Select all equations that are true. A. 3 4 − 1 2 = 1 4 B. 9 16 − 4 8 = 5 8 C. 7 8 − 3 4 = 1 8 D. 7 15 − 1 3 = 6 15 E. 1 2 − 1 20 = 10 20 HELP ASAP

A2 + 4a√b + 4b

____________

A2-4b

 By rationalizing the Denominator of \(\frac{a+\sqrt{4b} }{a-\sqrt{4b}}\)  we get \(\frac{a^{2} +2a\sqrt{4b} + 4b}{a^{2} -4b}\)

A radical or imaginary number can be removed from the denominator of an algebraic fraction by a procedure known as o learn more about . That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

To rationalise multiply numerator and denominator with \(a+\sqrt{4b}\) where a is an integer and b is a prime number.

we get  \(\frac{a+\sqrt{4b}}{a-\sqrt{4b}} * \frac{a+\sqrt{4b}}{a+\sqrt{4b}}\)

\(= \frac{(a+\sqrt{4b})^{2} }{a^{2} -(\sqrt{4b})^{2} }\)

by solving we get \(=\frac{a^{2} +2a\sqrt{4b} + 4b}{a^{2} -4b}\)

By rationalizing the Denominator of \(\frac{a+\sqrt{4b} }{a-\sqrt{4b}}\)  we get \(\frac{a^{2} +2a\sqrt{4b} + 4b}{a^{2} -4b}\)

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x + (-5)

x - 5

and so on

Dis work?

Using the concept of rational numbers, it is found that the best method Toby could use is a multiplication of fractions, as the product of two fractions(two rational numbers) is always a fraction(rational number).

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

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Answer:

n = -15

Step-by-step explanation:

Represent the number by n.

Then 2(n + 6) = n - 3

Performing the indicated multiplication, we get:

2n + 12 = n - 3

Combining like terms, we get n = -15

according to the question,

given data in the question'

there are 51 houses on a street'

each hoses has an address between 1000 and 1099

There are 51 residences and 1000 possible addresses, according to the pigeon hole principle. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)

Giving houses even numbers (leaving odd addresses as the buffer address) There are now 1000=50 addresses that can be used.

According to the pigeon hole principle, there must be at least one box that contains at least N

k things if N objects are put into k boxes.

Because of this, it is impossible to assign 50 distinct addresses to 51 separate homes without utilising a single consecutive integer.

So, at least one instance of a home must have consecutive integers, which.

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There are 2 houses that have at least consecutive integers .

According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.

According to the pigeonhole principle, if there are more pigeons than there are pigeonholes, then at least one pigeonhole must hold more than one pigeon. Although the underlying idea is clear, the ramifications are staggering. The explanation is that the principle establishes the reality (or absence) of a certain phenomena.

There are potential residences and addresses. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)

Houses are given even numbers, leaving odd addresses as the buffer address. As a result, we now have

50

addressable addresses

According to the "pigeon hole concept," if items are put into boxes, then there must be at least one box that contains at

[N/k]object.

As a result, it is impossible to assign distinct addresses to several dwellings without using at least one consecutive number.

Since there must be at least two homes with consecutive integer addresses, there must be at least one instance of consecutive integer addresses for houses.

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The fifth derivative of \(h(x)\) is \(h^{(5)}(x) = (243\cdot e^{3\cdot x})\cdot (\cos 4x +9) + 5\cdot (81\cdot e^{3\cdot x})\cdot (-4\cdot \sin 4x)+10\cdot (27\cdot e^{3\cdot x})\cdot (-16\cdot \cos 4x)+10\cdot (9\cdot e^{3\cdot x})\cdot (64\cdot \sin 4x)+5\cdot (3\cdot e^{3\cdot x})\cdot (256\cdot \cos 4x) + (e^{3\cdot x}-8)\cdot (-1024\cdot \sin 4x)\). \(\blacksquare\)

The Leibnitz rule states that the \(n\)-th derivative of the product of two functions equals:

