Product of two rational no. is 1 , if one of them is ⁵/²



, then the other no. is

a) ⅖



b) -1


c) 0​

Answer:

marla is 180m from the info center and she walked 240m from the parking lot to the lake

Answer:

19.63 in²

Step-by-step explanation:

Given:

\(\text{Diameter of circle: 5 inches}\)

Determine the radius of the circle:

The relationship between the diameter and the radius of the circle is that the diameter is two times larger than the radius. Thus, the diameter needs to be divided by two to obtain the radius of the circle.

Determining the area of the circle:

The area of the circle is πr². Let's substitute the measure of the radius to determine the area of the circle.

Simplify the square of 2.5:

Replace π with 3.14 (Approx.):

Furthermore, the question said to round to nearest hundredth...

⇒ 19.63 in² = Area of circle

Answer:

yes this quote isabsolutely right as

life is very innocent , we can make our life whatever we like

If the mass of bacteria multiplies by 3 every hour, then mass of bacteria after 5 hours is 1701mg and after 6 hours is 5103mg.

If the mass of bacteria multiplies by 3 every hour, then the mass after n hours is written by the expression ⇒ M = 7 × 3ⁿ;

Where, "M" is the mass of bacteria and "t" is time in hours;

To find the mass after 5 hours, we can substitute n = 5 in the formula:

We get,

⇒ M = 7×3⁵ = 7×243 = 1701 mg

So, the mass of bacteria after 5 hours will be 1701 mg.

To find the mass after 6 hours, we can substitute n = 6 in the formula:

We get,

⇒ M = 7×3⁶ = 7×729 = 5103 mg

So, the mass of bacteria after 6 hours will be 5103 mg.

Learn more about Bacteria here

https://brainly.com/question/14216887

#SPJ4

The equation of the line perpendicular to PQ passing through Z is:

y - ZY = 21/29(x - ZX)

To solve this problem, we can use the fact that the centroid of a triangle divides each median into two segments, where the length of the segment adjacent to the vertex is twice the length of the other segment.

Let M be the midpoint of WY, N be the midpoint of WX, and Z be the centroid of triangle WXY. Then, we know that:

WM = MY

WN = NX

ZM = 2ZC

ZN = 2ZB

where ZB and ZC are the lengths of the segments of the median from vertex W that intersect XY at points B and C, respectively.

We can use this information to set up a system of equations:

WM + WN = WY

ZM + ZN = ZW

ZC + ZB = ZX

Substituting the given values, we have:

(87/2) + (39/2) = WY

2ZC + 2ZB = WZ

48 + (87/2) = ZX

Simplifying each equation, we get:

WY = 63

ZC + ZB = WZ/2

ZX = 141

Now, we can use the fact that the sum of the lengths of the medians of a triangle is equal to three times the length of the segment connecting the centroid to the circumcenter. That is:

WX + WY + WZ = 3 × ZO

where O is the circumcenter of triangle WXY.

Substituting the given values and the values we found earlier, we have:

WX + 63 + 141 = 3 * ZO

Simplifying, we get:

WX = 3ZO - 204

To solve for WX, we need to find ZO. We know that the circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle. Let P be the intersection of the perpendicular bisectors of WY and WX, and Q be the intersection of the perpendicular bisectors of WY and XY. Then, ZO is the distance from Z to the line PQ.

We can find the equation of PQ by finding the midpoint of WY and WX, which is M. Then, the slope of PQ is the negative reciprocal of the slope of the line passing through M and Z.

We know that the slope of the line passing through M and Z is:

(ZM - MY) / (ZW - WM) = (2ZC - MY) / (WZ - WM)

Substituting the given values and the values we found earlier, we have:

(2ZC - 63/2) / (141/2 - 87/2) = (2ZC - 63/2) / 27

Solving for ZC, we get:

ZC = 117/2

Now, we can find the equation of PQ. The midpoint of WY is (0, 63/2), and the midpoint of WX is (87/2, 0). Therefore, the slope of PQ is:

(-87/2) / (63/2) = -29/21

The equation of PQ is therefore:

y - 63/2 = (-29/21)(x - 87/2)

Simplifying, we get:

29x + 21y = 1911

To find ZO, we need to find the distance from Z to the line PQ. We know that the equation of the line perpendicular to PQ passing through Z is:

y - ZY = 21/29(x - ZX)

Find out more about centroid of triangle

brainly.com/question/19593405

#SPJ1

Complete Question

If Z is the centroid of ΔWXY, WR=87, SY=39, and YT=48, find each measure.

a)WS=

b) WY =

c) WZ =

d) ZR =

e) ZT =

f) YZ =

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

know more about matrix method

https://brainly.com/question/32106604

#SPJ11

if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

To learn more on Angles click:

brainly.com/question/28451077

#SPJ1

Discrete mathematics has had a significant impact on reducing cultural distinctions by serving as a universal language that transcends cultural barriers. One way it has done this is by providing a common framework for communication and collaboration between mathematicians from different cultures.

