if a square has a side length of \( \sqrt{18} \)what is the area

Odpowiedź:

AB

Wyjaśnienie krok po kroku:

Biorąc pod uwagę współrzędne A = (7, -1), B = (2, 11), C = (-8, - 3), D = (4, - 3), chcemy wiedzieć, który segment ma dłuższy odcinek

Korzystanie ze wzoru na odległość

AB = √ (11 + 1) ² + (2-7) ²

AB = √12² + 5²

AB = √144 + 25

AB = √169

AB = 14 jednostek

Podobnie;

CD = √-3 - (- 3)) ² + (4 - (- 8)) ²

CD = √0² + 12²

CD = √12²

CD = 12 jednostek

Ponieważ AB> CD, stąd długość AB ma większą długość

The blanks that are missing in the sequence are -3 and 11

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

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

2018, 2004

Step-by-step explanation:

substitute C(t) for 1274 because it's the cost

1274=6(t-11)^2+980

6(t-11)^2=294

(t-11)^2=49

x-11=7 x-11=-7

x=18, x=4

Answer:

2018, and 2004.

Step-by-step explanation:

do the math "using Your heads".

whatever how much the money is for one day on the object just multiply the money by the days it's rented out and add together the snowboard total and the boots total

Answer:

358

Step-by-step explanation:

Answer: the last one

Step-by-step explanation:

the easiest way to do this is the vertical line test. Graph the relation separately and then roll a pencil over each one. If the pencil touches two points at the same time, then it is not a function. Or you can look at the x inputs and if any are the same, it’s not a function.

Answer:

17x20=340

Step-by-step explanation:

multiply 17x2 and you get 34 right? So then (just like multiplying by 10) just add a zero to the end.

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:

Step-by-step explanation:

Required equation is:

Solution:

Answer:

83 kids total

Step-by-step explanation:

There are 54 girls on the playground. There are 25 fewer boys than girls on the playground. How many kids are on the playground?

girls = 54

boys = 54 - 25 = 29

54 + 29 = 83 kids total

kids that are on the playground are 83.

Merging objects and identifying them since one big bunch is done through addition. In arithmetic, addition is the technique of adding two or more integers together. The product can meet are the quantities that are included, and the outcome of the operation, or the final response, is referred to as the sum.

The total number of girls that are present is 54

The data given is that there are

25 fewer boys taht are4 present

The total number of boys will be

boys = 54 - 25 = 29

The number of kids that are present will be the total of boys and girls that are present.

Kids = boys + girls

54 + 29 = 83 kids total

The quantity of kids that are present in the playground is 83.

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Answer:

The sequence converges to 5/9.

Step-by-step explanation:

Suppose we have a sequence \(a_{n}\)

Limit test:

\(L = \lim_{n \to \infty} a_{n}\)

If L is a constant number, the sequence converges to L.

If L = 0, the test is inconclusive.

Otherwise, the sequence diverges.

In this question:

\(a_{n} = \frac{5n}{1 + 9n}\)

Test:

\(L = \lim_{n \to \infty} (\frac{5n}{1 + 9n})\)

Infinity limit, we consider the term with the highest degree in the numerator and in the denominator.

\(L = \lim_{n \to \infty} (\frac{5n}{1 + 9n}) = \lim_{n \to \infty} \frac{5n}{9n} = \lim_{n \to \infty} \frac{5}{9} = \frac{5}{9}\)

The sequence converges to 5/9.

You can check whether the sequence is decreasing or not in this case and use them with the limit.

The answers are:

a) The sequence converges. The limit is 5/9

b) The sequence converges. The limit is 0

There are many methods to find that. But one reverse test to be sure that the given sequence is not converging is that the limit when n tends to infinity, won't come as a finite point.

