HELP ME MATH

Match each quadratic function to its graph.

Answer:

Step-by-step explanation:

The standard form of a circle is

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

where h, k an r are real numbers that can be added at the end.

First, to get to the general form of a circle, you have to expand the binomials. Meaning,

[tex](x-h)^2=x^2-2xh+h^2[/tex] and

[tex](y-k)^2=y^2-2yk+k^2[/tex].

After you do this, then the h^2, k^2, and r^2 terms can be added together to give you one number. Then put everything else in descending order, like this:

[tex]x^2+y^2-(2h)x-(2y)k+(h^2k^2r^2)=0[/tex]

It's very hard to describe when there are no values assigned to the h, k, and r in the equation.

Basic idea:

Expand the binomials and add like terms, setting the whole thing equal to 0.

The surface area of the sphere with radius 2 is found to be 16π, hence, option D is correct.

To find the surface area of the sphere, we will be using the formula,

Surface area = 4πr² Where r is the radius of the sphere. In this case, r = 2, so we have:

Surface area = 4π(2)²

Surface area = 4π(4)

Surface area = 16π

Therefore, the surface area of the sphere of radius 2 is 16π square units.

This suggests that we would require 16π square units of a substance to cover the whole surface of the sphere.

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Answer:

3 (cos 93 + i sin 93)

Step-by-step explanation:

We are to find the cube roots of the following:

27 (cos 279° + i sin 279°)

[tex](cosx + i sin x) = cos (nx)) + i sin (nx)[/tex]

[tex]27 \times (cos 279+i sin 279)\frac{1}{3} =27\frac{1}{3} \times (cos 279+i sin 279)\frac{1}{3}[/tex]

Simplifying this to get:

[tex]3\times (cos279+i sin279)\frac{1}{3}[/tex]

[tex]3\times(cos 279+i sin 279)13=3(cos \frac{279}{3} +i sin \frac{279}{3})[/tex]

We know that [tex]\frac{279}{3}=3[/tex]

So, cube root = [tex]3(cos 93 + i sin 93)[/tex]

Answer:

ABOUT 661 visitors per day

Step-by-step explanation:

There are 365 days in a year and they were not open 7 so you do

365-7=358  

Now, you know that out of those 358 days the total is 236758 visitors.

So you would divide 236758 by 358

236758/358 = 661.33519553072625698324022346369

I would recommend rounding this number to 661,

the amusement park had a average of ABOUT 661 visitors per day it was open.

ANSWER

The two lines are perpendicular if [tex]m_1 \times m_2 = - 1[/tex]

EXPLANATION

Given two lines:

[tex]y=m_1x+b_1[/tex]

and

[tex]y=m_2x+b_2[/tex]

We can tell wether these two lines are perpendicular to each other using their slopes.

If the product of their slopes is -1, the then the two line are perpendicular.

For example:

The line

[tex]y = 2x + 6[/tex]

has slope

[tex]m_1= 2[/tex]

and the line

[tex]y = - \frac{1}{2} x + 1[/tex]

has slope

[tex]m_2 = - \frac{1}{2} [/tex]

The product of the two slopes is

[tex]m_1 \times m_2 = 2 \times - \frac{1}{2} [/tex]

This implies that:

[tex]m_1 \times m_2 = - 1[/tex]

Therefore the two lines are perpendicular.

Answer:

They'll be negative reciprocals.

Step-by-step explanation:

A pex :)

Answer: The wavelength increases

Step-by-step explanation:

As frequency increases, wavelength decreases. Frequency and wavelength are inversely proportional. This basically means that when the wavelength is increased, the frequency decreases and vice versa.

Hope that this helps! Have a great day!

Answer:

1/5 or 20%

Step-by-step explanation:

Since the customer ordered a cold drink, that reduces our sampling population to 25 (8 + 12 = 5).

Out of those 25 people, 5 ordered a large size.

So, the probability that someone who has ordered a cold drink ordered a large one is 5 out of 25...

P = 5 / 25 = 1/5 or 20%

Answer:

x = ⅓ acos(y/7) + π/18, [-7, 7/2]

Step-by-step explanation:

y = 7 cos(3x − π/6)

Solving for x:

y/7 = cos(3x − π/6)

acos(y/7) = 3x − π/6

acos(y/7) + π/6 = 3x

x = ⅓ acos(y/7) + π/18

The domain of x is the same as the range of y.

