A square flower garden is surrounded by a brick walkway that is 1.8 m wide. The area of the walkway is equal to the area of the garden. Determine the dimensions of the garden to the nearest tenth of a metre.

Answer:

Adding 16 on both sides

Step-by-step explanation:

The first step would be adding 16 on both sides to isolate the 5r and find the value of r

Which means you were correct, good job!

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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Answer:

9c^2 - 30cd + 25d^2

Step-by-step explanation:

(3c - 5d)^2

= (3c - 5d) (3c - 5d)

= [3c * 3c] + [3c * -5d] + [-5d * 3c] + [-5d * -5d]

= 9c^2 - 30cd + 25d^2

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

\(\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}\)

Answer:

To prove AEB ≅ DEC by ASA (Angle-Side-Angle), the properties that can be used are:

1. Opposite angles are congruent: This property is necessary to establish that ∠AEB ≅ ∠DEC, as both angles are opposite each other in the square ABCD.

2. All sides are congruent: This property is necessary to establish that AE ≅ DE, as both sides are corresponding sides of the square ABCD.

So, the properties to use for proving AEB ≅ DEC by ASA are "Opposite angles are congruent" and "All sides are congruent."

Step-by-step explanation:

Therefore , the solution of the given problem of angle comes out to be  tangent is approximately 0.952 and its sine is roughly 0.729.

An angle is a shape in Euclidean geometry made up of two angles, or circular faces, that divide at the centre of the wall and the wall's apex. At their intersections, two rays can join to form an angle. Angle is another outcome of two entities interacting. They are known as dihedral angles. A two-dimensional curve can be created by arranging two line beams in various ways at their ends.

Here,

We must ascertain the values of y and x in order to determine the sine and tangent of the angle. We are aware of:

=> √(x² + y²) * cos(θ) = x/h * 21/29

When we square both edges, we obtain:

=> x² / (x^2 + y²) = 441/841

The result of multiplying both parts by (x² + y²) is:

=> x²= (441/841) (x²+ y²)

If we simplify, we get:

=> (400/841) x² = (441/841) y²

The result of dividing both parts by (441/841) is:

=> (400/441) x²/ y² = 1

=> (y/x)² = 400/441

When we square the two edges, we obtain:

=> y/x = ±(20/21)

=> y/x = 20/21

Therefore,

sin(θ) = y/√(x² + y²) = (20/21) / √(1 + (20/21)²) ≈ 0.729

=> tan(θ) = y/x = 20/21 ≈ 0.952

As a result, the angle's tangent is approximately 0.952 and its sine is roughly 0.729.

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The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

We have,

To solve the given ordinary differential equation (ODE) using Laplace transform, we'll follow these steps:

Step 1: Take the Laplace transform of both sides of the equation.

Step 2: Solve for the Laplace transform of the function ƒ(t).

Step 3: Take the inverse Laplace transform to obtain the solution in the time domain.

Let's go through these steps:

Step 1: Taking the Laplace transform of the ODE, we have:

L[f"(t)] + 6L[f'(t)] + 13L[f(t)] = 48L[t - 5]

Step 2: Applying the Laplace transform properties and using the initial conditions, we get:

\(s^2F(s) - sf(0) - f'(0) + 6(sF(s) - f(0)) + 13F(s) = 48(e^{-5s}/s)\)

Simplifying, we have:

\(s^2F(s) + 6sF(s) + 13F(s) - s(0) - 0 + 6sF(s) - 6(0) + 13F(s) = 48(e^{-5s}/s)\)

Combining like terms, we obtain:

\((s^2 + 6s + 13)F(s) = 48(e^{-5s}/s)\)

Step 3: Solving for F(s), we have:

\(F(s) = 48(e^{-5s}/s) / (s^2 + 6s + 13)\)

To find the inverse Laplace transform of F(s), we can use partial fraction decomposition, but the expression involves complex roots.

Therefore,

The final solution in terms of the inverse Laplace transforms:

\(ƒ(t) = L^{-1}[F(s)]\)

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A line segment that goes from one side of the circle to the other side of the circle and doesn't go through the center is called chord of circle.

Since,

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.

The diameter is the length of the line through the center that touches two points on the edge of the circle.

So, we can say that every diameter of a circle is always called chord (longest chord) but every chord of the circle is not a diameter because the diameter passes to the circle's center but it not necessay that evey chord will pass through the center of the circle. Some, line segment goes from one side of the circle to the other side and doesn't pass through centre then for this case the line segment is called chord of the circle.

Hence, a line segment that goes from one side of the circle to the other side of the circle and doesn't go through the center is called chord of the circle.

