At a snack bar, 3 hamburgers and a small drink cost $8.75. The cost of 2 hamburgers and 2 small drinks is $7.50. What is the cost of 4 hamburgers and 3 small drinks?

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:

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]

False.

The statement "11 more than 20 percent of a number" is best expressed as 11 + 0.20n, where n represents the number.

The appropriate translation of the phrase 11 more than 20 percent of a number is 0.2n + 11 is false.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

In order to derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

Given; 11 more than 20 percent of a number

The statement:"11 more than 20 percent of a number" is best expressed as 11 + 0.20n.

where n represents the number.

Therefore, The appropriate translation of the phrase 11 more than 20 percent of a number is 0.2n + 11 is false.

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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:

[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:

The quotient of v and twelve is equal to the product of 4 and the sum of v and three.

Step-by-step explanation:

The expression v/12 can be described several ways:

The product 4(v+3) can also be described several ways. The trick is to pick one that is not ambiguous.

The verbal expression written above is among the least ambiguous. (The least ambiguous way to write it is: v/12 = 4(v+3).)

Answer: The Correct Answer is  

A number divided by 12 is equal to 4 multiplied by the sum of that number and 3.

Step-by-step explanation:

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

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:

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.

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:

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.

[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.

Answer:

500

Step-by-step explanation:

They are asking what happens at x=0. Plug it in and you should see you get 500(1.2)^0=500(1)=500.

500 is the initial amount of fish

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.

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

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.

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:

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]

Final answer:

The probability that a randomly selected adult is 65 or older is 15.5% or 0.1550 in decimal form. The conditional probability that an adult is 65 or older, given that they take prescription drugs regularly, is approximately 24.63% or 0.2463 when rounded to four decimal places.

Explanation:

To answer these questions, we can use the information provided about the adult population and their prescription drug use.

Probability an Adult is 65 or Older

To calculate the probability that a randomly selected adult is 65 or older (Part a), we can subtract the percentage of the adult population that is age 18–64 from 100%. The provided statistics state that 84.5% of the adult population are 18 to 64 years old. Therefore, the probability that an adult is 65 or older is:

100% - 84.5% = 15.5%

This gives us a probability of 0.1550 (converted to decimal format).

Probability an Adult is 65 or Older Given They Take Prescription Drugs Regularly

For Part b, we are asked to find the probability that an adult is 65 or older, given that they take prescription drugs regularly. This is a conditional probability problem. We know the following:

54% of all adults take prescription drugs regularly.

85% of adults 65+ take prescription drugs regularly.

15.5% of all adults are 65 or older.

To find the required probability, we apply Bayes' theorem:

Probability (Adult is 65+ | takes prescription drugs) = (Probability (takes prescription drugs | Adult is 65+) * Probability (Adult is 65+)) / Probability (Adult takes prescription drugs)

Inserting our known values:

P(Adult is 65+ | takes prescription drugs) = (0.85 * 0.155) / 0.54 = 0.2463

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

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:

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: 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!

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!

Answer:

  B. Negative

Step-by-step explanation:

A line that has a negative "rise" (vertical change) for a positive "run" (horizontal change) has a negative slope. The slope is calculated from rise/run, so if the signs of rise and run are different, the slope is negative.

Any line that goes downward to the right has negative slope.

_____

Any line that goes upward to the right has positive slope.

Answer:

Width of the rectangular Park = 11 feet

Step-by-step explanation:

Given that the total length of the fencing is 62 feet. As has to be fenced around a rectangular park , it would be the perimeter of the rectangular park.

Also Shana wants the length of the run to be 20 feet. Hence the length of the park is 20 feet.

Here we will use the formula for perimeter to find the width of the run

Perimeter = 2(l+w)

62=2(l+w)

l+w = [tex]\frac{62}{2}[/tex]

l+w=31

20+w=31

w=31-20

w=11

Hence the width of the run for her dog in park would be 11 feet.

Answer:

The correct options are C, D and E.

Step-by-step explanation:

Consider the provided information.

Perimeter of a rectangular field  is:

[tex]P= 2 (length) + 2( width)\\P= 2 l + 2w[/tex]

Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet.

Substitute the L=20 and P=62 in above formula.

[tex]P= 2 l + 2w[/tex]

[tex]62= 2 (20) + 2w[/tex]

[tex]62= 40 + 2w[/tex]

Isolate the variable w by subtraction property of equality.

[tex]62-40= 40-40 + 2w[/tex]

[tex]22=2w[/tex]

[tex]w=11[/tex]

Hence, the length of width is 11.

Now consider the provided options.

Option A) The value of w is 10 feet.

This option is incorrect as the value of w is 11.

Option B) The value of w can be zero.

This option is incorrect as the value of w is 11.

Option C) The value of w cannot be a negative number.

This option is correct as the value of w is a positive number and length cannot be a negative number.

Option D) Substitution is used to replace the variable l with a value of 20.

This option is correct as we substitute L=20 in above calculation.

Option E) The subtraction property of equality is used to isolate the term with the variable w.

This option is correct as we use the subtraction property of equality in above calculation.

Hence, the correct options are C, D and E.

Answer:

Option. 7,000 − 24x

Step-by-step explanation:

Let

y ----> depreciated value of the car

x---> rate of depreciation

t ----> the time in months

we know that

The linear equation that represent this situation is

y=7,000-xt

For

t=2 years

Convert to months

t=2*12=24 months

substitute

y=7,000-x(24)

y=7,000-24x

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).

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].