\((f\cdot g)^{(n)} = \Sigma\limits_{k=0}^{n}\left(\begin{array}{cc}n\\k\end{array} \right) f^{(n-k)}\cdot g^{(k)}\) (1)

If we know that \(n = 5\), \(f(x) = e^{3\cdot x}-8\) and \(g(x) = \cos 4x + 9\), then the derivative of \(h(x)\) is:

\(f(x) = e^{3\cdot x}-8\), \(f'(x) = 3\cdot e^{3\cdot x}\), \(f''(x) = 9\cdot e^{3\cdot x}\), \(f'''(x)= 27\cdot e^{3\cdot x}\), \(f^{(4)}(x) = 81\cdot e^{3\cdot x}\), \(f^{(5)}(x) = 243\cdot e^{3\cdot x}\)

\(g(x) =\cos 4x +9\), \(g'(x) = -4\cdot \sin 4x\),\(g''(x) = -16\cdot \cos 4x\), \(g'''(x) = 64\cdot \sin 4x\),\(g^{(4)}(x) = 256\cdot \cos 4x\), \(g^{(5)}(x) = -1024\cdot \sin 4x\)

\(h^{(5)}(x) = \left(\begin{array}{cc}5\\0\end{array} \right)\cdot f^{(5)}(x)\cdot g(x) + \left(\begin{array}{cc}5\\1\end{array} \right)\cdot f^{(4)}(x)\cdot g'(x)+\left(\begin{array}{cc}5\\2\end{array} \right)\cdot f^{(3)}(x)\cdot g''(x)+\left(\begin{array}{cc}5\\3\end{array} \right)\cdot f^{(2)}(x)\cdot g'''(x)+\left(\begin{array}{cc}5\\4\end{array} \right)\cdot f(x)\cdot g^{(4)}(x)+\left(\begin{array}{cc}5\\5\end{array} \right)\cdot f(x)\cdot g^{(5)}(x)\)

\(h^{(5)}(x) = f^{(5)}(x)\cdot g(x) + 5\cdot f^{(4)}(x)\cdot g'(x)+10\cdot f'''(x)\cdot g''(x)+10\cdot f''(x)\cdot g'''(x)+5\cdot f'(x)\cdot g^{(4)}(x)+f(x)\cdot g^{(5)}(x)\)

\(h^{(5)}(x) = (243\cdot e^{3\cdot x})\cdot (\cos 4x +9) + 5\cdot (81\cdot e^{3\cdot x})\cdot (-4\cdot \sin 4x)+10\cdot (27\cdot e^{3\cdot x})\cdot (-16\cdot \cos 4x)+10\cdot (9\cdot e^{3\cdot x})\cdot (64\cdot \sin 4x)+5\cdot (3\cdot e^{3\cdot x})\cdot (256\cdot \cos 4x) + (e^{3\cdot x}-8)\cdot (-1024\cdot \sin 4x)\)

The fifth derivative of \(h(x)\) is \(h^{(5)}(x) = (243\cdot e^{3\cdot x})\cdot (\cos 4x +9) + 5\cdot (81\cdot e^{3\cdot x})\cdot (-4\cdot \sin 4x)+10\cdot (27\cdot e^{3\cdot x})\cdot (-16\cdot \cos 4x)+10\cdot (9\cdot e^{3\cdot x})\cdot (64\cdot \sin 4x)+5\cdot (3\cdot e^{3\cdot x})\cdot (256\cdot \cos 4x) + (e^{3\cdot x}-8)\cdot (-1024\cdot \sin 4x)\). \(\blacksquare\)

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The probability that a poisonous mushroom in the forest is red is 50%.

To find the probability that a poisonous mushroom in the forest is red, we need to consider the probabilities of a mushroom being red and poisonous, and compare it to the overall probability of a mushroom being poisonous.