When x = π/6:

y = 7 cos(3π/6 − π/6)

y = 7 cos(π/3)

y = 7/2

When x = 7π/18:

y = 7 cos(21π/18 − π/6)

y = 7 cos(π)

y = -7

So the domain of x as a function of y is [-7, 7/2].

Answer:

[tex]8\ years[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=?\ years\\ P=\$100\\A=\$150\\ r=0.05[/tex]  

substitute in the formula above  

[tex]150=100(e)^{0.05*t}[/tex]  

[tex]1.5=(e)^{0.05*t}[/tex]  

Applying ln both sides

[tex]ln(1.5)=(0.05t)ln(e)[/tex]  

[tex]ln(1.5)=(0.05t)[/tex]  

[tex]t=ln(1.5)/(0.05)[/tex]  

[tex]t=8\ years[/tex]  

Answer:

If you need all the answers for that assignment:

Step-by-step explanation:

1. Consider 8^x-4 = 8^10

Because the (blank a) are equal , the (blank b) must also be equal.

Answer: Bases, Exponents

The solution to the equation is 14

2.What equation is equivalent to 9^(x-3)=729?

Answer 3^x - 3 = 3^6  

Solve: 9x - 3 = 729

Answer: x = 6

3. To solve 5(2^x+4)=15, first divide each side by

Answer: 5

Solve 5(2^x+4) = 15. Round to the nearest thousandth.

Answer: -2.415

4. Which of the following is the solution of 5e^2x- 4 = 11?

Answer: x=In3/2

5. Select all of the potential solution(s) of the equation 2log5x = log54.

Answer: 2,-2

What is the solution to 2log5x = log54?

Answer: 2

6. Which equation is equivalent to log5x3 - logx2 = 2?

Answer: 10^log5^3/x^2=10^2

Solve: log5x3 - logx2 = 2

Answer: 20

7. What is the solution to ln (x2 - 16) = 0?

Answer: x=+-(17)

8. Solve: ln 2x + ln 2 = 0

Answer: ¼

Solve: e^ 2x+5 = 4

Answer: x=(In4) - 5/2

9. Consider the equation log(3x - 1) = log2(8). Explain why 3x - 1 is not equal to Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Answer: The bases are not the same, so you cannot set 3x - 1 equal to 8.You can evaluate the logarithm on the right side of the equation to get .You can use the definition of a logarithm to write 3x - 1 = 1000.

10. An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer: 8

Answer:

-[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

For linear equations that have been written in the form

y = mx + b,

m represents the slope

hence by comparing this equation to what you have in your question,

slope = m = -[tex]\frac{2}{3}[/tex]

All lines that are parallel to this line will have the same slope of m = -[tex]\frac{2}{3}[/tex]

Answer:

[tex]7x^3-2x^2-5[/tex]

Step-by-step explanation:

We need to add the two terms.

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)[/tex]

Solving,

Combine the like terms and adding those terms

[tex](6x^3+3x^2-2)+(x^3-5x^2-3)\\=6x^3+3x^2-2+x^3-5x^2-3\\=6x^3+x^3+3x^2-5x^2-2-3\\=7x^3-2x^2-5[/tex]

So, the answer is:

[tex]7x^3-2x^2-5[/tex]

Answer:

Probability of selecting someone who doesn't watch ABC 16/45 or 35.56%

Step-by-step explanation:

There are a total of 45 people in the survey.  Of those 45, the number that doesn't watch ABC is 12 + 4 = 16.  So the probability is 16/45.

The correct expressions are,

Because,  f + e=c

Therefore , a² + b² = c²

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

A right triangle ABC as shown in figure where CD is an altitude of the triangle.

Given that,  ΔABC and ΔCBD both are right triangle and both triangles have common angle B is same.

Therefore, Two angles of two triangles are equal.

Hence,  ΔABC ~ ΔCBD,  By using AA similarity.

