x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
General process of solving for an unknown angle.
1. Determine the type of angle: Determine whether the angle is a right angle (90 degrees), acute (less than 90 degrees), or obtuse (greater than 90 degrees).
2. Use geometric properties: If there are geometric properties or relationships given in the problem, such as angles formed by parallel lines or within a triangle, apply those properties to find the value of x.
3. Apply trigonometric functions: If the problem involves trigonometry, use sine, cosine, or tangent functions along with the given information to solve for x.
4. Apply algebraic equations: If there is an algebraic equation involving x, set up the equation and solve for x by isolating it on one side of the equation.
To find the value of x in the given triangle, we can use the inverse tangent function, which is tan^-1.
tan(x) = opposite/adjacent
tan(x) = 5/14
To isolate x, we take the inverse tangent of both sides:
x = tan^-1(5/14)
Using a calculator, we can find that x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
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This coordinate plane represents an area on a golf course. A sand hazard is located at (4, 6) and a water hazard is located at (7, 2).
Plot a point at each of the two locations. Plot only two points.
Answer:
See attached
Step-by-step explanation:
You want a graph with points plotted at (4, 6) and (7, 2), representing a sand trap and a water hazard, respectively.
CoordinatesThe ordered pair (4, 6) represents the coordinates (x, y). The x-coordinate is the number of units right of the point x=0, and the y-coordinate is the number of units up from y=0.
Both points have positive coordinates for both x and y, so will be located up and right from the origin. The plot is shown in the attachment.
<951414049393>
the sales tax rate in your city is 7.5%. What is the total amount you pay for a $6.84 item.
Answer:
$7.35
Step-by-step explanation:
Pythagorean theorem
I need help with my math
The height of the flagpole is 26.0 feet.
What is height?
Height is the vertical distance between two points.
To calculate the height of the flagpole, we use the formula below.
Formula:
h = √(l²-d²)............... Equation 1Where:
h = Height of the flagpolel = Length of the wired = Distance of the wire from the ground to the base of the poleFrom the question,
Given:
l = 300 feetd = 15 feetSubstitute these values into equation 1
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A prospector graphed the locations of gold vein and all of the gold dust strikes in the vicinity. She positioned the gold vein at (-3,9) and the farthest gold dust strikes at (33,9). If each unit on the graph represents 1 mile then how far away from the gold vein is the farthest gold dust strike?
Answer:
Step-by-step explanation:
The gold vein is at (-3,9) and the farthest gold dust strike is at (33,9). The distance between the two points is 36 miles.
PLEASE HELP WILL GIVE BRAINLEST !!!!
The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 40 who smoke. Step 2 of 2: Suppose a sample of 1089 Americans over 40 is drawn. Of these people, 806 don't smoke. Using the data, construct the 85% confidence interval for the population proportion of Americans over 40 who smoke. Round your answers to three decimal places
To construct a confidence interval for the population proportion of Americans over 40 who smoke, we can use the formula:
Confidence Interval = Sample Proportion ± (Critical Value) x Standard Error
where the sample proportion is the number of individuals who don't smoke divided by the total sample size (806/1089), the critical value can be found using a normal distribution table or calculator with the given confidence level (85%), and the standard error can be calculated using the formula:
Standard Error = √[ (Sample Proportion x (1 - Sample Proportion)) / Sample Size ]
Plugging in the given values, we get:
Sample Proportion = 806/1089 = 0.740
Sample Size = 1089
Standard Error = √[(0.740 x 0.260) / 1089] = 0.016
Critical Value (using a normal distribution table or calculator) = 1.440
Therefore, the 85% confidence interval for the population proportion of Americans over 40 who smoke is:
0.740 ± (1.440 x 0.016) = 0.740 ± 0.023
Rounding to three decimal places, the confidence interval is (0.717, 0.763). This means that we can be 85% confident that the true proportion of Americans over 40 who smoke falls between 71.7% and 76.3%.
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Doors&Windows, Inc. Makes, you guessed it, doors and windows. Each day, Doors&Windows orders 6,150 linear feet of framing material and has a few staff member who are able to work a collective 600 hours. For each window, Doors&Windows profits $40 requiring 6 labor hours and 30 linear feet of framing material. For each table, Doors&Windows profits $90 requiring 10 labor hours and 120 linear feet of framing material. Due to the availability of glass, they can only produce a maximum of 70 windows. When formulating this problem as a linear programming model, what are the decision variables?
Decision variables in Doors&Windows linear programming model.
