Help Please!

Solve the inequality and graph it’s solution.

Answer:

length=50m

width=25m

Step-by-step explanation:

perimeter is the distance all round,hence

2(l+w)=2(2x+x)=

4x+2x=6x=150

6x=150x

x=25

l=50m

w=25m

The inequality expression x < 7 is equivalent to the given inequality expression {x | x < 7}

The inequality expression is given as

{x | x < 7}

When the braces are removed, the inequality expression becomes

x < 7

This means that x < 7 is equivalent to the given inequality expression {x | x < 7}

Next, we represent the inequality expression on a plot

See attachment for the graph of the inequality expression

Read more about inequality at

https://brainly.com/question/24372553

#SPJ1

So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.

To find the y-coordinate of the solution of a system of equations, we can use one of the methods for solving systems of equations, such as substitution, elimination, or graphing. In this case, we will use substitution method.

The system of equations is:

3x + 2y = 7

y - 3x = 11

We can solve for y in the second equation and get:

y = 3x + 11

Now we can substitute this expression of y into the first equation:

3x + 2(3x + 11) = 7

3x + 6x + 22 = 7

9x + 22 = 7

9x = -15

x = -5/3

Now we can substitute this value of x into the second equation:

y = 3(-5/3) + 11

y = -5 + 11

y = 6

So, the y-coordinate of the solution of the system of equations 3x + 2y = 7 and y - 3x = 11 is 6.

To learn more about y-intercept

Visit; brainly.com/question/14180189

#SPJ4

Answer:

-20 < x < -3

Step-by-step explanation:

*math*

Answer:

314 cm

Step-by-step explanation:

If Keith's height is 15x and his nephew's height is 7x, we can write the following equation:

1.16 * 15x = 34 + 7x * 2 -- (We get the 1.16 from the 16% increase)

17.4x = 34 + 14x

3.4x = 34

x = 10 so Keith's current height is 1.16 * 15 * 10 = 174 cm and his nephew's height is 174 - 34 = 140 cm for a total current height of 174 + 140 = 314 cm.

The range of the graph is -4 ≤ y ≤ 2.

Option C is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

A coordinate plane with a segment going from the point (-3, 2) to (0, 1) and another segment going from the point (0, 1) to (5, -4).

This means,

(-3, 2) to (5, -4)

The range of the graph is the y-coordinate.

So,

-4 to 2

This can be written as,

-4 ≤ y ≤ 2

Thus,

The range is -4 ≤ y ≤ 2.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer:

The answer is B

Step-by-step explanation:

The statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is NOT true.

A. The statement is true. The ratios of the vertical rise to the horizontal run, also known as the slopes, of any two distinct nonvertical parallel lines are equal. This is one of the properties of parallel lines.

B. The statement is true. If two distinct nonvertical lines are parallel, then they have the same slope. Parallel lines have the same steepness or rate of change.

C. The statement is true. Given two distinct lines in the Cartesian plane, the two lines will either intersect at a point or they will be parallel and never intersect. These are the two possible scenarios for distinct lines in the Cartesian plane.

D. The statement is NOT true. Given any two distinct lines in the Cartesian plane, they may or may not be parallel or perpendicular. It is possible for two distinct lines to have neither parallel nor perpendicular relationship. For example, two lines that have different slopes and do not intersect or two lines that intersect but are not perpendicular to each other.

Therefore, the statement "D. Given any two distinct lines in the Cartesian plane, the two lines will either be parallel or perpendicular" is the one that is NOT true.

Learn more about cartesian plane here:

https://brainly.com/question/32222840

#SPJ11

Because of the negative new balance, the "client" still owes $\(0.01\),  the total amount deposited is $\(151.88\).

To answer mathematics issues involving proportional relationships, utilize the unitary technique. Finding the value of a quantity that is proportional to it includes utilising the value of one unit of the original quantity as a starting point. Many different mathematical problems, including those involving time, space, velocity, area, and volume, can be solved using the unitary technique. It is frequently utilised in everyday scenarios like shopping, cooking, and finance where two or more quantities are related to one another. The unitary method's fundamental steps are: Determine the problem's known and unknown quantities. Establish the connection between the quantities (e.g. if one quantity is twice another, or three times another, etc.).

given,

Let's start by calculating the greater deposit's amount using the given ratio:

If the smaller deposit is \(x\), then the larger deposit is \(7/2\) times x, or 3 1/2times the smaller amount.

After that, the total sum deposited is:

\(x\)\(+\) \(7/2x\)  \(=\)\(9/2x\)

Let's now calculate the new amount by adding the deposits and deducting the withdrawals:

Old balance minus New balance - Withdrawal plus all deposited funds

New balance is equal to \(-126.89\)$, \(-25\)$, \(+9/2x.\)

Simplifying:

New balance = \(-151.89\)$ plus \(9/2 x\)

Finding the value of x that brings the new balance to zero will help us determine how much extra the customer owes:

\(-151.89\)$ \(+\)\(9/2 x = 0\)

\(9/2 x\) \(=\)$\(151.89\)

\(x =\) $\(33.753\)

The lesser deposit is $\(33.75\), whereas the larger deposit is seven and a half times that amount, or $\(118.13\).

