One month Kevin rented 2 movies and 5 video games for a total of $30. The next month he rented 8 movies and 3 video games for a total of $35. Find the rental cost for each movie and each video game. Rental cost for each movie: s Rental cost for each video game

Answers

Answer 1

Answer:

M = $2.5; V = $5

Step-by-step explanation:

We need to set up a system of equations to find the price for both movies (M) and video games (V).

We can use 2M + 5V = 30 and 8M + 3V = 35

We can use elimination:

[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]


Related Questions

a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 5 48 22 Cold 8 12 5 What is the probability that a customer ordered a large given that he or she ordered a cold drink? Rounded to the nearest percent, [? ]% Enter

Answers

Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:

p = 5/25 = 0.2 = 20%.

20% probability that a customer ordered a large given that he or she ordered a cold drink.

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You have a credit card that charges an interest rate of 16.15% compounded monthly. The table below shows your activity for the month of April. Date Activity Amount Balance April 1 Beginning Balance 1,000.00 April 5 Purchase 29.10 1,029.10 April 12 Payment −225.00 804.10 April 15 Purchase 97.25 901.35 April 23 Purchase 19.00 920.35 April 26 Purchase 28.40 948.75 April 30 Ending Balance 948.75 What is the average daily balance for this account? $ What is the finance charge for the month of April? $

Answers

1. The average daily balance for this credit card account is $187.74.

2. The finance charge for the month of April is $249.22.

How is the average daily balance calculated?

The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.

A billing cycle for a credit card account is usually one month.

Data and Calculations:

Interest rate = 16.15% compounded monthly

Date       Activity            Amount     Balance  

April 1    Beginning Balance          $1,000.00

April 5   Purchase           29.10         1,029.10

April 12  Payment      −225.00           804.10

April 15  Purchase         97.25            901.35

April 23 Purchase         19.00           920.35

April 26 Purchase        28.40           948.75

April 30 Ending Balance                  948.75

Total                                            $5,632.05

Average daily balance = $187.735 ($5,632.05/30 days)

Daily interest rate = 0.04425 (16.15%/365)

Finance charge = $249.22 ($187.74 x 0.04425 30 days)

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Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.
What is the length of Line segment S R?

9 units
12 units
15 units
18 units

Answers

The length of the line segment SR is 15 units.

How to find the length of a line segment?

In Δ SRQ as seen in the attached image, we see that;

∠SRQ is a right angle

SQ is the hypotenuse

RT ⊥ SQ

Thus, by triangular rules, we know that;

(RQ)² = TQ × SQ

RQ = 20 units and TQ = 16 units

Thus;

(20)² = 16 × SQ

400 = 16 × SQ

SQ = 400/16

SQ = 25 units

By using Pythagoras theorem in Δ SRQ, we have;

(SR)² + (RQ)² = (SQ)²

RQ = 20 units and SQ = 25 units

Thus;

(SR)² + (20)² = (25)²

(SR)² + 400 = 625

(SR)² = 225

SR = √225

SR = 15 units

The length of the line segment SR is 15 units.

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Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to six mysteries and nine nonfiction books. If she randomly chooses three books from her selections, what’s the probability that they will all be nonfiction? Enter a fraction or round your answer to 4 decimal places, if necessary.
Please explain in detail

Answers

The probability that all 3 books would be nonfiction is 0.1846.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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If you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax
and you should tip the waiter 15%. How much should each person pay?
Tax $
Total meal cost
Tip $
Total cost of meal with tip
Price for each person

Answers

After the tax and the tip are counted, we conclude that each friend must pay $30.

How much should each person pay?

We know that the meal cost is $72.50.

Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).

Then the total meal cost is:

C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39

Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:

C' = $77.39*(1 + 15%/100%) = $88.998 = $90

(Where we rounded up).

Then, if there are 3 friends, each one must pay:

$90/3 = $30

Each friend must pay $30.

