You run 12 laps in 4 minutes. Your friend runs 18 laps in 8 minutes. Are the rates equivalent?

The equivalent expression is (x + 2√3i) (x - 2√3i).

What is a Polynomial Equation?

The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.

Given polynomial is,

x² + 12

We need to find it's equivalent expression for that see the options

Solve the option (a)

(x + 2√3i) (x - 2√3i)

Now, solve this if we get equal to x² + 12 that means that option is answer

x(x - 2√3i) + 2√3i(x - 2√3i)

x² - 2xi√3 + 2xi√3 -  2√3i *  2√3i

x²  -  12 i²

we know, i² = -1

so, we get

x² + 12

We get the answer by 1st option. If you solve other options you'll get different answer.

Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).

To read more about Polynomial Equation.

https://brainly.com/question/2833285

#SPJ1

Time taken by the bicyclist is 8 hours.

Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Given slope = 35 / 2 = 17.5

Distance = 140 miles.

then time is calculated by 140 /17.5

 = 8 hours

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.

To learn more about slope refer to:

https://brainly.com/question/3493733

#SPJ1

2/ ( 1 + x) ( 1 - x) is express  into partial fractions.

With an example, what is a partial fraction?

The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].

                        The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.

= 2/(1-(x^2))

= 2 / (1)² - (X)²

=  2/ ( 1 + x) ( 1 - x)

Learn more about partial fraction

brainly.com/question/29177355

#SPJ1

Answer: z=3x+1

Step-by-step explanation:

1. Distribute 6 through the parentheses

18x=6z-6

2. Move the z variable to the left side and x variable to the right

-6z= -6-18x

3. Divide both sides by -6 in order to get z by itself

z=1+3x

4. Reorder the terms using commutative property

z=3x+1

The value of (5x2−14x+24)÷(x−4)  is 5x + 6

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given ,

5x2 - 14x - 24

         x - 4    

  5x2 multiplied by 14x, then 24.

The first term is 5x2, and 5 is its coefficient.

The coefficient of the middle term, which is -14x, is -14.

"The constant," the final term, is -24.

Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.

Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.

    -120    +    1    =   -119  

    -60    +    2    =    -58  

    -40    +    3    =    -37  

    -30    +    4    =    -26  

    -24    +    5    =    -19  

    -20    +    6    =    -14    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6  

                   5x2 - 20x + 6x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                  5x • (x-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (x-4)

Step-5 : Add up the four terms of step 4 :

                 (5x+6)  •  (x-4)

Therefore  The value of (5x2−14x+24)÷(x−4)  is 5x + 6

To learn more about mathematical expression refer to :

https://brainly.com/question/1859113

#SPJ1

Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.

A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.

Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.

Factoring  5x2 - 14x - 24

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  -24

Multiply the coefficient of the first term by the constant   5 • -24 = -120

Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -14 .

-120    +   1   =   -119

-60    +   2  =   -58

-40    +   3  =   -37

-30    +   4  =   -26

-24    +   5  =   -19

-20    +   6  =  -14  

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6

5x2 - 20x + 6x - 24

Add up the first 2 terms, pulling out like factors :

                   5x • (x-4)

Add up the last 2 terms, pulling out common factors :

                   6 • (x-4)

Add up the four terms of step 4 :

                   (5x+6)  •  (x-4)

Which is the desired factorization

Cancel out  (x-4)  which appears on both sides of the fraction line.

 5x + 6

To learn more about Simplification refer :

https://brainly.com/question/28780542

#SPJ1

Answer:

5 cups

Step-by-step explanation:

6bananas =2cups

6(2cups)+6(2cups)+3(1cup)= 15 bananas

5cups of blueberries

Answer:

x = 222:2 and x = 2

Step-by-step explanation:

(2x-123):3=33

(2x – 123):3 = 33

2x – 123 = 33.3

2x – 123 = 99

2x = 99 + 123

2x = 222

x = 222:2

x = 111

200-8.(2x+7)=112

200 – 8.(2x + 7) = 112

-8.(2x + 7) = 112 – 200

-8.(2x + 7) = -88

2x + 7 = (-88):(-8)

2x + 7 = 11

2x = 11 – 7

2x = 4

x = 4:2

   x = 2

I hope my answer helps you.

The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28

From the given information, we are to determine the expression that is equivalent to the given expression

The given expression is

(ab⁷)⁴

To determine the expression that is equivalent to this expression, we will expand the given expression

Expanding the expression

(ab⁷)⁴

Applying the distributive exponent law of indices,

(a)⁴ × (b⁷)⁴

Simplifying

a⁴ × b²⁸

= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸

Learn more on Writing an equivalent expression here: https://brainly.com/question/28058543

#SPJ1

Answer:

I think it's a4b28

Step-by-step explanation:

Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given,

5 machines take 9 days,

5 x 9 = 45 machines day

45/15 = 3 days

Hence "Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines".

For more information about the work and time relation,

brainly.com/question/6912604

#SPJ1

The value of x = 3.8 cm and y = 3.44 cm

What are some examples of consistency?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

What are the five different types of congruence?
Two triangles are congruent if they satisfy all five conditions for congruence. Right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).

This can be solve by congruence

these two triangle can be congruent by AAS

so x = 3.8 com

in this triangle we have all angle 60 degree

so this is an equivalent triangle

hence down side = 3.8 cm

hence y = (3.8)^2-(1.6)^2 = 14.44 - 2.56 = √11.88 = 3.44

Learn more about congruence
brainly.com/question/2938476
#SPJ4

Answer:

John = 14 ; Van = 26

Step-by-step explanation:

V = 12 + J

V - 2 = 2(J-2)

12 + J - 2 = 2J - 4

J + 10 = 2J - 4

2J - J = 10 + 4

J = 14

V = 12 + 14

V = 26

Answer:(-6 5/6)

Step-by-step explanation:

-12.5=-12-1/2

-5 2/3= -5-2/3

=(-12 3/6)-(-5 4/6)

=(-6 5/6)

gimme brainlliest

Answer:

C(-6, -3)

Step-by-step explanation:

In a square, all four sides have the same length and all four angles have the same measure (90 degrees). Therefore, the line segments connecting the vertices of a square are all perpendicular to each other and all have the same length.

