A gardener already has 4 2/3 ft of fencing in his garage. he wants to fence in a square garden for his flowers. The length of one side of the garden is 3 1/4, how much more fencing will the gardener need to purchase? A. 8 1/3 B. 12 3/7 C. 13 1/4 D. 18 2/3​

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The domain of the function [tex]f(x) =log x[/tex] is (0, ∞) which means the given function is defined for all the values greater than 0.

The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.

Given function can also be written as   [tex]y=log_{10}x[/tex]

                                                             ⇒ [tex]10^{y}=x[/tex]

This means the domain of  [tex]logx[/tex]  is the set of all values that [tex]10^{y}[/tex] can be.Since 10 is a positive integer which means its power with any number will always be positive.Therefore domain of function [tex]logx[/tex] will always be positive.

                                     ∴ Domain of function = (0, ∞)

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Answer:

Below

Step-by-step explanation:

0 ≤ t ≤ + ∞

The value of x ≈ 8.0 rounded to the nearest tenth.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

In the right-triangle,

The cosine ratio,

cos37° = perpendicular / hypotenuse

cos37° = x / 10

Using cross multiplication,

10 × cos37° = x,

x = 0.7986 × 10

x = 7.986

x ≈ 8.0 rounded to the nearest tenth.

Therefore, x ≈ 8.0 rounded to the nearest tenth.

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After converting the given differential equation into first order we will get it as [tex]\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]

The equation dy/dx =f (x,y) with two variables x and y with its function f(x,y) specified on a region in the xy-plane defines a first-order differential equation. There are no higher-order derivatives since it only contains the one derivative, dy/dx, making it a first-order equation.

The given differential equation is

[tex]\left(1-x^2\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0----(i)[/tex] with y_1=x [tex]\Rightarrow & y^{\prime \prime}-\frac{2 x}{1-x^2} y^{\prime}+\frac{2}{1-x^2} y=0\end{aligned}$$[/tex]

Equation (1) is in the form of

[tex]$$y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0$$[/tex]

where [tex]$p(x)=\frac{-2 x}{1-x^2}, \quad q(x)=\frac{2}{1-x^2}$[/tex]

As we know that if y_1 is given, we can find y_2 as:

y_2=4y_1, where u is a function of x and can be determined by

[tex]$U=\int \frac{e^{-\int p d x}}{y_1^2} d x$[/tex]

[tex]=\int \frac{e^{-\int \frac{-2 x}{1-x^2}} d x}{x^2} d x\\=\int \frac{e^{-\ln \left|1-x^2\right|}}{x^2} d x\\=\int \frac{1}{x^2\left(1-x^2\right)} d x\\=\int \frac{\left(1-x^2\right)+x^2}{x^2\left(1-x^2\right)} d x\\=\int\left(\frac{1}{x^2}+\frac{1}{1-x^2}\right) d x[/tex]

[tex]$$\begin{aligned}& =\int \frac{1}{x^2} d x+\int \frac{1}{1-x^2} d x \\& =-\frac{1}{x}+\int \frac{1}{1-x^2} d x\end{aligned}$$[/tex]

Now, [tex]$\int \frac{1}{1-x^2} d x=\int f(x) d x$[/tex] (say)

Where, [tex]$f(x)=\frac{1}{1-x^2}=\frac{1}{(1+x)(1-x)}$[/tex]

[tex]=\frac{A}{1+\eta}+\frac{B}{1-x} \\[/tex]

1=A(1-x)+B(1+x)

Putting x = 1, we will get B = 1/2

x = -1, we will get it as: A = 1/2

[tex]\therefore \int \frac{1}{1-x^2} d x=\int \frac{1 / 2}{1+n} d x+\int \frac{1 / 2}{1-x} d x[/tex]

[tex]=\frac{1}{2} \ln |1+x|-\frac{1}{2} \ln |1-x|\\=\ln \sqrt{1+x}-\ln \sqrt{1-x}\\\\=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)\\\Rightarrow \int \frac{1}{1-x^2} d x=\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)[/tex]

Hence [tex]$u=-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)$[/tex]

[tex]\Rightarrow y_2=u \cdot y_1=x\left[-1 / x+\ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)=x \ln \left(\frac{\sqrt{1+x}}{\sqrt{1-x}}\right)-1\right.\\\Rightarrow y_2=\frac{1}{2} x \ln |1+x / 1-x|-1[/tex]

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Answer:

934−2s=214 and 2s=934−214

Step-by-step explanation:

To represent this situation, we need all three sides to add up to 934, which is the perimeter of the triangle. So we have:

[tex]214+2s=934[/tex]

Where s are the two remaining sides.