Similarity property: when two triangles are similar then their corresponding angles are equal and their corresponding side are in equal proportion.

a/f = c/a

Similarly ,  ΔABC ~ ΔACD by AA similarity property . Because both triangles are right triangles therefore, one angle of both triangles is equal to 90 degree and both triangles have one common angle A is same .

⇒ b/c = e/b

The corresponding parts of two similar triangles are in equal proportion  therefore , two proportion can be rewrite as;

⇒ a² = cf

and  b² = ce (II equation)

Adding b² to  both sides of first equation;

⇒ a² + b² = cf + b²

Because b² = ce and ce can be substituted into the right side of equation we can write as;

⇒ a² + b² = cf + ce

Applying the converse of distributive property we can write

⇒ a² + b² = c (f + e)

Distributive property:

a.(b+c)= a.c+a.b

Hence, We get;

⇒ a² + b² = c²

Because f + e = c²

Thus, The correct statement is,

⇒ a² + b² = c²

Because f + e = c²

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Final answer:

The answer explains how the principles of geometry and similarity of triangles are applied to arrive at the Pythagorean theorem. Through the use of similarity rules, algebra, and coordinate system properties, we demonstrate the derivation of a² + b² = c² for right-angled triangles.

Explanation:

The question provided revolves around the principles of geometry and similarity of triangles, specifically focusing on how to derive the Pythagorean theorem using similarity and proportions of triangular sides and angles.

By applying the condition that triangles ABC and CBD, as well as triangles ABC and ACD, are similar by AA (Angle-Angle similarity), we establish a foundation for comparing the lengths of sides within these triangles based on their geometric properties.

Through this comparison, and utilizing the properties of the coordinate system and the Pythagorean theorem, we arrive at the classic equation a² + b² = c², which is central to understanding right-angled triangles.

The process involves recognizing the equal ratios of corresponding sides in similar triangles, substituting values to reflect the equivalences in a coordinate context, and, through algebraic manipulation involving the distributive property, exemplifying how the sum of the squares of the lengths of the sides enclosing the right angle (a and b) equates to the square of the length of the hypotenuse (c).

This exploration elucidates the interconnectedness of geometry, algebra, and coordinate systems in proving fundamental theorems such as the Pythagorean theorem.

Answer:

  b.  42.875 units³

Step-by-step explanation:

The volume of a cuboid is the product of its edge dimensions (length×width×height):

  (3.5 units)(3.5 units)(3.5 units) = 3.5³ units³ = 42.875 units³

Hello There!

The volume for a cylinder is Pi*r^2*h

We are going to leave our Answer in terms of pi so first we need to square our radius which we know is 5

Our radius is 25 because we squared 5. Next, we need to multiply 25 by our height which is 11.

25 multiplied by 11 is 275 so our Answer would be 275[tex]\pi[/tex]

Answer:

23-m

Step-by-step explanation:

i took that test

Answer:

Step-by-step explanation:

The complete question is attached.

In the given table, we can observe that the variable x should represents the total time in minutes and free response questions.

However, if we use the table, we find that the total time in minutes can be obtained by multiplying 15-m and 8, because the first expression represents the total number of questions that are free response and 8 represents the time per question.

Therefore, the varible can be only replaced by the product 8(15-m).

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &3 \end{cases} \\\\\\ A=6500e^{0.06\cdot 3}\implies A=6500e^{0.18}\implies A\approx 7781.91[/tex]

Answer:

The answer is C) [tex]12\sqrt{2}[/tex].

Step-by-step explanation:

For a real number [tex]a[/tex],

[tex]\sqrt{a} \cdot \sqrt{a} = a[/tex].

In other words, multiplying a square root by itself gets rid of the square root.

How does this rule apply here?

[tex]24 = 2\times 12[/tex].

Similarly,

[tex]\sqrt{24} = \sqrt{2}\times \sqrt{12}[/tex].

That is:

[tex]\begin{aligned}\sqrt{24}\times \sqrt{12} &= (\sqrt{2}\times \sqrt{12}) \times \sqrt{12}\\&=\sqrt{2}\times (\sqrt{12}\times \sqrt{12}) && \begin{array}{l}\text{By the associative property}\\\text{of multiplication}\end{array}\\&=\sqrt{2} \times 12\\ &= 12\sqrt{2}\end{aligned}[/tex].

