Answers
Answer: [tex]\frac{10\sqrt{3}}{3}[/tex]
Step-by-step explanation:
To find this use TOA which is Tan = Opposite/Adjacent
so we have tan(30°) = y/10 and to isolate the "y" we multiply both sides by 10 to get 10tan(30°) = y
where y = [tex]\frac{10\sqrt{3}}{3}[/tex]
Related Questions
A worker is connecting a cable from the roof top of a school to a fence pole 7 ft away. The pole is 10 ft high. He uses 25 ft of cable to reach from the rooftop to the fence pole. How tall is the school? Show your steps taken to arrive at your answer.
Answers
The height of the school is given as follows:
34 ft.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The height of the school for this problem is given as follows:
h = x + 10 ft.
In which segment x is one of the sides of a right triangle, in which the other side is of 7 ft and the hypotenuse is of 25 ft, hence:
x² + 7² = 25²
x = sqrt(25² - 7²)
x = 24 ft.
Hence the height of the school is of:
24 ft + 10 ft = 34 ft.
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If an object lies below the horizontal plane and behind the vertical plane, what is its location?
A.
2nd Quadrant
B.
1st Quadrant
C.
4th Quadrant
D.
3rd Quadrant
E.
on the reference line
Answers
Answer:
third quadrant
its position with respect to reference planes will be behind Vertical Plane and below the Horizontal Plane.
The given figure shows different positions and their respective views
Find the union of each of the following pairs of the sets P={a,b,c,d} Q={a,e,i,o,u}
Answers
The union of the sets is written as;
P∪Q = { a, b, c, d,e , i, o, u}
How to determine the setFirst, we need to know that;
These signs of sets represents;
∩ represents the intersection of sets, where the common elements of the two or more sets are determined.∪ represents the union of sets where all the elements of the sets are written without repetition of elements.From the information given, we have that;
P={a,b,c,d}
Q={a,e,i,o,u}
The union of the sets is written as;
P∪Q = { a, b, c, d,e , i, o, u}
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Two identical trains, each with 31 cars, are traveling in opposite directions. When car Number 19 of one train is opposite car Number 19 of the other, which car is opposite car Number 12?
Answers
Car 12 of Train B is also 12 cars away from Car 19 on Train B.
How to explain the informationSince each train boasts 31 cars, we can ascertain the total amount of vehicles between Car 19 and Car 12 on Train A:
31 - 19 = 12
Thus, Car 12 on Train A is a dozen units distant from Car 19 on Train A.
Nevertheless, Train B is furthermore moving in an inverring direction and has its exclusive set of automobiles between Car 19 and Car 12. We comprehend that the matching figure of cars must be amongst Car 19 and Car 12 on Train B as with Train A.
In essence, Car 12 of Train B is also 12 cars away from Car 19 on Train B.
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In order to increase customer service, a muffler repair shop claims its mechanics can replace a muffler in 13 minutes. A time management specialist selected six repair jobs and found their mean time to be 12.3 minutes. The standard deviation of the sample was 2.3 minutes. At α=0.05, is there enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes?
Answers
There is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.
To determine whether there is enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes, we can conduct a one-sample t-test with the following hypotheses:
Null hypothesis: The true mean time in changing a muffler is equal to 13 minutes.
Alternative hypothesis: The true mean time in changing a muffler is less than 13 minutes.
Use the formula to calculate the test statistic,
[tex]t = \dfrac{(x - \mu)} { \dfrac{s} { \sqrt{n}}}[/tex]
where x is the sample mean, μ is the hypothesized population mean (13 minutes), s is the sample standard deviation, and n is the sample size (6).
Plugging in the numbers, we get:
t = (12.3 - 13) / (2.3 / √6) = -0.72
Using a t-distribution table with 5 degrees of freedom (n - 1), we find that the critical value for a one-tailed test with α = 0.05 is -2.571. Since our calculated t-value (-0.72) is greater than the critical value, we fail to reject the null hypothesis.
Therefore, there is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.
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7.6.AP-6
Find the surface area of the prism.