As a result, the total amount deposited is $\(151.88\)($\(33.75\)plus $\(118.13\)).

And following the withdrawal and the deposits, the new balance is:

-$\(151.89\)+ $\(151.88\)= -$\(0.01\)

Because of the negative new balance, the "client" still owes $\(0.01\),  the total amount deposited is $\(151.88\).

To know more about unitary method visit:

brainly.com/question/28276953

#SPJ1

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

Learn more about Radius of circle at:

https://brainly.com/question/28946570

#SPJ4

The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

learn more about trigonometric ratio from

https://brainly.com/question/24349828

#SPJ1

On solving the provided question, we can say that The maximum rank of a matrix is 2 and The maximum rank is min (5,2)=2.

A matrix is a set of numbers arranged in rows and columns. learns about the elements and dimensions of matrices and introduces them for the first time. A rectangular grid of numbers in rows and columns is known as a matrix. Matrix A, as an illustration, has two rows and three columns. Its single row and 1 n row matrix order are the reasons behind its name. A = [1 2 4 5] is a row matrix of order 1 by 4, for instance. P = [-4 -21 -17] of order 1-by-cubic is another illustration of a row matrix.

The maximum rank of a matrix is 2.

The maximum rank is min (5,2)=2.

Option c with the biggest rank is min(m,n).

To know more about matrix visit:

https://brainly.com/question/29995229

#SPJ4

The set of ordered pairs that represent 90 degrees counter clockwise rotation about he origin is

3) A' (-6, 1) B' (-6, 6) C' (-2, 1)

Rotation is a from of transformation that involves circular movement about an axis.

There two types of rotation

The transformation rule for 90 degrees clockwise rotation is as follows

(x, y) for a scale factor of r → (-y, x)

From the graph the coordinates are read and following the given transformation rule we have

preimage   image

A (1, 6)   →   A' (-6, 1)

B (6, 6)  →  B' (-6, 6)  

C (1, 2)  →   C' (-2, 1)

Learn more about rotation here:

https://brainly.com/question/29391174

#SPJ1

A total of 676 different three-letter initials combinations end with the letter Z using the uppercase characters in English alphabets.

We have three letters which have to be filled in.

English alphabets consist of 26 letters (A-Z). Let's suppose A1, A2 & A3 are the three initials.

For A1, we have 26 alphabets to choose from i.e. A-Z

For A2, we again have 26 alphabets to choose from i.e. A-Z

For A3, we have only one option i.e. Z

Thus, total different three-letter initials combinations for "**Z" pairings are:

26 x 26 x 1 = 676

Please note that combinations allow repetition of values. If one wants to avoid repetition, permutation needs to be calculated.

To learn more about combinations here https://brainly.com/question/11732255

#SPJ4

Answer:

(x + 3)(x + 2) = 9

x^2 + 5x + 6 = 9

x^2 + 5x = 3

Step-by-step explanation:

length * width = area

(x + 3)(x + 2) = 9

Expand

x^2 + 5x + 6 = 9

Subtract 6 from both sides

x^2 + 5x = 3

The topologies {∅, {x}, {y}, {z}, {x, y, z}} and {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}} satisfy both the Frechet and Hausdorff properties.

To find all possible topologies of the space  = {x, y, z}, we need to consider all the possible subsets of this set. Since the set has three elements, there are 2^3 = 8 possible subsets.
The possible topologies are as follows:
1. {∅, {x, y, z}}: This is the trivial topology, where the whole set and the empty set are the only open sets.
2. {∅, {x}, {y}, {z}, {x, y, z}}: This is the discrete topology, where every subset of the set is open.
3. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}}: This is the indiscrete or trivial topology, where only the whole set and the empty set are open.
4. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}}: This is a topology that is not discrete or indiscrete.

To determine which of these topologies satisfy the Frechet property and the Hausdorff property, we need to consider the limit points and the ability to separate points, respectively.
The Frechet property states that for every point x in a set A, there exists a sequence of points in A that converges to x. In other words, every point is a limit point.
The Hausdorff property states that for any two distinct points x and y in a set A, there exist disjoint open sets U and V such that x is in U and y is in V. In other words, every pair of distinct points can be separated by open sets.

Let's analyze each topology:
1. {∅, {x, y, z}}: This topology does not satisfy the Frechet or Hausdorff property because it does not have any limit points or allow for the separation of points.
2. {∅, {x}, {y}, {z}, {x, y, z}}: This topology satisfies both the Frechet and Hausdorff properties. Any point x can be approached by the sequence (x), and any two distinct points can be separated by open sets.
3. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}, {x, y, z}}: This topology does not satisfy the Frechet or Hausdorff property because it does not have any limit points or allow for the separation of points.
4. {∅, {x}, {y}, {z}, {x, y}, {y, z}, {x, z}}: This topology satisfies both the Frechet and Hausdorff properties. Any point x can be approached by the sequence (x), and any two distinct points can be separated by open sets.

