A tank has 55 gallons of water in it. The water drains from the tank at the rate of 3 gallons per minute. The function f(x) models the number of gallons of water in the tank after x minutes. Find f^-1(15) and explain what it represents.

Please help!!!!

The time that you will arrive in Nashville is 1:33.

From the information given, the person leaves Knoxville at 11:13, and the journey takes 2 hours and 20 minutes.

Therefore the time when the person will arrive will be the addition of the time given.

This will be:

= 11:13 + 2:20

= 1:33

Therefore, the person will arrive by 1:33.

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The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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The product that is represented with the algebra tiles is (2x + 2)(2x + 3)

From the question, we have the following parameters that can be used in our computation:

The algebra tiles

Representing the red tile with digit 1

So, we have

Vertical = 2x + 1 + 1 = 2x + 2

Horizontal = 2x + 1 + 1 + 1 = 2x + 3

The product that is represented with the algebra tiles is then calculated as

Product = Vertical * Horizontal

So, we have

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

Hence, the product is (2x + 2)(2x + 3)

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Since none of the functions have any restrictions, their domains are given as follows:

(-∞,∞).

The domain of a function is the set that contains all possible input values for the function.

In this problem, we are given these following functions:

Neither linear nor quadratic functions have any restriction in their domains, hence they are given as follows:

(-∞,∞).

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Answer: -x² - x

Step-by-step explanation:

Given expression

(x² + x) - (2x + 2x²)

Expand parentheses

=x² + x - 2x - 2x²

Combine like terms

=(x² - 2x²) + (x - 2x)

=\(\boxed{-x^2-x}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It's a cone

A teepee is in the shape of a cone

Answer:

\(Rate = 0.2167\ fl\ oz/hour\)

Step-by-step explanation:

Given

\(Rate = \frac{91\ fl\ oz}{2.5\ weeks}\)

Required

Express the rate as per hour

\(Rate = \frac{91\ fl\ oz}{2.5\ weeks}\)

There are 168 hours in  a week;

So, the rate becomes

\(Rate = \frac{91\ fl\ oz}{2.5 * 168\ hours}\)

\(Rate = \frac{91\ fl\ oz}{420\ hours}\)

\(Rate = 0.2167\ fl\ oz/hour\)

Hence;

The equivalent of the given rate is \(0.2167\ fl\ oz/hour\)

Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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Answer:

Step-by-step explanation: -3/2 divided by 9/6

= -3/2 multiply (to divide fractions we multiply by their recipical) 6/9
Then, simplify
= -3/3 = 1
Answer: -1

Hope this helps lol

The simplified result is -1. The correct option is b.

Given that:

Expression, -3/2 ÷ 9/6

To solve the given expression, follow as:

Rewrite the division as multiplication by the reciprocal of the second fraction.

-3/2 ÷ 9/6 = -3/2 × (6/9)

Now, simplify the fractions:

-3/2 × (6/9) = -3/2 × (2/3)

-3/2 × (6/9) = - (3 × 2)/(2 × 3)

-3/2 × (6/9) = -6/6

Finally, the simplified expression is -6/6. However, further simplify it by dividing the numerator and denominator by their greatest common divisor, which is 6:

-6/6 = -1

So, the simplified result is -1. The correct option is b.

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Complete question:

Simplify Negative 3 over 2 divided by 9 over 6.

a. −4

b. −1

c. 4

d. 1

Answer:

D

Step-by-step explanation:

Answer:

letter d

Step-by-step explanation:

a loss is negative do a loss of 18 would be -18

Answer:

D

Step-by-step explanation:

x - c = (r + d)/y                   for x

x = (r +d)/y + c          common denominator : (c/1) (y/1)  = yc

x = (r + d)/y + yc

x =   (yc + r + d)/ y                              

The solutions of the inequality are all numbers less than or equal to 3. Since we're looking for whole numbers less than 10, the solutions are: 0, 1, 2, and 3.

A statement that compares two numbers or expressions using an inequality symbol, such as (less than), > (greater than), (less than or equal to), or, is known as an inequality in mathematics (greater than or equal to). As contrast to an equation, which expresses equality, an inequality expresses a relationship between two quantities that may or may not be equal. Ranges of values, restrictions on variables, and requirements for optimisation are all described by inequalities. They are a cornerstone of calculus, algebra, and other areas of mathematics.

The whole numbers less than 10 are: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Now, for the given inequality:

4X -8 ≤4

4X - 8 + 8 ≤ 4 + 8

4X ≤ 12

X ≤ 3

Hence, the solutions of the inequality are all numbers less than or equal to 3. Since we're looking for whole numbers less than 10, the solutions are: 0, 1, 2, and 3.

