5. The lateral surfaces of the foam pit will be
lined with extra padding. How many square
feet will be lined with extra padding?

Answer:

A plant needing full sun can be placed from a fence 4.63 ft high at a distance of 10.75 meter if the lowest angle of elevation of the sun in winter is 23​° 18​'.

Explanation:

 The given figure shows the arrangement of sun, 4.63 ft high and plant needing full sun.

  By using trigonometric result, tan θ = Opposite side/Adjacent side.

   Substituting

                tan(23​° 18​') = 4.63 ft/x

                 x = 4.63 ft/ tan(23​° 18​') = 10.75 m

 So that a plant needing full sun can be placed from a fence 4.63 ft high at a distance of 10.75 meter.

The result is a polynomial in simplest form [tex]x^{2} -6x -27[/tex]

Polynomials are algebraic formulas with variables and coefficients. Variables are sometimes known as indeterminates.

To calculate (f - g)(x), subtract g(x) from f(x) as follows:

(f - g)(x) = f(x) - g(x)

When we substitute the given functions, we get:

(f - g)(x) =[tex](x^2 - 5x - 36)[/tex] - (x - 9)

When we expand and simplify, we get:

(f - g)(x) = [tex]x^{2} - 5x - 36 - x + 9[/tex]

(f - g)(x) = [tex]x^{2}[/tex] - 6x - 27

As a result, the polynomial is (f - g)(x):

(f - g)(x) = [tex]x^{2}[/tex] - 6x - 27

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the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.with  the sum of the first n terms of the arithmetic series formula we are able to solve it

what is arithmetic series  ?

An arithmetic series is a series of numbers in which each term is obtained by adding a fixed number to the preceding term (known as the common difference). The sum of the terms in an arithmetic series can be found by multiplying the average of the first and last

In the given question,

We know that the first term of the arithmetic series is given by (2t+1) and the common difference is 3. Therefore, the nth term can be written as:

a_n = a_1 + (n-1)d

(14r - 5) = (2t + 1) + (n-1)3

14r - 5 = 2t + 1 + 3n - 3

14r - 4 = 2t + 3n

7r - 2 = t + (3/2)n --------(1)

Now, we need to find the values of p, q, and r for the sum of the first n terms of the series, which is given by:

S_n = (n/2)[2a_1 + (n-1)d]

S_n = (n/2)[2(2t+1) + (n-1)3]

S_n = n(3n+4t+2)/2

We can simplify this expression by factoring out a 2 from the numerator:

S_n = n(3n+4t+2)/2 = (2n/2)(3n+4t+2)/2

S_n = (n/2)(3n+4t+2) = (3/2)n² + 2tn + n

Now, we need to write this expression in the form p(qt-1). To do this, we need to factor out (3/2):

S_n = (3/2)(n² + 4/3 tn + 2/3 n)

S_n = (3/2)[n² + 4/3 tn + (2/9)(3n)]

S_n = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n]

S_n = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/9)t² - (4/3)tn + (4/3)tn]

S_n = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)n + (4/3)tn]

S_n = (3/2)[(n + (2/3)t)² - (4/9)t² + (2/9)(3t*n)]

Now we can see that p=3/2, q=3t, and r=2/9. Therefore, the value of p is 3/2, the value of q is 3t, and the value of r is 2/9.

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The monthly payments for the loan to be paid off at the rate given would be = $1,504.4

The total cost of the house = $243, 950.

The time for the payment of the loan = 25 years.

The rate of the payment = 7.4%

The simple interest = principal×time×rate/100

Si = 243, 950.×25×7.4/100

si = 45130750/100

si = 451,307.50

The total number of months is 25 years = 300

The amount paid per month = 451,307.50/300 = $1,504.4

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Answer:

Step-by-step explanation: Isn't the 3rd one wrong

Answer:

hehe

Step-by-step explanation:

Answer:

[tex]2x = 20[/tex]

[tex]x = 10[/tex]

Step-by-step explanation:

you could answer the main complex question correctly by figuring out the resulting function g(x), but you don't understand the rather simple additional questions about some minor details ?

are you serious ?

so, what you have figured out :

g(x) = -f(x + 3) - 5

the reflection across the x-axis out the sign of the functionaries results upside-down. therefore, the "-" sign in front of f.

the downward shift by 5 units added the "- 5" at the end, because all functional result values are lowered by 5 units (that's what the shift downward by 5 units means).

and the shift left by 3 units made us transform x to x + 3 as the input value (because everything happens now 3 units earlier than for the original f(x)).