The surface area is
(Type an integer or a decimal.)
4 m
3.7 m-
3m
4 m
3.2 m
Answers
The Total surface area of the given prism is: 46.3 sq.m
What is the surface area of the prism?The surface area of the prism is gotten by finding the areas of all surfaces and adding up to get the total surface area. Thus:
We know that formula to find the area of a triangle is:
Area of triangle = ¹/₂*base*height
Area of rectangle = length * width
Thus:
Total surface area = 2(¹/₂* 3 * 3.7) + 2(4 * 3.2) + (3 * 3.2)
Total surface area = 11.1 + 25.6 + 9.6
Total surface area = 46.3 sq.m
Thus, that is the total surface area of the given prism with dimensions
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Carla has to construct the following figure using CADD. What value must she enter to construct angle ABX?
A.
50°
B.
40°
C.
120°
D.
130°
E.
180°
Answers
50 degrees is the value must she enter to construct angle ABX.
The given triangle is ABX
We have to find the value Karla has to enter to construct angle ABX.
By the given figure the angle at B is fifty degrees.
The value of ∠ABX is 50 degrees
Hence, 50 degrees is the value must she enter to construct angle ABX.
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4
Based on the March expense statement, what proportion of Maria's total expenses are for her car?
A. Less than one quarter.
B. More than a quarter but less than half.
O C. More than three-quarters.
D. More than half but less than three-quarters.
Auto
Check Number 87
Credit Card March)
Clothing
Marla's Expense 1
Get Card Mash
Food
Credit Card Mesh &
Sends Card March 11
Petal food
Cash Paya
Para Coch
Total
Answers
Based on the March expense statement, the proportion of Maria's total expenses that are for her car is D. More than half but less than three-quarters.
What is the proportion?The proportion refers to a portion or part of a whole number, value, or expression.
Proportions, which are ratios between two values, are depicted in decimals, fractions, or percentages.
The total expenses for March = $507.59
Auto expenses for March = $290.02
Proportion of auto expenses to the total expenses =0.57 ($290.02 ÷ $507.59)
One-half of $507.59 = 0.50 or $253.795)
Three-quarters of $507.59 = 0.75 or $380.69
Since $290.02 is more than $253.795 but less than $380.69, Option D is correct.
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help answer this pls
Answers
Answer:
it is 17.5
Step-by-step explanation:
you add 6.2 and 11.3 equal 17.5
Answer:
≈ 681.38 ft^2 when pi≈ 3.14
Step-by-step explanation:
2(3.14)(6.2^2)+(3.14)(12.4)(11.3)
241.4032+439.9768≈ 681.38
A composite figure is represented in the image.
A six-sided composite figure. A vertical line on the left is labeled 4 meters. The base is labeled 9 meters. There is a small portion from the vertical line that is parallel to the base that is labeled 3 meters. This portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled.
What is the total area of the figure?
a: 75 m2
b: 63 m2
c: 61.5 m2
d: 45 m2
Answers
To find the area of the figure, we need to break it down into simpler shapes. The figure consists of a trapezoid and a right triangle.
The area of the trapezoid is [(base1 + base2) / 2] x height.
The two bases of the trapezoid are 4 m and 9 m + 3 m = 12 m. The height of the trapezoid is 3 m.
Area of the trapezoid = [(4 + 12) / 2] x 3 = 48 m².
The area of the right triangle is (base x height) / 2.
The base of the triangle is 3 m and the height is 3 m.
Area of the triangle = (3 x 3) / 2 = 4.5 m².
The total area of the figure is the sum of the area of the trapezoid and the area of the triangle.
Total area = 48 + 4.5 = 52.5 m².
Therefore, the closest option is c: 61.5 m².
SQUARES The area of a square y can be modeled by the function y = x², where x is
the side length of the square. The perimeter of a square can be modeled by the
function y = 4x.
a. Solve the system of equations algebraically.
b. If the area of a square in square units is equal to the perimeter of the square in
units, what is the side length of the square? What are the area and perimeter of
the square?