How to formulate linear programming?The decision variables in the linear programming model for this problem are the number of windows (W) and the number of tables (T) that Doors&Windows should produce to maximize their profit while meeting the constraints. The objective function to maximize would be the total profit, which can be expressed as 40W + 90T. The constraints include the available linear feet of framing material (6150) and labor hours (600), which can be written as 30W + 120T ≤ 6150 and 6W + 10T ≤ 600, respectively. Additionally, the maximum number of windows that can be produced (W ≤ 70) due to glass availability is also a constraint. These decision variables and constraints can be used to create a linear programming model to optimize Doors&Windows' production and profit.
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|x-6|=-10
thanks in advance
Answer:
I guess you need the value of (x) if that's so then
x= -4
Step-by-step explanation:
Ration Recone
Question 4
Name and describe the transformation of Figure Q to Figure R.
Reflection Figure Q was flipped
over the y-axis, the line of reflection
Translation. Figure Q slid 6 units to
the right to Figure R.
Reflection Figure Q was flipped
over the x-axis, the line of reflection.
Fig
Fig R
Translation. Figure Q slid 4 units to
the right to Figure R.
Q to R transformation: Reflection, translation.
How were Figure Q and Figure R transformed?The transformation of Figure Q to Figure R involves a combination of reflection and translation. Firstly, Figure Q was flipped over the y-axis, which means that all the points of the figure on the left side of the y-axis were moved to the right side and vice versa.
Then, the figure was translated 6 units to the right, resulting in Figure R. Secondly, Figure Q was flipped over the x-axis, which means that all the points of the figure above the x-axis were moved below it and vice versa.
Finally, the figure was translated 4 units to the right, resulting in Figure R. These transformations are important in geometry as they allow us to create new figures that are related to the original ones.
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Jordy needs 20 cups of a certain shade of green paint. jordy created the shade of green paint by mixing 1/2 t of yellow paint with 1/3 t of blue paint. how many cups of yellow paint and how many cups of blue paint does jordy need?
The total number of yellow cups and blue cups paint that Jordy need is 10 t and (20/3) t, under the condition that he created the shade of green paint by mixing 1/2 t of yellow paint with 1/3 t of blue paint.
Here we have to apply the principles regarding basic multiplication of fraction.
Now to get 20 cups of green paint, Jordy requires 10 cups of yellow paint and 20/3 cups of blue paint.
Then the process of evaluating the number of blue paint cups needed is
Jordy created the shade of green paint by mixing 1/2 t of yellow paint with 1/3 t of blue paint.
To get 1 unit of green paint, Jordy needs 1/2 t of yellow paint and 1/3 t of blue paint.
To get 20 units of green paint,
Jordy needs
20 ×(1/2) t = 10 t of yellow paint
20 ×(1/3) t = (20/3) t of blue paint.
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A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
He concludes that she is not running fast enough to exceed her fastest time.
What errors did the coach make? Check all that apply.
He used an incorrect time ratio converting hours to minutes.
His units do not cancel.
He used an incorrect distance ratio converting miles to feet.
He incorrectly concluded that she is not running fast enough.
He cannot determine her average rate in miles per hour after only 15 minutes.
In a case whereby A bike wheel is 26 inches in diameter the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters) the the diameter is 660.4mm
How can the diameter be calculated?Note; the bike man do not make any calculation, so we can not know mat be he make any mistake.
Since the bike wheel is 26 inches in diameter then we can calculate the diameter of the bike wheel through the multiplication of the two numbers.
Diameter in milimeters = ( 26.0 x 25.4)
Diameter in milimeters = 660.4 mm.
Hence diameter of the bike wheel in millimeters will be 660.4.
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Mrs. Ross is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 902 books had no damage, 80 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 30,000 books in the collection should Mrs. Ross expect to have no damage? Round your answer to the nearest whole number. Do not round any intermediate calculations. Books 5 ? X
There would be 26,790 books. of the 30,000 books in the collection should Mrs. Ross expect to have no damage
Out of the random sample, 902 books had no damage. To estimate the number of books with no damage in the entire collection of 30,000 books, we can use the proportion of books in the sample that had no damage.
The proportion of books in the sample with no damage is:
902 / (902 + 80 + 43) = 0.893
Therefore, we can expect approximately:
30,000 x 0.893 = 26,790
books in the collection to have no damage. Rounded to the nearest whole number, the answer is:
26,790 books.
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I’m giving 10 points.