what is missing now is to use the original f(x) = 3^x

g(x) = -f(x+3) - 5 = -(3^(x+3)) - 5 = -(3^x)×3³ - 5 =

= -27×(3^x) - 5

either one of the last 3 expressions is the final g(x). pick the one you think your teacher is looking for the most.

the y-intercept of a curve/function is the functional value when x = 0 (that is what it intercepts the y-axis).

so,

y-intercept = g(0) = -27×(3^0) - 5 = -27×1 - 5 = -27 - 5 = -32

the domain of the function is the interval or set of all valid values for x.

do we need to exclude any negative or positive values that cannot be calculated in the expression, as it lead to an undefined value or situation ? 0 ?

no, any number we can think of is fine for x in the functional expression.

so, the domain is

x is in (-infinity, +infinity).

please note the round brackets, as the interval ends are not included. simply because infinity is not a defined number.

the range of a function is the interval or set of all build values for y, the functional results.

can the function ever deliver a positive value ?

no. -27×(3^x) - 5 will always be negative, no matter what number (positive it negative) we use for x.

can the function ever be 0 ?

no. only for x = -infinity. and remember, this is not a valid number. x will never reach -infinity (only in the infinity future or past), and therefore the functional value can get closer and closer to 0 bu will never reach it.

so, the range is

y in (-infinity, 0).

again with the round brackets, because the interval limits will never be included.

Approximately 20% of the 7th graders in the School of Rock play the keyboard. (This is the answer to the nearest whole number percent)

What is meant by whole number?

Whole numbers are integers that are greater than or equal to zero, and do not include fractions or decimals. They are used to represent quantities or values in counting and arithmetic operations.

What is meant by percent?

Percent is a mathematical concept that represents a value as a fraction of 100. It is often denoted with the symbol "%", and is commonly used to express ratios, rates, and percentages.

According to the given information

Here we can use the formula:

percentage = (part/whole) x 100

In this case, the part is the number of 7th graders who play keyboard (12) and the whole is the total number of 7th graders (60). So, we have:

percentage = (12/60) x 100 = 20

Therefore, approximately 20% of the 7th graders in the School of Rock play the keyboard.

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The statements that would be true if the length of each side of the square increased by one unit is that the area of the square would be a rational number and the area of the square would be a perfect square.

A perfect square is defined as the number that can be expressed as the product of two equal integers.

The area of the square given = 400

The sides of the square = 20

When an additional unit is added= 21

The new area = 441

This is a perfect square and equally a rational number because it's a real number.

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Answer:

Step-by-step explanation:

Answer:

the answer is 23

Step-by-step explanation:

the equation states that x=3

therefore you have to replace x with 3 so the equation is equal to

6×3= 18+5= 23

Therefore , the solution of the given problem of inequality comes out to be  less than 56, such as $30 or $45.

Due to the lack of an indication for this distinction in algebra, it can be represented by a combination or set two numbers. Equilibrium is typically followed by equity. The ongoing disparity in standards is the source of inequality. Disparity is not the same as equality. Despite knowing that the elements are frequently not related nor close to one another, as was my least favourite symbol. (). All deviations, no matter how slight, have an impact on value.

Here,

We must isolate the variable p on one side of the inequality sign in order to solve the inequality:

=> p - 25 < 31

To both sides, add 25:

=>  p - 25 + 25 < 31 + 25

Simplify:

=>  p < 56

Since the cost would be less than $31 after applying the shop credit, any value of p that is less than 56 would constitute a solution to Marilyn's inequality.

When the store credit is applied, Marilyn would pay $25 rather than $31 for a $50 gift, for instance.

Therefore, $50 is a potential expense for the present as well as a remedy for the inequality.

There are other other solutions that are less than 56, such as $30 or $45.

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Answer:

[tex]286\pi \: {in}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

d (diameter) = 22 in

l = 26 in

Find: A (lateral) - ?

First, let's find the length of the radius:

[tex]r = \frac{1}{2} \times d = \frac{1}{2} \times 22 = 11 \: in[/tex]

Now, we can find the lateral area:

[tex]a(lateral) = \pi \times r \times l[/tex]

[tex]a(lateral) = \pi \times 11 \times 26 = 286\pi \: {in}^{2} [/tex]

Answer: To show that the function has exactly one zero in the given interval, we need to show that the function changes sign exactly once on the interval.

First, we can see that the function is continuous on the interval (0, pi/2) as it is a polynomial of trigonometric functions.

