What is 63 ÷ 9 + 5y3 when y = 2?
37
47
72
96

a. C = 5.00 + 0.75t

b. It will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we can use the following equation:

C = 5.00 + 0.75t

In this equation, the constant term 5.00 represents the flat fee for parking, and the term 0.75t represents the additional cost per hour based on the number of hours (t) the car is parked. By adding the flat fee to the hourly cost, we get the total parking cost for t hours.

(b) To find out how much it will cost Elaine to park her car for a full 24 hours, we can substitute t = 24 into the equation:

C = 5.00 + 0.75 * 24

Calculating this expression, we get:

C = 5.00 + 18.00

C = 23.00

Therefore, it will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

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The equation of the perpendicular line passing through (0, -1) is y = -9x - 1.

To find the equation of a line that is perpendicular to the given line y = (1/9)x + 2 and passes through the point (0, -1), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The given line has a slope of 1/9. To find the slope of the perpendicular line, we take the negative reciprocal of 1/9, which is -9.

Using the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope and the coordinates of the given point (0, -1) into the equation.

y = -9x + b

Since the line passes through the point (0, -1), we can substitute the x-coordinate as 0 and the y-coordinate as -1 into the equation:

-1 = -9(0) + b

-1 = b

Therefore, the y-intercept (b) of the perpendicular line is -1.

Putting it all together, the equation of the line that passes through (0, -1) and is perpendicular to y = (1/9)x + 2 is:

y = -9x - 1

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)

=\(\frac{-10-+\sqrt{100-92} }{2}\)

=\(\frac{-10-+\sqrt{8} }{2}\)

then we form two equations according to negative and positive symbols

x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)

therefore x = \(-5+\sqrt{2}\)   or x=\(-5-\sqrt{2}\)

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

Honestly not sure what all the numbers you put down were (numbers for the graph?), but here is how to find the slope :)

First, find two "exact" points!

I am going to use (0, 1) and (2, 2)

We then go to our first point, (0, 1), and count how many points up it is until we are on the same x-axis of our y. This is 1. We then do the same thing for the y-axis. This is 2. It is rise over run, so the answer is \(\frac{1}{2}\)

(I hope this helps, have a nice day!)

The expressions that are equivalent to 3^8 are:

We have to solve these out

3^8. = 6561

From the options

A. 3^2x3^4

= 9 x 81

= 729

B  3²x3^6

= 9 x 729

= 6561

C.  3^16/3^2

= 43046721/9

= 4782969

d. 3^12/3^4

= 531441 / 81

= 6561

E.  (3^4)²

= 3⁴ x 3⁴

= 3⁴⁺⁴

= 3⁸

= 6561

F. (3¹)^7

= 3⁷

= 2187

The expressions that are equivalent to 3^8 are:

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The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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By using a Venn diagram, we can conclude that:

a. 10 businesses have a drive-up window and no outside seating

b. 4 Businesses have a drive-up window and outside seating, but no pay telephone

c. 20 businesses have no pay telephone

d. 9 businesses have only a drive-up window

e. 8 businesses have outside seating or a pay telephone

A Venn diagram is a diagram consisting of overlapping circles to illustrate the logical relationship between two or more sets of items.

In the question, there are 3 sets of criteria that describe the condition of the fast-food businesses in Valley Mills Drive: whether or not there is a drive-up window, outside seating, or a pay telephone.

Let d denotes the number of businesses that have the three criteria.

