Solve
- 5 3/4 - 3 1/2 = ???

The correct term to complete the sentence is "vertical asymptote."

In a rational function, the denominator represents the values of x for which the function is undefined or has vertical asymptotes. If a is a zero of the polynomial denominator, it means that the denominator equals zero when x equals a. As a result, the rational function has a vertical asymptote at x=a. In a rational function, the denominator plays a crucial role in determining the behavior of the function. If a is a zero of the polynomial denominator, it implies that the denominator equals zero when x equals a. This creates a vertical asymptote for the rational function. A vertical asymptote is a vertical line that the graph of the function approaches but does not cross. It represents the values of x for which the function is undefined or has a vertical discontinuity. When the denominator equals zero, it means that the function is not defined at that specific value of x. Hence, the rational function has a vertical asymptote at x=a.

In summary, if a is a zero of the polynomial denominator of a rational function, the function has a vertical asymptote at x=a. This indicates that the graph of the function approaches the vertical line x=a but does not cross it.

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2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

\((Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}\)

                        \((2.5)^{2}+(6)^{2}=(6.5)^{2}\)

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Rotating an image 90 degrees counterclockwise means turning the image so that it appears to be facing to the left. This can be done using various software programs, including image editors like Adobe Photoshop or online tools like PicMonkey.

In Adobe Photoshop, you can rotate an image 90 degrees counterclockwise by selecting the "Transform" option from the "Edit" menu. This will bring up a bounding box around the image, and you can then use the "Rotate" tool to turn the image counterclockwise.

If you are using an online tool, the process is similar. Simply upload the image you want to rotate, select the "Rotate" tool, and then choose the "90 degrees counterclockwise" option.

In conclusion, rotating an image 90 degrees counterclockwise is a straightforward process that can be done using various software programs and online tools. Whether you are editing photos for personal use or for a school project, understanding image manipulation is an important skill to have.

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the indefinite integral is: ∫(tan(x/14))^5 dx = (7/3) * (tan(x/14))^6 + C.

To find the indefinite integral of ∫ (tan(x/14))^5 dx, we can use the substitution method. Let u = x/14, then du/dx = 1/14 and dx = 14du. Substituting u and dx in the integral, we get:

∫ (tan(x/14))^5 dx = ∫ (tan(u))^5 (14 du)

Using the power rule of integration, we can simplify this expression as:

= (1/6) tan^6(u) + C

where C is the constant of integration. Substituting back u = x/14 and simplifying, we get:

∫ (tan(x/14))^5 dx = (1/6) tan^6(x/14) + C

Don't forget to use absolute values when appropriate, especially when dealing with trigonometric functions.
To find the indefinite integral of the given function, ∫(tan(x/14))^5 dx, we will perform a substitution. Let's set:

u = x/14, so du/dx = 1/14.

Now we can rewrite the integral in terms of u:

∫(tan(u))^5 * (14 du) = 14∫(tan(u))^5 du.

Next, we use integration by parts:

Let v = tan(u), so dv = (sec(u))^2 du.
Let w' = (tan(u))^4, so dw = 4(tan(u))^3(sec(u))^2 du.

Now, we can rewrite the integral as:

14∫v^5 dv = 14 * (1/6 * v^6 + C) = (7/3) * (tan(u))^6 + C.

Finally, we substitute x/14 back for u:

(7/3) * (tan(x/14))^6 + C.

So, the indefinite integral is:

∫(tan(x/14))^5 dx = (7/3) * (tan(x/14))^6 + C.

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Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= 4,000 + 10,000= $14,000

Unitary variable cost= $5.5

Selling price= $7.2

To calculate the number of units to be sold to break-even, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 14,000 / (7.2 - 5.5)

Break-even point in units= 8,235 units

In dollars:

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 14,000 / (1.7/7.2)

Break-even point (dollars)= $59,294

Now, imagine the company requires a profit of $50,000:

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units= 64,000/1.7

Break-even point in units= 37,647 units

Break-even point (dollars)= (fixed costs + desired profit) / contribution margin ratio

Break-even point (dollars)= 64,000 / (1.7/7.2)

Break-even point (dollars)= $271,059

By applying dilatation and congruency theorem, it can be concluded that the distance between points R and R' is 3 units (option A).

Dilation is a transformation of a geometric shape, either becoming larger or smaller, without changing the original shape using a certain scale factor.

Two shapes are said to be congruent if a pair of corresponding sides have the same ratio and the corresponding angles have the same measure.