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6x+2y=8
9x+3y=14
Skew
Neither
Perpendicular
Parallel

Answers

Answer: Parallel

I believe that if you set up these equations into y = mx + b form, you're able to notice that the slope is the same for each equation. That causes the answer to be parallel

An H0-scale model railroad engine is 9 inches long. The H0 scale is 87 feet to 1 foot. How long is a real engine?

Answers

The real engine is 65.25 feet long

How to determine the length?

The scale is given as:

Scale = 87 feet to 1 foot

The scale length is given as

Scale length = 9 inches

Convert inches to feet

Scale length = 9/12 feet

The actual length is then calculated as:

Actual = 87 * 9/12 feet

Evaluate

Actual = 65.25 feet

Hence, the real engine is 65.25 feet long

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The sum
of three numbers is 24. If two numbers are 16 and 22, what is the third?

Answers

Answer:

-14

Step-by-step explanation:

[tex]16+22+x=24\\38+x=24\\x=-14[/tex]

A procedure has an 81% success rate. The procedure is tried on 12 patients what is the probability that at least 8 patients show improvement

Answers

The probability that at least 8 patients show improvement is; 0.94

How to use Binomial Probability Distribution?

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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A body and tackle with a velocity ratio of 5 is used to raise a mass of 50kg through a vertical distance of 20n at a steady rate if the effort is equal to 80n. Determine (a) distance moved by effort (b)the workdone by the effort in lifting the load (c)the losses in energy involve the operating in machine​

Answers

A. The distance moved by the effort is 100 m

B. The workdone by the effort in lifting the load is 8000 J

C. The losses in energy involve the operating in machine 1800 J

A. How to determine the distance moved by the effortVelocity ratio = 5Load distance = 20 mEffort distance =?

Velocity ratio = Effort distance / Load distance

5 = Effort distance / 20

Cross multiply

Effort distance = 5 × 20

Effort distance = 100 m

B. How to determine the work done by the effortEffort distance = 100Effort = 80 NWorkdone by effort =?

Workdone = force × distance

Workdone by effort = 80 × 100

Workdone by effort = 8000 J

C. How to determine the losses in the energy

We'll begin by calculating the workdone in lifting the load. This is illustrated below:

Mass (m) = 50 KgAcceleration due to gravity (g) = 9.8 m/s²Height (h) = 20 mWorkdone =?

Workdone = mgh

Workdone = 50 × 9.8 × 20

Workdone = 9800 J

Now, we can determine the energy lost as follow:

Workdone = 9800 JWorkdone by effort = 8000 JEnergy lost =?

Energy lost = 9800 - 8000

Energy lost = 1800 J

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f f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?

Answers

hi

f°g  mean apply  g(x) and  then use result of  g(x) as  "x" in f(x)

so as  g(x) = x² +1   and  f(x) = 3x+2

so if we call  g(x)   X  we have  

f( X) =  3 X +2

now we replace  " X"  for it's value

f(X) =  3 ( x² +1) +2

f(X) =  3x² +3 +2

f(X) = 3x² +5

so  f°g = 3x² +5

If a boat with a value of $23, 000 depreciates at a rate of 18% per year, what is the value
after 5 years?

Answers

The value of the car after 5 years is 8527.02 dollars

How to find the value after depreciation?

Depreciation is the reduction in the value of an asset over time due to elements such as wear and tear. For example a car is said to "depreciate" in value after a discovery of a faulty transmission.

The value after 5 years can be found as follows:

Rate = 18% = 18 / 100 = 0.18

Initial Value  = $23,000

time = 5 years

Therefore,

y = 23000(1 + 18%)⁵

y = 23000(1 - 0.18)⁵

y = 23000(0.82)⁵

y = 23000 × 0.3707398432

y = 8527.0163936

y = 8527.02 dollars

Therefore, the value of the car after 5 years is 8527.02 dollars

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Using an exponential function, it is found that the value of the car after 5 years will be of $8,527.

What is an exponential function?

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

A(0) is the initial value.r is the decay rate, as a decimal.

For this problem, the initial cost and the decay rate are given as follows:

A(0) = 23000, r = 0.18.