Answer:  The correct answer is:  [C]:

______________________________________________

                   →   " 12sqroot " ;   or, write as:  " 12√2 " .

______________________________________________

Step-by-step explanation:

______________________________________________

√24 * √12 = ?

Let us start by simplifying:  " √24 " ;

   24 = 4 * 6 ;

So;  √24 = √4 *√6  ;

  √4 = 2 ;

So:  " √24  = √4 *√6  =  2√6 " .

______________________________________________

Now, let us simplify:  " √12 " :

______________________________________________

   " √12  = ?  "

       12 = 4 * 3 ;

So:  "√12 = √4 *√3  " ;

    √4 * √3 = 2√3 ;

So:  "√12 = √4 *√3 = 2√3 " .

______________________________________________

We are asked to solve—"simplify"— "√24 * √12 " .

 √24 = 2√6 ; as we simplified above.

 √12 =  2√3  ; as we simplified above.

______________________________________________

So:  " √24 * √12 " ;

     = 2√6  * 2√3 ;  

     = ?  ;  Note:  "2 * 2 = 4 " ; and:  "√6 * √3 = √(6*3) = √18 ;

So;    2√6  * 2√3 ;

     =  4√18 ;

Now, we can simplify this value further:

   by simplifying:  " √18 " ;

       18 = 9 * 2 ;

So:    " √18 = √9 *√2  = 3 √2 " ;

So:  " 4√18 = 4 * (3√2) =  12√2 " .

     →  which  is our answer:  " 12√2 " .

    →  which corresponds to:  

     →  Answer choice:  [C]:  " 12 * sq root 2 " .  {or, write as:  " 12√2 ".}.

_____________________________________________

Hope this answer and explanation is of help to you!

       Wishing you the best in your academic endeavors

                    — and within the "Brainly" community!

_____________________________________________

Answer:

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Step-by-step explanation:

Find the volume of the large cone and the volume of the small cone. The subtract the small volume from the large volume.

Large cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(9 in.)^2(15 in.)

V = 405pi in.^3

Small cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(3 in.)^2(5 in.)

V = 15pi in.^3

Difference in volumes:

volume of part = 405pi in.^3 - 15pi in.^3 = 390pi in.^3

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Answer:

see below

Step-by-step explanation:

Let r = number of rides

total amount of money spent has to be less than  or equal to 50

costs are admission and food and rides

rides cost 1.50 each

50≥ admission + food + rides

50 ≥ 15 +10 + 1.50r

Combine like terms

50 ≥25 + 1.50 r

Subtract 25 from each side

50-25 ≥25-25 + 1.50 r

25  ≥ 1.50 r

Divide by 1.5 on each side

25/1.5 ≥ 1.5r/1.5

50/3  ≥ r

Changing this to a mixed number

16 2/3  ≥r

We can only take a whole number of rides

r = 16

Beverly has not spent all of her 50 dollars since there was a fraction for the rides

cost =  15 +10 + 1.50r

        15+10 + 1.5*16

            25+24

           49

She has 1 dollar left

Hello!

To first solve this problem, let's look at how much the workers would've finished when they were still a group.

Since the job could've been originally done in 11 days with 7 people, and they only worked for 3 days (with 7 people), they originally finished 3/11 of the job.

Now, let's look at how much each person finishes of the job in one day.

Since 7 workers can finish the job in 11 days, this means that 1 worker can finish the job in 77 days, translating to that one worker does 1/77 of the job in one day.

Let's connect these ideas. There is 8/11 of the project remaining, and this was finished in 14 days. This means, every day, 4/77 of the project was finished. (8/11 divided by 14)

Since we know one worker does 1/77 of the job per day, and every day, 4/77 of the job was finished, 4 workers were on the team.

Therefore, 7-4, 3 workers left the team.

Hope this helped!