If a denotes the number of businesses that have drive-up window and outside seating only, then:

drive-up window and outside seating = a + d

                                                           12 = a + 4

                                                             a = 8

If b denotes the number of businesses that have outside seating and a pay telephone only, then:

outside seating and a pay telephone = b + d

                                                           6 = b + 4

                                                            b = 2

If c denotes the number of businesses that have drive-up window and a pay telephone only, then:

drive-up window and a pay telephone = c + d

                                                             5 = c + 4

                                                              c = 1

If x denotes the number of businesses that have drive-up window only, then:

have a drive-up window = a + c + d + x

                                    18 = 4 + 1 + 4 + x

                                    18 = 9 + x

                                      x = 9

If y denotes the number of businesses that have outside seating only, then:

have outside seating = a + b + d + y

                                17 = 4 + 2 + 4 + y

                                17 = 10 + y

                                  y = 7

If z denotes the number of businesses that have pay telephone only, then:

Have pay telephone = b + c + d + z

                               8 = 2 + 1 + 4 + z

                               8 = 7 + z

                                z = 1

Then we can draw a Venn diagram to illustrate those numbers to get a better illustration in answering the questions.

a. a drive-up window and no outside seating = c + x = 1 + 9 = 10

b. a drive-up window and outside seating, but no pay telephone = a = 4

c. no pay telephone = x + y + a = 9 + 7 + 4 = 20

d. only a drive-up window = x = 9

e. outside seating or a pay telephone = y + z = 7 + 1 = 8

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If the value of |A| is 48 the possible values for x in the matrix is 4 or -2.

The determinant of the matrix A is as follows:

|A| = 48

Therefore,

48 = (3x × 2x) - (4x × 3)

48 = 6x² - 12x

6x² - 12x - 48 = 0

3x² - 6x - 24 = 0

x² - 2x - 8 = 0

x² + 2x - 4x - 8 = 0

x(x + 2 -4(x + 2) = 0

(x - 4)(x +2) = 0

Therefore,

x = 4 or -2

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Answer:

X        -8          0          8         16        24

Y       -8         -5         -2          1           4

When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

It is also known as the object's capacity. The fundamental equation for volume is length, width, and height, as opposed to the fundamental equation for the area of a rectangular shape, which is length, breadth, and height. The math is the same regardless of how you refer to the different dimensions. For example, you can substitute "depth" for "height." Volume is used to describe an object's capacity.  Volume can also be used to describe how much space a three-dimensional object occupies.

given

The ratio of their volumes is always one to three

Since the volume of a prism is 108 cubic meters,

a pyramid's volume is 1/3 * 108, or 36 cubic meters.

When the pyramid is cut out of the prism, it has a volume of 36 cubic meters and the same base and height.

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Answer:

B. y = x² + 1

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Algebra II

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

Slope Fields

Solving Differentials - Integrals

Integration Constant C

U-Substitution

ln Integration: \(\displaystyle \int {\frac{1}{x}} \, dx = ln|x| + C\)

Step-by-step explanation:

*Note:

When solving differential equations in slope fields, disregard the integration constant C for variable y.

Step 1: Define

\(\displaystyle \frac{dy}{dx} = \frac{2xy}{x^2 + 1}\)

Point (0, 1)

Step 2: Rewrite Differential

Rewrite Leibniz Notation using Separation of Variables.

Step 3: Integrate Pt. 1

Solving general form of differential using integration.

Step 4: Identify Variables

Set up u-substitution for right integral.

u = x² + 1

du = 2xdx

Step 5: Integrate Pt. 2

General Form: \(\displaystyle |y| = C|x^2 + 1|\)

Step 6: Solve Particular Solution

Since both sides have absolute value, assume that the particular solution will be positive.

Substituting integration constant C into the general form:

Particular Solution: \(\displaystyle y = x^2 + 1\)

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Differentials and Slope Fields

Book: College Calculus 10e

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

Answer:

A and C are Functions

Step-by-step explanation:

They pass the vertical line test.

The way you know if a set of coordinates are not a function is if they have multiple points that have the same Y value.

Answer:

it is 3(x+2)

Answer:

3(x+2)

Step-by-step explanation:

You first find the common factor.

3x+6

3(x+2) solution.

The parameters of the exponential function in this problem are given as follows:

The standard format of an exponential function is given as follows:

y = c(1 - a)^t.

This is the case for a decaying exponential function, and the meaning of each parameter is given as follows:

In this problem, the function is given as follows:

f(x) = 1.1(0.44)^x.