From the problem we obtained the following information:

QR is dilated to create Q'R' ⇒ QR // Q'R'

The dilatation factor is 1.5 ⇒ Q'R'/QR = 1.5

Now we look at the ΔTRQ and ΔTR'Q':

QR // Q'R'

∠TRQ = ∠TR'Q'

So ΔTRQ is congruent to ΔTR'Q' and TR'/TR = Q'R'/QR

Now we can calculate y using this equation:

   TR'/TR = Q'R'/QR

(6 + y) / 6 = 1.5

      6 + y = 9

            y = 3

Thus, the distance between points R and R' is 3 units.

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We have shown that P(N < aJ) ≤ 1 - J for nonnegative values aj.N is a nonnegative integer-valued random variable

To prove the given inequality, let's start by defining the indicator random variable Ij, which takes the value 1 if aj ≤ N and 0 otherwise.

We have:

Ij = {1 if aj ≤ N; 0 if aj > N}

Now, we can express the expectation E(Ij) in terms of the probabilities P(aj ≤ N):

E(Ij) = 1 * P(aj ≤ N) + 0 * P(aj > N)

= P(aj ≤ N)

Since N is a nonnegative integer-valued random variable, its probability distribution can be written as:

P(N = n) = P(N ≤ n) - P(N ≤ n-1)

Using this notation, we can rewrite the expectation E(Ij) as:

E(Ij) = P(aj ≤ N) = P(N ≥ aj) = 1 - P(N < aj)

Now, let's consider the sum of the expectations over all values of j:

∑ E(Ij) = ∑ (1 - P(N < aj))

Expanding the sum, we have:

∑ E(Ij) = ∑ 1 - ∑ P(N < aj)

Since ∑ 1 = J (the total number of values of j) and ∑ P(N < aj) = P(N < aJ), we can write:

∑ E(Ij) = J - P(N < aJ)

Now, let's look at the expectation E(∑ Ij):

E(∑ Ij) = E(I1 + I2 + ... + IJ)

By linearity of expectation, we have:

E(∑ Ij) = E(I1) + E(I2) + ... + E(IJ)

Since the indicator random variables Ij are identically distributed, their expectations are equal, and we can write:

E(∑ Ij) = J * E(I1)

From the earlier derivation, we know that E(Ij) = P(aj ≤ N). Therefore:

E(∑ Ij) = J * P(a1 ≤ N) = J * P(N ≥ a1) = J * (1 - P(N < a1))

Combining the expressions for E(∑ Ij) and ∑ E(Ij), we have:

J - P(N < aJ) = J * (1 - P(N < a1))

Rearranging the terms, we get:

P(N < aJ) = 1 - J * (1 - P(N < a1))

Since 1 - P(N < a1) ≤ 1, we can conclude that:

P(N < aJ) ≤ 1 - J

Therefore, we have shown that P(N < aJ) ≤ 1 - J for nonnegative values aj.

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Answer:

they are equal and act in opposite directions

Step-by-step explanation:

if it wants to reduce the dollars flowing out of the country, the United States can limit the number of Japanese cars being imported by imposing an Import Quota.

Import Quota:

An import quota is a type of trade restriction that places a physical limit on the amount of goods that can be imported into a country during a specific period of time. Like other trade restrictions, quotas are generally used to the benefit of commodity producers in a given economy (protectionism). The essence of import quotas is to limit the amount of foreign goods that can be brought into a country. Quotas work by allowing only those authorized through a license or government contract to bring in the amount specified in the contract. When the quantity specified in the quota is reached, no more goods can be imported during this period.

There are also quota insurance programs where liability and premiums are distributed proportionately among insurers. For example, three companies have a $1,000,000 fire insurance policy per quota, Company A receives 50% ($500,000), Company B receives 30% ($300,000), and Company C receives 20% ($200,000). If the annual bonus is $5,000, Company A will receive $2,500, Company B will receive $1,500 and Company C will receive $1,000. Company A pays 50%, company B 30% and company C 20% for each claim.

Complete Question:

To reduce dollars flowing out of the country, the United States can take measures to limit the number of foreign cars imported from Japan by imposing a(n).

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The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.

Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0

Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x

Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).

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Answer:

Since Paula has her own business of making cakes for special occasions, and the total price (P) of one of Paula's cakes is represented by the equation P = 0.75S +10, where S is the number of people the cake serves, for determine what does the 0.75 represent in this situation and what does the 10 represent in this equation, the following mathematical reasoning must be carried out:

P is the price of the cake

S is the number of servings

Therefore, 0.75 is the value of each serving, which can be variable (the number of servings can vary)

In turn, 10 is the fixed cost of each cake.

Answer:

Yes

Step-by-step explanation:

1. A graph of two similar, but not equal, right triangles using segments of line AB as the hypotenuse of each triangle is shown below.

2. The three pair of corresponding angles and sets of proportionate sides include:

ΔACE ≅ ΔBDF, ΔAEC ≅ ΔBFD, and ΔCAE ≅ ΔDBF.