\(a_n = \dfrac{5n}{1+9n}\)

We have this sequence upper bounded by: \(\dfrac{5n}{9n} = \dfrac{5}{9}\)  (assuming n starts from 1) since the less the denominator, the bigger the term is (since 9n is positive and 1 is positive so 1 + 9n > 9n )

The sequence is lower bounded by  \(\dfrac{5n}{n + 9n} = \dfrac{5n}{10n} = \dfrac{5}{10} = \dfrac{1}{2}\)

Checking if the sequence is monotonic:

\(a_{n+1} - a_n = \dfrac{5(n+1)}{1+9(n+1)} - \dfrac{5n}{1+9n} = \dfrac{(5n + 5)(1+9n) - (5n)(10 + 9n)}{(10 + 9n)(1+ 9n)} \\\\=a_{n+1} - a_n = \dfrac{5}{(10+9n)(1+9n)} > 0\)

Thus the sequence is monotonically increasing sequence.

Thus, since the sequence is bounded and monotonic, thus it is converging.

The limit of this sequence is found by:

\(lim_{n \rightarrow \infty}\dfrac{5n}{1+9n} = lim_{n \rightarrow \infty}\dfrac{5}{1/n+9} = \dfrac{5}{9}\)

Thus, the limit of this sequence is 5/9

Checking the convergence of second given sequence:

Since the given sequence is always bigger than 0, thus it is lower bounded by 0.

Now the given sequence is monotonic decreasing since each term is less than or equal to previous term. Thus, due to it being monotonic decreasing and being bounded (and all terms are smaller or equal to 1, thus upper bounded too), we have this sequence as converging.

The limit of this sequence is taken by:

\(a_n = \dfrac{1}{mod(n, 2)}\\\\\rm As \: n \rightarrow \infty, \text{ we have mod(n,2)} \rightarrow \infty\\Thus, a_{\infty}= 0\)

Thus, the given sequence converges to 0.

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Answer:

The left side of the histogram has a cluster.

Step-by-step explanation:

The others don't make since.

It's not evenly distributed,

it's not symmetrical, and

it is definitely not a mirror image of the right side.

Answer:

A

Step-by-step explanation:

Answer:

-72 y^4

Step-by-step explanation:

(8y^2)(-9y^2)​

Multiply the coefficients

8*-9 = -72

Add the exponents since the bases are the same

y^2 * y^2 = y^(2+2) = y^4

(8y^2)(-9y^2)​ = -72 y^4

As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

It is possible either multiply, distribute, add, or negate in mathematics. The trying to follow is how a expression is put together: Number, expression, and scientific operator The ingredients of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) It is possible to combine expressions and phrases. An expressions, often known as an arithmetic operation, is any mathematical statement that contains variables, numerals, and a numerical operation between them. That instance, the word m there in given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

To address this issue, we just need to determine the total or difference that yields 2x2 + 2x + 2

Option A: ( x2 + 4x -2) + (x2 - 2x - 4) = 2x2 + 2x - 6

Option B: ( x2 + 4x - 2 ) + ( x2 + 2x + 4 ) = 2x2 + 6x + 2

Option C: ( x2 + 4x - 2) - ( -x2 + 2x - 4)= x2 + 4x - 2 + x2 - 2x + 4

= 2x2 + 2x + 2

As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

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The complete question is:-

Select the correct answer.

Which sum or difference is modeled by the algebra tiles?

A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2

B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2

C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2

D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

y = -2+1/3x

Step-by-step explanation:

Slope = -2

x - intercept = -3

To make the x-intercept positive you make it 1/3.  

y = -2 +1/3x

Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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Answer:

\({ \bf{ \bar {MN}} \: means \: length \: between \: M \: and \: N}\)

MN means line joining point M to point N.

Answer:

10,400 or 9360

Step-by-step explanation:

I'm currently doing permutations and combinations, actually I'm finishing it. I'm doing my test rn so I'm finishing geometry today for the whole grade. So I hope I got this right:

26*4*10*10 = 10,400

26 = 26 letters possible as to be the Capital letter

4 = 4 possible special characters

10 = 10 digits are possible, unless you can't repeat numbers, then it's:

26*4*10*9 = 9360

Answer:

bxjfjxucjkkdndjkjhkjjnn

Answer:

10. x ≈ 15,9

11. x ≈ 17,5

Step-by-step explanation:

10. Use the Pythagorean theorem:

\( {x}^{2} = {17}^{2} - {6}^{2} = 289 - 36 = 253\)

\(x > 0\)

\(x = \sqrt{253} ≈15.9\)

11.

