4y + 14x = -10 and 5y – 7x = 12

There are infinitely many possible solutions to a continuous linear function graph or equation.

A constant rate of change here in the coordinate plane describes a straight line. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) = 3x - 2 since y can be substituted with f(x).

An unlimited number of solutions exist for a linear function. Therefore, we may replace the domain with an endless amount of values.

A table lists all of the possible solutions.

All of the solutions are represented by an equation or graph.

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A certain corner of a room is selected as the origin of a rectangular coordinate system. A fly has coordinate (1.7, 0.6). The distance of the fly from the corner of the room is 1.8 meters.

Suppose we have a point having coordinate (x,y). Then the horizontal axes, vertical axis,  and the distance from the origin form a right triangle which its base is x and y.

Hence, we can find the distance of the point (x,y) from the origin using the Pythagorean Theorem.

In this case, the origin is a certain corner of the room. The coordinate of the fly is (1.7, 0.6) meters.

Using the Pythagorean Theorem:

distance = sqrt (1.7² + 0.6²)

distance = sqrt (2.89 + 0.36)

distance = sqrt (3.25)

distance = 1.8 meters

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.

The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.

There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:

Use math to avoid constructing improbable trees

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The results of the study examining the relationship between years spent smoking and attitudes toward quitting should show a negative relationship between these variables. This means that as the number of years spent smoking increases, participants' optimism for the success of a treatment program should decrease.

In the study, participants were asked to rate their optimism for the success of a treatment program, which serves as a proxy for their attitudes toward quitting. The variable being measured is the level of optimism, which can be quantified using a numerical rating scale or likert scale. The independent variable is the number of years spent smoking, which represents the duration of smoking behavior.

To determine the relationship between these variables, researchers would likely conduct statistical analyses, such as correlation or regression analysis. These analyses would examine the association between the number of years spent smoking and participants' optimism ratings. A negative relationship would be indicated by a statistically significant negative correlation coefficient or a negative regression coefficient.

The study's results should demonstrate that as the number of years spent smoking increases, participants' optimism for the success of a treatment program decreases. This suggests that individuals who have been smoking for a longer duration may be less hopeful about quitting successfully.

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Answer:

27

Step-by-step explanation:

Answer:

ST=27   (Hope this helps)

Step-by-step explanation:

         RS+ST=100

           2x+7+x-6=100

             3x+1=100

               3x=99

                 x=33

         ST=33-6

           ST=27

This problem involves finding the probability that the actual costs for maintenance and repairs in a certain electricity company will exceed the budgeted amount of C450.

We can standardize the distribution of the weekly costs using the z-score formula given:

z = (x - μ) / σ

where x is the budgeted amount, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (450 - 400) / 20 = 2.5

Using the z-table, we can find the probability that the actual costs will exceed the budgeted amount as:

P(z > 2.5) = 1 - P(z < 2.5)

From the z-table, we find that P(z < 2.5) = 0.9938

Therefore:

P(z > 2.5) = 1 - 0.9938 = 0.0062

Hence, the probability that the actual costs for maintenance and repairs in the electricity company will exceed the budgeted amount of C450 is 0.0062 or approximately 0.62%.

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Answer:

well if you're looking for angles then

angle ADB = 30°

angle CBD = 80°

angle CDB = 120°

but they asked to classify triangle ADC ,whose measurements are 90° , 40° and 50° ...so of they're asking what type of triangle then it is a right angled triangle.

Answer:

Triangle ADC is a right triangle.

Step-by-step explanation:

Triangles Classification

An acute triangle is a triangle with three acute angles or with less than 90° each.

An obtuse triangle has one obtuse angle or more than 90°.

A right triangle has one right angle of 90°

From the figure, we can see angle D is marked as a right angle (90°), thus triangle ADC is a right triangle.

To complete the answer, triangle ADB is obtuse (has an angle of 100°), and triangle ABD is acute.