Next, we can evaluate the function at the endpoints of the interval:

R(0) = sec^2(0) - cos(0) - 1 = 1 - 1 - 1 = -1

R(pi/2) = sec^2(pi/2) - cos(pi) - 1 = undefined

We can see that R(0) is negative, and since the function is continuous on the interval, by the Intermediate Value Theorem, the function must pass through zero at some point in the interval.

To show that it passes through zero only once, we can take the derivative of the function:

R'(theta) = 2sec^2(theta)sin(theta) + 2sin(2theta)

We can see that R'(theta) is positive for all theta in the interval (0, pi/2), as sec^2(theta) and sin(theta) are positive and sin(2theta) is non-negative. Therefore, the function R(theta) is strictly increasing on the interval, and can cross the x-axis at most once.

Thus, we have shown that the function R(theta) has exactly one zero in the interval (0, pi/2).

Step-by-step explanation:

The value of the quadratic equation when x = 3 is 67.

What is a quadratic equation?

Any algebraic equation that can be expressed in standard form as where x represents an unknown number and where a, b, and c represent known values, with a ≠ 0, is a quadratic equation.

We are given a quadratic equation as 3[tex]x^{2}[/tex] + 5x + 25.

Now, when x = 3, we get

⇒ 3* [tex]3^{2}[/tex] + 5 (3) + 25

⇒ 3 (9) + 5 (3) + 25

⇒ 27 + 15 + 25

⇒ 67

Hence, the value of the quadratic equation when x = 3 is 67.

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Question: Evaluate : 3x² + 5x + 25 when x = 3.

Using the exponential probability density function in the given situation the required formula for P(x ≤ x0) would be P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵.

The exponential distribution, sometimes known as the negative exponential distribution, is the probability distribution of the interval between events in a Poisson point process, that is, an event-producing process where events happen continuously and independently at a fixed average rate.

The memoryless feature of the exponential distribution states that future probabilities are independent of any prior knowledge.

According to mathematics, P(X > x + k|X > x) = P(X > k).

The probability that a random variable will fall into a specific range of values as opposed to taking on any value is defined by the probability density function (PDF).

In the given function:

f(x) = 1/5⁻ˣ⁺⁵ for x

Then, the formula for P(x ≤ x0) would be:

P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵

Therefore, using the exponential probability density function in the given situation the required formula for P(x ≤ x0) would be P(x ≤ x0) = 1 - e⁻ˣ⁰⁺⁵.

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Complete question:

Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0. Write the formula for P(x ≤ x0)

Answer:

2°
one solution
(a) The system has no solution

Step-by-step explanation:

Let the smaller angle be x. According to the given condition, the larger angle is forty-four times the smaller angle, which is 44x. Since the angles are complementary, their sum is 90°.

x + 44x = 90

45x = 90

x = 90/45

x = 2

So, the smaller angle is 2°, and the larger angle is 44 times that, which is 88°.

The given system of equations is:

20y = -24x + 40

6x + 5y = 10

To determine the nature of the system, we can compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.

Let's find the slopes of the two equations:

20y = -24x + 40

Dividing by 20, we get: y = (-24/20)x + 2

6x + 5y = 10

Dividing by 5, we get: (5/5)y = (6/5)x + (10/5)

y = (6/5)x + 2

Comparing the slopes, we see that they are equal (both are 6/5), and the y-intercepts are also equal (both are 2). So, the system has infinitely many solutions. The correct answer is (b) The system has infinitely many solutions.

The given system of equations is:

19 = 4y + 12x

12x + 4y = 15

To determine the nature of the system, we can again compare the slopes of the two equations. If the slopes are equal and the y-intercepts are also equal, the system has infinitely many solutions. If the slopes are equal but the y-intercepts are not equal, the system has no solution. If the slopes are not equal, the system has one solution.

Let's find the slopes of the two equations:

19 = 4y + 12x

Dividing by 4, we get: (1/4)(4y + 12x) = 19/4

y + 3x = 19/4

12x + 4y = 15

Dividing by 4, we get: (1/4)(12x + 4y) = 15/4

3x + y = 15/4

Comparing the slopes, we see that they are equal (both are 1/3), but the y-intercepts are not equal. So, the system has no solution. The correct answer is (a) The system has no solution.

There is a 65.54% probability that the average age of those doctors is under 48.8 years.

Science uses a figure called the probability of occurrence to quantify how likely an event is to occur.

It is written as a number between 0 and 1, or between 0% and 100% when represented as a percentage.

The possibility of an event occurring increases as it gets higher.