Discrete mathematics is a branch of mathematics that deals with discrete objects, such as numbers, graphs, and algorithms. It provides a basis for computer science, information technology, and other fields that rely on computational methods and mathematical models.

These fields have become increasingly important in our interconnected world, and their growth has helped to reduce cultural distinctions by bringing mathematicians from different cultures together to work on common problems and develop a shared understanding of mathematical concepts and methods.

Another way discrete mathematics has reduced cultural distinction is by providing a common language for representing and solving problems in various fields, such as engineering, finance, and biology.

Learn more about the  discrete mathematics, please visit the link given below;

https://brainly.com/question/30409326#

#SPJ11

This matrix has exactly one (real) eigenvalue of 2, and the 2-eigenspace is the line spanned by the vector [1, 0, 0].

To find a 3x3 matrix with exactly one (real) eigenvalue 2, such that the 2-eigenspace is a line, we can start by constructing a diagonal matrix with a 2 in the top left corner, a 1 in the middle, and a 0 in the bottom right corner. This matrix would have a single eigenvalue of 2, since the other two entries do not affect the determinant.

Next, we can choose a non-zero vector v that lies in the 2-eigenspace. Since the eigenspace is a line, any non-zero vector in that line will suffice. Let's choose v = [1, 0, 0] for simplicity.

Finally, we can construct our desired matrix A by using the formula A = PDP^-1, where P is the matrix whose columns are the eigenvectors of A, and D is the diagonal matrix of eigenvalues. Since we only have one eigenvalue of 2, D will be [2 0 0]. We already have one eigenvector v = [1, 0, 0] in the 2-eigenspace, so we need two more linearly independent eigenvectors to complete P.

One option is to choose any two linearly independent vectors that are orthogonal to v. Let's choose u = [0, 1, 0] and w = [0, 0, 1]. These vectors are clearly orthogonal to v and to each other.

We can then construct the matrix P by placing the eigenvectors v, u, and w as the columns of P:

P = [1 0 0; 0 1 0; 0 0 1]

Finally, we can compute the inverse of P by swapping the rows and columns:

P^-1 = [1 0 0; 0 1 0; 0 0 1]

Putting it all together, we have:

A = PDP^-1 = [1 0 0; 0 1 0; 0 0 1][2 0 0; 0 1 0; 0 0 0][1 0 0; 0 1 0; 0 0 1]

A = [2 0 0; 0 1 0; 0 0 0]

Know more about diagonal matrix here:

https://brainly.com/question/28217816

#SPJ11

A diameter is a straight line that connects two points on the circumference of a circle and passes through the center. It is a fundamental concept in the study of circles and is used to calculate various properties and measurements associated with circles.

A straight line that passes through one side of a circle to the other is called a diameter.

In geometry, a circle is a closed curve consisting of all points in a plane that are equidistant from a fixed center point.

The diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circumference.

It is the longest chord of the circle and divides the circle into two equal halves called semicircles.

The diameter plays a significant role in the properties and measurements of circles.

One important property is that the diameter is twice the length of the radius, which is the distance from the center of the circle to any point on the circumference.

In mathematical terms, if r represents the radius and d represents the diameter, then d = 2r.

The diameter of a circle has several important applications and implications.

It is used to calculate the circumference of a circle using the formula C = πd, where C represents the circumference.

Additionally, the diameter is crucial in determining the area of a circle, which is given by the formula \(A = \pi r^2,\)

where A represents the area.

For similar question on straight line.

https://brainly.com/question/25969846

#SPJ11

Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

To learn more about Polyhedron, refer:

https://brainly.com/question/27231951

#SPJ4

The decay Σ+→Λ0+�+Σ+→Λ0+π+is allowed based on conservation laws and rules.

Here's the reasoning:

Conservation of charge: The total charge on the left-hand side (Σ+Σ+) is +1, and on the right-hand side (Λ0+�+Λ0+π+) is also +1. Therefore, the decay is consistent with the conservation of charge.

Conservation of baryon number: The total baryon number on the left-hand side is +1 (since Σ+Σ+has baryon number +1), and on the right-hand side, the sum of the baryon numbers ofΛ0Λ0and�+π+is also +1.

Hence, baryon number is conserved in this decay.

Conservation of strangeness: The strangeness quantum number is conserved separately for each particle in the decay. The strangeness of

Σ+Σ+is 0, whileΛ0Λ0has strangeness -1 and�+π+has strangeness 0. The sum of the strangeness values on the right-hand side is -1 + 0 = -1, which matches the strangeness of the Σ+Σ+on the left-hand side. Therefore, strangeness is also conserved.