Hence the values for the parameters are given as follows:

Then the percent of change is of -56%, as it is a decaying exponential function with a = 0.56.

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Answer: 0.3063 * 10^-1

Step-by-step explanation: hope this helps!

Answer:

it something i know that much

Step-by-step explanation:

Solution:

We know that the formula to write the equation of a circle is (x – h)² + (y – k)² = r², where:

First, let's find the radius of the circle. We know that the diameter of the circle is ten units. The radius is half of the diameter. This means that the radius is five units because it is half the diameter, which is ten units.

Creating the equation:

Hence, the equation to form a circle with center (-6, 2) and diameter 10 is (x + 6)² + (y – 2)² = 5².

Image attached~

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Answer:

Integer: 9

Nearest 10th: 9.5

Step-by-step explanation:

Answer:

Scale Factor: 6, for every one inch there is 2 feet.

Step-by-step explanation:

Hi there!

Let’s find the scale factor first.

Since the width is 18, divide that by 3 to find the scale factor, which is 6.

To find the scale, we divide 6 by 3, so we know that for every 1 inch, the actual size is 2 feet.

I hope this helps!

Answer:

x = 1

Step-by-step explanation:

5(2x - 8) + 15 = -15

First, let's move the 15 to the opposite side of the equation. We'll do this by subtracting 15 from BOTH sides of the equation.

5(2x - 8) + 15-15 = -15-15

5(2x-8) + 0 = -30

5(2x-8) = -30

Now let's expand that first term.

5(2x)-5(8) = -30

10x - 40 = -30

Now let's move the -40 to the opposite side of the equation. We'll do this by ADDING 40 to both sides of the equation.

10x - 40 + 40 = -30 + 40

10x -0 = 10

10x = 10

Now to solve for x, we divide BOTH sides by 10 to "isolate the variable" aka get x alone.

10x/10 = 10/10

x = 1

The answer is x = 1.

Let's check if our answer is correct!

Original equation: 5(2x - 8) + 15 = -15

Substitute 1 for x.

5(2*1-8) + 15 =

5(2-8) + 15 =

5(-6) + 15 =

-30 + 15 = -15 >>> which is exactly what we started with! So x is 1.

The area of the triangle with angle B = 128°, side a = 86, and side c = 37 is approximately 2302.7 square units.

To find the area of a triangle when one angle and two sides are given, we can use the formula for the area of a triangle:

Area = (1/2) * a * b * sin(C),

where a and b are the lengths of the two sides adjacent to the given angle C.

In this case, we have angle B = 128°, side a = 86, and side c = 37. To find side b, we can use the law of cosines:

c² = a² + b² - 2ab * cos(C),

where C is the angle opposite side c. Rearranging the formula, we have:

b² = a² + c² - 2ac * cos(C),

b² = 86² + 37² - 2 * 86 * 37 * cos(128°).

By substituting the given values and calculating, we find b ≈ 63.8.

Now, we can calculate the area using the formula:

Area = (1/2) * a * b * sin(C),

Area = (1/2) * 86 * 63.8 * sin(128°).

By substituting the values and calculating, we find the area of the triangle to be approximately 2302.7 square units.

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Answer:

The answer is the last line below.

Step-by-step explanation:

g(x) = 4x

h(x) = -3x^2 + 4

(g + h)(x) = 4x - 3x^2 + 4

Answer:

A = $446,068.00

Step-by-step explanation:

A = $446,068.00

I = A - P = $88,068.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 8.2%/100 = 0.082 per year.

Solving our equation:

A = 358000(1 + (0.082 × 3)) = 446068

A = $446,068.00

The total amount accrued, principal plus interest, from simple interest on a principal of $358,000.00 at a rate of 8.2% per year for 3 years is $446,068.00.

Answer:

12. 5

11.

10

10

15. 7

14. 11

2

=

16

16

18. 3

+

11

17

3

4

co

loo

8

Step-by-step explanation:

12. 5

11.

10

10

15. 7

14. 11