The output of the MATLAB function is value = 12; taylor_val = 12, n = 2; n is the required order.

syms x % defining independent variable x

f= (x) x*x+x; % defining input function

tol=0.1; % defining  toleration

a=2; % defining center/expansion point

b=3; % defining calculation point

n=1; % initializing the order of taylor polynomial

value=f(b); % value of original function at point b

taylor_val=inf; % initializing value of taylor polynomial function with infinity

% defining loop to reduce error below toleration point

while(abs(value-taylor_val)>tol) % defining condition to calculate error above toleration to continue looping

   Taylor = taylor(f,x,'Order',n+1,'ExpansionPoint',a); % calculating taylor polynomial of order n at expansionpoint a

   taylor_val=subs(Taylor,x,b); % calculating taylor polynomial value at point b

   n=n+1; % increasing order by 1

end

n=n-1; % reducing order by 1 to get correct order

display(value)% displaying value of original function at point b

display(taylor_val) % displaying value of taylor polynomial function at point b

display(n) % displaying required order

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The function of the water balloon is an illustration of a quadratic function.

The balloon will splat on the ground after 2.5 seconds

The function is given as:

\(h(t) = -6t^2 + 13t + 5\)

When the balloon splats on the ground, the value of h(t) is 0.

So, we have:

\(-6t^2 + 13t + 5 = 0\)

Expand the expression

\(-6t^2 + 15t- 2t + 5 = 0\)

Factorize the above expression

\(-3t(2t - 5)- 1(2t - 5 )= 0\)

Factor out 2t - 5 in the 2t - 5

\((-3t - 1)(2t - 5 )= 0\)

Split the equation into 2

\(-3t - 1 = 0\ or\ 2t - 5= 0\)

Rewrite as:

\(-3t = 1\ or\ 2t = 5\)

Solve for t

\(t = -\frac 13\ or\ t = \frac 52\)

The value of t cannot be less than 0 i.e. negative.

So, we have

\(t = \frac 52\)

Divide 5 by 2

\(t = 2.5\)

Hence, the balloon will splat on the ground after 2.5 seconds

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Step 1: Suppose, for the sake of contradiction, that there are integers A and B such that A2 = 3B2 + 2015. Let N = A2. Then, N ≡ 1 (mod 3).

Step 2: By the Legendre symbol, since (2015/5) = (5/2015) = -1 and (2015/67) = (67/2015) = -1, we know that there is no integer k such that k2 ≡ 2015 (mod 335).

Step 3: Let's consider A2 = 3B2 + 2015 (mod 335). This can be written as A2 ≡ 195 (mod 335), which can be further simplified to N ≡ 1 (mod 5) and N ≡ 3 (mod 67).

Step 4: However, since (2015/5) = -1, it follows that N ≡ 4 (mod 5) is a contradiction.

Therefore, there are no integers A, B such that A2 = 3B2 + 2015.

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Answer:

-1.5

Step-by-step explanation:

The common difference of the given arithmetic sequence is -1.5.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The common difference is calculated by subtracting the next term from the previous term.

Common diference = 5 - 6.5

Common difference = -1.5

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A basis for the orthogonal complement w⊥ of w = span{v1, v2} is {(-4, -5, 2, -1), (-5, -4, 1, 2)}. The dimension of w⊥ is 2.

To find a basis for the orthogonal complement w⊥ of w = span{v1, v2}, where v1 = (-1, 2, 3, 0) and v2 = (2, 0, -1, 1), we can use the Gram-Schmidt process. This process allows us to find an orthogonal basis for a subspace.

Step 1: Set the first vector u1 = v1 = (-1, 2, 3, 0).