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Answer:

35

Step-by-step explanation:

5(3+4)

5x7=35

Answer:78

Step-by-step explanation:

Answer:

<p

Step-by-step explanation:

Answer: <p

Step-by-step explanation: I did the quiz

There are 240 different ways to paint a cube such that one side is blue, two sides are red and three sides are green.

In the given problem, we can imagine the different possible configurations for painting different sides of a cube. We can consider the number of cubes that would be painted with one blue face, two red faces, and three green faces. In total, we could paint any of the six faces with blue, any of the remaining five faces with red, and any of the remaining four faces with green.

Therefore, the total number of different cubes that can be painted with one blue face, two red faces and three green faces is the product of the number of ways to choose one blue face from the six faces, times the number of ways to choose two red faces from the remaining five faces, times the number of ways to choose three green faces from the remaining four faces.

So, the number of possible cubes can be calculated as:

6C1 x 5C2 x 4C3 = 6 x 10 x 4 = 240

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The Arizona Department of Real Estate takes its rules and regulations from three basic sources: The Arizona State Constitution, Arizona Revised Statutes, and the Arizona Administrative Code.

The Arizona Department of Real Estate derives its rules and regulations from three primary sources. Firstly, the Arizona State Constitution serves as a fundamental legal document that outlines the framework and principles upon which the state operates.

Secondly, the Arizona Revised Statutes (ARS) provide the statutory laws enacted by the Arizona State Legislature. These statutes specifically address real estate matters and govern the activities and conduct of individuals and organizations involved in the real estate industry.

Lastly, the Arizona Administrative Code (AAC) contains the administrative rules and regulations established by various state agencies, including the Arizona Department of Real Estate. The AAC provides detailed guidelines and procedures for implementing and enforcing the laws set forth in the Arizona Revised Statutes, ensuring compliance and facilitating the proper functioning of the real estate sector within the state.

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The answer in fractions is 59/100

When a statistic is given as a percentage, we assume that the sample size of the survey is

100

persons.

So, in the aforementioned question, we simply need to express the percentage as a fraction where the

numerator

represents the number of people who are in favor of the argument that their teens are addicted to cell phones which is

59

the denominator of the fraction represents the total number of people in the sample survey size which is

100.

simply using the above logic we can deduce the percentage into a fraction which is

59/100

.

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Answer:

Y = 44

Step-by-step explanation:

44/4 - 2 = 9

11 - 2 = 9

Y = 44

<3

Answer:

1

Step-by-step explanation:

hope this helps!

Answer:

There are 4 possible scenarios where given relation could not be a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Step-by-step explanation:

From Function Theory, we remember that a relation is not a function when at least one element from domain (x-coordinate) is related to one or more elements from range (y-coordinate). Hence, there are four possibilities of making the relation not a function:

i)  \((-1, 4), (0,4), (2,5), (3,-6), (-1, 7)\)

ii) \((-1, 4), (0,4), (2,5), (3,-6), (0, 7)\)

iii) \((-1, 4), (0,4), (2,5), (3,-6), (2, 7)\)

iv) \((-1, 4), (0,4), (2,5), (3,-6), (3, 7)\)

Answer:

-2c + 8d - 6

-6 + 5d - 2c + 3d

Step-by-step explanation:

When multiplying terms in a bracket, you need to multiply the term outside the bracket to all the terms in the bracket.

-\(\frac{2}{5}\)(15-20d+15c) = (-\(\frac{2}{5}\) × 15) + (-\(\frac{2}{5}\) × -20d) + (-\(\frac{2}{5}\) × 15c)

Two minuses make a plus. One minus and one plus make a minus.

(-\(\frac{2}{5}\) × 15) + (-\(\frac{2}{5}\) × -20d) + (-\(\frac{2}{5}\) × 15c) = (-6) + (8d) + (-2c)

Note that the terms can be presented in any order and still be correct.

(-6) + (8d) + (-2c) = -6 + 8d - 2c

Let us go through the options to see which ones are correct:

-2c + 8d - 6: Since all the terms are there, this option is correct!

-c + 40d - 8: Since none of the terms is there, this option is wrong.

-4c + 40d - 8: Since none of the terms is there, this option is wrong.

-3c + 8d - 3: Since (-3c) and (-3) are not the correct terms, this option is wrong.

-6 + 5d - 2c + 3d: If we evaluate the like terms (5d and 3d), the final answer would be -6 + 8d - 2c so this option is also correct!

Answer:

V = 396 cubic inches

Step-by-step explanation:

width = w; length = l; height = h; volume = V; area of smallest face = a

base units are inches

w = 2 + l

h = l - 5

Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.

a = h × l = (l - 5) × l

36 = l^2 - 5l ==> l^2 - 5l - 36 = 0

Factor ==> (l - 9) × (l + 4) = 0

l = 9 and l = -4

Since length cannot be negative, 9 is the only Real answer.

l = 9

h = l - 5 = 9 - 5 = 4

w = 2 + l = 2 + 9 = 11

Volume of rectangular prism/box is length times width times height.