Answer:
12
Step-by-step explanation:
-3(b - 5) + 7a - (9 - a) ^6 a = 7 and b = -4
-3(-4 - 5) + 7(7) - (9 - 7)^6
= -3(-9) + 49 - (2)^6
= 27 + 49 - (64)
= 27 + 49 - 64
= 76 - 64
= 12
15. Given that M ={x:x^2-5x+2x+8=0}
show that
P(A)= (1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}.
The powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
Given that, M = {x: x² - 5x + 2x + 8 = 0}
This is a quadratic equation and it can be written in the form of (x - a)(x - b) = 0, where a and b are the roots of the equation.
Substituting x² - 5x + 2x + 8 = 0 in (x - a)(x - b) = 0, we get
(x - a)(x - b) = (x - (-3))(x - 5) = 0
Therefore, the roots of the equation are a = –3 and b = 5.
Now, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
Here,
(1, 2) represents the set containing only the root ‘–3’,
(2, 1) represents the set containing only the root ‘5’,
(2, 4) represents the set containing both the roots
Therefore, the powerset of M can be written as P(M) = {(1, 2), (1, 4), (2, 1), (2, 4), (2, 4, 1), (1, 4), (4, 2}, {}}.
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Estimate first, then compute Increase $120 by 160% and give the total. Estimate: Calculate:
The estimate increase for $120 by 160% is 192. The calculated increase for $120 by 160% is 192.
What is percent?Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase "per centum", which means "per hundred". Percentages are often used to describe a part of a whole. Percentages are used in many areas of life, such as finance, business, and statistics. They are used to calculate interest rates, taxes, discounts, and many other important figures.
Here,
Estimate: To estimate 160% of 120, we can first find 10% of 120, which is 12. Then, we can find 100% of 120 by multiplying 12 by 10, which is 120. Finally, we can add 60% of 120, which is 72 (since 60% is 6 times 10%), to get an estimate of 192.
Calculate: To calculate 160% of 120, we can first convert the percentage to a decimal by dividing it by 100, which gives us 1.6. Then, we can multiply 120 by 1.6 to get:
120 x 1.6 = 192
So the total increase is 192.
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Which statement about the transformation is true? it is rigid because all side lengths and angles are congruent. It is rigid because no side lengths or angles are congruent. It is nonrigid because all side lengths are congruent. It is nonrigid because no side lengths or angles are congruent.
The statement "It is rigid because all side lengths and angles are congruent" is true.
In mathematics, a transformation is considered rigid if it preserves distances and angles. For example, a translation, rotation, or reflection is a rigid transformation because it preserves distances and angles. If a transformation preserves side lengths and angles, then it is considered rigid, regardless of whether the side lengths and angles are congruent or not.
Answer: A. it is rigid because all side lengths and angles are congruent.
Step-by-step explanation: RIGHT ON EDGE 2023
The ingredients for your braised greens cost $1.32. you sell it for $4. what is your contribution margin?
select one:
a.
$2.68
b.
$4
c.
$3.18
d.
0.31
The contribution margin for braised greens is $2.68.
The contribution margin is a financial metric that helps businesses determine the profitability of a product or service. It represents the amount of revenue that is left over after deducting the variable costs of producing that product or service.
In this case, the ingredients for the braised greens cost $1.32, and the selling price is $4, so the contribution margin would be $2.68 ($4 - $1.32 = $2.68).
This means that for every sale of the braised greens, the business earns $2.68 towards covering fixed costs and generating profit. By calculating the contribution margin, businesses can determine the pricing strategy that is necessary to achieve their desired profit margins while remaining competitive in the market.
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I want solve this help me
Using circle theorems the angles in triangle ΔABM are
∠BMA = 30°∠BAM = 30° and∠ABM = 120°What are circle theorems?Circle theorems are theorems that govern circle peoperties
To find the angles in triangle ABM, we notice that in ΔABO, since OB = OA (radius of the circle), then ΔABO is an isoceles triangle.
So, ∠OAB = ∠ABO (Base angles of an isoceles triangle)
Now, ∠OAB = ∠ABO = ∠A = 30°
Also ∠OAB + ∠ABO = ∠BOM (sum of opposite interior angles)
30° + 30° = ∠BOM
∠BOM = 60°
Now since OB is the radius and touches MV at B, and thus perpendicular to it. so, ∠OBM = 90°
Now, ∠OAB + ∠OBM = ∠ABM
30° + 90° = ∠ABM
∠ABM = 120°
Now in triangle ΔABM
∠BAM + ∠ABM + ∠BMA = 180° (sum of angles in a triangle)
Now
∠BAM = ∠OAB = 30°, ∠ABM = 120°So, making ∠BMA subject of the formula, we have that
∠BMA = 180° - ∠BAM + ∠ABM
So, substituting the values of the variables into the equation, we have that
∠BMA = 180° - ∠BAM + ∠ABM
∠BMA = 180° - 30° - 120°
∠BMA = 180° - 150°
∠BMA = 30°
So, the angles are
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The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters, how long is the gauge needle? Round to the nearest centimeter.
a.) 2cm
b.) 3cm
c.) 4cm
d.) 5cm
The value of the gauge needle is, 9.01 cm
Given that;
The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters.
