What is the solution to the system of equations? 2x – y = 7 y = 2x 3

1260

Just as 12 is to 72. 210 is to x

setup ratio, cross multiply, and solve for x:

Answer is 1260

The product of the polynomial expression 3·a² × (8·a² + 8·a + 2) is the option B) 24·a⁴ + 24·a³ + 6·a²

The correct option is therefore option B

A polynomial is an expression that consists of a number of terms with positive integer exponents joined by addition, subtraction and or multiplication symbols.

The specified expression is; 3·a²·(8·a² + 8·a + 2)

The above polynomial expression can be evaluated by expanding as follows;

3·a²·(8·a² + 8·a + 2) = 3·a² × 8·a² + 3·a² × 8·a + 3·a² × 2

3·a² × 8·a² + 3·a² × 8·a + 3·a² × 2 = 24·a⁴ + 24·a³ + 6·a²

Therefore, 3·a²·(8·a² + 8·a + 2) = 24·a⁴ + 24·a³ + 6·a²

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The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

Answer:

q= 11

Step-by-step explanation:

25-14= 11

Answer:

q= 11

Step-by-step explanation:

25=q+14

25-14=q+14-14

11=q

hope it's helpful ❤❤❤

THANK YOU.

To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.

This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.

In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.

So, the matrix A must have the following form:

A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

where each aij is a scalar.

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The Skubic family and the Shaw family went on a safari tour in which they drove their own vehicles through the park to view the animals. The cost of the tour was $5. 25 per vehicle plus an additional amount for each person in the vehicle is $12.75.



We know that the cost of the tour is $5.25 per vehicle plus an additional amount for each person in the vehicle. Let's start by finding out how much the Skubic family paid per person:

$22.75 (total cost) - $5.25 (vehicle fee) = $17.50 (amount for people)

$17.50 ÷ 7 (number of people) = $2.50 per person

Now we can use this information to find out how much the Shaw family paid:

$5.25 (vehicle fee) + $2.50/person x 3 people = $12.75

Therefore, the Shaw family paid $12.75 for the safari tour.



To summarize, the Skubic family paid $22.75 for the safari tour with 7 people in their vehicle, and the Shaw family paid $12.75 for the safari tour with 3 people in their vehicle. The cost of the tour is $5.25 per vehicle plus an additional amount for each person in the vehicle.
Main Answer: The Shaw family paid $12.75 for the safari tour.


1. First, we need to find the additional amount per person. Since the Skubic family had 7 people in their vehicle and paid $22.75, we can write the equation:

$5.25 + 7x = $22.75

2. Subtract $5.25 from both sides of the equation:

7x = $17.50

3. Divide both sides by 7:

x = $2.50 (additional amount per person)

4. Now, we can calculate the cost for the Shaw family with 3 people in their vehicle:

$5.25 (base cost) + 3($2.50) = $5.25 + $7.50 = $12.75

The Shaw family paid $12.75 for their safari tour.

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The product of the 5/8 and 4 is 2.5.

What is the product of numbers?

In mathematics, a product is an outcome of multiplying two or more numbers together.

We have,

5/8 and 4

When looking to find what the product of a number is, you can find each product of a number by multiplying it by another number.

For example, 27 is a product of 9 and 3, because 9 x 3 = 27.

= 5/8 × 4

= 5/8 × 4/1

= 20/8

= 5/2

= 2.5

Hence, the product of the 5/8 and 4 is 2.5.

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The expected value of the treatment mean square for a completely randomized design experiment is given by E(MS Trt) = σ2 + m∑Ti2 / (L-1).

Let L be the number of treatments, and R be the number of replications per treatment.

According to the model, yij is the response from the jth replication of the ith treatment.

Therefore, the total number of observations is given by N = LR. Therefore, we assume the following linear model to estimate the treatment effects: yij=μ+Ti+Eij Where yij is the observed value for the jth replication in the ith treatment. μ represents the population mean.