Hence the value of the boat after t years is given as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 23000(1 - 0.18)^t[/tex]

[tex]A(t) = 23000(0.82)^t[/tex]

The value after 5 years will be of:

[tex]A(5) = 23000(0.82)^5 = 8527[/tex]

The value of the car after 5 years will be of $8,527.

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Jan and Jo live 1,170 miles apart. At the same time, they start driving toward each other on the same road. Jo’s constant rate is 60 mph. Jan’s is 70 mph. How long will it take them to meet?
A. 8 hours
B. 9 hours
C. 16 hours
D. 19 hours

Answers

Answer: B. 9 hours

Step-by-step explanation:

Question analysis (Optional if you can understand the question)

Since they are 1170 miles apart, with their speed, the question is asking how long would it take them to travel 1170 miles together.

In other words, the distance that Jo and Jan together add up to 1170 miles.

Given information

Total distance = 1170 miles

Jo's rate = 60 mph

Jan's rate = 70 mph

Set variables

Let x be the time they took to meet each other

Set equation

60x + 70x = 1170

Solve equation

130x = 1170

Divide 130 on both sides

130x / 130 = 1170 / 130

[tex]\boxed{x=9 \: hrs}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Someone please help with this question!

Answers

The value of angle 20 is as follows:

m∠20 = 50.9 degrees.

How to find angles when parallel lines are cut by a transversal?

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line l and m are parallel lines cut by the two transversal.

Hence,

m∠6 ≅ m∠20 (alternate angles)

Therefore, alternate angles are congruent

m∠20 = 2x - 4

m∠19 + m∠20 = 180 (angles on a straight line)

5x - 8 + 2x - 4 = 180

7x - 12 = 180

7x = 180 + 12

7x = 192

x = 192 / 7

x = 27.4285714286

x = 27.43

Therefore,

m∠20 = 2(27.43) - 4

m∠20 = 50.8571428571

m∠20 = 50.9 degrees.

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You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y = –x2 + 9x + 8 and the path of the dog is modeled by y = 3x + 8, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?

Yes, they intersect at the coordinates (0, 8) and (3,17)

Yes, they intersect at the coordinates (0, 8) and (4, 20)

Yes, they intersect at the coordinates (0, 8) and (6, 26)

No, the paths do not cross

Answers

Solving a quadratic equation, the correct option is given by:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

What is a quadratic function?

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are:

x1 = (-b + sqrt(Delta))/2a

x2 = (-b - sqrt(Delta))/2a

In which:

Delta = b² - 4ac

The equation for this system if:

-x² + 9x + 8 = 3x + 8

x² - 6x = 0

x(x - 6) = 0

Then:

x = 0 -> y = 3 x 0 + 8 = 8.x - 6 = 0 -> x = 6, y = 3 x 6 + 8 = 26.

Which means that the correct option is:

Yes, they intersect at the coordinates (0, 8) and (6, 26).

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Solve the following system of equations.

d + e = 6
d – e = 4


infinite number of solutions

infinite number of solutions

(5, 1)

(5, 1)

no solution

no solution

(3, –1)

(3, –1)

Answers

Answer: (5,1)

Step-by-step explanation:

Adding the equations gives 2d=10, and thus d=5.

So, it follows e=1.

Therefore, the solution is (5,1).

The solution is (5,1)

Given that d+e =6 and d-e =4

We need to find the solution of the given equations

Elimination method is used to eliminate a variable in an equation to find the value of another variable

Now here ,

We we will solve the equation i.e

d+e = 6

d-e = 4

Solving this equation We get,

2d = 10

Therefore,

d= 5

Now substituting the value of d in equation d+e =6

therefore,

5+e =6

Therefore e = 1

Hence the solution is (5,1)

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solve the equation 13Z/Z+1 =11-3i, Z£C where Z=X+yi X&Y£R?​

Answers

Presumably you mean the equation

[tex]\dfrac{13z}{z+1} = 11-3i[/tex]

Observe that for [tex]z\neq-1[/tex],

[tex]\dfrac{13z}{z+1} = \dfrac{13(z+1) - 13}{z+1} = 13 - \dfrac{13}{z+1}[/tex]

so we can simplify the equation to

[tex]13 - \dfrac{13}{z+1} = 11 - 3i \implies \dfrac{13}{z+1} = 13 - (11 - 3i) = 2+3i[/tex]

Multiply both sides by [tex]\frac{z+1}{2+3i}[/tex].