Since the line segment AB has a length of 8 (the difference in the y-coordinates is 8) and a horizontal component (the difference in the x-coordinates is 0), the line segment CD must also have a length of 8 and a horizontal component of 0. This means that the x-coordinate of point C is the same as the x-coordinate of point A, which is 2.

The line segment CD also has a vertical component equal to the difference in the y-coordinates of points D and A, which is 5 - (-3) = 8. Therefore, the y-coordinate of point C is the same as the y-coordinate of point D minus 8, or -3.

Therefore, the coordinates of point C are (-6, -3).

Answer:

Step-by-step explanation:

Although the answer is correct, the Step 3 is not correct.

The missing numbers are 3 hours = 180 minutes 24 hours = 1 day

24 months = 2 years

What are numbers ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.

1. 5 × x = 45

   45 / 5 = x

    x = 9

45 ÷ 5 = 9

2. 200 + 600 = 800

300 + 400 = 700

3. 3 hours = 180 minutes

     3 * 60 minutes

24 hours = 1 day

24 months = 2 years

12 * 2 = 24

To learn more about numbers from the given link  

https://brainly.com/question/24644930

#SPJ1

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

Since the length of 15 is divided between the circumference of the circle and the perimeter of the square,

2πr + 4s = 15 ⇒ s = (15 - 2πr ) / 4

A = πr2 + s2 = πr2 + [ (15 - 2πr ) / 4]2 = πr2 + (225 - 60πr + 4π2r2) / 16

A = π(1 + π/4)r2 - (15/4)πr + 225/16

dA/dr = 2π(1 + π/4)r - (15/4)π = 0 ⇒ r = (15/4)π / [2π(1 + π/4)] = 15 / (8 + 2π)

Since A(r) is concave up, it has a minimum at

r = 15 / (8 + 2π)

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

To learn more about circumference visit:

https://brainly.com/question/28757341

#SPJ4

Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

Learn more about the PEMDAS rule here :

https://brainly.com/question/20876480

#SPJ1

Answer:Pemdas

Step-by-step explanation:Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

The following excel commands would give you the critical value is T.INV(0.95,25)

What is excel commands?

The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.

Population sd is not available so we have to use t test.

0.95 is for upper bound and 25 is df of t test.

To learn more about excel commands visit:https://brainly.com/question/10053162

#SPJ4

Share of the each person is 1/12. And the above situation can be represented in the given picture.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.

When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.

To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.

First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.

Here we have

6 people equally share 1/2 a pan of macaroni and cheese  

As we know 1/2 means half

By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts

=> (1/2) ÷ 6 =  [tex]\frac{ \frac{1}{2} }{6}[/tex]  = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]  

Therefore,

Share of the each person is 1/12. And the above situation can be represented in the given picture.

Learn more about Fractions at

https://brainly.com/question/8482939

#SPJ1    

The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Given,
To determine the value of the unknowns in the matrix,

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,

2z -18 = 12
z = 15

10 - 6 = 4y
y = 1

Thus,  the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Learn more about matrix here:
https://brainly.com/question/28180105
#SPJ1

The percentage of the council members who voted in favor of the tax is 50%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the council has 76 members out of which 38 members voted in favor of the tax.

The percentage amount of members who favor the tax is:
(38/76) × 100%

= 50%

Hence, the percentage of the council members who voted in favor of the tax is 50%.

Learn more on percentages here:

https://brainly.com/question/14979505

#SPJ1

The decision for rejecting the null hypothesis is μ = 8.4

In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.

Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.

Here we have to determine the decision for rejecting the null hypothesis.

While we looking into the the given question we have identified the following values,

Standard deviation = 1.0

Mean pressure = 8.4 pounds/square

Level of significance = 0.05

Sample size = 24

According to these values the null and alternative hypothesis is written as,

H0 = μ = 8.4

Hx = μ ≠ 8.4

Therefore, H0 = μ = 8.4 is the decision for this one.

To know more about hypothesis here.

https://brainly.com/question/29576929

#SPJ4

Answer:

c. |11|

Step-by-step explanation:

When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.

|11-0|=11

|0-19|=19-0=19

|0-34|=34-0=34

Answer: 1/2

Step-by-step explanation:

Use rise over run. Up 1, over 2.

And so on. Find nice points on the graph to practice slope with!

Answer:

q. point of intersection

Step-by-step explanation:

Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.

The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane

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

f(x) = 0.48 ln(x + 2) + 27

Also from the question, we have

Pressure = 28 inches

This means that

f(x) = 28

So, we have the following equation

0.48 ln(x + 2) + 27 = 28

Subtract 27 from both sides

0.48 ln(x + 2) = 1

Divide 0.48 from both sides

ln(x + 2) = 2.083

Take the exponent of both sides

x + 2 = 8.03

So, we have

x = 6.03

Hence, the distance is 6.03 miles

Read more about functions at

https://brainly.com/question/28277110

#SPJ1

Answer:

C.

Step-by-step explanation:

For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.

For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.

Answer:

                  1

log₂√2 = ------

                  2

Step-by-step explanation:

I'm assuming the equation looks like this:

2¹⁽² = √2

                  1

log₂√2 = ------

                  2

I hope this helps!