Mathematics College

A rental car company charges $20 per day to rent a car and $0.10 for every mile driven. Addison wants to rent a car, knowing that:
She plans to drive 100 miles.
She has at most $80 to spend.

Answers

Answer 1

Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

An inequality contains one or more unknown values called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.

This case

A rental car company charges $20 per day to rent a car and $0.10 for every mile driven.

Addison wants to rent a car, knowing that:

She plans to drive 100 miles.She has at most $80 to spend.

On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.

Then, the inequality that can be used to determine x is:

20x + 0.1×100≤ 80

So:

20x + 10≤ 80

In summary, the inequality that can be used to determine x is 20x + 10≤ 80

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Related Questions

Real World Scenario: Sara and Kim are both three years old. Both have recently talked to their parents about doing chores around the house to earn some money. Both Sara and Kim's parents have agreed to start giving them a constant allowance every week. Sara currently has $1 in her piggy bank. Her parents have agreed to give her $.60 per week for doing her chores. Kim currently has $2.20 in her piggy bank. Her parents have greed to give her $.20 per week for doing her chores.

What equation and graph help support scenario?

Answers

The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.

The equation that represents the amount of money in Sara's piggy bank over time can be written as

Y = 0.6x + 1

Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.

Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as

Y = 0.2x + 2.2

Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.

To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.

Here is a graph that represents the scenario

In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.

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Need help on please

Answers

Answer:

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

what is the resultant displacement of 6m north 8m east and 10m north west?

Answers

The resultant displacement is approximately 13.071m north and 8m east.

To find the resultant displacement, we need to combine the given displacements in a vector-like manner.

Let's break down the displacements into their components and then add them up.

The first displacement is 6m north.

Since it is purely in the north direction, its components would be 6m in the north direction (along the y-axis) and 0m in the east direction (along the x-axis).

The second displacement is 8m east.

As it is purely in the east direction, its components would be 0m in the north direction and 8m in the east direction.

The third displacement is 10m northwest.

To find its components, we can split it into two perpendicular directions: north and west.

The northwest direction can be thought of as the combination of north and west, each with a magnitude of 10m.

Since they are perpendicular, we can use the Pythagorean theorem to find the components.

The north component would be 10m multiplied by the cosine of 45 degrees (45 degrees because northwest is halfway between north and west).

Similarly, the west component would be 10m multiplied by the sine of 45 degrees.

Calculating the components:

North component = 10m [tex]\times[/tex] cos(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

West component = 10m [tex]\times[/tex] sin(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m

Now, let's add up the components:

North component: 6m (from the first displacement) + 7.071m (from the third displacement) = 13.071m north

East component: 8m (from the second displacement).

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By using the trapezoidal rule with 5 ordinates, approximate [sin(x²+1) dx to 4 decimal places.

Answers

Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) + 2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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Select the correct answer. Consider this function. Which graph represents the inverse of function f? f(x)= x+4

Answers

The inverse of the function f(x) = x + 4 is given as f⁻¹(x) = x - 4

What is inverse of a function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, the function given is f(x) = x + 4;

We can find the inverse of the function as;

y = x + 4;

Let's switch the variables by replacing x as y and y as x;

x = y + 4

Solving for y;

y = x - 4

f⁻¹(x) = x - 4

The graph of the function is attached below

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i need the answer for this asap Please!

Answers

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

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What is the instantaneous rate of change at x=2 for the function
f(x)= 2x - 5

Answers

The instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

How to solve for the rate of change

The derivative of f(x) = 2x - 5 with respect to x can be found by applying the power rule of differentiation, which states that the derivative of x^n is n*x^(n-1).

Taking the derivative of f(x) = 2x - 5:

f'(x) = 2 * (d/dx)(x) - (d/dx)(5)

= 2 * 1 - 0

= 2.

The derivative of f(x) with respect to x is a constant, 2, indicating that the function has a constant slope.

Therefore, the instantaneous rate of change at x = 2 is equal to the derivative, which is 2.

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more equation things

Answers

For the given linear equation y = (1/4)*x + 5/4.

(1, 1.5) is a solution.(12, 4) is not a solution.The x-intercept is (-16/5, 0).

Are these points solutions of the linear equation?

Here we have the linear equation:

y = (1/4)*x + 5/4.

to check if (1, 1.5) is a solution we need to evaluate this in x = 1 and see if we get 1.5.

y = (1/4)*1 + 5/4

y = 6/4 = 3/2 = 1.5

Then (1, 1.5) is a solution.

For the second point we evaluate in x = 12.

y = (1/4)*12 + 5/4

y = 3 + 5/4 = 4.25

So (12, 4) is not a solution.

Finally, to find the x-intercept, we evaluate in y = 0.

0 = (1/4)*x + 5/4

-4/5 = (1/4)*x

4*(-4/5) = x

-16/5 = x

The x-intercept is (-16/5, 0).

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1.
A 50 foot rope is stretched tight from the roof of a building to a spot 20 feet from the base of the
building. How tall is the building? Round your answer to TWO decimal places.

Answers

The required height of the building is approximately 45.82 feet.

Given that, a 50-foot rope is stretched from a building's top to a point 20 feet from the building's base.

We can use the Pythagorean theorem to solve the question.

Let h be the height of the building.

Pythagoras's theorem states that in a right-angled triangle, "the square of one side is equal to the sum of the squares of the other two sides".

Then, we have:

h² + 20² = 50²

Simplifying and solving for h, we get:

h² = 50² - 20²

h² = 2500 - 400

h² = 2100

h = √(2100)

h ≈ 45.82

Therefore, the height of the building is approximately 45.82 feet.