The first and third choice resembles this exact equation, but rearranged:

First equation:

[tex]934-2s=214\\934=214+2s[/tex]

Third equation:

[tex]2s=934-214\\214+2s=934[/tex]

The other two choices either have different operations or different values.

sdfasdfasdfAnswer:a

Step-by-step explanation:

asdfasdfsdfsdf

Answer:

x = 49

Step-by-step explanation:

180 - 112 = 68

68 - 19 = 49

x = 49

Have a good day!

Answer:

[tex] {12}^{2} - {10}^{2} = 44 \\ \sqrt{44} = 2 \sqrt{11} [/tex]

If you have problems in mathematics you can text me if you want

Considering the graph of g(x) which is a transformation of the graph of

f(x) = 3ˣ, the equation for g(x) is

g(x) = 3ˣ ⁺ ¹- 2

Translation say x units to the left is represented by positive x units while to the right is represented by negative x values. the left and right translation is restricted to the x values.

Translation say x units up is represented by positive x units while to the down is represented by negative x values. the top and down translation is restricted to the y values or the function itself.

The transformation of f(x) = 3ˣ include

translation 1 unit to the left = x + 1 putting to the equation yields 3ˣ ⁺ ¹

translation 2 units to the down = "the equation itself" - 1 putting to the equation yields 3ˣ ⁺ ¹- 2

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Answer:

Critical point

Step-by-step explanation: A critical point of a function y = f (x) is a point (c, f (c)) on the graph of f (x) at which either the derivative is 0 (or) the derivative is not defined. But how is a critical point related to the derivative? We know that the slope of a tangent line of y = f (x) at a point is nothing but the derivative f' (x) at that point.

Using Denise's schedule and he explicit formula (an = 1 + (n-1) 0,5) . At 10 weeks, the distance the students will swim is 5.5 km

The training schedule will get them ready to swim 5 km in time for the half-marathon is Denise's schedule

The formula given for the calculation of how far the students will swim is an = 1 + (n-1) 0,5

where:

n = 10

substituting and solving gives

an = 1 + (n - 1) 0.5

an = 1 + (10 - 1) * 0.5

an = 1 + 9 * 0.5

an = 5.5 km

Ernest's schedule is given by the expression: an = 1 + (n - 1) 0.25. In 10 weeks the students will swim

an = 1 + (10 - 1) 0.25 = 3.25 km still less than 5 km

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The range of the function g(x) = √-(x2 + 4) is |x| ≥ 2

Range of the function g of x is equal to negative square root of the quantity x squared plus 4.

The range of the function g(x) = √-(x2 + 4) can be determined by solving the inequality g(x) ≤ 0.

To solve the inequality, we need to first simplify the expression by squaring both sides:

(√-(x2 + 4))2 ≤ 0

-x2 - 4 ≤ 0

-x2 ≤ 4

x2 ≥ -4

Now, we can take the square root of both sides to get the final expression:

|x| ≥ √-4

|x| ≥ 2

Therefore, the range of the function g(x) = √-(x2 + 4) is |x| ≥ 2.

We can also express this range in interval notation as [2, ∞).

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The range of given function is (-∞ ,-2] . Range is calculated  using the concept of Maximum and minimum value of the function.here maximum value is -2 and minimum value is –∞.

In this question, we have asked about a range of an function so let's try to understand what is range of an function.

The set of numbers that a function can produce is known as its range. With all potential x-values plugged into the function, it is the set of y-values that results. The domain is the set of feasible x-values. If you're interested in learning how to determine a function's range.