Based on the conservation laws of charge, baryon number, and strangeness, we can conclude that the decay

Σ+→Λ0+�+Σ+→Λ0+π+is allowed.

To know more about decay, visit

https://brainly.com/question/33268082

#SPJ11

El Sr negron tiene que redactar una serie de cartas en su oficina. A Lourdes le toma 6 horas pasar todas las cartas. A su compañera rosabel, le toma 9 horas en realizar la misma tarea. Si ambas trabajan juntas para hacer todo el trabajo d ela oficina,

a. Cuánto tiempo le tomará a ambas realizar el trabajo?

Answer:

3.6 horas

Step-by-step explanation:

Sea el número total de horas que ambos trabajaron = T

Deje que la cantidad total de letras por las que pasaron = 1

De la pregunta, se nos dice:

Lourdes necesitó 6 horas para revisar las cartas.

Esto significa que, cada 1 hora, Lourdes revisaba 1/6 de las letras

Rosabel tardó 9 horas en leer las letras.

Esto significa que, cada 1 hora, Rosabel revisó 1/9 de las letras

Por lo tanto,

(1/6 × 1) T + (1/9 × 1) T = 1

(1/6 + 1/9) T = 1

(3 + 2/18) T = 1

(18/5) T = 1

5T / 18 = 1

Cruz multiplicar

5T = 18

T = 18/5

T = 3.6 horas

Por lo tanto, les tomó a ambas 3.6 horas hacer el trabajo.

So the solution of the given question is,  the correct answer is D) Both data sets represent multiplicative relationships. from the given conditions.

In mathematics, a multiplicative relationship between two variables means that the ratio of their values remains constant as the values of the variables change. In other words, the product of the two variables is a constant. For example, if we have two variables x and y such that xy = k, where k is a constant, then x and y have a multiplicative relationship. If we increase the value of one variable, we must decrease the value of the other variable proportion in order to maintain the constant product. This type of relationship is often seen in situations involving rates, ratios, and proportions, such as in growth or decay processes, population dynamics, and financial calculations.

In Table A, y is 2.5 times x, and in Table B, y is 3 times x. In both tables, the relationship between x and y is a constant ratio, which is a characteristic of multiplicative relationships. In Table A, the ratio of y to x is always 2.5, meaning that y is always 2.5 times greater than x. In Table B, the ratio of y to x is always 3, meaning that y is always 3 times greater than x. Therefore, both tables represent multiplicative relationships between x and y.

To know more about Proportion visit:

https://brainly.com/question/29157395

#SPJ1

Answer:

− ( q p 4 − 12 q p 2 + 36 q − p 2 + 6 )

Step-by-step explanation:

When we measure a ECG waveform the large boxes represents 0.2 seconds.

To determine the measurements of the big box on ECG paper, we need to consider the standard calibration of ECG paper.

In most ECG papers, the standard calibration is as follows:

These measurements allow for accurate interpretation of the ECG waveform and analysis of heart activity.

Learn more about ECG here:

https://brainly.com/question/30410077

#SPJ1

Answer:

d = 102 below the surface of the sea.

Step-by-step explanation:

65 Seconds -- Direction down

d = ?

r = 4.9 feet / second

t = 65

d = 4.9 * 65 = 318 feet below sea level.

60 seconds -- direction up

t = 60 seconds

r = 2.1 feet/second

d = 2.1 *60 = 126 upwards.

Answer

The answer is neither one of the two distances.

d = 318 - 216

d = 102 below the surface of the sea.

Note: you might be asked to use a minus sign in your answer. I would dispute that. You are not told which sign down and up should take. All you can do is record the distance as I have.

Answer:

13.5*pi = 42.412

Step-by-step explanation:

ecplanation in picture

A stack of 35 cups would have a height of 30 units.

To determine the height of a stack of 35 cups using the equation S(n) = 0.5n + 12.5, we can substitute n = 35 into the equation and evaluate the function.

Given that S(n) represents the height of the stack and n represents the number of cups in the stack, we want to find S(35), which represents the height of the stack when there are 35 cups.

Substituting n = 35 into the equation S(n) = 0.5n + 12.5, we have:

S(35) = 0.5(35) + 12.5

Now we can perform the calculations:

S(35) = 17.5 + 12.5

S(35) = 30

Therefore, a stack of 35 cups would have a height of 30 units.

In the given equation S(n) = 0.5n + 12.5, the term 0.5n represents the contribution to the stack's height from the cups themselves, and 12.5 represents a constant height added to account for the base or any other additional height.

By substituting n = 35 into the equation, we calculate the height of the stack when there are 35 cups. In this case, the height is determined to be 30 units.

Understanding and utilizing function notation allows us to express mathematical relationships and evaluate them for specific values. It provides a concise and standardized way of representing mathematical functions and their corresponding outputs.

