If SLED ~ PARK which of the following statements are correct?

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Therefore, additivity and homogeneity of T are satisfied, T is linear.

T must be linear for both b and c to be true. T is linear, hence additivity is true for every p, q, and P. (R). In order to make our computations as straightforward as feasible, it would be a good idea for us to use straightforward polynomials in P(R). p, q ∈ P(R), where p(x) = \(\frac{\pi }{2}\) and q(x) =  \(\frac{\pi }{2}\) for all x ∈ R and so we have

T(p + q) =(3(p + q)(4) +5(p + q)'(6)+b(p + q)(1)(p + q)(2) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p + q)(x) d(x) +               c sin((p + q)(0))

           = (3(p(4)+q(4)) + 5(p'(6)+q'(6))+b(p(1)+q(1))(p(2)+q(2)) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p(x)+q(x))d(x)+ c sin(p(0)+q(0)))

           = (3(\(\frac{\pi }{2}\) +\(\frac{\pi }{2}\))+5(0+0)+b(\(\frac{\pi }{2}\)+\(\frac{\pi }{2}\))(\(\frac{\pi }{2}\)+\(\frac{\pi }{2}\)),  \(\int\limits^2_ {-1} \,\) \(x^{3}\)(\(\frac{\pi }{2}\)+\(\frac{\pi }{2}\))d(x)+c sin(\(\frac{\pi }{2}\)+\(\frac{\pi }{2}\)))

           = (3(\(\pi\))+b\(\pi ^{2}\),\(\frac{15\pi }{4}\))

and

Tp + Tq = (3p(4) +5(p)'(6)+bp(1)(p)(2) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p)(x) d(x) + c sin((p)(0)) +(3(q)(4) +5(q)'(6)+b(q)(1)(q)(2) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(q)(x) d(x) +c sin(q(0)))

           = (3(\(\frac{\pi }{2}\))+5(0)+b(\(\frac{\pi }{2}\))(\(\frac{\pi }{2}\)),  \(\int\limits^2_ {-1} \,\) \(x^{3}\)(\(\frac{\pi }{2}\))d(x)+c sin(\(\frac{\pi }{2}\))) +  (3(\(\frac{\pi }{2}\))+5(0)+b(\(\frac{\pi }{2}\))(\(\frac{\pi }{2}\)),  \(\int\limits^2_ {-1} \,\) \(x^{3}\)(\(\frac{\pi }{2}\))d(x)+c sin(\(\frac{\pi }{2}\)))

           =(3(\(\frac{\pi }{2}\))+\(\frac{\pi b}{4}\),\(\frac{\pi }{2}\)  \(\int\limits^2_ {-1} \,\) \(x^{3}\)d(x) + c) +(3(\(\frac{\pi }{2}\))+\(\frac{\pi b}{4}\),\(\frac{\pi }{2}\)  \(\int\limits^2_ {-1} \,\) \(x^{3}\)d(x) + c)

           =(3\(\pi\)+ \(\frac{\pi b}{2}\),\(\frac{15\pi }{4}\)+2c)

Since T is linear, additivity of T holds and implies that we have

              (3(\(\pi\))+b\(\pi ^{2}\),\(\frac{15\pi }{4}\)) = T(p+q)

                                     =Tp+Tq

                                     =(3\(\pi\)+ \(\frac{\pi b}{2}\),\(\frac{15\pi }{4}\)+2c)

from which we can equate the coordinates to obtain the equations 3π + πb/2= 3π +πb/2 and 15π/4 =15π/4+2c, which imply b = 0 and c = 0, respectively.

Backward direction: If b = 0 and c = 0, then T is linear. Suppose b = 0 and c = 0. Then the map T : R ^3 → R^2 becomes

Tp = (3p(4) +5(p)'(6) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p)(x) d(x) )

we need to prove that T is linear

• Additivity: For all p, q ∈ P(R), we have

 T(p+q) = (3(p + q)(4) +5(p + q)'(6) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p + q)(x) d(x))

             =(3(p(4)+q(4)) + 5(p'(6)+q'(6)) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p(x)+q(x))d(x))

             =  (3p(4) +5(p)'(6)+3q(4)+5q'(6) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p)(x) d(x) + \(\int\limits^2_ {-1} \,\) \(x^{3}\)q(x) d(x))