True mean = mean (or average)+/- Z*SD/sqrt (sample population)

Then,

Mean (average) = 48.0 years

The true mean must be less than 48.8 years.

SD = 6.0 years, and

Sample size (n) = 9 doctors

Using Z as the formula's subject:

Z= (True mean - mean)/(SD/sqrt (n))

Inserting values:

Z=(48.8-48.0)/(6.0/sqrt (9)) = 0.4

From the table of normal distribution probabilities:

At Z= 0.4, P(x<0.4) = 0.6554 0r 65.54%

Therefore, there is a 65.54% probability that the average age of those doctors is under 48.8 years.

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Complete question:

The average age of doctors in a certain hospital is 48.0 years old. suppose the distribution of ages is normal and has a standard deviation of 6.0 years. if 9 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 48.8 years. assume that the variable is normally distributed.

The equation that is true for all value is : 4(x - 3) = 0

A linear equation is one that has the following form of expression:

y = mx + b

If m is the line's slope, b is the y-intercept, x and y are variables. In this equation, m indicates the steepness of the line and b the point at which it crosses the y-axis to show a straight line on a graph.

The equation that is true for all values of x is:

4(x - 3) = 0

To see why, we can simplify the equation as follows:

4(x - 3) = 0

4x - 12 = 0 (distributing the 4)

4x = 12 (adding 12 to both sides)

x = 3 (dividing both sides by 4)

So we see that the equation simplifies to 4 times the quantity (x - 3), which is equal to 0 if and only if x = 3. Therefore, the equation is true for all values of x if and only if x = 3.

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Answer:

2 3/8

Step-by-step explanation:

I am not completely sure because I did it a long while back but correct me if I'm wrong I want to learn please mark me brainliss

Answer:

1 / 20 or 0.05

Step-by-step explanation:

1/5 ÷ 4

= 1/5 × 1/4

= 1 / 20

The area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

What is rectangle?

A rectangle is a four-sided two-dimensional geometric shape in which all angles are right angles (90 degrees) and opposite sides are parallel and equal in length. This means that a rectangle has two pairs of congruent sides and its opposite sides are parallel.

To find the area of each part of the figure and the whole figure, we need to use the formulas for the area of a triangle and the area of a rectangle.

First, we can find the area of the triangle:

Area of Triangle A = (1/2) x base x height = (1/2) x 4 x 6 = 12 square units.

Next, we can find the area of the rectangle:

Area of Rectangle B = length x width = 5 x 6 = 30 square units.

To find the area of the whole figure, we can add the area of Triangle A and Rectangle B:

Area of Whole Figure = Area of Triangle A + Area of Rectangle B

= 12 + 30

= 42 square units.

Therefore, the area of Triangle A is 12 square units, the area of Rectangle B is 30 square units, and the area of the whole figure is 42 square units.

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a) The problem can be formulated as a Linear Programming Model (LPM) as follows:

Maximize Z = 400x + 100y

Subject to:

4x + 2y ≤ 1600

2.5x + y ≤ 1200

4.5x + 1.5y ≤ 1600

Where x is the number of units of model A produced, y is the number of units of model B produced, and the constraints represent the production capacities of each department.

b) The LPM can be solved using the graphical method by plotting the constraints on a graph and finding the feasible region, which is the region of the graph where all constraints are satisfied. The corner points of the feasible region are then evaluated to find the optimal solution.

After plotting the constraints and finding the feasible region, the corner points are (0, 0), (0, 800), (266.67, 533.33), (400, 200), and (355.56, 0). Evaluating the objective function at each corner point, we find that the maximum profit of Birr 133,333.33 is achieved at the point (266.67, 533.33), which represents producing 266.67 units of model A and 533.33 units of model B.

The slack time in each department can be found by subtracting the time used for production from the available time. The slack times are 533.33 hours in Department I, 466.67 hours in Department II, and 66.67 hours in Department III.

P(x<69.3) = 0.9082. (Rounded to four decimal places.)

P(x ≥ 66.3) = 0.2486. (Rounded to four decimal places.)

(b) We have X ~ N(65, 4²), where μ = 65 and σ = 4. Therefore,

Z = (X - μ) / σ = (69.3 - 65) / 4 = 1.325

Using a standard normal table or calculator, find P(Z < 1.325) = 0.9082. Therefore,

P(X < 69.3) = 0.9082.

(c) Using the same standard normal table or calculator, find P(Z ≥ 0.675) = 0.2486. Therefore,

P(X ≥ 66.3) = 0.2486.