AC = BD, EC = FD, and AE = BF

3. Yes, the slope of line is the same between any two points on the line.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Part 1.

In this exercise, we would use an online graphing tool to create two similar, but not equal, right triangles by using line segments AB as the hypotenuse of each triangle.

Part 2.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent (similar) triangles and sets of proportionate sides:

Part 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using this formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope AC = (0 + 1)/(-3 + 5)

Slope AC = 1/2.

Slope BD = (3.5 - 2)/(4 - 1)

Slope BD = 1/2.

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The eigenspace corresponding to the eigenvalue λ = -2 is { = [ (1/3)₃ ; (1/3)₃ ; ₃ ] | ₃ ∈ ℝ }. Therefore, a basis for the eigenspace is the vector [ (1/3) ; (1/3) ; 1 ].

The eigenspace corresponding to the eigenvalue λ = -2 for matrix A = [ 1 0 -1 ; 1 -3 0 ; 4 -13 1 ] can be found by solving the equation (A - λI) = , where I is the identity matrix and is a vector.

To find the eigenspace, we subtract λ = -2 from the diagonal elements of A and set up the equation:

[ 1-(-2) 0 -1 ; 1 -3-(-2) 0 ; 4 -13 1-(-2) ] = .

This simplifies to:

[ 3 0 -1 ; 1 -1 0 ; 4 -13 3 ] = .

To find the basis for the eigenspace, we perform row reduction on the augmented matrix [ 3 0 -1 ; 1 -1 0 ; 4 -13 3 | ]:

[ 1 0 -1/3 ; 0 1 -1/3 ; 0 0 0 ].

The system of equations is given by:

₁ - (1/3)₃ = 0,

₂ - (1/3)₃ = 0,

₃ is a free variable.

Simplifying, we have:

₁ = (1/3)₃,

₂ = (1/3)₃,

₃ is a free variable.

Thus, the eigenspace corresponding to the eigenvalue λ = -2 is given by:

{ = [ (1/3)₃ ; (1/3)₃ ; ₃ ] | ₃ ∈ ℝ }.

Therefore, a basis for the eigenspace is the vector [ (1/3) ; (1/3) ; 1 ].

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From the truth table, we can see that p->q and ¬p∨q have the same truth values for all possible combinations of truth values for p and q. Therefore, we can conclude that p->q is logically equivalent to ¬p∨q. In summary, we can see that p->q is logically equivalent to both !q->!p and ¬p∨q.

To prove the logical equivalence of the given statements, we can show that they have the same truth values in all possible cases. We'll use a truth table to demonstrate this.

p | q | p->q | !q | !p | !q->!p | p->q = !q->!p

-------------------------------------------------

T | T |   T  |  F |  F |    T   |      T

T | F |   F  |  T |  F |    F   |      F

F | T |   T  |  F |  T |    T   |      T

F | F |   T  |  T |  T |    T   |      T

From the truth table, we can see that for all possible combinations of truth values for p and q, the statements p->q and !q->!p have the same truth values. Therefore, we can conclude that p->q is logically equivalent to !q->!p.

Now let's consider the second statement, p->q. We can rewrite it as ¬p∨q using the logical equivalence of implication.

The truth table for p->q and ¬p∨q is as follows:

p | q | p->q | ¬p | ¬p∨q

-----------------------------

T | T |   T  |  F |   T

T | F |   F  |  F |   F

F | T |   T  |  T |   T

F | F |   T  |  T |   T

From the truth table, we can see that p->q and ¬p∨q have the same truth values for all possible combinations of truth values for p and q. Therefore, we can conclude that p->q is logically equivalent to ¬p∨q.

In summary, we have shown that p->q is logically equivalent to both !q->!p and ¬p∨q.

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Answer:

8.75

Step-by-step explanation:

\(\frac{3}{4} +\sqrt{64} \\\\\frac{3}{4} +8\\\\\frac{3+32}{4} \\\\\\\\\frac{35}{4}\) 35/4 simply(8\(\frac{3}{4}\)) then turn into a decimal which would be 8.75

Since A1, A2, ..., Am are mutually exclusive and exhaustive, answers to both parts of the question is;

a) We can use the same argument to show that P(A2) = P(A3) = ... = P(Am) = 1/m.
b) We have proved that if A = A1 ∪ A2 ∪ ... ∪ Ah and (a) holds, then P(A) = h/m.

(a) Since A1, A2, ..., Am are mutually exclusive and exhaustive, we have:

P(S) = P(A1) + P(A2) + ... + P(Am)

Since P(A1) = P(A2) = ... = P(Am), we can rewrite the above equation as:

P(S) = m * P(A1)

Since S is the sample space and its probability is 1, we have:

P(S) = 1

Therefore, we can solve for P(A1) as:

P(A1) = 1/m

Similarly, we can use the same argument to show that P(A2) = P(A3) = ... = P(Am) = 1/m.