[tex]\dfrac{13}{z+1}=2+3i \implies \dfrac{13}{2+3i} = z+1 \implies z = \dfrac{13}{2+3i} - 1[/tex]

Rationalize the denominator by introducing its complex conjugate.

[tex]z = \dfrac{13(2-3i)}{(2+3i)(2-3i)} - 1 = \dfrac{26-39i}{2^2+3^2} - 1 = \boxed{1 - 3i}[/tex]

Which of the following functions are discontinuous?

Answers

Answer:

D.  I, II, and III

Step-by-step explanation:

A discontinuous function is a function which is not continuous.  

If f(x) is not continuous at x = a, then f(x) is said to be discontinuous at this point.

To prove whether a function is discontinuous, find where it is undefined.

A rational function is undefined when the denominator is equal to zero.

Therefore, to find the values that make a rational function undefined, set the denominator to zero and solve.

Function I

Denominator:  x - 2

Set to zero:  x - 2 = 0

Solve:  x = 2

Therefore, this function is undefined when x = 2 and so the function is discontinuous.

Function II

Denominator:  4x²

Set to zero:  4x² = 0

Solve:  x = 0

Therefore, this function is undefined when x = 0 and so the function is discontinuous.

Function III

Denominator:  x² + 3x + 2

Set to zero:  x² + 3x + 2 = 0

Solve:  

⇒ x² + 3x + 2 = 0

⇒ x² + x + 2x + 2 = 0

⇒ x(x + 1) + 2(x + 1) = 0

⇒ (x + 2)(x + 1) = 0

⇒ x = -2, x = -1

Therefore, this function is undefined when x = -2 and x = -1, and so the function is discontinuous.

Therefore, all three given functions are discontinuous.

Solve the inequality by the method of intervals

Answers

The solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

What is the solution of the given inequality problems ?

The first inequality is (x² - 25)/(x + 10) ≥ 0

⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

∴ x ≥ 5

Thus the domain of the given inequality from method of interval is x = [5,∝).

The second inequality is (x + 2)(x² - 64)/(x² + 45) ≤ 0

⇒ (x + 2)(x² - 64)≤ 0

Either (x + 2)≤ 0 or (x² - 64)≤ 0

Either x ≤ -2 or x ≤ 8

Thus , the combined domain of the given inequality from method of interval is x = [-2,0]∪[8,-∝) .

Therefore, the solution of the inequality by method of interval is x = [5,∝) and x = [-2,0]∪[8,-∝).

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The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?

Answers

the value of sin ∅ is 12/ 13

Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.

From the given question,

We have,  cos ∅= 5/13

From the trigonometric identities, we have that

[tex]sin^2\alpha + cos^2\alpha = 1[/tex]

Then , let's substitute the value of cos ∅

[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]

Let make sin the subject of formula and find the squares of the fraction

sin²∅ = [tex]1 - \frac{25}{169}[/tex]

Find the LCM

sin²∅ = [tex]\frac{169 - 25}{169}[/tex]

Find the difference

sin²∅ = [tex]\frac{144}{169}[/tex]

Find the square root

sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]

sin∅ = [tex]\frac{12}{13}[/tex]

In quadrant II , sin is positive, so we have

sin ∅ = 12/ 13

Thus, the value of sin ∅ is 12/ 13

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Rewrite 1/2 x 1/2 x 1/2 as an exponential expression with a base of 2.

Answers

The equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

How to rewrite the expression?