Step 2: Subtract the projection of v2 onto u1 from v2 to obtain a new vector u2 orthogonal to u1. The projection of v2 onto u1 is given by proj(u1, v2) = (v2⋅u1) / (u1⋅u1) * u1, where ⋅ denotes the dot product. In this case, proj(u1, v2) = ((2⋅(-1) + 0⋅2 + (-1)⋅3 + 1⋅0) / ((-1)⋅(-1) + 2⋅2 + 3⋅3 + 0⋅0)) * (-1, 2, 3, 0) = (-4/14) * (-1, 2, 3, 0) = (2/7, -4/7, -6/7, 0). Therefore, u2 = v2 - proj(u1, v2) = (2, 0, -1, 1) - (2/7, -4/7, -6/7, 0) = (12/7, 4/7, 1/7, 1).

Step 3: Normalize u1 and u2 to obtain the orthonormal basis for w⊥. The normalized vectors are (-4/7, -5/7, 2/7, -1/7) and (-5/7, -4/7, 1/7, 2/7), which form a basis for w⊥.

Therefore, a basis for the orthogonal complement w⊥ of w = span{v1, v2} is {(-4/7, -5/7, 2/7, -1/7), (-5/7, -4/7, 1/7, 2/7)}. The dimension of w⊥ is 2, as it has two linearly independent vectors in its basis.

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Answer:

212

Step-by-step explanation:

85 here is 100%

And 900 is also 100%

That's for the different comparisons. So now, what we do is, we should divide 85 by 900, and then, whatever is our answer, multiply that by 20.

That is surely going to equal how many students are going to say that Math is Awesome for 900 student survey.

Step 1

85/900=10.5882352941

Let's round that to make it

10.5

Step 2

10.5x20=210

That means, if we go exactly, like multiplying all of those numbers, then our answer should be 212 or 200.

Just to be sure that our answer is correct, we will do it with 10.58 now.

Step 3

10.58x20=211.6

So now it looks like it's most probably going to be 212

But still, let's do 10.588 now.

Step 4

10.588x20=211.76

Okay, let's do it again, with 10.5882

Step 5

10.5882x20=211.764

Okay, so I just multiplied the whole number this time, and I still got a decimal, so that means that your answer is 212 basically.

Answer: a

Step-by-step explanation:a

A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities.

What are inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

A system of equations has one solution for each variable, whereas a system of inequalities has a range of possible values for each variable.

Set up the equations as follows:

ax + by = c

dx +ey = f

Let the inequitable system exist:

ax + by <c

dx +ey > f

The same technique, such as graphing, substitution, and elimination, can be used to solve both systems.

But there's a difference because:

A system of equations can only have one solution for each variable, whereas a system of inequalities can have any number of solutions for each variable.

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Answer:

First you would make 62% into \(\frac{62}{100}\)

\(7893+82-\)\(\frac{62}{100}\)

Than you would do 7893+82 which is 7975

\(7975-\frac{62}{100}\)

You would than simplify \(\frac{62}{100}\) which is \(\frac{31}{50}\)

\(7975- \frac{31}{50}\)

Therefore your answer will be \(\frac{398719}{50}\) or in decimal form it will be \(7974.38\)

Hope that helps :>

Answer:

42 plants

might be easier to find how many plants are planted in 1 hour then multiply that by 6. In this case, 7 plants will be planted within an hour. So, multiply 7 x 6 to get 42.

Answer:

42.50

Step-by-step explanation:

bill + tip = total bill

The tip is based on the bill

tip = bill * 20%

tip = bill * .20

Replace in the original equation

bill + .20 bill = total bill

Combine like terms

1.20 bill = total bill

The total bill was 51 dollars

1.20 bill = 51

Divide each side by 1.20

1.20 bill / 1.2 = 51/ 1.2

bill =42.50

Answer:

$42.50

Step-by-step explanation:

If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:

0.2x+x=51

1.2x=51

x=42.5

Therefore, the bill (w/o tip) was $42.50

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Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.

To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.

1. We must calculate how much you would earn with option A in a week.

$28 * 40 = $1,120

2. We must make a rule of three to find a value of which 4% is equal to 1,120

Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.

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Answer:

See below.