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HELP PLEASE PHOTO INCLUDED

Answers

Answer:

Eat that cookie and you will not regret about it

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles. The same map shows that the movie theater is 20 inches from the school.

What is the actual distance from the movie theater to the school, rounded to the nearest mile?

A: 15
B:27
C:30
D:60

Answers

The actual distance from the movie theater to the school is given as follows:

A. 15 miles.

How to calculate the actual distance?

The actual distance from the movie theater to the school is obtained applying the proportions in the context of the problem.

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles, hence the scale factor is of:

2 inches = 1.5 miles

1 inch = 0.75 miles.

The same map shows that the movie theater is 20 inches from the school, hence the actual distance is given as follows:

20 x 0.75 = 15 miles.

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Use the following sets to answer the question.
A={1,2,3,4,5}
B={5,6,7,8}
Which answer shows the union of sets A
and B?
{5}
{1,2,3,4,6,7,8,9}
{1,2,3,4,5,6,7,8}
{2,4,8}

Answers

The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

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someone please answer this its confusing me

Answers

24. opposite sides of a parallelogram are always congruent

the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9

line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12

if gender would not have mattered, what would have been the number of males that would have survived, given the data for the number of females who survived (296/402) and the total number of passengers on the ship (1207).

Answers

If gender did not matter then the number of males who would have survived would be 593 males

How to find the number who would have survived ?

If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.

First, calculate the survival rate of the females:

Survival rate = Number of females who survived / Total number of females

= 296 / 402

= 0.737

Expected number of male survivors = Number of males * Female survival rate

= 805 x 0.737

= 593 males

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i dont know the answer to this

Answers

combine like terms. D) 2x+7

879 divided by 8 with remainder as fraction

Answers

in mixed number form 109 7/8
in decimal form 109.875

a) The monthly basic salary of the married Chief of Army Staffs (COAS) General is Rs 79,200 with Rs 2,000 dearness allowance. He gets Dashain allowance which is equivalent to his basic salary of one month. He contributes 10% of his basic salary in Employee's Provident Fund (EPF) and he pays Rs 50,000 as the premium of his life insurance. Given that 1% social security tax is levied upon the income of Rs 6,00,000, 10% and 20% taxes are levied on the next incomes of Rs 2,00,000 and up to Rs 3,00,000 respectively. Answer the following questions. (i) What is his monthly basic salary? (ii) Find his taxable income.

Answers

(i). His monthly basic salary is Rs 79,200.

(ii) His taxable income is Rs 1,02,480.

(i) The monthly basic salary of the married COAS General is given as Rs 79,200, with an additional Rs 2,000 as a dearness allowance.

Total salary = Basic salary + Dearness allowance

Total salary = Rs 79,200 + Rs 2,000

Total salary = Rs 81,200

So his monthly basic salary is Rs 79,200.

(ii)

Total income = Basic salary + Dearness allowance + Dashain allowance

Total income = Rs 79,200 + Rs 2,000 + Rs 79,200

Total income = Rs 1,60,400

From this, we subtract his EPF contribution and life insurance premium:

Taxable income = Total income - EPF contribution - Life insurance premium

Taxable income = Rs 1,60,400 - 10% of Rs 79,200 - Rs 50,000

Taxable income = Rs 1,60,400 - Rs 7,920 - Rs 50,000

Taxable income = Rs 1,02,480

So his taxable income is Rs 1,02,480.

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Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver

Answers

A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay

The cost of insurance

Auto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).

The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.

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XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.

Answers

The values of the constants m and c include the following:

m = -1.3

c = 7.1

What is the slope-intercept form?

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c ...equation 1.

-11 = 3m + c ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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In a class of 26 students, 15 play an instrument and 5 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport and an instrument?

Answers

Answer:

3:26

Step-by-step explanation:

If r = 5 units and x = 11units then what is the volume if the cylinder shown above

Answers

The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.

A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.

The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;

Given that the radius is 5 units and the height is 11 units,

Substituting the values,

We get,

V = π × (5)² × (11);

V = 275π cubic units;

V = 275×3.14 = 863.5 cubic units;

Therefore, the required volume is = 863.5 cubic units.

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The given question is incomplete, the complete question is

If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.

what is the co efficient of x in(2.x+3)²

Answers

What is the Coefficient of x mean?

A coefficient is any constant or numerical term that is in front of one or more variables and is defined as a fixed number that is multiplied by a variable. For example, in the expression 3x+2y+4, 3 is the coefficient of x, 2 is the coefficient of y but 4 is not a coefficient, as it is not being multiplied by a variable.

How do you find the coefficient of x?

To find the coefficient of x, we can encircle it or underline it. Then, take everything else except for x, i.e. 5y. So, the coefficient of x in the term 5xy is 5y. Similarly, the coefficient of y in the term 5xy is 5x.

Solving it with Binomial Theorem

(2.x+3)² = (2x+3)(2x+3)

2x(2x+3)+3(2x+3)=

4x²+6x+3(2x+3)=

4x²+12x+9

so if your using the binomial theorem it would equal 4x²+12x+9

if you just want the coefficient of x that would be 4 ↑

Help My Daughter we not understanding?

Answers

Representation of a number in three different ways:

133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]

678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]

877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]

543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]

453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]

341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]

555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]

485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]

789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]

864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]

652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]

Here given an example to write a particular number in different representations.

13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.

14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.

1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.

So three representations are of number 142.

Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.

Representations for some numbers: