Properties of Operations
Use your knowledge of properties of operations to fill in the blanks.
HELP PLEASE

The inequality for solving the problem is d * cost per day + 275 * $0.10 ≤ $140

To solve this problem, we need to write an inequality that represents the total cost of renting the car and driving the planned miles. The total cost is the sum of the daily rental fee (d times the cost per day) and the cost of driving the planned miles (275 times $0.10 per mile). We can write the inequality as follows:

d * cost per day + 275 * $0.10 ≤ $140

Next, we need to solve for d, the number of days Salma can afford to rent the car. To do this, we can rearrange the inequality to isolate d on one side:

d * cost per day ≤ $140 - 275 * $0.10

d ≤ ($140 - 275 * $0.10) / cost per day

Now we can plug in the given cost per day for the car rental and solve for d. For example, if the cost per day is $30, we would have:

d ≤ ($140 - 275 * $0.10) / $30

d ≤ ($140 - $27.50) / $30

d ≤ $112.50 / $30

d ≤ 3.75

Since Salma cannot rent the car for a fraction of a day, we need to round down to the nearest whole number. Therefore, Salma can afford to rent the car for at most 3 days while staying within her budget.

Learn more about inequalities:

https://brainly.com/question/25275758

#SPJ11

The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is π/77 (243 - 9sqrt(3)).

To find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis, we can use the method of cylindrical shells. This involves integrating the circumference of a cylindrical shell times its height to obtain the volume of each shell, and then adding up the volumes of all the shells to get the total volume.

First, let's find the points of intersection of the two curves:

2/7 x^2 = 9/7 - x^2

9/7 = 9/7 x^2 + 2/7 x^2

9/7 = 11/7 x^2

x^2 = 9/11

x = ±sqrt(9/11)

The solid we obtain by rotating this region about the x-axis will have cylindrical shells with height dx, radius x, and circumference 2πx. Therefore, the volume of each shell will be:

dV = 2πx × h × dx

where h is the difference between the y-values of the curves at x:

h = (9/7 - x^2) - (2/7 x^2) = 9/7 - 9/7 x^2

Therefore, the total volume of the solid will be:

V = ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) 2πx * (9/7 - 9/7 x^2) dx

V = 2π/7 ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) x(9 - 9x^2) dx

We can simplify the integrand by setting u = 9x^2:

du/dx = 18x

dx = du/18x

Substituting:

V = 2π/7 ∫(from u = 9/11 to u = 81/11) (1/2)u^(1/2) (9/2) (du/18x)

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / x du

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / sqrt(9/11 - u/11) du

This integral can be evaluated using a trigonometric substitution. Let u = 9/11 sin^2 θ, then:

du/dθ = (18/11) sin θ cos θ dθ

Substituting:

V = π/7 ∫(from θ = π/6 to θ = π/2) (81/121) sin^3 θ dθ

V = π/7 [(81/121) * (3/4) - (9/121) × (sqrt(3)/2)]

V = π/77 (243 - 9sqrt(3))

Learn more about volume here

brainly.com/question/26621824

#SPJ4

Diane's monthly payment for borrowing $3,000 at 13.5% APR over 36 months is $101.81.

We can use an online finance calculator to compute the monthly payment, setting the following parameters.

The monthly payment shows the periodic payment that must be made to settle the loan with the finance charges.

N (# of periods) = 36 months

I/Y (Interest per year) = 13.5%

PV (Present Value) = $3,000

FV (Future Value) = $0

Results:

Monthly payments (PMT) = $-101.81

Sum of all periodic payments = $-3,665.01

Total Interest = $665.01

Thus, Diane will pay $101.81 monthly for 36 months.

Learn more about the monthly payment at https://brainly.com/question/28106777.

#SPJ1

Answer:

x+y-200=0

Step-by-step explanation:

ax = x

by = y

c = 200 but we convert it to negative 200 after moving it from the RHS to LHS

So x+y=200 will be x+y-200=0 in the form ax + by + c =0

When t = 4, the expression 3⋅2ᵗ evaluates to 48.

Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the given expression, all of which are separated by the arithmetic sign +.

An expression consists of one or more numbers or variables along with one more operation.

When t=4, the expression 3⋅2ᵗ evaluates to:

3⋅2⁴ = 3⋅16 = 48

Hence, when t = 4, the expression 3⋅2ᵗ evaluates to 48.

To learn more about expression, Visit

https://brainly.com/question/1859113

#SPJ1

We can expect 40 defective parts in a shipment of 1,000 parts.

We can use proportions to solve this problem.

The proportion of defective parts in the first shipment is:

16/400 = 0.04

This means that 4% of the parts in the first shipment are defective.

We can use this proportion to estimate the number of defective parts in a shipment of 1,000 parts.

If 4% of the parts are defective, we can set up the following proportion:

4/100 = x/1000

where x is the number of defective parts in the shipment of 1,000.

Simplifying the proportion, we get:

0.04 = x/1000

To solve for x, we can multiply both sides by 1000:

0.04 * 1000 = x

x = 40

Therefore, we can expect 40 defective parts in a shipment of 1,000 parts.

Learn more about defective parts here :

brainly.com/question/21999703

#SPJ4

The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

The set of values that can be satisfies the given condition in the equation is known as the solution.  We can solve the equation by adding or subtracting the same integer from both sides. Here adding or subtracting doesn't change the value of the equation.

Here we have

√(x - 1) - 5 = x - 8  

Solve the above equation to get the solutions

√(x - 1) - 5 = x - 8    

Add 5 on both sides

√(x - 1) - 5 + 5 = x - 8 + 5

√(x - 1)  = x - 3  

Do squaring on both sides

[√(x - 1) ]² = (x - 3)²    

[ x - 1 ] = (x² + 9 - 6x)    

x² + 9 - 6x - x + 1 = 0

x² - 7x + 10 = 0  

Now factorize the above equation

x² - 5x - 2x + 10 = 0      

x(x - 5) - 2(x - 5) = 0

(x - 5) (x - 2) = 0

(x - 5) = 0     and     (x - 2) = 0

x = 5                       x = 2      

at x = 2 => √(2 - 1) - 5 = 2 - 8    

=> √1 - 5 = 2 - 8    

=>   - 4 = -6 [ which is not true ]

at x = 5 => √(5 - 1) - 5 = 5 - 8      

=> √(4 - 1) - 5 = - 3  

=> 2 - 5 = -3  [ which is true ]

Therefore,

The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

Learn more about Equations at

https://brainly.com/question/30222034  

#SPJ1

According to the standard conversion rates 1.78 is equal to 5.696 feet.

We measure the distance between any two bodies in the terms of meter but when the distance is a small one, we can also use the unit called foot and these two units are interconvertible.

According to the standard us conversion rates one meter is equal to 3.2 ft.

We can use this same conversion rate to find the measurement of 1.78 m into ft.

So, we will write,

1 m = 3.2ft

1.78m = 1.78 x 3.2 ft

1.78m = 5.696 ft.

So, we have found that 1.78 m is equal to 5.696 feet.

To know more about unit conversion, visit,

https://brainly.com/question/97386

#SPJ4

the lateral surface area of the triangular prism with measurement of 5cm, 5cm, 4cm, 6cm and 12cm is 140 cm².

To find the lateral surface area of a triangular prism, we need to calculate the sum of the areas of all the rectangular faces of the prism. In this case, the triangular prism has two triangular faces and three rectangular faces. The triangular faces have dimensions of 5 cm (base) and 4 cm (height), while the rectangular faces have dimensions of 5 cm (width), 6 cm (height), and 12 cm (length).

To calculate the area of one of the triangular faces, we use the formula for the area of a triangle:

Area = (1/2) x base x height

In this case, the base is 5 cm and the height is 4 cm, so the area of one triangular face is:

Area = (1/2) x 5 cm x 4 cm = 10 cm²

Since there are two triangular faces, the total area of the triangular faces is: Total area of triangular faces = 2 x 10 cm² = 20 cm²

To calculate the area of one of the rectangular faces, we use the formula for the area of a rectangle: Area = length x width

In this case, the dimensions of the rectangular faces are 6 cm (height) x 5 cm (width) and 12 cm (length) x 5 cm (width), so the areas of these faces are: Area of one rectangular face = 6 cm x 5 cm = 30 cm²

Area of another rectangular face = 12 cm x 5 cm = 60 cm²

Since there are three rectangular faces, the total area of the rectangular faces is: Total area of rectangular faces = 30 cm² + 60 cm² + 30 cm² = 120 cm²

Finally, the lateral surface area of the triangular prism is the sum of the areas of the triangular and rectangular faces:

Lateral surface area = Total area of triangular faces + Total area of rectangular faces

Lateral surface area = 20 cm² + 120 cm² = 140 cm²

Therefore, the lateral surface area of the triangular prism is 140 cm².

To learn more about lateral surface area click here

brainly.com/question/14001755

#SPJ4

Input x (0 1 2)-  Output y( 2 -1 -4) is ​represents the function y = -3x+2.The relationship between such a collection of input data and each output is how a function is defined.

A function is, to put it simply, a relationship between outputs in which each input is connected to exactly one output. For each function, there is a range, made the request, and domain. Typically, a function is written as f(x), where x stands for the output. It is possible for a function to be declared inside of a class, module, or other function.

To determine Function , we obtain,

y = -3x+2

y = -3(0)+2=2

y = -3(2)+2=-1

y = -3(2)+2=-4

To know more about function visit:

https://brainly.com/question/30721594

#SPJ1

The value of the exponential equation is A = ( 8/7 ) x ^ -15/2

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = 8 / ( 7√x¹⁵ )   be equation (1)

On simplifying the equation , we get

The value of √x¹⁵ = x ^ 15/2

Now , the equation will be

A = ( 8/7 ) x ^ -15/2

Hence , the exponential equation is A = ( 8/7 ) x ^ -15/2

To learn more about exponents click :

https://brainly.com/question/28966438

#SPJ1

None of the given equations gives the correct answer, the answer is none of the options.

The equation from the calculation is:

y = 375(0.9834)ˣ

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The data gives the relation between time and temperature.

We are asked to find the time and temperature relation as an equation.

We are given five equations as options.

a) T(x) = 375(0.5)ˣ

x is time and T is temperature.

Now we will give the value of x = 10 in this equation.

T(10) = 375 * 0.5¹⁰ = 0.366

This is not the value given in the table.

So this is not the equation.

b) T(x) = -50x + 375

  T(10) = -50 * 10 + 375 = -500 + 375 = -125

This is not the equation.

c) T(x) = -25x² + 375

   T(10) = -25 * 10 * 1 0 + 375 = -2500 +375 = -2125

This is not the equation.

d) T(x) = 50x - 375

   T(10) = 50 * 10 - 375 = 500 - 375 = 125

This is not the equation.

e) T(x) = 25x² -75x + 375

  T(10) = 25 * 10 * 1 0 -75 * 10 + 375 = 2500 -750 +375 = 2125

The general form of the exponential equation is:

y = abˣ

375 = ab⁰= a

325 = ab¹⁰

275 = ab²⁰

275/325 = b¹⁰

b = 0.9834

So the equation for this data is:

y = 375(0.9834)ˣ

Since none of the given equations gives the correct answer, the answer is none of the options.

To learn more about the equations, follow the link.

https://brainly.com/question/22688504

#SPJ1

The total number of miles that Parker would have to run is given as follows:

88.41 miles.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

As the number of miles increases by 5% each week, the common ratio is obtained as follows:

100% + 5% = 105% = 1.05.

Hence the number of miles each week is given as follows:

Then the total number of miles is given as follows:

16 + 16.8 + 17.64 + 18.52 + 19.45 = 88.41 miles.

More can be learned about geometric sequences at https://brainly.com/question/24643676

#SPJ1

The slope of the line passing through the points (2, 8) and (2, -4) is undefined.

The slope of the line passing through the points (-7, 8) and (2, 8) is zero.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-4 - 8)/(2 - 2)

Slope, m = (-12)/0

Slope, m = undefined.

Since the change in the y-axis equals to zero, the slope of this line is equal to zero:

Slope, m = (8 - 8)/(2 - (-7))

Slope, m = 0/9

Slope, m = 0

Read more on slope here: brainly.com/question/3493733

#SPJ1

The solution for n of the expression in this problem is given as follows:

n = 5.

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

The mistake in the solution was applying the distributive property to 3(2n - 7), as 3 has to multiply both terms, 2n and -7, hence:

3(2n - 7) = 6n - 21.

Thus the solution to the expression is obtained as follows:

6n - 21 = 9

6n = 30

n = 30/6

n = 5.

More can be learned about the distributive property at brainly.com/question/2807928

#SPJ1

The inverse of the given function could be; y = √x / 7 + 8

Suppose that the given function is [tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

This simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

We have been given the function as g(x)=7(x-8)² +3 for 8 ≤ x < ∝

Function that can reverse into another function is known as an inverse function or anti function to find y when x is swapped with another variable, we must first determine the inverse function.

On the other hand, the inverse function and the original function have interchangeable domains and ranges.

y = 7(x-8)²

(x-8)² = y/7

x - 8 = y / 7

x = √y / 7 + 8

Or

y = √x / 7 + 8

Learn more about inverse function here:

https://brainly.com/question/19425567

#SPJ1

Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.

Here,

We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:

3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)

= -9x - 21x² + 3x² + 24 + 3x

= -21x² - 6x + 24

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

Answer:

122.5 feet

Step-by-step explanation:

[tex]\frac{4}{35}[/tex] = [tex]\frac{14}{x}[/tex]  cross multiply and solve for x

4x = 490  Divide both sides by 4

x = 122.5

The sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

A recursive rule is a mathematical rule that describes how to calculate the value of a term in a sequence or function based on the values of previous terms. In other words, a recursive rule defines a sequence or function in terms of itself.

To apply a recursive rule, we start with one or more initial terms and then use the rule to generate the subsequent terms. The rule involves a formula that expresses each term in the sequence or function as a function of the previous terms. This process continues indefinitely, generating an infinite sequence or function.

Recursive rules are often used in mathematics to define sequences and functions that have a recursive structure, such as the Fibonacci sequence or the factorial function. They can also be used to define algorithms for solving problems in computer science and other areas.

One advantage of recursive rules is that they can provide a concise and elegant way of defining complex sequences or functions. However, they can sometimes be difficult to work with, as they can lead to complicated and recursive formulas that are hard to evaluate or simplify.

To generate the sequence 1, 0.5, 0, -5, ... recursively, we can use the following rule:

a_n = (a_{n-1} - 3a_{n-2})/2

where a_n represents the nth term in the sequence.

Using this rule, we can generate the sequence as follows:

a_1 = 1 (given)

a_2 = 0.5 (given)

To find the next term, we use the recursive rule:

a_3 = (a_2 - 3a_1)/2 = (0.5 - 3(1))/2 = -1

Continuing in the same way, we can find the next terms:

a_4 = (a_3 - 3a_2)/2 = (-1 - 3(0.5))/2 = -2.5

a_5 = (a_4 - 3a_3)/2 = (-2.5 - 3(-1))/2 = 2

and so on. Thus, the sequence generated recursively by the rule is 1, 0.5, 0, -5, -2.5, 2, 7.25, ...

To know more about sequence visit:

https://brainly.com/question/30240118

#SPJ1

Answer:

1 = 37° 2= 53° 3=106° 4=74°

Step-by-step explanation:

I apologize in advance since I am not the best at explaining but I'll do my best:

All triangles add up to 180° since you already know 106° you can subtract 106° from 180° to get 74° so you divide that by 2 to get angle 1 since both angles will be the same (since all the triangles are isosceles triangles) now since it's a rectangle all angles add up to 90° so subtract 37° from 90° to get angle 2 now you only have 3 and 4 left 3 is 106° since it's the same as the first triangle now to find four since you know angle 2 you know both of the bottom angles are 53° now 53 times 2 equals 106° so you subtract 106° from 180° and get 74°

The surface area of the given prism above would be = 606cm²

To calculate the surface area of the given prism is to add all the area of the faces.

The area of the two triangles = 2(1/2 base×height)

where base = 12 cm

height = 8cm

area = 1/2× 12×8

= 48 × 2 = 96cm²

Area of rectangle =3( l×w )= 3(17×10)

= 3×170 = 510cm²

Therefore the surface area of the prism = 96+510 = 606cm².

Learn more about multiplication here:

https://brainly.com/question/28768606

#SPJ1

Answer:1st and 3rd

Step-by-step explanation:

Answer: (-4, -2) and (-13, 0)

Used a calculator

For some values, such as the speed of light or the separation between the Earth and the sun, scientists and mathematicians long ago realized they needed a simpler way to write and refer to these large numbers.

They developed/created scientific notation at that time.

For us to estimate the order of magnitude:

Firstly, write the number in scientific notation.

Secondly, Round up to the nearest integer times a power of ten or power of ten.

Thirdly, Apply these estimates to your calculations.

Fourthly, If possible, compare the result to the exact one.

Example question, How many orders of magnitude are there in one million, for instance?

Answer will be, In order to represent the number 1,000,000, we will move the decimal to the left, stopping just before the first digit. The order of magnitude is determined by the quantity of left moves you make. Since we moved it six times, there are six orders of magnitude between ten and one million, which means that ten times six is equal to one million.

To learn more about order of magnitude: https://brainly.com/question/30460426

#SPJ4

The simplest form is (-2 ±√12)/2.

What is simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: x = (-4 ±√48)/4

We have to simplify the given term.

x = (-4 ±√48)/4

x =  (-4 ±√12×4)/4

x =(-4 ±2√12)/4

Now, we take 2 as common and get

x = (-2 ±√12)/2

Hence, the simplest form is (-2 ±√12)/2.

To learn more about the simplification from the given link

https://brainly.com/question/28008382

#SPJ1

The value of the converting 148 pounds to kilograms is given by               ( 67.1328 ) kilograms.

One kilograms is equal to 2.20462 pounds.

⇒ 2.20462 pounds = One kilograms

⇒ One pounds = ( 1 / 2.20462 ) kilograms

⇒ One pounds = ( 0.4536 ) kilograms

Substitute the required value we have,

⇒ 148 pounds = ( 148 × 0.4536 ) kilograms

⇒ 148 pounds =  ( 67.1328 ) kilograms

Therefore, the conversion of the 148 pounds to kilogram is equal to  ( 67.1328 ) kilograms .

learn more about kilograms here

brainly.com/question/28844288

#SPJ4

Answer: The value of sinB is b/c

Step-by-step explanation:since sinB =P/H

Here, P=perpendicular

         H=hypotenuse

so here, P=b and H=c

sinB=b/c

To know more about trigonometric ratios:

https://brainly.in/question/52160034#:~:text=Answer%3A%20Trigonometric%20Ratios%20are%20defined%20as%20the%20values,as%20the%20trigonometric%20ratios%20of%20that%20particular%20angle.

The actual distance from Ferris to Butte is 10 miles shorter than the distance found by Wayne.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The actual distance is the hypotenuse of the right triangle, hence it is obtained as follows:

d² = 15² + 20²

d = sqrt(15² + 20²)

d = 25 miles.

The distance found by Wayne from the diagram is of 15 + 20 = 35 miles, then the difference is of:

35 - 25 = 10 miles.

More can be learned about the Pythagorean Theorem at brainly.com/question/30203256

#SPJ1

The angle of depression from the top of the taller building is equal to the angle of elevation from the top of the shorter building.

The angle of depression from the top of the taller building is the angle between the line of sight from the top of the taller building and the base of the shorter building. This angle is equal to the angle of elevation from the top of the shorter building, which is the angle between the line of sight from the top of the shorter building and the top of the taller building. Both angles are measured from the horizontal and are equal in b. This is because the two buildings are the same distance apart and the line of sight from the top of one building to the base of the other is the same as the line of sight from the base of one building to the top of the other.

Learn more about angle here

https://brainly.com/question/28451077

#SPJ4