1. Write the equation of the circle, (x-2)²+(y-5)²=7² in general form.​

The domain and the range of the relations are

What is domain?

In mathematics, the domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

In other words, the domain of a function is the set of values that can be plugged into the function and produce a valid output.

What is range?

In mathematics, the range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for a given input value from its domain.

In other words, the range of a function is the set of values that the function takes on as its input variable varies over its domain.

Using the above definitions, we have the domain and the range of the relations to be:

Graph 9:

Domain = [0, 6]

Range = [-3, 3]

Relation = Yes

Function = No

Graph 10:

Domain = (-∝, ∝)

Range = (-∝, ∝)

Relation = Yes

Function = Yes

Graph 11:

Domain = (-∝, ∝)

Range = [0, ∝)

Relation = Yes

Function = Yes

Graph 12:

Domain = [-3, 3]

Range = [-4, 4]

Relation = Yes

Function = No

Graph 13:

Domain = (-∝, ∝)

Range = [-2, 4]

Relation = Yes

Function = Yes

Graph 13:

Domain = (-∝, ∝)

Range: y = 1

Relation = Yes

Function = No

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[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }.[/tex]

[tex]f(x)=2x+\frac{3}{5} \\ \\[/tex]

[tex]y=2x+\frac{3}{5} \\ \\[/tex]

[tex]x=2y+\frac{3}{5} \\ \\[/tex]

[tex]x-\frac{3}{5} =2y+\frac{3}{5} -\frac{3}{5} \\\\x-\frac{3}{5} =2y[/tex]

[tex]\frac{x-\frac{3}{5}}{2} =\frac{2y}{2} \\ \\\frac{x-\frac{3}{5}}{2} =y[/tex]

[tex]y =\frac{x-\frac{3}{5}}{2}[/tex]

[tex]y =\frac{x}{2} -\frac{\frac{3}{5} }{2}[/tex]

[tex]y =\frac{x}{2} -\frac{3}{5} }*\frac{1}{2} \\ \\y =\frac{x}{2} -\frac{3*1}{5*2} }\\ \\y =\frac{x}{2} -\frac{3}{10} }[/tex]

[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }[/tex].

To verify if this is the correct expression for the inverse of the function, simply see if the "x" values and "y" values of the function are inverses as well. For example, a value of x = 2 returns 4.6 on the original function. Therefore, the inverse function should return 2 when a value of x = 4.6 is used. Check the attached image to see this comparison using the table of values of the original function and it's inverse.

Hello and greetings KingDanny2xx.

Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.

 [tex]\boldsymbol{\sf{f(x)=2x+\dfrac{3}{5} }}[/tex]

We substitute f(x) for y.

          [tex]\boldsymbol{\sf{y=2x+\dfrac{3}{5} }}[/tex]

We interchange x and y.

       [tex]\boldsymbol{\sf{x=2y+\dfrac{3}{5} }}[/tex]

We interchange the sides of the equation. We want to swap sides because mathematicians agreed to the convention that the unknown variable in equations and inequalities must always be on the left-hand side.

If there is a variable on both sides, we do it to facilitate a later calculation.

        [tex]\boldsymbol{\sf{2y+\dfrac{3}{5}=x }}[/tex]

We multiply both sides of the equation by 5. We want to multiply an equation to get rid of fractions and/or rational expressions, doing a lot more calculations later.

Both sides of the equation must be multiplied by the same value to preserve equality between all sides, according to the Multiplication Property of Equality.

        [tex]\boldsymbol{\sf{5\left(2y+\dfrac{3}{5}\right)=5x }}[/tex]

We distribute the 5 to the terms in parentheses. The distributive property is that each term in an expression between parentheses is multiplied by the expression outside the parentheses.

          [tex]\boldsymbol{\sf{5x2y+5x\dfrac{3}{5} =5x}}[/tex]

We calculate the product.

            [tex]\boldsymbol{\sf{10y+\not{5}x\dfrac{3}{\not{5}}=5x }}[/tex]

We cancel the greatest common divisor 5.

            [tex]\boldsymbol{\sf{10y+3=5x}}[/tex]

We move the constant to the right side and change its sign. We want to move a constant to the right because it is customary for constants in equations to be on the right hand side.

The sign of the constant must be changed because in the process of "moving the constant", we are adding its opposite to both sides.

We move the constant to the right by adding its opposite to both sides.