Let's denote the events as follows:

R: Mushroom is red

P: Mushroom is poisonous

P(R) = 20% = 0.20 (probability of a mushroom being red)

P(P|R) = 20% = 0.20 (probability of a red mushroom being poisonous)

P(P|not R) = 5% = 0.05 (probability of a non-red mushroom being poisonous)

We want to calculate:

P(R|P) = ? (probability that a poisonous mushroom is red)

We can use Bayes' theorem to calculate this probability:

P(R|P) = (P(P|R) * P(R)) / P(P)

To calculate P(P), the overall probability of a mushroom being poisonous, we can use the law of total probability:

P(P) = P(P|R) * P(R) + P(P|not R) * P(not R)

P(not R) = 1 - P(R) = 1 - 0.20 = 0.80 (probability of a mushroom not being red)

Now, we can calculate P(P):

P(P) = P(P|R) * P(R) + P(P|not R) * P(not R)

      = 0.20 * 0.20 + 0.05 * 0.80

      = 0.04 + 0.04

      = 0.08

Finally, we can calculate P(R|P) using Bayes' theorem:

P(R|P) = (P(P|R) * P(R)) / P(P)

      = (0.20 * 0.20) / 0.08

      = 0.04 / 0.08

      = 0.50

Therefore, the probability that a poisonous mushroom in the forest is red is 50%.

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Answer:

Step-by-step explanation:

Let the side be s and diagonal be d.

The relationship between the side and diagonal of a square is:

Substitute the value of s to find d:

Answer:

4,0

Step-by-step explanation:

Try 4,0.

Hope this helps!  :)

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures

Calculate the volume of the container:

Volume = πr2h

Volume = π x (5 cm)2 x 20 cm

Volume = 3,142 cm3

Calculate the total volume of liquid A and B:

Total volume of A and B = 4:11

Total volume of A and B = 4 + 11 = 15 cm3

Calculate the volume of liquid A:

Volume of A = 4/15 x 15 cm3

Volume of A = 4 cm3

Calculate the volume of liquid B:

Volume of B = 11/15 x 15 cm3

Volume of B = 11 cm3

Calculate the mass of liquid A:

Mass of A = Volume of A x Density of A

Mass of A = 4 cm3 x 1.05 g/cm3

Mass of A = 4.2 g

Calculate the mass of liquid B:

Mass of B = Volume of B x Density of B

Mass of B = 11 cm3 x 1.27 g/cm3

Mass of B = 13.97 g

Calculate the total mass of liquid C:

Total mass of C = Mass of A + Mass of B

Total mass of C = 4.2 g + 13.97 g

Total mass of C = 18.17 g

The mass of the liquid in the container is 18.17 g, correct to 3 significant figures.

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1. nβ₀ + β₁Σxi = Σyi

β₀Σxi + β₁Σxi² = Σxiyi

These are simultaneous linear equations in β₀ and β₁. Solving these equations will give us the critical values of β₀ and β₁ that minimize the RSS. The exact solution depends on the specific values of Σxi, Σyi, Σxi², and Σxiyi.

2.  The solution depends on the specific values of Σxi, Σyi, Σ(xi - X), and Σ(xi - X)(yi - α₀ - α₁(xi - X)).

1. To derive the critical values of β₀ and β₁ that minimize the residual sum of squares (RSS) for the sample regression model Yi = β₀ + β₁X₁ + ei, we need to find the partial derivatives of the RSS with respect to β₀ and β₁ and set them equal to zero.

The RSS is defined as the sum of the squared residuals:

RSS = Σ(yi - β₀ - β₁xi)²

To find the critical values, we differentiate the RSS with respect to β₀ and β₁ separately and set the derivatives equal to zero:

∂RSS/∂β₀ = -2Σ(yi - β₀ - β₁xi) = 0

∂RSS/∂β₁ = -2Σ(xi)(yi - β₀ - β₁xi) = 0

Simplifying the above equations, we get:

Σyi - nβ₀ - β₁Σxi = 0

Σxi(yi - β₀ - β₁xi) = 0

Rearranging the equations, we have:

nβ₀ + β₁Σxi = Σyi

β₀Σxi + β₁Σxi² = Σxiyi

These are simultaneous linear equations in β₀ and β₁. Solving these equations will give us the critical values of β₀ and β₁ that minimize the RSS. The exact solution depends on the specific values of Σxi, Σyi, Σxi², and Σxiyi.

2. To derive the critical values of α₀ and α₁ that minimize the RSS for the sample regression model Yi = α₀ + α₁(Xi - X) + ei, we follow a similar approach as in the previous question.

The RSS is still defined as the sum of the squared residuals:

RSS = Σ(yi - α₀ - α₁(xi - X))²

We differentiate the RSS with respect to α₀ and α₁ separately and set the derivatives equal to zero:

∂RSS/∂α₀ = -2Σ(yi - α₀ - α₁(xi - X)) = 0

∂RSS/∂α₁ = -2Σ(xi - X)(yi - α₀ - α₁(xi - X)) = 0

Simplifying the equations, we get:

Σyi - nα₀ + α₁(Σxi - nX) = 0

Σ(xi - X)(yi - α₀ - α₁(xi - X)) = 0

Again, these are simultaneous linear equations in α₀ and α₁. Solving these equations will give us the critical values of α₀ and α₁ that minimize the RSS. The solution depends on the specific values of Σxi, Σyi, Σ(xi - X), and Σ(xi - X)(yi - α₀ - α₁(xi - X)).

In both cases, finding the exact critical values of the parameters involves solving the equations using linear algebra techniques such as matrix algebra or least squares estimation.

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I don't see the picture. Can you send it in the message.

a) Null hypothesis: There is no significant difference in the grades between the students who participated in the yoga workshop and those who did not participate.

Research hypothesis: There is a significant difference in the grades between the students who participated in the yoga workshop and those who did not participate.

b) IV is the participation in the yoga workshop and DV is the grades of the students.

c) The conclusion that can be made about the null hypothesis is that it should be rejected because p-value is less than the conventional significance level of 0.05.

The null (H0) and research (H1) hypotheses can be formulated based on the information provided as follows:

H0 (Null hypothesis): There is no significant difference in the grades between the students who participated in the yoga workshop and those who did not participate.

H1 (Research hypothesis): There is a significant difference in the grades between the students who participated in the yoga workshop and those who did not participate.

In this case, the independent variable (IV) is the participation in the yoga workshop. It represents the condition or factor that is manipulated or varied to observe its effect on the dependent variable (DV).

The dependent variable is the grades of the students. It represents the outcome or variable that is measured to assess the effect of the IV.

The provided statistical information indicates a t-value of 6.3, with a corresponding p-value of 0.005. A t-value measures the magnitude of the difference between the means of two groups, while the p-value indicates the probability of obtaining such a difference by chance.

In this case, the p-value is less than the conventional significance level of 0.05, suggesting strong evidence against the null hypothesis.

Therefore, the conclusion that can be made about the null hypothesis is that it should be rejected.

The low p-value indicates that the observed difference in grades between the students who participated in the yoga workshop and those who did not participate is highly unlikely to have occurred due to random chance alone.

Instead, the evidence supports the research hypothesis, which states that there is a significant difference in grades between the two groups.

The provided t-value of 6.3 suggests a substantial difference between the means of the two groups, with the group that participated in the yoga workshop having higher grades on average.

The statistical significance further strengthens this conclusion, indicating that the observed difference is not likely to be a result of sampling variability.

In summary, based on the given information, the null hypothesis is rejected, and it can be concluded that there is a significant difference in grades between the students who participated in the yoga workshop and those who did not participate.

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Complete question:

Here are the results of the grades of students who participated in a yoga workshop (M = 78.4, SD = 4.3) and the grades of students who did not participate in the workshop (M = 67.8, SD = 6.2), t (54) = 6.3, p= .005.

a) What are the null (H0) and research (H1) hypotheses? (2pts)

b) What is the IV and DV? (2pts)

c) What conclusion should be made about the null hypothesis? Why? (1pt)

Answer: 73414.2

Step-by-step explanation:

There are three zeros in 1,000, so you have to move the decimal point to the right 3 places.