Learn more about topologies

https://brainly.com/question/31913704

#SPJ11

Answer:

140

Step-by-step explanation:

20+4(s)=

20+4(30)=

20+ 120=

140

Answer:

48 + 87 + 20x - 10 = 180

125 + 20x = 180

20x = 55

x = 2.75

45 + 48 + 87 = 180

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

Given,

Total distance for the marathon = 26 miles

Distance she add each day =2

She starts with 6 miles

Then,

Equation of nth term in the arithmetic sequence

\(t_{n}=a+(n-1)d\)

Substitute the values and find the value of n

26=6+(n-1)2

26=6+2n-2

26=4+2n

2n=22

n=11

To find the total distance she run to achieve her 26 miles goal, we have to apply the sum of n terms of arithmetic sequence,

\(S=\frac{n}{2}[2a+(n-1)d]\\ S=\frac{11}{2}[2(6)+(11-1)2]\\ S=\frac{11}{2}[12+20]\\ S=\frac{11}{2}[32]\\ S=176\)

If she starts with 6 miles today and add 2 miles each day to her distance until she achieves her goal and  then she has to run 176 miles in total to achieve her 26 miles goal.

Learn more about Arithmetic sequence here

brainly.com/question/20795790

#SPJ4

Answer:

There would be 15 unsuccessful rolls

Step-by-step explanation:

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

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

The chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample.V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

To find E(Y1 + Y2), we first find the marginal distribution of Y1 and Y2 by integrating the joint density function over the other variable as follows:

f1(y1) = ∫f(y1,y2)dy2 = ∫2dy2 from 0 to 1-y1 = 2(1-y1) for 0 ≤ y1 ≤ 1

f2(y2) = ∫f(y1,y2)dy1 = ∫2dy1 from 0 to 1-y2 = 2(1-y2) for 0 ≤ y2 ≤ 1

Now we can find E(Y1 + Y2) as follows:

E(Y1 + Y2) = ∫∫(y1 + y2)f(y1,y2)dy1dy2

= ∫∫(y1 + y2)2dy1dy2 over the region 0 ≤ y1 ≤ 1-y2, 0 ≤ y2 ≤ 1

E(Y1 + Y2) = ∫0^1∫0^(1-y1) (y1 + y2)2dy2dy1

= ∫0^1[y1(y1/2 + 2/3) + 1/3]dy1

= 7/12

To find V(Y1 + Y2), we can use the fact that V(Y1 + Y2) = V(Y1) + V(Y2) + 2Cov(Y1, Y2), where Cov(Y1, Y2) is the covariance of Y1 and Y2. First, we need to find the variances of Y1 and Y2:

Var(Y1) = E(Y1^2) - [E(Y1)]^2 = ∫∫y1^22dy1dy2 - [∫∫y1f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y1) y1^22dy2dy1 - [∫0^1(2y1-2y1^2)dy1]^2

= 1/18

Var(Y2) = E(Y2^2) - [E(Y2)]^2 = ∫∫y2^22dy1dy2 - [∫∫y2f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y2) y2^22dy1dy2 - [∫0^1(2y2-2y2^2)dy2]^2

= 1/18

Now we need to find the covariance of Y1 and Y2:

Cov(Y1, Y2) = E(Y1Y2) - E(Y1)E(Y2) = ∫∫y1y2f(y1,y2)dy1dy2 - (∫∫y1f(y1,y2)dy1dy2)(∫∫y2f(y1,y2)dy1dy2)

= ∫0^1∫0^(1-y1) 2y1y2dy2dy1 - (7/12)(7/12)

= 1/144

Therefore, V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

Learn more about proportion here:

https://brainly.com/question/31548894

#SPJ11

The coordinates of the point dividing the segment in the ratio 3:1 will be ( 38 / 4, 6 / 4).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that point A is (2,0) and point B is (2,12) and the line is divided in the ratio of 3:1. the coordinate of the point will be calculated as,

Point = { ( mx₂ + nx₁ ) / ( m + n ) }, { ( my₂ + ny₁ ) / ( m + n ) }

Point = { ( 3 x 12 0 + ( 1 x 2 ) / ( 3 + 1 )], { ( 3 x 2 ) + 0 ) / ( 3 + 1) }

Point = { 38 / 4, 6 / 4 }

Hence, the coordinates of the point dividing the segment by a factor of three will be (38 / 4, 6 / 4).

To know more about coordinate geometry follow

https://brainly.com/question/29212773

#SPJ1

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

To learn more about arithmetic operations,

Visit; brainly.com/question/16679150

#SPJ4

Answer:

g=10

b=1

m=1

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

This is your posted line:

4 3/4 = 19 / 4

2 1/3 = 7/3

19/4  * 7/3  =  (19*7) /(4*3) = 133/12  = 11  1/12

BUT the question in the picture shows

2 4/7 * 2/3 =

18/7   * 2/3 =  (18*2) / ( 7*3) = 36/21 = 1  15/21   =    1 5/7

you know he made 5 deliveries for $16 each.  5*16=80.  So to find his salary you have 215-80=$135.

So he makes $135 no matter what plus $16 times the number of deliveries.

so, S=16d+135