     [tex]\boldsymbol{\sf{10y+3-3=5x-3}}[/tex]

Since two opposite numbers add up to 0, we remove them from the expression. The additive inverse property states that two opposite numbers add up to 0.

Since adding or subtracting 0 doesn't change the value of the expression, we can simply remove them.

      [tex]\boldsymbol{\sf{10y=5x-3}}[/tex]

We divide both sides of the equation by 10. We want to divide an equation to isolate the unknown variable on one side or to transform the equation in a certain way.

Both sides of the equation must be divided by the same number to preserve equality between the sides, according to the Division Property of Equality.

         [tex]\boldsymbol{\sf{10y\div10=(5x-3)\div10}}[/tex]

Any equation divided by itself is equal to 1.

         [tex]\boldsymbol{\sf{y=(5x-3)\div10}}[/tex]

We distribute the 10 to the terms in parentheses. The distributive property is that each term of an expression between the parentheses is multiplied by the expression that is outside the parentheses.

        [tex]\boldsymbol{\sf{y=5x\div10-3\div10 }}[/tex]

We write the division as a fraction. A fraction is another way of writing division.

One more way to remember it is the division symbol.

We notice that the division symbol looks like a fraction where the dots represent the numerator and denominator.

         [tex]\boldsymbol{\sf{y=\dfrac{5}{10}x-3\div10 \iff y=\dfrac{\not{5}}{\not{10}}x-\dfrac{3}{10} }}[/tex]

We divide by the common factor 5. The object of canceling a common factor is to rewrite a fraction in the simplest form to facilitate a later calculation.

We can cancel a common factor because it will still represent the same value.

         [tex]\boldsymbol{\sf{y=\dfrac{1}{2}x-\dfrac{3}{10} }}[/tex]

Substitute y for f⁻¹ (x). Substitution means to replace one algebraic expression with another or with a specific value.

         [tex]\boldsymbol{\sf{f^{-1}(x)=\dfrac{x}{2}-\dfrac{3}{10} }}[/tex]

Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.

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This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get , x ≈ 1.29

Tο sοlve linear equatiοns with fractiοns, we need tο multiply bοth sides οf the equatiοn by the least cοmmοn multiple (LCM) οf all the denοminatοrs tο eliminate the fractiοns¹.

When an equatiοn invοlves fractiοns οn bοth sides, multiply each side by the denοminatοrs' lοwest cοmmοn multiple (LCM).

The LCM οf 4 and 3 is 12. Multiplying bοth sides by 12, we get:

12(x - (3x-2)/4) = 12((6-5x)/3)

Simplifying, we get:

12x - 3(3x-2) = 4(6-5x)

Expanding and cοllecting like terms, we get:

-6x + 6 = -20x + 24

Adding 20x tο bοth sides, we get:

14x + 6 = 24

Subtracting 6 frοm bοth sides, we get:

14x = <cοde>**18**</cοde>

Dividing bοth sides by <cοde>**14**</cοde>, we get:

<cοde>**x = 18/14**</cοde>

This is an imprοper fractiοn. Tο simplify it, we divide the numeratοr by the denοminatοr and get:

<cοde>**x = <u>9</u>/<u>7</u>**</cοde>

This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get:

x ≈ 1.29

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Answer:

Step-by-step explanation:

The range of the uniform distribution is from 23 to 47, so the minimum value (a) is 23 and the maximum value (b) is 47.

The probability density function for a uniform distribution is:

f(x) = 1 / (b - a) if a ≤ x ≤ b

= 0 otherwise

We want to find the probability that a random vehicle gets between 28 and 36 miles per gallon. This is the same as finding the area under the probability density function between x = 28 and x = 36.

Since the distribution is uniform, the probability density function is a horizontal line between x = 23 and x = 47, with height equal to 1 / (47 - 23) = 1/24.

The area under the probability density function between x = 28 and x = 36 is:

P(28 ≤ x ≤ 36) = (36 - 28) * 1/24 = 8/24 = 1/3

Therefore, the probability that a random vehicle gets between 28 and 36 miles per gallon is 1/3, or 0.3333 rounded to four decimal places.

