The scale of this blueprint of an art gallery is 1 in 48 ft. find the actual lengths of the following walls.

As per the given details, the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

To rewrite the equation y+5=5(x-4) in Ax+By=C form, we need to simplify and rearrange the equation to isolate y on one side:

y + 5 = 5(x - 4)

y + 5 = 5x - 20 (Distribute 5 on the right side)

y = 5x - 20 - 5 (Subtract 5 from both sides)

y = 5x - 25

Now the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To rewrite it in Ax + By = C form, we need to rearrange the terms to get the x and y terms on the left side and a constant on the right side:

y = 5x - 25

-5x + y = -25

So the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

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Answer:

D

Step-by-step explanation:

Subtract 60 from 80 to get 20, and divide 20 by 80 to get 1/4, which can be converted to 25%.

Answer:

i think its D but im not exactly sure

Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

Answer:

t=-132

Step-by-step explanation:

multiply -12 on both sides.

-12x11=t

t=-132

Answer:

1/3

Step-by-step explanation:

Since there is 3 sections it could land anywhere

Answer:1/3

Step-by-step explanation:

Answer:

perimeter ( in cm )

= 4+13+9+5+5+5+10+3

= 54 cm

1 cm = 3 yards

54 cm = 54×3

= 162 yards

The pair of integers with the greatest sum where the sum of two consecutive integers is less than 55 is 26 and 27

The statement is given as:

the sum of two consecutive integers is less than 55.

Let the consecutive integers be x and y

Where y is greater than x

So, we have

y = x + 1

x + y < 55

Substitute y = x + 1 in the inequality x + y < 55

x + x + 1 < 55

Evaluate the sum

2x + 1 < 55

Subtract 1 from both sides

2x < 54

Divide both sides by 2

x < 27

The greatest integer less than 27 is 26.

So, we have

x = 26

Substitute x = 26 in y = x + 1

y = 26 + 1

Evaluate the sum

y = 27

So, we have

(26, 27)

Hence, the pair of integers with the greatest sum where the sum of two consecutive integers is less than 55 is 26 and 27

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Answer:

20 units

Step-by-step explanation:

If we line this up, we have A as the up-left, B as the up-right, C as the lower right, and D as the lower-left. Perimeter is 2(length+width), and the length is 8, the width is 2. 2+8=10, and 10*2= 20.

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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The measurement of angle 5 is equivalent to 76°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram.

We can write -

∠A = 76° + ∠1

∠C = 37° + ∠5

In a parallelogram, the opposite angles are equal. Therefore, we can write -

∠A = ∠C

76° + ∠1 = 37° + ∠5

37° + ∠5

∠1 = 37° (Alt. interior angles)

76° + 37° = 37° + ∠5

∠5 = 76°

Therefore, the measurement of angle 5 is equivalent to 76°.

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We will call the amount of each candy as X and Y.

Candy X sells for $1.20 per pound.

Candy Y sells for $2.00 per pound.

The total mix weights 26 pounds, so we can write:

Then, the final price of the mix will be 26 pounds * 1.65 $/pound = $42.9. This final price is equal to the sum of X by its price and Y by its price:

Now we have a system of equations with two unknowns.

We can replace X in the second equation knowing that:

With the value of Y, we can calculate X as:

Answer:

The amount of the $1.20 candy is 11.38 pounds and the amount of the $2 candy is 14.62 pounds.

The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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The total number of juice bottles is given by the equation J = 3400 bottles

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as a : b : c

Now , the ratio of mango juices to tomato juice to passion fruit be 4 : 4 : 3

The total number of mango juice = 4x

The total number of tomato juice = 4x

The total number of passion fruit juice = 3x

The total number of passion fruit juice = 1020

Substituting the values in the equation , we get

3x = 1020

Divide by 3 on both sides of the equation , we get

x = 340 bottles

Now , the total number of bottles = 4x + 3x + 3x = 10x bottles

So , substituting the value of x in the equation , we get

The total number of juice bottles = 340 ( 10 ) = 3400 bottles

Hence , the proportion is 40 : 40 : 30

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Answer:

r = \(\frac{7}{8}\)

Step-by-step explanation:

the sum to infinity of a geometric progression is

S∞ = \(\frac{a_{1} }{1-r}\) : | r | < 1

where a₁ is the first term and r the common ratio

given S∞ = 8a₁ , then

\(\frac{a_{1} }{1-r}\) = 8a₁ ( multiply both sides by 1 - r )

\(a_{1}\) = 8a₁(1 - r) ( divide both sides by 8a₁ )

\(\frac{a_{1} }{8a_{1} }\) = 1 - r

\(\frac{1}{8}\) = 1 - r ( subtract 1 from both sides )

\(\frac{1}{8}\) - 1 = - r

\(\frac{1}{8}\) - \(\frac{8}{8}\) = - r

- \(\frac{7}{8}\) = - r ( multiply both sides by - 1 ) , then

r = \(\frac{7}{8}\)

DFS can be used because the graph is directed and all of the edge weights are positive.

What is Algorithms?

An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially. All aspects of IT employ algorithms extensively.