[tex]\text{Hey there!}[/tex]

[tex]\text{Question reads: What was the sensitive, well-insulated tool Willard F.}[/tex] [tex]\text{ Libby used to date artifacts with known ages?}[/tex]

[tex]\bf{Choices\downarrow}\\\bf{A) X-ray\ machine}\\\bf{B) Richter\ Scale}\\\bf{C)Geinger-Muller\ tubes}\\\bf{D)Petri\ dish}[/tex]

[tex]\boxed{\boxed{\bf{Answer: C. Geiger-Muller\ tubes}}}\checkmark[/tex]

[tex]\text{Your explanation}\downarrow[/tex]

[tex]\text{The people of the University of Berkeley were succeeding to make a(n)}[/tex] [tex]\text{energy to make the interest for the atomic energy force.}[/tex][tex]\text{. Some people thought this was delicate to handle.}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C. Geiger-Müller tubes

Step-by-step explanation:

Geiger-Müller tubes was the sensitive, well-insulated tool Willard F. Libby used to date artifacts with known ages.

Question 1:

For this case we have that the function [tex]f (x) = \frac {5x} {x ^ 2-25}[/tex] is undefined or discontinuous where the denominator equals 0.

[tex]x ^ 2-25 = 0\\x ^ 2 = 25\\x = \pm \sqrt {25}\\x_ {1} = + 5\\x_ {2} = - 5[/tex]

Thus, the function is undefined or discontinuous at +5 and -5.

To find the zeros of the function we match the function to zero and clear "x":

[tex]\frac {5x} {x ^ 2-25} = 0[/tex]

Factoring the denominator, taking into account that the roots are -5 and +5:

[tex]\frac {5x} {(x + 5) (x-5)} = 0[/tex]

We multiply by[tex](x + 5) (x-5)[/tex]on both sides of the equation:

[tex]5x = 0\\x = 0[/tex]

ANswer:

Discontinuity: + 5, -5

Zero: x = 0

Question 2:

For this case we propose a system of equations:

x: Be the variable that represents the yellow fish

y: Be the variable that represents the green fish

[tex]x = y-6\\x = 0.4 (x + y)[/tex]

We manipulate the second equation:

[tex]x = 0.4x + 0.4y\\x-0.4x = 0.4y\\0.6x = 0.4y\\y = \frac {0.6} {0.4} x\\y = 1.5x[/tex]

We substitute in the first equation:

[tex]x = y-6\\x = 1.5x-6\\x-1.5x = -6\\-0.5x = -6\\x = \frac {-6} {- 0.5}\\x = 12[/tex]

So, we have 12 yellow fish in the aquarium.

[tex]y = 1.5 * 12\\y = 18[/tex]

So, we have 18 green fish.

Answer:

12 yellow fish

18 green fish

Answer: x = 20

Step-by-step explanation:

Multiply by 10 ( next LCF )

10 ( x / 2 + 2x / 5 ) = 18 * 10

5x + 4x = 180

9x = 180

x = 20

Answer:

[tex]\dfrac{x}{2} + \dfrac{2x}{5} = 18[/tex] has the unique solution x = 20.

Step-by-step explanation:

The equation has the equivalences

[tex]\displaystyle\frac{x}{2} + \frac{2x}{5} = 18 \Leftrightarrow x\left( \frac{1}{2} + \frac{2}{5} \right) = 18 \Leftrightarrow x \left( \frac{9}{10} \right) = 18 \Leftrightarrow x = 18 \cdot \frac{10}{9} = 20.[/tex]

Answer:I think its the third answer

ANSWER

The correct answer is B.

EXPLANATION

The cosine rule can be used to find the relation for b.

According to the cosine rule:

[tex] {b}^{2} = {a}^{2} + {c}^{2} - 2ac \cos( B ) [/tex]We have that a=4 and c=5 and B=60°

We plug in these values to get:

[tex]{b}^{2} = {4}^{2} + {5}^{2} - 2(4)(5) \cos( 60 \degree ) [/tex]

[tex]{b}^{2} = 16+ 25 - 40 ( \frac{1}{2} ) [/tex]

[tex]{b}^{2} = 16+ 25 - 20[/tex]

Take positive square root.

[tex]b = \sqrt{25 + 16 - 20} [/tex]

The correct answer is B

Answer:

1. x

=

5

2

−

5

y

4

x=5/2-5y/4

2. x

=

15

4

−

5

y

8

x=15/4-5y/8

Step-by-step explanation:

Answer:

[tex]x=5[/tex]

[tex]y=-2[/tex]

Step-by-step explanation:

Given the system of equations [tex]\left \{ {{4x+5y=10} \atop {8x+5y=30}} \right.[/tex], you can use the Elimination Method to solve it.