Ti represents the effect of the ith treatment and is assumed to be a fixed effect. Eij is the error term for the jth replication of the ith treatment, and is assumed to follow a normal distribution with a mean of 0 and a variance of σ2.

We now turn to the analysis of variance for the CRD with L treatments and R replications per treatment.

The total sum of squares is given by: SST = ∑∑yij2 - (T..)2/N Where T.. is the total sum of observations.

It has (L-1)(R-1) degrees of freedom.

The total mean square is given by: MST = SST / (L-1)(R-1)

The treatment sum of squares is given by: SSTR = ∑n(T.)2/R - (T..)2/N Where T. is the sum of the observations in the ith treatment, and n is the number of observations in the ith treatment.

It has L-1 degrees of freedom. The treatment mean square is given by: MSTR = SSTR / (L-1)

The error sum of squares is given by: SSE = SST - SSTR It has (L-1)(R-1) degrees of freedom.

The error mean square is given by: MSE = SSE / (L-1)(R-1)

Therefore, E(MS Trt)=σ2+ m∑Ti2/t-1  since E(Ti)=0 for all i.

To show that E(MS Trt) = σ2 + m∑Ti2 / t-1

We start by using the definition of expected value E() to derive the expected value of the treatment mean square

(MS Trt): E(MS Trt) = E(SSTR / (L-1))

Next, we can express SSTR in terms of the Ti's as follows:

SSTR = ∑n(T.)2/R - (T..)2/N= 1/R ∑Ti2n - (T..)2/N

We can then substitute this expression into the expression for MS Trt:

MS Trt = SSTR / (L-1)

Substituting SSTR = 1/R ∑Ti2n - (T..)2/N, we get:

MS Trt = [1/R ∑Ti2n - (T..)2/N] / (L-1)

Simplifying the expression, we get:

MS Trt = [1/R ∑Ti2n] / (L-1) - [(T..)2/N] / (L-1)E(MS Trt)

= E([1/R ∑Ti2n] / (L-1)) - E([(T..)2/N] / (L-1))

Next, we can apply the linearity of expectation to the two terms:

E(MS Trt) = 1/(L-1) E[1/R ∑Ti2n] - 1/(L-1) E[(T..)2/N]

Simplifying the expression, we get:

E(MS Trt) = 1/(L-1) E(Ti2) - 1/(L-1) [(T..)2/N]

We note that E(Ti) = 0 for all i, since the treatments are assumed to have no effect on the population mean.

Therefore, we can simplify the expression further:

E(MS Trt) = E(Ti2) / (L-1) - [(T..)2/N] / (L-1)

Substituting the expression for Ti2 from the model, we get:

E(MS Trt) = σ2 + m∑Ti2 / (L-1)(R-1) - [(T..)2/N] / (L-1)

Simplifying the expression, we get:

E(MS Trt) = σ2 + m∑Ti2 / (L-1)

Since we have derived the expected value of MS Trt in terms of the Ti's, we can now use this result to derive E(MS Err). By definition, we have E(MS Err) = σ2.

Therefore, the expected value of the treatment mean square for a completely randomized design experiment is given by E(MS Trt) = σ2 + m∑Ti2 / (L-1). When Ti = 0 for all i, the treatments have no effect on the population mean, and hence all the observations will be independent and identically distributed with a common variance. Therefore, the experiment reduces to a randomized complete block design with one block, and the standard analysis of variance can be used to estimate the treatment effects.