Answer:73414.2

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

1/2 * 600 = 300

There are 300 times would you predict getting an even number.

We have to given that,

The probability of spinning an even number is 1/2.

And, you spin 600 times.

Hence, Number of times would you predict getting an even number is,

⇒ 1/2 of 600

⇒ 1/2 × 600

⇒ 600 / 2

⇒ 300

Therefore, There are 300 times would you predict getting an even number.

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Answer:

the answer is m=19

Step-by-step explanation:

5^(m-7)=5^12

m-7=12(5 is cancelled because it is common in both sides)

m=19

A trade of securities between a bank and an insurance company without using the services of a broker-dealer would take place on the over-the-counter (OTC) market, also known as the fourth market.

The first market refers to the primary market, where newly issued securities are bought and sold directly between the issuer and investors. This market is typically used for initial public offerings (IPOs) and the issuance of new securities.

The second market refers to the organized exchange market, such as the New York Stock Exchange (NYSE) or NASDAQ, where securities are traded on a centralized platform. This market involves the buying and selling of already issued securities among investors.

The third market refers to the trading of exchange-listed securities on the over-the-counter market, where securities that are listed on an exchange can also be traded off-exchange. This market allows for direct trading between institutions, such as banks and insurance companies, without the involvement of a broker-dealer.

Therefore, in the scenario described, the trade of securities between the bank and insurance company would take place on the fourth market, which is the over-the-counter market.

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Answer:

0.38

Step-by-step explanation:

The given expression is

We will multiply at first -5 by 3

Then we will multiply x^2 by x^4 by adding their powers

And multiply y by 1 as there is no y in the second bracket, then

The answer is C

Answer:

1.25 lawns/per hour

Step-by-step explanation:

Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

A Type II error, in the context of hypothesis testing, occurs when the null hypothesis (H₀) is not rejected even though it is false. In other words, it's the failure to reject a false null hypothesis.

In this scenario, the null hypothesis states that the complaint rate is 8%, and the alternative hypothesis (Hₐ) states that the complaint rate is less than 8%.

A Type II error would occur if the chef believes that the complaint rate is not less than 8% (failing to reject the null hypothesis), when in fact it is less than 8% (the alternative hypothesis is true).

Consequences of a Type II error in this context:

The consequence of a Type II error would be that the chef continues to use the new gluten-free recipe for the topping even though the actual complaint rate is less than 8%.

This means that the chef would miss out on an opportunity to improve the recipe and potentially satisfy more customers.

In this case, the chef might continue to experience a significant number of unsatisfied customers who might have been pleased with an improved recipe.

This could lead to negative customer reviews, loss of customer loyalty, and a potential negative impact on the restaurant's reputation and business.

To summarize:

Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%.

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers, potentially harming the restaurant's reputation and business.

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A Type II error in this scenario would occur if the chef wrongly assumes the complaint rate is less than 8%, leading to continued use of the disliked recipe and unsatisfied customers.

In this context, a Type II error in the chef's hypothesis test would occur if the chef believes the complaint rate for the new gluten-free recipe is less than 8%, when in fact, it is not. That means the chef is under the false impression that the customers are more satisfied with the new recipe than they truly are. The consequence would be that the chef continues to use the new recipe, despite a higher complaint rate. This would lead to a significant number of unsatisfied customers because the recipe is not meeting their taste preferences as much as the chef thinks. This could subsequently affect the restaurant's reputation and customer loyalty.

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Answer:

y=x+1

Step-by-step explanation:

The slope of the equation is 1, you can try the rise over run method or picking 2 points and subtracting them for example 2,3 and 3,4

2,3-3-4=1,1. The y-intercept is 1 because that is the point where the line crosses the y axis.