Steps can be taken. There may be a path from v to z* but not from z* to v or different from each with different weights, so we just need to apply DFS, dijkstras twice, starting with vertex v, to find the path length until z*. Then we need to add the path weights.

The problem is clear in that we need to find path weight from v to z* and z* to v. There may be more than one path that leads from v to z*, thus we must locate them all and store some of them because each loop will require a time complexity of O(V+E).

where, in the given graph, E stands for edges and V for vertex. When a graph is complete, meaning there is a path connecting every vertex to every other vertex, we must execute this technique V times to determine the total number of paths. As a result, the time complexity is O(V(V+E)).

Then we must repeat the process from z* to v, but this time we must choose every path whose weights satisfy the specified condition. In the worst case, we must repeat this process (V-1) times, thus the time complexity will be the same as before. As a result, our time complexity will be O(V(V+E)) overall.

Since the graph is directed and every edge weight is positive, DFS may be used.

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

Step-by-step explanation:

The perimeter is given by the formula ...

  P = 2(L +W) . . . where L and W are the length of the sides of the rectangle

Filling in the given values, we have ...

  8(2x +1) = 2((3x +4) +(4x +3))

  4(2x +1) = 7x +7 . . . . . . . . . . . . divide by 2, collect terms on the right

  8x +4 = 7x +7 . . . . . . eliminate parentheses

  x = 3 . . . . . . . . . . . . . subtract 7x+4

The side lengths are ...

  (3x +4) = 3(3) +4 = 13

  (4x +3) = 4(3) +3 = 15

The lengths of the sides are 13 inches and 15 inches.

__

Check

The perimeter is 8(2(3) +1) = 56 = 2(13 +15).

The conclusion is valid in this experiment because the sample is homogenous and an experimental study was performed.

It should be noted that an experimental study is one in which there is a dependent variable and there is a dependent variable. Also a control is used to establish the validity of the results.

In this case, the dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.

The conclusion is valid in this instance because the sample is homogenous and an experimental study was performed.

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Answer:Threefourths of the fudge at the fudge shop on Monday morning contain nuts. Helena works at the fudge shop and prepares 12 3/4 pounds of fudge containing walnuts to fulfill a special order Monday afternoon. With this 29 5/8 pounds of fudge containing nuts at the fudge shop on additional amount of fudge, there are at least Monday (a) Write an inequality that represents the scenario. Begin by defining your variable (b) Solve the inequality Show your work . (C) Fudge is packaged into 1-pound boxels. What is the fewest number of boxes of fudge at the fudge shop Monday morning?​

Step-by-step explanation:

12 3/4 pounds of fudge containing walnuts to fulfill a special order Monday afternoon. With this 29 5/8

Answer:

x=0

Step-by-step explanation:

The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.

To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).

We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.

We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.

Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.

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The amount of money in account A is decreasing by 8% per year.

The account that recorded a greater percentage change in amount of money over the previous year is account B.

From the information, the amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 9,628(0.92)x

Therefore, this shows a decrease and the percentage will be:

= 1 - 0.92

= 0.08

= 8%

The account that recorded a greater percentage change will be:

Account B = (8,972 - 8,074.80) / 8,972 × 100

= 10%

Therefore, B has a higher percentage.

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Answer:

no solution

Step-by-step explanation:

2x - 2x - 24 = 0

2x - 2x = 24

0x = 24

0 = 24

Answer:

I think its -- linear postulate

Step-by-step explanation:

The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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Answer:

(-11/2; -4)

Step-by-step explanation:

The point that lies on the line is symmetry is the middle point of the segment

M(x) = (-8-3)/2 = -11/2

M(y) = -4

Answer:

(-11/2; -4)

Step-by-step explanation: The point that lies on the line is symmetry is the middle point of the segment

M(x) = (-8-3)/2 = -11/2

M(y) = -4

Answer:

  (d)  (1, 2)

Step-by-step explanation:

You want to know which of the given points satisfies the inequality.

We find it easiest to plot the given points on a graph of the solution. This shows us that (1, 2) is a solution to the inequality. (It lies in the solution area.)

__

Additional comment

Another way to choose the answer is to try each of the points in the inequality.

If you can visualize the boundary line (without plotting it) as a line with positive slope and a y-intercept of 2, you can more readily reject the first choice and accept the last choice. (0, 3) is above the y-intercept, and (1, 2) is to the right of it (in the solution space).

You may also recognize the x-intercept will be -3, so the second choice lies above the boundary line.

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer:

After applying the distributive property, Ezra's expression was 8y + 16

After he used the commutative property, his expression was 16 + 8y

Step-by-step explanation:

Distributive property rule: a(x+y) = ax + ay
   Not much to explain here

Commutative property rule: a + b = b + a   or  xy = yx
   We use addition rule in this case, simply place 16 in front of 8y

-8/8 is an integer

By mathematical definition, an integer is a whole number, whether positive or negative.

In other terms, we can say integers are numbers without fractional parts that can be negative or positive

Hence, decimals are not integers

Looking at the question, -8/8 is the same as -1

-1 is a whole number which does not have a decimal or any other frcational part

With this, we can classify -1 as an integer