\( {x}^{2} = {9}^{2} + {15}^{2} = 81 + 225 = 306\)

\(x > 0\)

\(x = \sqrt{306} ≈17.5\)

Answer:

4a²

Step-by-step explanation:

(2a)²

Distribute the square to all the terms in the bracket.

2²a²

Solve the powers if possible.

4a²

Answer:

4a²

Step-by-step explanation:

=> \((2a)^2\)

=> \((2^2*a^2)\)

=> 4 * a²

=> 4a²

The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = \(πr^2\)

A ≈ 3.14 × \((2^2)\)

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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Answer:

Step-by-step explanation:

Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.

1) (2-6i)+(4+2i)

open the parenthesis

= 2-6i+4+2i

collect like terms

= 2+4-6i+2i

= 6-4i

2)  (6+5i)(9-2i)

= 6(9)-6(2i)+9(5i)-5i(2i)

= 54-12i+45i-10i²

= 54+33i-10i²

In complex number i² = -1

= 54+33i-10(-1)

= 54+33i+10

= 54+10+33i

= 64+33i

3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i

= 2/3-9i*3+9i/3+9i

=2(3+9i)/(3-9i)(3+9i)

= 6+18i/9-27i+27i-81i²

= 6+18i/9-81(-1)

= 6+18i/9+81

= 6+18i/90

= 6/90 + 18i/90

= 1/15+1/5 i

4) For (3 − 5i)(7 − 2i)

open the parenthesis

= 3(7)-3(2i)-7(5i)-5i(-2i)

= 21-6i-35i+10i²

= 21-6i-35i+10(-1)

= 21-41i-10

= 11-41i

  Simplified form of the given expressions will be,

1). 6 - 4i

2). 64 + 33i

3). \(\frac{1}{15}+\frac{1}{5}i\)

4). \(\frac{31}{53}-\frac{31}{53}i\)

1). In a complex number (a + bi),

    a = Real part of the complex number

   bi = Imaginary part

     Expression given in the question → (2 - 6i) + (4 + 2i)

Rule to solve the given expression,

"Add real part and imaginary part of two complex numbers separately"

(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)

                         = 6 + (-4i)

                         = 6 - 4i

  Therefore, simplified form of the given expression will be (6 - 4i).

2). Given expression → (6 + 5i)(9 - 2i)

Rule to solve the expression → i² = -1

(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)

                       = 54 - 12i + 45i - 10i²

                       = 54 - 12i + 45i + 10 [Since, i² = -1]

                       = (54 + 10) + (45i - 12i)

                       = 64 + 33i

     Therefore, simplified form of the given expression will be (64 + 33i).

3). Given expression → \(\frac{2}{3-9i}\)

Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).

\(\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}\)

       \(=\frac{2(3+9i)}{3^2-(9i)^2}\)

       \(=\frac{6+18i}{9-81(-1)}\)

       \(=\frac{6+18i}{9+81}\)

       \(=\frac{6+18i}{90}\)

       \(=\frac{6(1+3i)}{90}\)

       \(=\frac{1}{15}+\frac{1}{5}i\)

    Therefore, simplified form of the given expression will be \(\frac{1}{15}+\frac{1}{5}i\)

4). Given expression → \(\frac{(3-5i)}{(7-2i)}\)

Multiply numerator and denominator with the conjugate of the denominator.

\(\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}\)

         \(=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}\)

         \(=\frac{21+4i-35i-10i^2}{49-4(-1)}\)

         \(=\frac{21-31i+10}{53}\)

         \(=\frac{31-31i}{53}\)

         \(=\frac{31}{53}-\frac{31}{53}i\)

  Therefore, simplified form of the given expression will be \(\frac{31}{53}-\frac{31}{53}i\).

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The value of the functions at f(-4) = 21 and f(0) = 13.

To evaluate f(x)=-2x+13 for f(-4) and f(0), we need to substitute the values into the equation and solve:

f(-4) = -2(-4) + 13 = 8 + 13 = 21

f(0) = -2(0) + 13 = 13

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