              = (3p(4) +5(p)'(6) , \(\int\limits^2_ {-1} \,\) \(x^{3}\)(p)(x) d(x)) +(3(q)(4) +5(q)'(6), \(\int\limits^2_ {-1} \,\) \(x^{3}\)(q)(x) d(x))

             =Tp+Tq

• Homogeneity: For all λ ∈ F and for all (x, y, z) ∈ R^3, we have

                 T(λp) = (3(λp)(4) + 5(λp)'(6), \(\int\limits^2_ {-1} \,\) \(x^{3}\)(λp)(x) d(x))

                           =(3λp(4) + 5λp'(6), \(\int\limits^2_ {-1} \,\) \(x^{3}\)λ(p)(x) d(x))

                          =(λ(3p(4) + 5p'(6)),λ \(\int\limits^2_ {-1} \,\) \(x^{3}\)p)(x) d(x))

                          =λ(3p(4) + 5p'(6), \(\int\limits^2_ {-1} \,\) \(x^{3}\)p)(x) d(x))

                         =λTp

 Therefore, additivity and homogeneity of T are satisfied, T is linear.

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Answer:

C

Step-by-step explanation:

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

Answer:

Step-by-step explanation:

14 mins

this is because if we divide 2 but 1/2 you would get 4

since she can run 1/2 a mile in 3 1/2 mins

we should multiply the 3 1/2 buy 4

this would lead to the answer 14

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

A. x=8 B. x=25

Step-by-step explanation:

for a.

70/50=1.4

60*1.4=11x-4

84=11x-4

88=11x

x=8

for b.

72/27=2/3

64/(2/3)=-4+4x

96=-4+4x

100=4x

x=25

Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

q = 4

Step-by-step explanation:

4q + 4 = 20

or, 4q = 20 - 4

or, q = 16/4

or, q = 4

The shape of the population sample means is large, the mean and standard deviation is 6 and 0.2155, the probability of sample mean is 0.37172 and it is conclude that mean is less than 6.

Given that sample of 107 waiting times provides evidence to support the claim that µ is less than 6 and for the waiting times mean is \(\bar{x}\)=5.27 and standard deviation is 2.23.

(a) It is observed that the sample size n=107, population mean μ=6, sample mean \(\bar{x}\)=5.27, and population standard deviation σ=2.23.

The Central Limit Theorem (CLT) states that for a large number of samples, the sample mean tends to approximate the standard value. Using this, it can be asserted that the sample mean follows an approximate normal distribution with μ and variance σ²/n. So, this data will follows a normal distribution because it is very large.

(b) The given mean of all samples is μ=6.

The standard error (SE) is same as the standard deviation of the sample mean. SE is computed as shown below:

SE=√(σ²/n)

SE=σ/√n

SE=2.23/√107

SE=0.2155

In notations,

\(\bar{x}\sim N(\mu=6,SE=0.2155)\)

(c) For a single mean (n=1), the z-score is given as follows:

\(\begin{aligned}z&=\frac{\bar{x}-\mu}{\sigma}\sim N(0,1)\\ &=\frac{\bar{x}-6}{2.23}\end{aligned}\)

Then, the probability less than or equal to 5.27 is computed as given below:

\(\begin{aligned}P(\bar{x}\leq 5.27)&=P\left(\frac{\bar{x}-6}{2.23}\leq \frac{5.27-6}{2.23}\right)\\ &=P(z\leq -0.3273)\\ &=P(z > 0.3273)\\ &=1-P(z \leq 0.3273)\end{aligned}\)

Using the normal table, it is found out that  P(z≤0.3273)=0.6282

\(\begin{aligned}P(\bar{x}\leq 5.27)&=1-0.62828\\&=0.37172\end\)

d. If the population mean =6 and sample mean is 5.27 then there is 3.71% that sample mean is less than 5.27 hence we conclude that means is less than 6.

Hence, when  the mean of the sample of 107 waiting times is = 5.27 and assume that σ, the standard deviation is known to be 2.23. the shape of the population sample means is large, the mean and standard deviation is 6 and 0.2155, the probability of sample mean is 0.37172 and it is conclude that mean is less than 6.

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Answer:

x = - 13/29 OR x = - -0.44827586

Step-by-step explanation:

We use PEMDAS to evaluate the equation.

P stands for parenthesis. In this case we distribute the 8 to the equation in parenthesis.