Now, We can formulate;
A = θ/360 πr
10.6 = (135/360) 3.14 x r
3816 = 423.5r
r = 9.01
Thus, The value of the gauge needle is, 9.01 cm
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This table represents rico's check register. a transfer of $30.00 was made on august 15 from his savings account into his checking
account
how should the august 15th transaction be recorded on his check register?
This will ensure that his check register accurately reflects his current account balance and transaction history.
This table represents Rico's check register, and on August 15th, he made a transfer of $30.00 from his savings account into his checking account.
To record this transaction on his check register, Rico should enter it as a deposit in his checking account column, and also include a note indicating that the deposit was a transfer from his savings account.
This will ensure that his check register accurately reflects his current account balance and transaction history.
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According to these three facts, which statements are true? Circle D has center (2, 3) and radius 7. Circle F is a translation of circle D, 2 units right. Circle F is a dilation of circle D with a scale factor of 4. Select each correct answer. Responses Circle F and circle D are similar. Circle , F, and circle , D, are similar. The radius of circle F is 28. The radius of circle , F, is 28. The center of circle F is (0, 3). The center of circle , F, is , begin ordered pair 0 comma 3 end ordered pair,. Circle F and circle D are congruent. Circle , F, and circle , D, are congruent
Answer:
The answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
Step-by-step explanation:
How to find the radius:
A = π × [tex]r^{2}[/tex]
But the radius of a circle from diameter. If you can recall the diameter d, the radius is r = d / 2.
By looking at our facts we can actually see ( if we use the comparing method ) that the circles, F & D are very much similar.
Thus the answer to your problem is:
The radius of circle F is 28.
Circle F and circle D are similar.
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What is the value of x in degrees?
Please show work if you can!
Answer: 72
Step-by-step explanation:
Q is same as M = 72
N=36
L=x
All 3 angles of a triangle add to 180
72+36+x=180
x=72
The probability of an event is given. Find the odds in favor of the event.
0. 5
The odds in favor of the event are 1.
The probability of an event is the ratio between the total number of favorable outcomes and the total number of outcomes.
The odds in favor of an event are the ratio of the total number of favorable outcomes and the total number of unfavorable outcomes. If the probability of the event is given, we can find the odds in favor by using the formula of odds in favor:
odds in favor = probability of event/probability of not event
In this case question, the probability of an event is given as 0.5 which means that the total number of favorable outcomes is 50 out of 100
So the probability of not having an event is also 0.5 (the other half of the part.)
So, odds in favor = 0.5/0.5 = 1
The probability of the happening of an event is the same as the probability of not happening of an event. This means that the odds in favor of the event are 1 to 1, or simply 1.
Therefore, the odds in favor of the event are 1.
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If you charge more than your limit in your credit card
If you charge more than your limit on your credit card, you will likely face several consequences, including:
1. Over-limit fees: Many credit card companies charge a fee if you exceed your credit limit. This fee can vary depending on the issuer, but it's typically around $25 to $35.
2. Increased interest rates: If you go over your credit limit, your credit card company may increase your interest rate, making it more expensive to carry a balance on your card.
3. Lower credit score: Exceeding your credit limit can negatively impact your credit score, as it's an indication of risky financial behavior.
4. Reduced credit availability: Your credit card company may reduce your credit limit if you consistently go over the limit, making it harder for you to access credit in the future.
5. Declined transactions: If you're significantly over your limit, your credit card company may start declining transactions to prevent further over-limit spending.
To avoid these consequences, it's important to monitor your spending and ensure you stay within your credit limit. If you find yourself consistently approaching your limit, consider requesting a credit limit increase or using other methods to manage your spending.
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A rectangular box will have a square cross section and a volume of 500 cubic centimeters. A. Sketch the box and sketch a net for the box. Assume the box will have an open top. Label the dimensions. B. Using w for the width and h for the height, find an expression in h and w for w the surface area of the box. C. Find the width and height that will make the surface area as small as possible
The expression for the surface area of the box is if w is A = x² + 2(xh) + 2(h²) the width of the box and h is the height. The dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.