Note that we use the complement rule here, since P(X ≥ 66.3) = 1 - P(X < 66.3), and we have already calculated P(X < 66.3) in part (b).

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Based on the information provided, the direction of rotation appears to be a 270° clockwise rotation.

This is because the point A has been rotated to a new point A' at (5, -1), which is 270° clockwise from the original point A at (1, 5) with respect to the origin. A 270° clockwise rotation will also cause point B to move to the right and down, point C to move further down and to the right, and point D to move to the right and up.

A 90° counterclockwise or 180° clockwise rotation would not result in the point A being mapped to the point A'. Similarly, a 270° counterclockwise rotation would cause point A to end up in quadrant 3, which is not consistent with the given information.

Answer:

270° clockwise rotation.

Step-by-step explanation:

The answer is -77x⁶y⁷z² = -7x⁴yz * 11x²y⁶z

What is factor?

In mathematics, a factor is a number or expression that divides another number or expression evenly without leaving a remainder.

To complete the factoring of -77x⁶y⁷z², we need to divide it by -7x⁴yz, as it is a common factor:

-77x⁶y⁷z² / (-7x⁴yz) = 11x²y⁶z

Therefore, the complete factoring of -77x⁶y⁷z² is:

-77x⁶y⁷z² = -7x⁴yz * 11x²y⁶z

or

-77x⁶y⁷z² = 7x⁴yz * -11x²y⁶z

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The quadratic equations are classified as follows:

If the discriminant of the quadratic equation is positive, then the equation has two real solutions.

If the discriminant is zero, then the equation has one real solution.

If the discriminant is negative, then the equation has no real solutions (but may have complex solutions).

Let's classify the given quadratic equations based on the number of solutions:

20² +5 = 9 is not a quadratic equation because it does not have a variable with a degree of two. Instead, it is just a number that evaluates to a false statement.

Therefore, it has no solution.

2x² + 3x = 5 is a quadratic equation with a = 2, b = 3, and c = -5. The discriminant is 3² - 4(2)(-5) = 49, which is positive.

Therefore, the equation has two real solutions.

3x² + 2x = 22 is a quadratic equation with a = 3, b = 2, and c = -22. The discriminant is 2² - 4(3)(-22) = 100, which is positive.

Therefore, the equation has two real solutions.

4x² + 12x = 19 is a quadratic equation with a = 4, b = 12, and c = -19. The discriminant is 12² - 4(4)(-19) = 400, which is positive.

Therefore, the equation has two real solutions.

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Drag each equation to the correct location on the table.

Classify the quadratic equations based on the number of solutions.

20² +5 = 9

2x² + 3x = 5

3x² + 2x = 22

4x² + 12x = 19

One Solution

Two Solutions

No Solution

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

The value of X for which 70.54% of the area under the normal curve lies to the right of it is 7.88 (rounded to two decimal place)

To solve this problem, we need to find the value of X such that 70.54% of the area under the normal curve lies to the right of it.

We know that the total area under the normal curve is 1 or 100%. So, if 70.54% of the area lies to the right of X, then 29.46% of the area must lie to the left of X.

We can find the Z-score corresponding to the left tail area of 29.46% using a standard normal distribution table or calculator.

The Z-score is -0.53 (rounded to two decimal places).

Now, we can use the formula for converting a Z-score to an X-value for a normal distribution:

X = μ + Zσ

where;

μ is the mean of the distribution,

σ is the standard deviation, and

Z is the Z-score.

Plugging in the values, we get:

X = 10 + (-0.53)(4)

X = 7.88

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Therefore, the value of m = 1/ 3, b = -11/6. equation in the form [tex]y = mx+b[/tex].

"Slope-intercept" refers to a method of expressing a linear equation in the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept.

The "slope" of a line refers to how steeply it rises or falls as it moves from left to right. It is calculated by dividing the change in y by the change in x between any two points on the line.

The "y-intercept" is the point where the line intersects the y-axis. It is the value of y when x equals zero.

By expressing a linear equation in slope-intercept form, you can easily identify the slope and y-intercept, which can provide useful information about the line's behavior.

To write the equation in the form y = mx + b, we need to solve for y:

[tex]-2x + 6y = -11[/tex]

[tex]6y = 2x - 11[/tex]

[tex]y = (2/6)x - (11/6)[/tex]

[tex]y = (1/3)x - (11/6)[/tex]

So, the equation in slope-intercept form is. [tex]y = (1/3)x - (11/6)[/tex], where the slope m is 1/3 and the y-intercept b is -11/6.

Therefore,

m = 1/3

b = -11/6

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