8(-8x - 6)

-64x - 48 = -6x - 22 we will move the terms to their proportional sides

-64x + 6x = 22 + 48 (remember we do the opposite equation to move to the other side of the equals to sign)

-58x = 70 we divide both sides by -58 to isolate x

x = - 13/29 OR x = - -0.44827586

Answer: I got 3.18 repeating

Step-by-step explanation:

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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The total principal and interest payment that Nelson will have to pay after 2 months is $4665.50.

To calculate the total principal and interest payment, we need to determine the interest amount and add it to the principal.

First, let's find the interest amount:

Interest = Principal x Interest Rate x Time

Given:

Principal = $4650

Interest Rate = 2% per year

Time = 2 months

Since the interest rate is given on an annual basis, we need to convert the time from months to years. There are 12 months in a year, so 2 months is equivalent to 2/12 = 1/6 years.

Interest = $4650 x 0.02 x (1/6) = $15.50

Now, we can calculate the total principal and interest payment:

Total Payment = Principal + Interest

Total Payment = $4650 + $15.50 = $4665.50

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Answer:

C. 1324.7 cm³

Step-by-step explanation:

Volume of cylinder = πr²h

π = 3.14

radius (r) = ½ of 15 = 7.5 cm

Height (h) = 7.5 cm

Plug in the values

Volume = 3.14*7.5²*7.5 = 1324.7 cm³

Answer:

C 18 feet:D

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Hope you have a fantastic day, and do well on your test!!!!!!!!!!!!!!

the flux of curI(F) through the surface area in the figure as with integral:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

First, we calculate the curl of F: curI(F) = (2z, -2x, 2y).

Next, we apply Stokes' Theorem to calculate the flux of curI(F) through the surface in the figure. We start by computing the line integral of F around the boundary of the surface. This is given by:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

We can now evaluate this line integral by splitting it into a sum of integrals:

flux of curl(F) = 2 ∫ (x + 2yz) dx + 2 ∫ (x√(y^2 + 1))dy - 2 ∫ (16 - 2yz)dz

= 2∫x dx + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32∫dz + 4∫yz dz

= 2x^2/2 + 4∫yz dx + 2∫x√(y^2 + 1) dy - 32z + 4yz^2/2

= x^2 + 4yz∫dx + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

Finally, we can evaluate the flux of curI(F) through the surface in the figure as:

flux of curl(F) = x^2 + 4yz(2) + 2∫x√(y^2 + 1) dy - 32z + 2y^2z

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Money made during peak season = 1,800,000 * p

1. Expression for money made during peak season:

During peak season, the zoo has about 1,800,000 visitors. To calculate the money made during peak season, we multiply the number of visitors by the price of one peak season ticket (p):

Money made during peak season = 1,800,000 * p

2. Expression for money made during the off season:

The zoo wants to sell tickets in the off season for half the price of tickets in the peak season. Therefore, the price of one off season ticket would be p/2. To calculate the money made during the off season, we multiply the number of visitors by the price of one off season ticket:

Money made during the off season = 1,200,000 * (p/2) = 600,000 * p

3. Inequality for breaking even:

To break even, the zoo needs to make at least as much money as they spent on the animals. Let's represent the amount spent on animals as A. The money made during peak season plus the money made during the off season should be greater than or equal to the amount spent on animals:

1,800,000 * p + 600,000 * (p/2) ≥ A

Simplifying the inequality:

3,600,000p + 300,000p ≥ 2A

3,900,000p ≥ 2A

Solving for p:

p ≥ (2A) / 3,900,000

This determines the minimum price of one peak season ticket to break even.

The price of one off season ticket would be half the price of one peak season ticket, so the off season ticket should be (p/2).

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According to the properties of the standard normal distribution, approximately 99.7% of the values lie within three standard deviations of the mean. Therefore, the answer is 99.7%.

To determine the percentage of videos on the streaming site that are between 264 and 489 seconds, we need to calculate the area under the normal curve within that range. Since the distribution is approximately normal with a mean of 264 seconds and a standard deviation of 75 seconds, we can use the properties of the standard normal distribution to find the desired percentage.

First, we need to convert the values 264 and 489 to z-scores, which represent the number of standard deviations a particular value is away from the mean. The z-score formula is given by:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z1 = (264 - 264) / 75 = 0

z2 = (489 - 264) / 75 = 3

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between z = 0 and z = 3. The area represents the percentage of videos falling within that range. The answer is 99.7% .

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Answer:

a. Experiment

b. yes

Step-by-step explanation:

The study being conducted in this scenario is an experiment because different groups are being created and both an independant variable and dependant variable are being introduced. This means that there is researcher involvement and therefore makes this an experiment and not an observational study.