The sketch of the box and the sketch of the net of the box is attached below. The box has a square base of side length x, and height h. The volume of the box is given as 500 cubic centimeters, therefore
x × x × h = 500
The surface area of the box can be found by summing the areas of each of the six faces. The top face is a square of side length x, so its area is x². The other five faces are all rectangles. The area of each of these rectangles is given by its length times its width. Therefore, the surface area of the box is
A = x² + 2(xh) + 2(h²)
To find the dimensions that minimize the surface area, we can use calculus. We can first solve the equation for x in terms of h
x² = 500/h
x = √(500/h)
Substituting this expression for x into the equation for the surface area, we get
A = 500/h + 2h×√(500/h) + 2h²
We can find the derivative of this expression with respect to h
dA/dh = -500/h² + sqrt(500/h) - 4h
Setting this derivative equal to zero and solving for h, we get
-500/h² + sqrt(500/h) - 4h = 0
Using a calculator or computer, we can find that this value is approximately 6.19. Substituting this value back into the equation for x, we get
x = √(500/6.19) ≈ 11.68
Therefore, the dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.
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What is the osmotic pressure for a 4. 50% by a mass aqueous solution of glucose (C6H12O6) at 300 K?
The osmotic pressure for a 4.50% by mass aqueous solution of glucose (C6H12O6) at 300 K is 0.616 atm.
To calculate the osmotic pressure of a solutionWe can use the equation:
π = MRT
where:
π = osmotic pressure
M = molarity of the solution
R = gas constant
T = temperature in Kelvin
We must translate the proportion by mass to molarity in order to determine the molarity of the glucose solution. Glucose (C6H12O6) has a molecular weight of 180 g/mol.
So, for a 4.50% by mass solution of glucose, we have:
4.50 g glucose / 100 g solution = (4.50 g glucose / 180 g/mol) / (Molarity of solution)
Solving for molarity, we get:
Molarity of solution = 0.025 mol/L
Now we can plug in the values into the equation for osmotic pressure:
π = (0.025 mol/L) * (0.0821 L atm / mol K) * (300 K)
π = 0.616 atm
Therefore, the osmotic pressure for a 4.50% by mass aqueous solution of glucose (C6H12O6) at 300 K is 0.616 atm.
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Eric throws a biased coin 10 times. He gets 3 Tails. Sue throws the same coin 50 times. She gets 20 Tails. Aadi is going to throw the coin once. (i) Which one of the following statements is correct about the probability of Aadi getting Tails? (1) A Sue's estimate is best because she throws it 50 times. B Sue's estimate is best because she gets more Tails. C Sue's estimate is best because she throws it more times than Eric (ii) Use Eric's and Sue's results to work out an estimate for the probability that Aadi will get Tails. Write your fraction in the form a/b (1)
(i) The correct statement about the probability of Aadi getting Tails is B - Sue's estimate is best because she gets more Tails. The number of times a coin is flipped affects the accuracy of the probability estimate, but getting more Tails in fewer trials does not necessarily mean that the probability of getting Tails is higher.
(ii) Eric got 3 Tails in 10 trials, so the proportion of Tails is 3/10. Sue got 20 Tails in 50 trials, so the proportion of Tails is 20/50 or 2/5. We can use the average of these two proportions as an estimate for the probability that Aadi will get Tails.
(3/10 + 2/5) / 2 = 0.35
So the estimated probability of Aadi getting Tails is 0.35 or 7/20 in fraction form.
SIMPLIFYYY THIS EXPRESSION
Answer:
x - 5y
Step-by-step explanation:
6x - 8y - 5x + 3y =
= 6x - 5x - 8y + 3y
= x - 5y
Answer:
1x + 11y
Step-by-step explanation:
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a.) the equation for g(x) is g(x) = 1.1x + 1.1
b.) The equation for g(x) is x = 10 which is the equation for a vertical line passing through (10, 15).
How do we calculate?An equation for g(x) in point-slope form is:
y - 15 = m(x - 10)
We have that g(x) = f(x) = -11 and that g(x) passes through the point (-1, 0),
use point-slope form to write the equation for g(x):
y - 0 = (-11)(x - (-1))
We simplify and then solve for y
y = -11x - 11
In conclusion, the equation for g(x) in slope-intercept form is:
g(x) = -11x - 11
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What are the slopes and y-intercept of a graph?
The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.
The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.
The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.
Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.