V = l × w × h = 9 × 11 × 4 = 396

The volume of the box with the given dimensions is;

Volume = 396 in³

Let us denote the properties of the box as follows;

Length of box = l

Width of box = w

Height of box = h

Area of the smallest face of box = a  

We are told that the width is 2 inches more than the length. Thus;

w = 2 + l

We are told that the height is 5 inches less than its length. Thus;

h = l - 5

Since length is smaller than width but bigger than height, the height and length are the 2 smallest faces

Thus,

a = h × l

plugging in the relevant values gives;

a = (l - 5) × l

a = l² - 5l

We are told that the area of the two smallest faces is 36 in². Thus;

l² - 5l = 36

l² - 5l - 36 = 0

Using online quadratic equation solver, we have; l = 9 inches

Plugging in 9 for h in; h = l - 5  

h = 9 - 5

h = 4

Also, plugging in 9 for l into; w = 2 + l, we have;

w = 2 + 9

w = 11

Volume of box is given by;

Volume = length × width × height

Volume = 9 × 11 × 4

Volume = 396 in³

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what are the answer choices?

The hybrid car will travel 38 miles on 7.4 gallons of gas, therefore, she will not be able to make it home.

The problem is solved applying the proportions in it's context.

A hybrid car averages 630 miles on a 122-gallon tank of gas, hence the number of miles per gallon is given as follows:

630/122 = 5.16 miles per gallon

Ramona has enough money to put 7.4 gallons of gas in her hybrid, hence the distance that she can travel is obtained as follows:

7.4 x 5.16 = 38 miles.

Hence she will not be able to make it home.

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Step-by-step explanation:

-4 + 2 + 4f = 8 - 3f

-2+4f=8-3f

7f=10

f=10/7

Step-by-step explanation:

\( - 4 + 2 + 4f = 8 - 3f \\ - 2 + 4f = 8 - 3f \\ - 4f - 3f = - 2 - 8 \\ \frac{ - 7f }{ - 7} = \frac{ - 10}{ - 7} \\ f = \frac{10}{7} \)

We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.

Let's evaluate f(1) and f(7) to determine their signs:

f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4

f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332

From the calculations, we can see that f(1) = -4 and f(7) = 332.

Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.

According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.

Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.

Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

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Answer:

c=30 -9over 4 f f= 40 over 3 negative 4 over 9 c

Step-by-step explanation:

hopefully that helps you

The resultant answer of the given equation [-1/2n² + 18 = 0] is n = 6.

So, -1/2n² + 18 = 0:

Solve for 'n' as follows:

Therefore, the resultant answer of the given equation [-1/2n² + 18 = 0] is n = 6.

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The complete question is given below:

Type the correct answer in the box. use numerals instead of words. what is the solution to this equation?

Check the picture below.

since the cliff is 48 feet tall, thus that its initial height.

\(~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&8\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&48\\ \qquad \textit{of the object}\\ h=\textit{object's height}&\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+8t+48\)

well, as you can see in the picture, its maximum is at its vertex, so

\(\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+8}x\stackrel{\stackrel{c}{\downarrow }}{+48} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 8}{2(-16)}~~~~ ,~~~~ 48-\cfrac{ (8)^2}{4(-16)}\right)\implies \left(\cfrac{1}{4}~~,~~48-\cfrac{64}{-64} \right)\)

\(\left( \frac{1}{4}~~,~~48+1 \right)\implies \stackrel{\textit{the ball is at highest}}{\left(\frac{1}{4}~~,~~\stackrel{\downarrow }{49} \right)}\)

well, it hits the ground when y = 0.

\(\stackrel{h(t)}{0}=-16t^2+8t+48\implies 0=8(-2t^2+t+6)\implies 2t^2-t-6=0 \\\\\\ (2t+3)(t-2)=0\implies t= \begin{cases} -\frac{3}{2}\\\\ 2~~\textit{\large \checkmark} \end{cases}\)

notice, we didn't use the negative value, since "t" must be greater than 0.

A unit of measurement which is equal to one thousands meters is known as one kilometers.

Therefore, the given units of measurement equal to one thousand meters is called one - kilometers.

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The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1and interval = [4]

since function text is continuous in a given interval. And also

+(4) = 42+4 = 4-1

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simple, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated proved.

Now,

= 6 C-1

C-5c +6 = 0

C=2 or c=3

1=3 or

C= 2, 3

<= 2

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