Yes, a case can be made for such a claim. This is because the music being played is the dependent variable in each of the groups. Meaning that the only difference in each of the groups was the music. Therefore, any differences in the data gathered can be connected to the music.

$ 119.607

Explanation

we can easily solve this by using a rule of three

Step 1

Let

actual price(2020)=price of 2019 + 2%

so

actual price(2020)= 102 % and

price ( 2019)=100 %

let x represents the cost for 2019, so

the proportion would be

therefore, the cost in January of 2019 is

$ 119.607

I hope this helps you

A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

If A = 136 when \(b_{1}\) = 7 and h = 16, find \(b_{2}\)

We are given the equation that we are working with:

A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

We are given certain values that the variables, in this case, are equal to:

A = 136

\(b_{1}\) = 7

h = 16

Substitute the given variables in the given equation for the corresponding numbers:

A = \(\frac{1}{2}h(b_{1} +b_{2} )\)

136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))

We know all the values in the equation except  \(b_{2}\). In order to find  \(b_{2}\) we must isolate it on one side of the equation

136 = 8 (7 + \(b_{2}\))

\(\frac{136}{8}\) = \(\frac{8 (7 + b_{2}) }{8}\)

17 = 7 + \(b_{2}\)

17 - 7 = 7 - 7 + \(b_{2}\)

10 =   \(b_{2}\)

If   \(b_{2}\) is equal to 10 then if we plug it back into the given equation both sides of the equation should equal each other. Remember to use PEMDAS

136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))

136 = \(\frac{1}{2}\) * 16 (7 + 10)

136 = \(\frac{1}{2}\) * 16 (17)

136 = 8 (17)

136 = 136

\(b_{2}\) = 10

Answer:

a dilation is different from a translation because it enlarges an image or shrink them instead of moving them. it's also different from rotation since it doesn't rotate but enlarge or shrink. it's way far from reflection because it enlarges or shrinks.

Answer: A diliation is a non rigid transformation, whereas reflections, transitions and rotations are rigid transformations. This means that dilations do not preserve the size of the shape.

Answer:

There are a total of 840 possible different teams

Step-by-step explanation:

Given

Number of boys = 6

Number of girls = 8

Required

How many ways can 4 boys and 5 girls be chosen

The keyword in the question is chosen;

This implies that, we're dealing with combination

And since there's no condition attached to the selection;

The boys can be chosen in \(^6C_4\) ways

The girls can be chosen in \(^8C_5\) ways

Hence;

\(Total\ Selection = ^6C_4 * ^8C_5\)

Using the combination formula;

\(^nCr = \frac{n!}{(n-r)!r!}\)

The expression becomes

\(Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}\)

\(Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}\)

\(Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}\)

\(Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}\)

\(Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}\)

\(Total\ Selection = \frac{30}{2} * \frac{336}{6}\)

\(Total\ Selection =15 * 56\)

\(Total\ Selection =840\)

Hence, there are a total of 840 possible different teams

Answer:

3

Step-by-step explanation:

The entire triangle shifts 2 to the left and up 6, the lengths of the sides remain the same, therefore:

AC = A'C' = 3

Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.

You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,

we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).

However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.

Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.

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Answer:

No.of cups for one soup : 2 cups

No.of cup for 3 soups: 2×3

=6

So , 6 cups of vegetable

HOPE IT HELPS U :)

A specific X-value for the solution ,-4 is not equal to -3/2.

The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.

We can rewrite this equation in terms of y:

4y = -2x

y = (-2/4)x

y = (-1/2)x

Now, let's use the data from the table to create a system of equations:

For the first data point (-1, 8):

y = (-1/2)x

8 = (-1/2)(-1)

8 = 1/2

Since 8 is not equal to 1/2, the first data point does not satisfy the equation.

For the second data point (3, -4):

y = (-1/2)x

-4 = (-1/2)(3)

-4 = -3/2

Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.

We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.

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The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.

Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.

Let the slope of the line joining A (7,-6)  and B(6,-6)  be m.

We know that the slope of a line is given by:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line

= (6-7) / (-6+6)

= -1 / 0

= undefined

Since the slope is undefined we can say that the straight line is parallel to the y axis.

we know that tan 90° = ∞

So any line parallel to this line will have the same slope as the y axis.

Hence the slope of the given line is undefined or infinity.

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