Answer:

Slope intercept form:

y = mx + b

Where 'y' is the independent variable and 'x' is the dependent variable.

'm' represents the slope(rise/run), and 'b' represents the y-intercept(where the line meets the y-axis).

If we look at this graph, we can see the line meets the y-axis at 1. So 1, will be our y - intercept.

We can also see, that from the point 1, it rises 1 and goes over 1. So 1, will be our slope as well.

To double check this, we select two fixed points on this graph and subtract the y-coordinates from each other and divide the result of that by the x-coordinates subtracted from each other.

y2(second y-coordinate) - y1(first y-coordinate)

_____________________________________

x2(second x-coordinate) - x1(first x-coordinate)

We pick the two points to be, (1,2) and (2,3).

 3 - 2              1

______ = _______, which is equal to 1, so 1 is the slope.

 2 - 1               1

Now we insert these values into our slope intercept form equation:-

y = mx + b

y = 1x + 1 or y = x + 1.

Where 1 is the slope, and the y-intercept is 1.

you didn't attach the figure....

Answer:

12 and 48

Step-by-step explanation:

let n be the larger number , then \(\frac{1}{4}\) n is the smaller number and their sum is

x + \(\frac{1}{4}\) x = 60 ( multiply through by 4 to clear the fraction )

4x + x = 240 , that is

5x = 240 ( divide both sides by 5 )

x = 48

smaller number = \(\frac{1}{4}\) × 48 = 12

The 2 numbers are 12 and 48

Weierstrass M-test is a way of determining the uniform convergence of a series of functions on a closed interval.

Let Aₙ(x) be a sequence of functions on a closed interval [a,b]. If there is a sequence of positive numbers Mₙ that satisfies |Aₙ(x)| ≤ Mₙ for all x in [a,b] and all n in the domain of Aₙ(x) and the series ΣMₙ converges, then ΣAₙ(x)converges uniformly on [a,b].

Since the power series in question converges absolutely at the point zo, the definition implies that the series converges when |x−zo| < R for some positive R and diverges when |x−zo| > R.

Hence, the power series has a radius of convergence that can be expressed as R = ∞ if the series converges everywhere or R = 1/lim sup_{n→∞} |aₙ|¹/ⁿ if the series is finite. The series converges uniformly on a closed interval [-c,d] with c = |zo| and d is the minimum of (R, 2−|zo|).

Using the Weierstrass M-test, if we let Mₙ = |aₙ|/2ⁿ, then ΣMₙ converges absolutely because ΣMₙ = Σ|aₙ|/2ⁿ is a geometric series with a common ratio of 1/2, so it is easy to compute its sum as Σ|aₙ|/2ⁿ = 2|zo| ≤ ∞.

By definition, we have |aₙ xⁿ| ≤ |a_n|/2ⁿ for all x in [-c,d] and n in the domain of a_n.

Thus, using the inequality Σ|aₙ|/2ⁿ, we can conclude that the power series Σaₙ xⁿ converges uniformly on [-c,d].

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Answer:

de=104

fe=76

def=180

cfd=284

dfe=256

Answer:

y = - x - 18

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

the equation of a line in point- slope form is

y - b = m (x - a)

m is the slope and (a, b ) a point on the line

y + 3 = - (x + 2) ← is in point- slope form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation

to find c substitute (- 10, - 8 ) into the partial equation

- 8 = 10 + c ⇒ c = - 8 - 10 = - 18

y = - x - 18 ← equation of line s

The equation in slope-intercept form is y=-x-18.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, Line r has an equation of y + 3 = -(x + 2).

y+3=-x+2

y=-x+2-3

y=-x-1

Here, slope m=-1

Line s includes the point (-10, -8) and is parallel to line r.

The slope of a line parallel to given line is m1=m2

Substitute m=-1 and (x, y)=(-10, -8) in y=mx+c, we get

-8=-1(-10)+c

c=-18

So, the equation is y=-x-18

Therefore, the equation in slope-intercept form is y=-x-18.

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