Multiply the first equation by -1, add both equations and then solve for the variable "x":

[tex]\left \{ {{-4x-5y=-10} \atop {8x+5y=30}} \right.\\........................\\4x=20\\\\x=\frac{20}{4}\\\\x=5[/tex]

And finally, substitute the value of the variable "x" into any original equation and solve for the variable "y". Then:

[tex]4x+5y=10\\\\4(5)+5y=10\\\\20+5y=10\\\\5y=10-20\\\\y=\frac{-10}{5}\\\\y=-2[/tex]

[tex]p+b=27\\p=4b-3\\\\4b-3+b=27\\5b=30\\b=6\\\\p+6=27\\p=21[/tex]

21

Final answer:

To determine the number of purple marbles, we can use a system of linear equations derived from the problem's conditions. Solving these gives us 21 purple marbles in the bag.

Explanation:

To solve the problem, let's denote the number of blue marbles as x and the number of purple marbles as y. According to the problem, the total number of marbles is 27, which is our first equation, x + y = 27. Additionally, the number of purple marbles is 3 less than 4 times the number of blue marbles, giving us a second equation, y = 4x - 3.

Now, we'll solve for x using substitution. We place the expression for y from the second equation into the first equation:

x + (4x - 3) = 27

5x - 3 = 27

5x = 30

x = 6

Since x is 6, we can find y by substituting back into the second equation:

y = 4(6) - 3

y = 24 - 3

y = 21

There are therefore 21 purple marbles in the bag.

Answer:

d

Step-by-step explanation:

Answer:

Option d

Step-by-step explanation:

Consider the parent function y =sinx which has amplitude 1 and period 2pi.

Compare this with out graph passing through 3 points given as

(0.5,5) (1.5,-15) and (0,5)

Since maximum value is 5 and min value is -15 amplitude = 1/2 (20) = 10

Also period =2 instead of 2pi.

Hence pi must be coefficient for x

Also the curve does not pass through origin but passes through (0,-5)

So vertical shift of 5 units down.

Hence the curve equation is

[tex]y=10sin \pi x -5[/tex]

For this case we convert the mixed numbers to fractions:

Dwight:[tex]1 \frac {1} {3} = \frac {3 * 1 + 1} {3} = \frac {4} {3} = 1.33[/tex]

Mike:[tex]3 \frac {1} {5} = \frac {5 * 3 + 1} {5} = \frac {16} {5} = 3.2[/tex]

It is observed, that in fact, Mike takes more time to travel the road.

We subtract to know how much more time it takes Mike:

[tex]\frac {16} {5} - \frac {4} {3} = \frac {48-20} {15} = \frac {28} {15}[/tex]

So, Mike takes [tex]\frac {28} {15}[/tex] hours more than Dwight to walk the road.

Answer:

Mike takes[tex]\frac {28} {15}[/tex]hours longer than Dwight to walk the road.

It takes Mike 2.4 times as long to walk the trail as it takes Dwight to run it.

To determine how many times as long it takes Mike to walk the trail as it takes Dwight to run it, we first need to convert the mixed numbers into improper fractions.

Dwight takes: 1 ÷ 1÷3 hours. Converting to an improper fraction:
1 ÷ 1÷3 = 4÷3 hours

Mike takes: 3 ÷ 1÷5 hours. Converting to an improper fraction:
3 ÷ 1÷5 = 16÷5 hours

Next, we find the ratio of the time it takes Mike to walk the trail to the time it takes Dwight to run the trail:

Ratio = (Time taken by Mike) \ (Time taken by Dwight)
= (16÷5) ÷ (4÷3)
= (16÷5) * (3÷4)
= (16 * 3) ÷ (5 * 4)
= 48÷20
= 2.4

It takes Mike 2.4 times longer to walk the trail than it does for Dwight to run it.

Answer:

x³ - 6x² + 18x - 10

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

= x³ - 2x² + 12x - 6 - (4x² - 6x + 4)

= x³ - 2x² + 12x - 6 - 4x² + 6x - 4 ← collect like terms

= x³ - 6x² + 18x - 10