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9514 1404 393

Answer:

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

Answer:

Step-by-step explanation:

surface area of the given image

= 1/2 (24) 35 (2 sides)  = 840 cm²

= 44 x 37 (2 sides)       = 3256 cm²

= 24 x 44 (bot base)   = 1053 cm²  

total                             = 5152 cm²          

Answer:

Inequalities in the explanation

Step-by-step explanation:

Inequalities

Is a relation that makes a non-equal comparison between two mathematical expressions using comparators as >, <, ≤, and ≥, among others.

Some usual operations performed in equations cannot be done in the same way in inequalities, especially multiplying or dividing by negative numbers. When we need to multiply or divide by a negative number, the inequality sign must be flipped.

Let's start off with the inequality

4>-3

a) Add 3 to each side:

4+3>-3+3

7>0

b) Subtract 2 from each side:

4-2>-3-2

2>-5

c) Multiply each side by 2:

2*(4)>2*(-3)

8>-6

d) Multiply each side by -3. We must flip the sign:

-3(4)<(-3)(-3)

-12<9

All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The solution is, fraction of Polygon P's area with Q's area is,

=4/1.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

given that,

1 Polygon Q is a scaled copy of Polygon P , using a scale factor of  1/2.

let, area of P = x^2

so, area of Q = x/2^2

                      = x^2/4

fraction of Polygon P's area with Q's area =

x^2 : x^2/4

=1/ 1/4 = 4

Hence,  The solution is, fraction of Polygon P's area with Q's area is,

=4/1.

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Answer:

2/3

Step-by-step explanation:

0.666666

times by 10

6.66666

10x-x=9x

9x=6

x=2/3

Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

<95141404393>

Answer:

Answer 4

Step-by-step explanation:

Rise 9, Run 8

Answer: 2 is the answer

Step-by-step explanation:

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

The expression (ab + ac + bc)^3 - a^3*b^3 is factored to give a³b³ (1 + a³c³ + b³c³ - 1)

Index forms are described as mathematical forms of representing numbers that are too large or too small in more convenient forms.

They are also termed scientific notation or standard forms.

They are identified as exponents of variables or numbers.

From the information given, we have that;

(ab + ac + bc)^3 - a^3*b^3

expand the bracket, we have;

a³b³ + a³c³ + b³c³ - a³b³

Now, we have to factor the common terms, we get;

a³b³ (1 + a³c³ + b³c³ - 1)

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Our negative number means that the government owes you $413.75. We would have to pay the government money if it weren't a negative number.

In order to pay for general government services, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.

Since ancient times, paying taxes to governments or officials has been a fundamental aspect of civilization.

So, to address this issue, utilize the Single column.

You must first calculate her taxes before deducting the tax credit.

She earns $17,000 in taxable income. She now falls into the 15% category.

The amount owed on the first 9275 dollars that are subject to the tax must first be determined.

.10 * 9275 =  927.50

The remainder of her debt, which is in the 15% range, must then be collected.

.15 * (17000 - 9275) = 1158.75

Add up all of our taxes on the money, then deduct our tax credit of $2500.

(927.50 + 1158.75) -  2500

(2086.25) -  2500 = -413.75

Therefore, our negative number means that the government owes you $413.75. We would have to pay the government money if it weren't a negative number.

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Answer:

6.986.

Step-by-step explanation:

6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000

We do the multiplications first    ( according to PEMDAS):-

= 6 + 9 * 0.1 + 8 * 0.01 + 6 * 0.001

= 6 + 0.9 + 0.08 + 0006

= 6.9 + 0.086

= 6 986.

The value of the equation in the decimal form is A = 6.986

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 6 x 1 + 9 x 1/10 + 8 x 1/100 + 6 x 1/1000

On simplifying the equation , we get

The value of 6 x 1 = 6

The value of 9 x 1/10 = 0.9

The value of 9 x 1/100 = 0.08

The value of 6 x 1/1000 = 0.006

So , substituting the values in the equation A , we get

A = 6 + 0.9 + 0.08 + 0.006

On simplifying the equation , we get

A = 6.986

Therefore , the value of A is 6.986

Hence , the value of the equation is 6.986

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bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

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Answer:

2x + 1 = 15

Step-by-step explanation:

Answer:

D or 2x+1

Step-by-step explanation:

first we have to distribute the 7 to the 2x+1

14x+7-2(6x+3)=15

now distribute the -2

14x+7-12x-6=15

combine like terms on the left side

2x+1=15

your answer would be D

hope this helps!