Answer:

To find the perimeter of the quadrilateral, we need to find the distance between its vertices and then add them up. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can find the distance between each pair of adjacent vertices:

Distance between (-3, 1) and (2, 1):

d = sqrt((2 - (-3))^2 + (1 - 1)^2) = sqrt(25) = 5

Distance between (2, 1) and (2, -2):

d = sqrt((2 - 2)^2 + (-2 - 1)^2) = sqrt(9) = 3

Distance between (2, -2) and (-3, -2):

d = sqrt((-3 - 2)^2 + (-2 - (-2))^2) = sqrt(25) = 5

Distance between (-3, -2) and (-3, 1):

d = sqrt((-3 - (-3))^2 + (1 - (-2))^2) = sqrt(9) = 3

Now we can add up these distances to get the perimeter:

perimeter = 5 + 3 + 5 + 3 = 16

Therefore, the perimeter of the quadrilateral is 16 units.

Answer:[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:The line is diagonal to the left(\) , so the slope is negative.

[tex]\frac{rise}{run}[/tex]

Rise one(up), Run two(left)

So the CORRECT answer is [tex]-\frac{1}{2}[/tex]

Answer:

Step-by-step explanation: There are 60 minutes in each hour. You can do 162.44/60 and will get 2 with a remainder of 42.44 and the 42 goes towards minutes will the 0.42 left is for seconds. Your not converting to seconds so we can leave that as a decimal.

This will give you a total of 2 hours 42.44 minutes. If you want to check your work, you can do (2*60)+42.44=162.44.

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To convert 162.44 minutes to hours and minutes, we can follow these steps:

Divide the number of minutes by 60 to get the total number of hours:

162.44 ÷ 60 = 2.7073 hours (rounded to 4 decimal places)

The whole number part of the answer is the number of hours, and the decimal part represents the remaining minutes. In this case, we have:

2 hours and 0.7073 hours (or 42.438 minutes)

To convert the decimal part to minutes, we can multiply it by 60:

0.7073 × 60 = 42.438 minutes (rounded to 3 decimal places)

Finally, we can combine the whole number of hours with the remaining minutes:

2 hours and 42 minutes

Therefore, 162.44 minutes is equal to 2 hours and 42 minutes.

Step-by-step explanation:

the 2 angles are supplementary. that means together they have 180°

4x + 29 = 180 - (12x + 55) = 180 - 12x - 55 = 125 - 12x

16x = 96

x = 96/16 = 6

Juan paid Rs. 4.35 for the grapes. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

The four fundamental operations, frequently referred to as "arithmetic operations," are claimed to be able to explain all real numbers. The four mathematical operations that come after division, multiplication, addition, and subtraction are quotient, product, sum, and difference.

We are given that Juan bought 24 ounces of grapes and the grapes cost 2.90 per pound.

We know that 1 pound = 16 ounces.

So, 24 ounces = 1.5 pounds

Now, using multiplication operation, we get

⇒ 1.5 * 2.9 = Rs. 4.35

Hence, Juan paid Rs. 4.35 for the grapes.

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Answer:

shape?Draw a tree diagram to display all the possible outcomes that can occur when you flip a coin and then toss a six-sided die.(b) How many outcomes contain a head and a number greater than 2?(c) Assuming the outcomes displayed in the tree diagram are all equally likely, what is the probability that you will get a head and a number greater than 2 when Sure, I can help you with that! Here's a tree diagram showing all the possible outcomes of flipping a coin and rolling a six-sided die: ``` H T / \ / \ 1 2 3 4 / \ / \ / \ / \ 1 2 3 4 5 6 1 2 ``` Each branch represents a possible outcome, with the first letter indicating the outcome of the coin flip (H for heads, T for tails), and the second number indicating the outcome of the die roll. (b) To find the number of outcomes that contain a head and a number greater than 2, we can look at the branches that start with H and have a 3, 4, 5, or 6 on the second level. There are four of

Answer: There are 3 outcomes that contain greater than 2

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Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.

A mathematical equation is an expression that describes the relationship between two other expressions and is expressed as an equality on both sides of the equal to sign. The equation 3y = 16 is an illustration.

Kami has 3 choices for the color of her shoes and 3 choices for the type of heel, so the total number of possible shoe combinations is:

3 colors × 3 types of heels = 9 shoe combinations

The list of all possible choices for Kami's new shoe purchase is:

1.Black flat

2.Black small heel

3.Black high heel

4.White flat

5.White small heel

6.White high heel

7.Red flat

8.Red small heel

9.Red high heel

Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.

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Miguel has to put up the equation r = 72/16.

4.5% is the interest rate.

For calculating how long it would take for an investment to double in value, the rule of 72 is utilised. To get the doubling time, divide 72 by the interest rate.