The collection of each function's results.

You say:

range, function, and domain

Example: The range is 1,4,9,... when the function f(x) = x^2 is given the values x = 1,2,3,...

Given function in this question is f(x) = [tex]-\sqrt{x^2+4}[/tex] .

This is a negative sqaure root function . here let's try to understand properties of square root function.

The square root symbol √ is used in the square root function (which is read as "square root of"). A integer "y" such that y^2 = x is said to be a number "x's square root.

For calculating range we have to find what is the minimum value of function and what is the maximum value of function.

we know sqaure root function always gives positive value.

negative square root function will give negative value.

Minimum value is –∞.

For maximum value x = 0 f(x) = [tex]-\sqrt{4}[/tex]  = -2

So the range of given function is (-∞ ,-2].

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The flat fee that the store charges for renting a vacuum cleaner can be found by substituting 0 into the equation f(x) = 6x + 14. Doing this yields f(0) = 14, meaning the store charges a flat fee of 14.

The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner. This equation can be used to calculate the total rental cost of the vacuum cleaner. The equation is solved by substituting the number of hours the vacuum cleaner is rented for, x, into the equation. The flat fee that the store charges can be found by setting x equal to 0 in the equation, f(x) = 6x + 14. When x is set to 0, the equation becomes f(0) = 6(0) + 14. Simplifying the equation yields f(0) = 14. This means that the flat fee the store charges is 14.

To summarise, the flat fee that the store charges for renting a vacuum cleaner can be found by substituting 0 into the equation f(x) = 6x + 14. Doing this yields f(0) = 14, meaning the store charges a flat fee of 14.

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Answer:

(6 x 20) (6 x 5)

Step-by-step explanation:

We know

Earning per week $25

Earning 8 weeks

25 x 8 = ( 20 + 5) 8 = 20 x 8 + 5 x 8

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Answer: circular charts divided up into segments which each represent a value

Step-by-step explanation:

The area of the large rectangle shown in the image is (2 + 3 + 4)a unit square

An equation is an expression that shows the relationship between two or more numbers.

Area is the amount of space occupied by a two dimensional shape or object.

The area of a rectangle is the product of its length and width. It is given by the equation:

Area of a rectangle = length * width

From the diagram:

Width = a; length = 2 + 3 + 4

Area = length * width

Substituting the terms into the equation:

Area = (2 + 3 + 4)a

Further simplification gives:

Area = 2a + 3a + 4a

The area of the rectangle is 2a + 3a + 4a

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According to the question, Triangles are said to be in SSS (Side-Side-Side) congruence if their third sides are the same length as the third sides of another triangle.

One of the following conditions must be satisfied for two triangles to be considered congruent: There is equality between all three pairs of corresponding sides. Two matching side pairs have identical angles between them, as well as equal sides between them. The corresponding sides between two sets of corresponding angles and their two pairs are equal.

If both of a triangle's three sides and three angles are equal in any orientation, the two triangles are said to be congruent.

When all three corresponding sides are the same length and all three corresponding angles are the same size, two triangles are said to be congruent. Slides, rotations, flips, and turns can be used to make these triangles appear identical.

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The system of inequality that models the fencing of the garden as desired by the local citizen is

the graph is attached

The inequality equation is written by deucing some information given in the problem

The length of the garden should be at least 110ft

length, x ≥ 110 feet

the distance around should be no more than 380ft

the distance around is the perimeter, P ≤ 380 ft

let the width be y

P = 2(L + w)

2(x + y)  ≤ 380

the required equations is are x ≥ 110 feet and 2(x + y)  ≤ 380

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If you are paid biweekly a total of $108.50 is deducted, thus leaving with a total of $1,569.50

Biweekly pay means you are paid once every two weeks, resulting in 26 paychecks per year.