Step-by-step explanation:

A. <2 is congruent to <3

B. <3 is congruent to <7

There are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

To find out how many of the desserts with yogurt also include fruit, we need to use the concept of intersection in set theory. We can create two sets: one for desserts with yogurt and another for desserts with fruit.

The set of desserts with yogurt has 8 elements, and the set of desserts with fruit has 7 elements. We can represent these sets as follows:

Y = {yogurt desserts} = {1, 2, 3, 4, 5, 6, 7, 8}
F = {fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

Now we need to find the intersection of these sets, i.e., the desserts that have both yogurt and fruit. To do this, we can count the number of elements in the set Y ∩ F:

Y ∩ F = {yogurt and fruit desserts} = {1, 2, 3, 4, 5, 6, 7}

So there are 7 desserts that have both yogurt and fruit. Therefore, the answer to your question is 7.

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Answer:

A=7

B=10

C=2

D=2

Surface area= 208

Pretty sure this is correct.

Answer: The ASAP Math program provides an opportunity for additional small group instruction for students who find the math program challenging. Students in grades 1 to 4 will come to the ASAP room two to three times a week during the math block.

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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a. Calculation errors resolved through double-checking and verification process.

b. Different-sized eigenspaces due to repeated eigenvalues or computational errors.

a. The discrepancy in eigenvectors between you and your classmate could be attributed to calculation errors or misinterpretation of the problem.

Mistakes in performing matrix operations or solving characteristic equations can lead to different results.

However, when both of you obtain the same solution upon reevaluation, it suggests that the initial differences were due to errors rather than fundamental disagreements.

To resolve the discrepancy, you can suggest comparing the steps of the calculations with each other, checking for mistakes, and verifying the correctness of the eigenvector solutions obtained.

b. If your classmate computed a different-sized eigenspace for matrix M compared to your calculation, it could be due to a few factors.

One possibility is that the matrix M has repeated eigenvalues, leading to a larger eigenspace with multiple linearly independent eigenvectors. Another reason could be computational errors made during the process of finding eigenvectors.

It is important to note that eigenvectors are only determined up to scalar multiples, so the specific scaling of eigenvectors might differ.

Additionally, if your classmate used a different method or approach to compute eigenvectors, it can also result in differences in the size or composition of the eigenspace.

To understand the discrepancy, it would be helpful to compare the methodologies and calculations used by your classmate and review any errors or alternative techniques employed.

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Answer:

D) |−8,000 − (−50)|

Step-by-step explanation:

When we are dealing with questions involving above or below sea level,

The formula for the Absolute value expression representing the distance = | Height above sea level -(Distance below sea level|

Height of Cameron above sea level = 8000ft = -8000

Distance of the whale below sea level = 50ft = -50

Hence, we have:

|−8,000 − (−50)|.

Option D is the correct option

Solution is y = e^v, where v satisfies the linear equation v' + P(x) = Q(x)v(x).

To show that the substitution v = In y transforms the differential equation y' + P(x)y = Q(x)(ylny) into the linear equation v' + P(x) = Q(x)v(x), we need to substitute y = e^v into the original equation:
y' + P(x)y = Q(x)(ylny)
e^v dv/dx + P(x) e^v = Q(x) e^v
Now divide both sides by e^v:
dv/dx + P(x) = Q(x) v
This is the linear equation v' + P(x) = Q(x)v(x) that we were asked to show.
To solve the equation xy' – 4x²y + 2y In y = 0, we can use the substitution v = In y. Taking the derivative of v with respect to x, we get:
dv/dx = 1/y dy/dx
Substituting this and y = e^v into the equation, we get:
x(1/y dy/dx) e^v - 4x² e^v + 2e^v v = 0
Dividing both sides by e^v yields:
x(1/y dy/dx) - 4x² + 2v = 0
Now substitute v = In y back into the equation to get:
x(1/y dy/dx) - 4x² + 2In y = 0
Multiplying both sides by y and rearranging, we get:
xy' - 4x²y + 2y In y = 0
which is the original equation we started with.

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here, it's not clear , but visible