The expression is given as:

1/2 * 1/2 *1/2

Apply the product law of indices

1/2 * 1/2 *1/2 = (1/2)^3

Apply the power law of indices

1/2 * 1/2 *1/2 = (2^-1)^3

This gives

1/2 * 1/2 *1/2 = 2^-3

Hence, the equivalent expression of 1/2 * 1/2 *1/2 is 2^-3

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(02.04 LC)

Determine the equation of the line shown in the graph:

graph of a vertical line with an x intercept of negative 1

y = −1
y = 0
x = −1
x = 0

Answers

Answer:

x = - 1

Step-by-step explanation:

the equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

the line passes through the x- intercept of - 1 , then

x = - 1 ← equation of vertical line

The ratio of the weight of an object

Answers

The weighing of the man on the earth given the ratio is 174 pounds

Ratio

ratio of the weight of an object on the earth to the moon = 6:1

Weight of a man on the moon = 29 poundsWeight of the man on Earth = x

Equate the ratio

6 : 1 = x : 29

6/1 = x/29

cross product

6 × 29 = 1 × x

174 = x

x = 174 pounds

Complete question:

The ratio of the weight of an object on the earth to the moon is 6:1. If a man weighs 29 pounds on the moon, calculate his weighing on the earth.

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An animal shelter has a total of 5 * 47 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one half the number of cats, and there are 20 more cats than dogs, how many dogs are at the shelter?

Answers

The number of dogs in the animal shelter which comprise of cats, dogs, and rabbits is 84 dogs.

Equation

Total animals = 5 × 47

= 235

Number of rabbits = 1/2(d + 20) - 5Number of cats = d + 20Number of dogs = d

235 = d + (d + 20) + 1/2(d + 20) - 5

235 = d + d + 20 + 1/2d + 10 - 5

235 = 2 1/2d + 25

235 - 25 = 2 1/2d

210 = 2 1/2d

d = 210 ÷ 2 1/2

d = 210 ÷ 5/2

= 210 × 2/5

= 420/5

d = 84 dogs

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Which of the following functions has an initial value of -1/2 and a rate of change of -2?

Answers

Which of the following functions has an initial value of -1/2 and a rate of change of -2?

Answer is the B.
y
=



1
2

4/3*(1/2-6)=(4/3*1/2)-(4/3-6)

Answers

Answer:

The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)

50 POINTS!!!!!!!!!!!!!!!!!!!!!!!! SOLVE THIS QUICKLY WITH AN EXPLANATION

Answers

Answer:

x = 30 degrees

Step-by-step explanation:

angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees

KNL = 30 degrees

angle KLN is 90 degrees, a triangle is equal to 180 degrees

2x+30+90 = 180

2x = 60

x = 30 degrees

Kristina wants to invest $6200 in a savings account that pays 7.6% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.

Answers

The number of years it would take the investment to double in value is 13.2 years.

How long will it take for the investment to double?

When the amount doubles, the interest earned would be $6200.

Time = interest earned / (amount invested x simple interest)

$6200 / (6200 x 0.076) = 13.2 years

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Given the functions f(x) = x3 + x2 – 3x + 4 and g(x) = 2^x– 4, (Consider domain, range, x-intercepts, and y-intercepts.)

Answers

The first function is a type of cubic function and the second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The function given in the problem is:

f(x) = x³ + x² – 3x + 4

The highest degree (power) of this function is 3. Thus, this function is a type of cubic function.

The second function given in the problem is:

g(x) = 2x – 4

The highest degree (power) of this function is 1. Thus, this function is a type of linear function.

Both the function has the value of domain and range from -∞ to ∞ (-∞,∞).

Thus, the first function is a type of cubic function  and second function is a type of linear function. The key feature(s) do f(x) and g(x) have in common as they both have value of domain and range as (-∞, ∞).

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Explain how to draw a line segments that measures 2 7/16 inches.

Answers

The line segment which represents 2 7/16 inches should first be drawn with the use of a ruler.

What is a Ruler?

This is referred to an instrument which is used to measure distances between points or draw straight lines and also usually graduated in inches.

On the inches graduation, the zero mark should be located and the 1/16 inch which is found before the half-inch mark between 2 and 3 inches. When this is done, a line should be drawn to meet both points which will therefore measure 2 7/16 inches long.

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