(b) Since A1, A2, ..., Am are mutually exclusive and exhaustive, we have:

P(S) = P(A1) + P(A2) + ... + P(Am)

Using (a), we know that P(Ai) = 1/m for i = 1, 2, ..., m. Therefore, we can rewrite the above equation as:

1 = m * (1/m) + P(Ah+1) + ... + P(Am)

Simplifying this equation, we get:

P(Ah+1) + ... + P(Am) = (m - h) * (1/m)

Since A = A1 ∪ A2 ∪ ... ∪ Ah, we can write:

P(A) = P(A1) + P(A2) + ... + P(Ah) = h * (1/m)

Therefore, we have proved that if A = A1 ∪ A2 ∪ ... ∪ Ah and (a) holds, then P(A) = h/m.

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The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

270

Step-by-step explanation:

assuming that Britt earned the same amount since they didn't give enough information you can just multiply 45x6 and that gets you 270

Answer:

Step-by-step explanation:

a rectangular tree lot must have a perimeter of 100 yards and an area of at least 500 square yards. Describe the possible lengths of the tree lot

Answer:

Lol. I like life how it is right now though

Answer:

Lol I get what your saying, but I kinda like having the right to my own body and stuff.

Step-by-step explanation:

3Answer:

7%, 1/12, 0.1, 2/9, 0.26, 1/3

Step-by-step explanation:

To solve this question, the first step is converting all numbers into decimals.

7% = 0.07

1/3 = 0.33

0.1

0.26

1/12 = 0.083

2/9 = 0.2222

Now we can sort them, from least to greatest, leaving us with:

7%, 1/12, 0.1, 2/9, 0.26, 1/3

Converting fractions to decimals

1/3

1/3 is one divided by three

1/12

This is one divided by 12.

Answer:

x > 1

Step-by-step explanation:

15 - 1 = 14

The inequality is 15 - 1 < 14, but this is incorrect. 14 can not be less than 14. In order for the left side to be less than 14, the x value (currently representing 1) should be larger than what it currently is to make the statement true.

Therefore, x>1

Answer:

The composition is undefined.

Step-by-step explanation:

The output of f of 2 is -5 because -5 is not listed as the input in g of x the function is undefined.

A solution of \(y" + 2y' + 2y = 3f1(t) + f2(t)\) using the superposition principle is given by: \(y = ((3-f2(t))/8) y1 + ((1+3f1(t))/8) y2\)

It be found by taking a linear combination of the two given solutions y1 and y2. Let c1 and c2 be constants, then the solution y can be expressed as y = c1y1 + c2y2.  To find c1 and c2, we differentiate y twice and substitute it into the given differential equation:

\(y' = c1(2cos(3t) - 6tsin(3t)) + c2(-6e^-{t sin(6t)} - e^{-t cos(6t)})\)

\(y" = c1(-18sin(3t) - 36tcos(3t)) + c2(-36e^{-t sin(6t)} + 12e^{-t cos(6t)})\)

Substituting these expressions for y and its derivatives into the differential equation and simplifying, we get: \((3c1 + c2) f1(t) + (c1 + 3c2) f2(t) = 0\)

Since this must hold for all t, we can equate the coefficients of f1(t) and f2(t) to zero to get the system of equations: \(3c1 + c2 = 3, c1 + 3c2 = 1\)

Solving for c1 and c2, we get \(c1 = (3-f2(t))/8\) and \(c2 = (1+3f1(t))/8.\)

Note that this solution is valid only if f1(t) and f2(t) are continuous and differentiable.

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Four special two digit numbers exist: 1, 2, 145, and 40585.

A special two-digit number is one in which the original two-digit number is equal to the sum of the number's digits plus the product of its digits. Take the number's initial and last digits out, then add and multiply each digit independently. After that, multiply the two-digit number by the sum and product of its digits and then compare the result to the original value. If they match, it qualifies as a special two-digit number; otherwise, it does not.

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the quotient of 5 and y:   5÷y

added to 3:   3 + 5÷y

is at least (AKA is greater than or equal to) 5:  3 + 5÷y  ≥ 5

Answer:   3 + 5÷y ≥ 5

The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let the number of days = x, and the water level = y.

Given that,

Water level of river = 34 ft (initial value/y-intercept)

Rate of change = -0.5 ft per day (slope)

The equation of the line is given as:

y = mx + c

where, m is the slope

c is the y-intercept.

Substituting the values we have:

y = (-0.5)x + 34

The number of days in which the water level will reduce to 26 ft is:

26 = (-0.5)x + 34

26 - 34 = -0.5x

x = 16 days.

Hence, it will take 16 days for the water level to be 26 feet.

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