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Answer:

The profit function P(x) is defined as the difference between the revenue function R(x) and the cost function C(x): P(x) = R(x) - C(x). Substituting the given functions for R(x) and C(x), we get:

P(x) = (-31.72x^2 + 2030x) - (-126.96x + 26391) = -31.72x^2 + 2156.96x - 26391

To find the maximum profit, we need to find the vertex of this quadratic function. The x-coordinate of the vertex is given by the formula x = -b/(2a), where a = -31.72 and b = 2156.96. Substituting these values into the formula, we get:

x = -2156.96/(2 * (-31.72)) ≈ 34

Substituting this value of x into the profit function, we find that the maximum profit is:

P(34) = -31.72(34)^2 + 2156.96(34) - 26391 ≈ $4,665

The selling price of the dog food is given by the revenue function divided by x: R(x)/x = (-31.72x^2 + 2030x)/x = -31.72x + 2030. Substituting x = 34 into this equation, we find that the selling price of the dog food should be set to:

-31.72(34) + 2030 ≈ $92

So, the maximum profit of $4,665 can be made when the selling price of the dog food is set to $92 per bag.

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.

Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.

A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.

You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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the difference between the approximation and the actual value of f′(0.5)

is D) 1

To approximate f'(0.5) using the given table, we can use the finite difference approximation. The finite difference approximation of the derivative is calculated as:

f'(0.5) ≈ (f(1) - f(0)) / (1 - 0)

Given the values in the table:

f(0) = 1

f(1) = 2

Plugging these values into the finite difference approximation formula:

f'(0.5) ≈ (2 - 1) / (1 - 0) = 1 / 1 = 1

what is derivative?

In mathematics, the derivative represents the rate at which a function changes as its input (usually denoted as x) changes. It measures the instantaneous rate of change of a function at a particular point. Geometrically, it corresponds to the slope of the tangent line to the graph of the function at that point.

The derivative of a function f(x) is denoted as f'(x) or dy/dx and is calculated by taking the limit of the difference quotient as the change in x approaches zero:

f'(x) = lim Δx→0 [f(x + Δx) - f(x)] / Δx

The derivative provides important information about the behavior of a function, such as whether it is increasing or decreasing, concave up or concave down, and the location of extrema (maximum and minimum points). It is a fundamental concept in calculus and is widely used in various fields of mathematics, science, engineering, and economics to analyze and solve problems involving rates of change and optimization.

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Answer:

B

Step-by-step explanation:

\(\boxed{area \: of \: sector = \frac{1}{2} {r}^{2} θ }\)

Radius= diameter ÷2

r= 32 ÷2

r= 16

\( \frac{1}{2} {r}^{2} θ = \frac{512\pi}{3} \)

Substitute r= 16,

\( \frac{1}{2} ( {16}^{2} )(θ) = \frac{512\pi}{3} \)

\(128 \: θ = \frac{512\pi}{3} \\ θ = \frac{512\pi}{3} \div 128 \\ θ = \frac{512\pi}{384} \)

Divide the denominator and numerator by 128:

\(θ = \frac{4\pi}{3} \)

Thus, the answer is B.

Answer:

-9/6 divided by -1/8 equals 12

Step-by-step explanation:

. A negative divided by a negative is a positive so... 9/6 divided by 1/8

. To divide by a fraction, multiply by the reciprocal of that fraction so... 9/6 times 8

. Reduce the fraction with 3 so... 3/2 times 8

. Reduce the numbers with the greatest common factor 2 so... 3 times 4

. Multiply the numbers so... 3 times 4 equals 12

Answer:

0.06

Step-by-step explanation:

To find the particular solution that satisfies the given differential equation and initial condition, we need to integrate the derivative of f(x) with respect to x to obtain the function f(x).

Given: f'(x) = 7x and f(0) = 6

Integrating f'(x) with respect to x:

∫7x dx = (7/2)x^2 + C

Here, C represents the constant of integration.

To find the value of C, we can use the initial condition f(0) = 6:

f(0) = (7/2)(0)^2 + C

6 = C

Therefore, C = 6.

Substituting the value of C back into the integrated function, we have:

f(x) = (7/2)x^2 + 6

Thus, the particular solution that satisfies the given differential equation f'(x) = 7x and initial condition f(0) = 6 is f(x) = (7/2)x^2 + 6.

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Answer:

The two lines are perpendicular.  They have slopes of -(1/3) and 3.