To use the rule of 72, you simply divide the number 72 by the annual interest rate. For example, if the interest rate is 6%, the rule of 72 predicts that it will take approximately 12 years (72 ÷ 6 = 12) for the investment to double in value.

Part2:

equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires is n = 72 / r

Part3:

annual interest rate does Miguel need to double his money by the time he retire

r = 72 / n

72 / 16 = 4.5%

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Therefore , the solution of the given problem of area comes out to be  a.720 sq. ft, b.$227.94 , c.64,800 BTUs. and d.2,592 sq in.

Calculating how much space would be needed to fully enclose its exterior will reveal its overall size. The neighboring area is considered when selecting a comparable good for the rectangular design. The surface area of something determines its overall measurements. The number of sides between a cuboid's four trapezoidal shapes determines how much water it can hold.

Here,

A.

=>  2(144 sq. ft.) + 2(162 sq. ft.) =  720 sq. ft.

b.

16 *  18 = 288 square feet

The entire region that needs painting is:

=> 720 square feet +  288 square feet = 1008 square feet.

We need to apply two layers of paint to the following surface area:

=>  2 * 1008 square feet =  2016 square feet.

5.04 gallons are obtained by multiplying 2016 square feet by 400 square feet per gallon.

=> $6 liters* $37.99/gallon = $227.94

c. 16 feet by 18 feet by 9 feet equals 2,592 cubic feet

As a result, the room's necessary cooling capacity is:

=> 2,592 cubic feet*25 BTUs per cubic foot =  64,800 BTUs.

Rounding up to the next greatest thousand BTUs, we need an air conditioner with a capacity of 65,000 BTUs.

d.

=> 16 ft x 144 sq in/ft = 2,304 sq in by

=>  18 ft x 144 sq in/ft = 2,592 sq in

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Answer:

Cost per lawnmower = total earnings / number of lawnmowers sold

Cost per lawnmower = €23,380 / 10

Cost per lawnmower = €2,338

Therefore, the cost per lawnmower was €2,338.

Note that in the above Theoretical Probability prompt, the P(A, D) if two cards are randomly selected with replacement is 2/9. (Option C)

Theoretical probability is a branch of mathematics that deals with predicting the likelihood of events based on mathematical reasoning and assumptions, rather than empirical evidence or observations.

Where it is required to determine the P(A, D) if two cards are randomly selected from cards (A,D,D) with replacement:

P (A) = 1/3

P (D) = 2/3


Thus, P (A, D) = 1/3 * 2/3

= 1/3 × 2/3

= (1×2) / (3×3)

= 2/9

Thus, it is correct to state that the probability, if two cards A, and D are randomly selected with replacement is 2/9. (Option C)

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Answer:

Step-by-step explanation:

You want the side lengths in a right triangle geometry when the altitude to the hypotenuse of length 25 cuts off a segment of length 6.

All of the right triangles in this configuration are similar. The proportional relationships between the sides give rise to three geometric mean relations.

In effect each of the segments x, y, z is the geometric mean of the two segments of the hypotenuse it touches.

  x = √(6·(25-6)) = √114 ≈ 10.68

  y = √(6·25) = 5√6 ≈ 12.25

  z = √((25 -6)·25) = 5√19 ≈ 21.79

__

Additional comment

To see how these arise, consider the ratio of long side to hypotenuse:

  z/25 = 19/z

  z² = 25·19

  z = √(25·19) . . . . . the geometric mean of 25 and 19

The "geometric mean" of n numbers is the n-th root of their product. For two numbers, it is the square root of their product.

Answer:

(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:

E(X) = 5(1-p)^10 (since each box has the same probability of being empty)

Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,

E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328

So, the expected number of boxes that do not have any balls is approximately 0.328.

(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:

P(exactly one ball in a box) = 10p(1-p)^4

where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:

E(Y) = 5(10p(1-p)^4)

Substituting p = 1/5, we get:

E(Y) = 5(10/5^5) = 1/25

So, the expected number of boxes that have exactly one ball is 1/25.

Answer:

(1) 63 odd - and - 28 even

(2) 49 odd - and - 76 even

Step-by-step explanation:

We have been given the function We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.

Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.

Therefore, the range of the function is given by y>0B is the correct option.

The correct option is (b) i.e. The cosecant of an angle is defined as the length of the hypotenuse over the length of the side opposite.

What is Trigonometric ratio?