To know more about function notation refer here:

https://brainly.com/question/20755259

#SPJ11

Answer:

0.00043 in standard form is 0.00043

0.00043 in scientific notation is \(4.3*10^{-4}\)

Step-by-step explanation:

or zero and forty three hundred thousandths

Answer:

Proportional

Step-by-step explanation:

6 2/3 liters of water should be mixed with 10 juiced lemons to obtain the same result as Four liters of water are mixed with 6 juices lemons to make lemonade.

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.

A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).

By using unitary method, 4 liters was water has 6 lemons

1 lemon will have 4/6 liter of water.

So 10 lemon will have

(4/6)*10=40/6

=20/3

=6 2/3 liters

Mix 10 freshly squeezed lemons with 6 2/3 liters of water to make lemonade as needed to combine the juice of six lemons with four liters of water.

To know more about unitary method,

https://brainly.com/question/28276953?referrer=searchResults

#SPJ13

This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.

\(\lambda = \frac{-6±\sqrt{-164} }{4} \\\)

Now, According to the question:

Nontrivial Solutions of a System:

System of equations has a form:

AX = 0, X = (x , y, z)

System of equations has a nontrivial solutions if a determinant of a system is zero. If the determinant is not zero than the matrix has inverse and a nontrivial solution x=0. This can be said differently: The homogeneous system has the trivial solution if rank of A in the row reduced form of matrix is equal to the number of unknown variables. If rank of A is less than the number of variables then the system has nontrivial solutions.

λx + 2y + z = 0

x + 5y + 2z = 0

3x - λy + z= 0

So, we calculate and determinant :

\(\left[\begin{array}{ccc}\lambda&2&-1\\1&5&2\\3&-\lambda&1\end{array}\right]\)  \(= \lambda det\left[\begin{array}{ccc}5&2\\-\lambda&1\end{array}\right]\) \(-2det\left[\begin{array}{ccc}1&2\\3&1\end{array}\right]\) \(det\left[\begin{array}{ccc}1&5\\3&-\lambda\end{array}\right]\)

\(=2\lambda^2+6\lambda+25=0\)

This equation has complex solutions and that means the system has no nontrivial solutions for real value of lambda.

\(\lambda = \frac{-6±\sqrt{-164} }{4} \\\)

Learn more about Non-trivial solution at:

https://brainly.com/question/29910424

#SPJ4

The given question is incomplete, complete question is :

For which values of ? does the following system have nontrivial solutions

λx + 2y + z = 0

x + 5y + 2z = 0

3x - λy + z= 0

-3 < x - 10​

10 is subtracting on the right, then it will add on the left.

-3 + 10 < x

7 < x

The slope of the line passing through the point (1, 2) and (-1, -3) is 2.5

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The slope between two points A(x₁, y₁) and B(x₂, y₂) is given as:

Slope = (y₂ - y₁) / (x₂ - x₁)

Given that the line passes through the point (1, 2) and (-1, -3):

Slope = (-3 - 2)/(-1 - 1) = 2.5

The slope is 2.5

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

Know more about bottleneck  here,

https://brainly.com/question/32590341

#SPJ11

Answer:

k=15/4

Step-by-step explanation:

so you have to do y=Kx and then find you constant witch would give you the answer witch the answer is above.

hope this helped you

Answer:

False

Step-by-step explanation:

B is not subset of A because all the elements of B are not in A.

We will use Green's theorem to evaluate the line integral ∮C (2xy) dx + (xy²) dy, where C is the closed curve formed by traveling between specified points.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. It states that for a vector field F = (P, Q), the line integral ∮C P dx + Q dy around a closed curve C is equal to the double integral ∬R (Qx - Py) dA over the region R enclosed by C.

In this case, the vector field F = (2xy, xy²). To apply Green's theorem, we need to find the partial derivatives of P and Q with respect to x and y.

∂P/∂y = 2x and ∂Q/∂x = y²

Now, we can evaluate the double integral over the region R. The region R is the triangle formed by the points (-1, 2), (-1, -5), and (4, -4).

∬R (Qx - Py) dA = ∫∫R (y² - 2xy) dA

Using the given points, we can determine the limits of integration for x and y.

Finally, we evaluate the double integral using these limits of integration to obtain the value of the line integral ∮C (2xy) dx + (xy²) dy.

In summary, we use Green's theorem to relate the line integral to a double integral over the region enclosed by the curve. By evaluating this double integral, we can find the value of the line integral over the given closed curve.

Learn more about double integral here:

https://brainly.com/question/27360126

#SPJ11

Answer:

Step-by-step explanation:

Given that the total time taken to practice is given by the expression as

y=7(15+x)

Simplifying the expression we have

y=105+7x

Solving for x (that is making x subject of formula we have)

7x=y-105

Divide both sides by 7 we have

x=(y-105)/7

Therefore the expression is

x=(y-105)/7