Step-by-step explanation:

See attached graphic for the details and explanation.

Answer:

$8.99

Step-by-step explanation:

1 pound = 16 ounces

y pound = 8 ounces

\(\frac{1}{16} :\frac{y}{8}\)

y · 16 = 1 · 8

16y = 8

16y ÷ 16 = 8 ÷ 16

y = 0.5

0.5 pound = 8 ounces

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

1 pound = $17.98

0.5 pound = y

\(\frac{1}{17.98} :\frac{0.5}{y}\)

y · 1 = 17.98 · 0.5

y = $8.99

The amount of zinc in the chemical compound is 60 grams.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

In a chemical compound there are 3 parts zinc for every 16 parts copper by mass a piece of the compound contains 320 grams of copper.

Now,

Since, The ratio of zinc and copper is,

Zn : Cu = 3 : 16

And, The available mass a piece of the compound contains 320 grams of copper.

So, We can formulate;

⇒ 3 / 16 = Zn / 320

⇒ Zn = 0.1875 × 320

⇒ Zn = 60 grams

Thus, The amount of zinc in the chemical compound is 60 grams.

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The number of triangles that can be formed from a common vertex on the polygon shown is three triangles.

To form triangles on polygons, you can draw diagonals connecting the vertices of the polygon. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. By drawing diagonals, you can create triangles within the polygon.

From a hexagon, we can draw three diagonals from each vertex. So, from a common vertex, we can draw three diagonals and form three triangles. Since there are six vertices in a hexagon, we can choose any one of these vertices as the common vertex and form three triangles.

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In between 2 and 2.5 seconds, the rock lands.

Because the zero is included in the range from 0.4 to -10.6, the ground level is when h(t) = 0. Therefore, the issue is the question of when, in terms of time, does the rock touch the ground. We just need to search for t-values between 0.4 and -10.6.

t            h(t)

0           20

0.5        18.8

1             15.1

1.5          9

2            0.4

2.5        -10.6

3           -24.1

Therefore, the issue is the question of when, in terms of time, does the rock touch the ground. We just need to search for t-values between 0.4 and -10.6.

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Answer:

2, 2.5

Step-by-step explanation:

Answer:

\((a)\ Area = 24in^2\)

\((b)\ Area = 60in^2\)

Step-by-step explanation:

Given

See attachment for the dimension of the block

Solving (a): Area of the front face

From the attachment, the front face has the following dimension.

\(Length = 4in\)

\(Width = 6in\)

The area is calculated as:

\(Area = Length *Width\)

\(Area = 4in * 6in\)

\(Area = 24in^2\)

Solving (b): Area of the top and bottom faces

The top and bottom faces have the same dimension

From the attachment, the top face has the following dimension.

\(Length = 5in\)

\(Width = 6in\)

The area of the top is calculated as:

\(Area = Length *Width\)

\(A_1 = 5in * 6in\)

\(A_1 = 30in^2\)

The area of the top and the bottom faces is:

\(Area = 2 *A_1\) ---- because the top and bottom faces have the same dimension

\(Area = 2 *30in^2\)

\(Area = 60in^2\)

The equation of the line in point-slope form is y + 3 = (1/2)(x - 6), and in slope-intercept form is y = (1/2)x - 6.

To write the equation of a line in point-slope form and slope-intercept form given a point (6, -3) and a slope of 1/2:

1. Point-Slope Form:

The point-slope form of a linear equation is given by: \(y - y_1 = m(x - x_1)\), where (\(x_1, y_1\)) is a point on the line and m is the slope.

Substituting the values into the equation:

y - (-3) = 1/2(x - 6)

y + 3 = 1/2(x - 6)

2. Slope-Intercept Form:

The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

Using the given slope (1/2) and the point (6, -3), we can solve for the y-intercept (b).

-3 = (1/2)(6) + b

-3 = 3 + b

b = -6

The equation in slope-intercept form is:

y = 1/2x - 6

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