According to the question,

The total amount we are paid = $1750

The social security tax = 6.2%

So, the deduction will be = 6.2% of$1750 = 0.062 * 1750

The deduction amount = $108.50

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[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0\hspace{5em}\textit{we also know that} \begin{cases} x=-4\\ y=1 \end{cases} \\\\\\ 1=a(-4-0)^2 + 0\implies 1=16a\implies \cfrac{1}{16}=a~\hfill \boxed{y=\cfrac{1}{16}x^2}[/tex]

The value that shows the occupancy for the cobalt ion is -1. Option B

We know that the electrons can be found in the orbitals that are contained in the atom. The d orbital diagram is the image that shows the occupancies of the d orbital of the atom. This is the number of the electrons that can be found in a particular orbital.

Let us note that the elements that have a d level that is not completely occupied as said to be the transition elements. As such the transition elements are the elements that have d orbitals that are incompletely filled.

We have a transition metal complex here and the number or the magnitude of the charge that is carried by the complex is what has been designated as n in the image that has been attached here.

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There are 18 hours would the server have to work to earn $135 in tips.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A restaurant server averages $30 in tips for a 4 hour shift.

Now,

Since, A restaurant server averages $30 in tips for a 4 hour shift.

Hence, The time for a restaurant server averages in tips $1 = 4/30

So, The time for a restaurant server averages in tips $135 = 4/30 × 135

                                                                                        = 18 hour

Thus, The time for a restaurant server averages in tips $135= 18 hours

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Answer:

Yes, t=9 is a solution to the inequality t ≤ 10. When t is equal to 9, the inequality is satisfied because 9 is less than or equal to 10.

Step-by-step explanation:

Answer:

I thing yes! because ≤ means less than or equal to, which 9 is less than 10.

Step-by-step explanation:

Hope it helps!

[tex]f^{-1}{x} = \sqrt{(x+4)} + 1[/tex], is the inverse function of f(x) = (x-1)² - 4

What is an inverse of a function?

In mathematics, an inverse function is a function that undoes the effects of another function. Given a function f(x), the inverse function of f(x) is denoted as f^-1(x) or as f^1(x). The inverse function f^-1(x) satisfies the condition that f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain of the function.

To find the inverse of a function, one common way is to algebraically manipulate the function and the relationship between the function and its inverse.

To identify the inverse of the function f(x)=(x-1)^2-4, we can start by swapping x and y in the original function:

y = (x-1)^2-4

Then we need to solve for x:

x = (y+4)^0.5 + 1

To check that this is indeed the inverse function, you can substitute x = (y+4)^0.5 + 1 into f(x) and check that you get back y:

f((y+4)^0.5 + 1) = (((y+4)^0.5 + 1)-1)^2-4 = y

Hence, [tex]f^{-1}{x} = \sqrt{(x+4)} + 1[/tex], is the inverse function of f(x) = (x-1)² - 4.

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The applicants that would have to apply in order to meet the target is 52. Option 4 is correct.

We have to define x as the applications to meet target

The number of persons to hire is 30

10 percent do not meet requirements. Hence 90 meets the requirements. 90% of x

= 0.9X

12% fail the pre screening stage. Hence 88% have passed it. This would be 88% of 0.9x. = 0.792x

23% Did not come for the interview, hence 77% showed up. This would be 0.77*0.792x = 0.60984x

then 5% are said to have failed the background test. This means that 95% passed the test.

0.95 * 0.60984x = 0.579348X

We have to equate this to 30 in order to get the value of x

0.579348X = 30

divide through by 0.579348

X = 30 / 0.579348

X = 51.78

X ~ 52

The number of applicants is 52

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Analyzing the provided total storage for the CD and amount of pictures stored in it, Using simple difference , The answer is 581.28 megabytes.

Storage refers to the process of preserving data in a computer or other electronic device for later retrieval. This can include both short-term storage, such as in RAM, and long-term storage, such as on a hard drive or in the cloud. Data can be stored in various formats, including text, images, videos, and audio. Storage devices come in different forms including internal storage, external storage, removable storage, and cloud storage.

