rule and the Formula of the Right Angled Triangle

What is the Right Angled Triangle?

The hypotenuse is the longest side of a right triangle, a "opposite" side is the one across from a given angle, and a "adjacent" side is the one close to a given angle. Right triangle sides are described using specific terminology. A right triangle's hypotenuse is always the side opposite the right angle.

To find the area of the triangle we must obtain, the Base and the Height, that is FD and A F.

Note that we have

∠F = 90°

∠D = 30°

Since the sum of angles in a Δ = 180°,

∠A = 180 - (90 + 30)

∠A = 60°

To find the area of the triangle we must obtain, the Base and the Height, that is F D and A F.

To obtain F D, we must use the Sine rule which states:
Sine θ = O/H; that is


Sin ∠A = F D/AD

Sin 60° = F D/14

0.86602540378 = FD/14

F D = 14 * 0.86602540378

F D = 12.1243556529

F D [tex]\approx[/tex] 12. 12

Using the above Cos Rule (CAH) we can find the Adjacent Side (that is height). Thus

Cos A = A F/AD

Cos 60° = A F/14

0.5 = A F/14; multiply both sides by 14

A F = 0.5 * 14

A F = 7

Now we have Adjacent Side  (Height) = 7; and the Opposite Side (Base) = 12.12

The area of the Triangle according to the Pythagorean Rule is:

1/2 B * H

= 1/2 * 12.12 * 7

= 42.42

Thus the Area of the above triangle [tex]\approx[/tex] 42

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Which measure of center should Raul use to calculate his overall performance if he hits a line drive to the outfield on each pitch?

Answers

Since the distribution of the 10 distances is not uniform, Raul should use the median to determine his total performance.

What is median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income.

Given that it is the most resilient statistic, the median is crucial to strong statistics.

According to our question-

The home run is an outlier in the data set even if nine lengths are grouped together.

The median is the most accurate indicator of the middle of a data collection including outliers.

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Mario and Russell plot a triangle on a coordinate grid and then perform a
rotation and a translation. Russell thinks the original triangle and final triangle
are congruent but Mario disagrees. Which student is correct and why?
Russell is correct. Since neither rotations no translations preserve distance, the
triangles are congruent.
O Mario is correct. Since neither rotations not translations preserve distance, the
triangles are not congruent.
Mario is correct. Since both rotations and translations preserve distance, the triangles
are congruent.

Russell is correct. Since both rotations and translations preserve distance, the
triangles are congruent.

Answers

The right answer is SSS since two triangles are said to be congruency when each of their three sides and Mario is correct.

How can you show a triangle is congruent?

Triangles are said regarded as being congruent if their size and shape actually match exactly. The word "congruent" contains the sign. When a triangle's three sides and three angles match those of a another triangle's three sides and three angles, two triangle are said to be congruent.

Here,

begin by writing the names of the triangles' vertices, beginning with triangles DAB and BCD, as shown below.

AB = CD

DA = BC

In both triangles, side BD is the same, therefore

BD = BD

We can infer that the triangles DAB & BCD are congruent that use the SSS feature of a congruence triangle because they have the same number of sides on each side.

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!!!!50 POINTS!!!!

It will take you t seconds to carry the water, which
you will do y times a day. What is the total amount of
time you will be carrying water?
How many hours would you spend carrying water in a
year?
I need an expression, evaluation, and explanation! ASAP

Answers

Answer:

1. t*y

2. 365*t*y

Step-by-step explanation:

Identify variables

T (time) seconds

Y amount of times per day

T * Y = amount of time you would spend carrying water in a day, 24 hrs

365 * t * y = 365 (amount of days per year, multiplied by the amount of time you carry water per day.)

Rewrite the expression with rational exponents √6

Answers

We can rewrite the expression by using a rational exponent as:

[tex]\sqrt{6} = 6^{1/2}[/tex]

How to rewrite the expression?

We know that all roots can be written as exponents, such that:

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

Particularly, if there is no upper index on the root, then it is a square root, and the exponent corresponding to the square root is 1/2.

Here we want to rewrite the expression:

[tex]\sqrt{6}[/tex]

Using what we saw above, we can rewrite this as:

[tex]\sqrt{6} = 6^{1/2}[/tex]

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What is change of base formula example?

Answers

Change of base formula is used to rewrite a logarithmic operation as a ratio of two logarithms each with the same base that is different from the base of the original logarithm, for example, log₆₄8 = log 8 / log 64.

Logarithm is the inverse function of an exponential. The logarithm of x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

Change of base formula is used to rewrite a logarithmic operation as a ratio of two logarithms each with the same base that is different from the base of the original logarithm. It can be written as follow:

[tex]Log_{b} a = \frac{Log_{d} a}{Log_{d} b}[/tex]

For example:

We want to find the value of log₆₄8 using the change of base formula.

log₆₄8 = log 8 / log 64

          = log 8 / log 8²

          = log 8 / 2 log 8

          = 1/2

Thus the log₆₄8 is 1/2

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