Trigonometric ratios are mathematical functions used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles. The three main trigonometric ratios are sine, cosine, and tangent

All statements contain some sort of mistake except the statement (b).

The statements should be corrected as given below:

A). The cosine of an angle is defined as the length of the side adjacent over the length of the hypotenuse.

C). The cotangent function is defined as the length of the side adjacent over the length of the side opposite.

D). The sine function is defined as the length of the side opposite over the length of the hypotenuse.

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Answer:

Step-by-step explanation:

From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.

Our model is

[tex]y=a(x-h)^2+k[/tex] where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:

[tex]-1=a(-4+5)^2-2[/tex] and

[tex]-1=a(1)^2-2[/tex] and

-1 = a - 2 so

a = 1.

Now we can fill in the equation with the coordinates of the vertex and the value found for a to get

[tex]y=(x+5)^2-2[/tex] You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.

Answer:

49

Step-by-step explanation:

P: Parenthesis

E: Exponent

M: Multiplication

D: Division

A: Addition

S: Subtraction

Start by solving what is inside the parenthesis first:

Next, solve for the exponent:

7² (which means 7 multiplied by itself twice)

Now you can multiply 49 and 4:

49 × 4 = 196

Finally, divide 196 by 4:

196 ÷ 4 = 49

Therefore, the answer to the expression 7² (4) ÷ 4 is 49.

Answer:

36 square inches.

Step-by-step explanation:

volume is given by 1 by 3, into base into height is based. His height and volume and area of the base is given by area of the ashe area of the base is given by 3 into 60 by 5. As given in the question on solving it, we get it equals to 36 square inches.

Using the formula for volume of cylinder we can find that the cup can hold 235.5cm³ volume of water.

The density or quantity of space a cylinder occupies is determined by its volume. Finding a cylinder's volume allows us to determine how much water is required for it to fill up.

Volume of a cylinder equals circle's area times height.

Volume equals πr² h

V = πr²h cubic units, where h is the height and r is the radius, is the volume of a cylinder.

Let's assume the cup is a cylinder. The pencil length is simulating a diagonal (hypothenuse), which forms a right triangle with the height of the cylinder and the diameter at the bottom. So, we apply Pythagorean's Theorem.

13² = 12² + d²

⇒ d² = 169-144

⇒ d = √25

⇒ d =5cm.

Radius = d/2

= 5/2

=2.5cm.

Now,

Volume of the cup = π × r² × h

= 3.14 × 2.5² × 12

= 235.5cm³.

Therefore, the cup can hold 235.5cm³ volume of water.

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The complete question is:

Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.

Anna's monthly payment for principal and interest is $1,117.78.

a) The amount of the required down payment can be calculated as follows:

Down payment = 15% of $245,000

Down payment = 0.15 x $245,000

Down payment = $36,750

Therefore, Anna is required to make a down payment of $36,750.

b) The amount of the mortgage can be calculated as follows:

Mortgage = Total price of the house - Down payment

Mortgage = $245,000 - $36,750

Mortgage = $208,250

Therefore, Anna's mortgage amount is $208,250.

c) The monthly payment for principal and interest can be calculated using the formula for a fixed-rate mortgage:

[tex]$M = P\left[\frac{i(1+i)^n}{(1+i)^n-1}\right][/tex]

Where:

M = Monthly Mortgage

P = Principal (amount of the loan)

i = Monthly interest rate (5% / 12 = 0.0041667)

n = Total number of payments (30 years x 12 months = 360)

Plugging in the values, we get:

[tex]$M = \frac{\$208,250 \left[0.0041667(1+0.0041667)^{360}\right]}{\left[(1+0.0041667)^{360}-1\right]}[/tex]

M = $1,117.78

Therefore, Anna's monthly payment for principal and interest is $1,117.78.

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Opens down with a vertex at (3, −8)

Term οr phrase used tο describe the factοrs Geοrge is "quality οf life."

In grammar, a phrase—called expressiοn in sοme cοntexts—is a grοup οf wοrds οr singular wοrd acting as a grammatical unit. Fοr instance, the English expressiοn "the very happy squirrel" is a nοun phrase which cοntains the adjective phrase "very happy".

Phrases can cοnsist οf a single wοrd οr a cοmplete sentence. In theοretical linguistics, phrases are οften analysed as units οf syntactic structure such as a cοnstituent. An adjective phrase is a phrase that mοdifies (explains) a nοun.

The term used tο describe the factοrs Geοrge is cοnsidering is "quality οf life."

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