The term "difference" in mathematics can refer to a few different concepts, depending on the context. In subtraction, the difference between two numbers is the result of subtracting one number from the other. For example, the difference between 8 and 3 is 8 - 3 = 5. In set theory, the difference between two sets is a new set that contains all the elements that are in the first set, but not in the second set. In geometry, the difference between two shapes is the area left over when one shape is subtracted from the other.

total = 700 MB

used by pictures = 53 * 2.24 = 118.72 MB

Space left = 700 - 118.72 = 581.28 MB

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The homeowner is responsible for paying the first $5,000 of the damages, and the insurance company would cover the remaining $165,000 amount . The premium of $150 would remain the same, and the limit of $300,000 would not be affected.

You would be responsible for paying the first $5,000 of the damages, and the insurance company would cover the remaining $165,000. The premium of $150 would stay the same, and the limit of $300,000 would not be affected.

1. Determine the damages: The home suffers $170,000 in damages.

2. Determine the deductible: The deductible is $5,000.

3. Determine the limit of coverage: The limit of coverage is $300,000.

4. Calculate the amount of coverage: The insurance company would cover the remaining $165,000 (the difference between the damages and the deductible).

5. Determine the premium: The premium of $150 would stay the same.

The homeowner is responsible for paying the first $5,000 of the damages, and the insurance company would cover the remaining $165,000. The premium of $150 would remain the same, and the limit of $300,000 amount would not be affected.

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Answer:

143 degrees, 37 degrees

Step-by-step explanation:

Let's say the angle is x and the supplementary angle is x-106:

x + (x-106) = 180  ==> supplementary angles add up to 180 degrees

x + x - 106 = 180

2x - 106 = 180

2x = 286 ==> isolate x by adding 106 to both sides

x = 143 ==> divide 2 on both sides

x-106=

143-106 = 37

Answer: 143 degrees, 37 degrees

The student is not correct when he forms a triangle with side lengths 3 ,5 ,9 inches.

A triangle contains of  3 sides and 3 angles

The Triangle Inequality Theorem, which asserts that the total of any two sides must be greater than the third side, must be followed in order to determine whether a collection of integers is a legitimate measure of a triangle's sides.

as per the details stated above

Let a is 3 inches , b is 5 inches c is 9 inches

According to the triangle Inequality theorem

a + b > c

that is 8>9

which is incorrect

a + c > b

that is 12 > 5

which is correct

b + c > a

14 > 3

which is correct

as the theorem it does not satisfy one case so we can say that it will form a triangle

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No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle.

No, the student is not correct. To form a triangle, all three sides must follow the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is not greater than 9, making it impossible to form a triangle. This theorem is based on the idea that the longer side of a triangle must always be opposite the largest angle. Therefore, the longest side of the triangle must be less than the sum of the other two sides. Essentially, this means that in order for a triangle to be formed with side lengths of 3 in, 5 in, and 9 in as the student suggests, the longest side must be less than 8 in, which is not possible. Therefore, the student is incorrect, and it is impossible to form a triangle with the side lengths they have provided.

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Health club B cost $17 more in monthly membership than health club A.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

y = 48x + 40

Write the equation for the charges of club B as shown below,

y = 36x + 35

Calculate the charge for one month for both clubs,

Charges for club A = 48 × 1 + 40

Charges for club A = 88

Charges for club B = 36 × 1 + 35

Charges for club B = 36 + 35

Charges for club B =71

Thus, the charge of club B is $17 more than club A.

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The sum of the infinite series is approximately 0.6740, calculated to four decimal places.

The sum of the series can be approximated by adding up the first few terms.

1/4 + (-1/16) + (1/384) + (-1/18432) + (1/798336)

= 0.673975

Therefore, the sum of the series is approximately 0.6740, calculated to four decimal places.

The sum of the infinite series can be approximated by adding up the first few terms. The series is of the form (−1)^n/4^n n! with n = 1,2,3,4,… The first term is 1/4, which is the sum when n=1. The second term is then (-1/16), which is the sum when n=2. This pattern continues, with the next terms being 1/384 and -1/18432, respectively. After adding up the first five terms, we get a sum of 0.673975. Therefore, the sum of the series is approximately 0.6740, calculated to four decimal places.

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