Answers
y = x² (equation 1)
y = 4x (equation 2)
Substituting equation 1 into equation 2, we get:
x² = 4x
Rearranging and factoring, we get:
x(x - 4) = 0
Therefore, x = 0 or x = 4. However, a square cannot have a side length of 0, so the only solution that makes sense is x = 4.
Substituting x = 4 into equation 1, we get:
y = 4² = 16
Therefore, the side length of the square is 4 units, the area of the square is 16 square units, and the perimeter of the square is 4x4 = 16 units.
b. If the area of the square is equal to its perimeter, then we can set the two equations equal to each other:
x² = 4x
Rearranging and factoring, we get:
x(x - 4) = 0
Therefore, x = 0 or x = 4. However, a square cannot have a side length of 0, so the only solution that makes sense is x = 4.
Therefore, the side length of the square is 4 units, the area of the square is 16 square units, and the perimeter of the square is 4x4 = 16 units.
Aleks topic data analysis and probability really need help with this
Answers
To draw the histogram we have to find the frequency of the data
Here are the heights of a sample of 15 adults
66,71,76,63,75,77,74,73,64,62,78,80,67,72,68
We have to draw the histogram by taking height on x axis
Let us find the frequency of given heights
62-66 , the frequency is 4
67-71, the frequency is 3
72-76, the frequency is 5
77-81 , the frequency is 3
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What is the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815?
Answers
Answer:
Step-by-step explanation:
To calculate the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815, you can use the following formula1:
Rate of Return = (Proceeds - Cost - Commission) / Cost
where Proceeds is the amount received from selling the shares, Cost is the amount paid for the shares, and Commission is the commission paid on the sale1. Plugging in the values, we get:
Rate of Return = (815 - (35 * 20) - 6) / (35 * 20) = 0.2875
Multiplying by 100 to convert to a percentage, we get a rate of return of 28.75%1.
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account. To achieve this goal, how much money does the couple need to have in this account by the time they retire?
Answers
The amount (present value) that the couple needs to have in this retirement account by the time they retire in 35 years to enable them withdraw $6,000 monthly for 25 years is $777,387.14.
How is the present value determined?The amount in 35 years' time when the couple retire that they should have can be described as the present value (in 35 years).
Based on the above conclusion, the present value can be determined using an online finance calculator as follows:
With the monthly withdrawal of $6,000 and compounded interest of 8% APR monthly, the future value of the account in 60 years' time will be $0.
N (# of periods) = 300 months (25 years x 12)
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = $-6,000
FV (Future Value) = $0
Results:
Present Value in 35 years (PV) = $777,387.14
Sum of all periodic payments = $-1,800,000 ($-6,000 x 300 months)
Total Interest = $1,022,612.86
Thus, the couple should save up to $777,387.14 in 35 years' time when they retire to achieve their goal.
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i need help with the last two i cant get it
Answers
a) There are no values of x for which h'(x) is undefined.
b) The critical numbers of h(x) = sin²(x) + cos(x) in the domain 0 < x < 2π are x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers.
a) To find the values of c for which h'(c) = 0 or is undefined, we first need to find the derivative of h(x):
h'(x) = 2sin(x)cos(x) - sin(x)
Now we can set h'(x) equal to 0 and solve for x:
2sin(x)cos(x) - sin(x) = 0
sin(x)(2cos(x) - 1) = 0
This equation is satisfied when sin(x) = 0 or 2cos(x) - 1 = 0. The first equation has solutions x = kπ, where k is an integer. The second equation has solutions x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.
Next, we need to check if there are any values of x for which h'(x) is undefined. Since h'(x) is a combination of sin(x) and cos(x), it is defined for all values of x in the given domain.
b) The critical numbers of h(x) are the values of x at which h'(x) = 0 or h'(x) is undefined. From part (a), we have the solutions x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers. These are the critical numbers of h(x) in the given domain.
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Evaluate the expression. (7 − 3)!
Answers
Answer: The expression (7 − 3) can be simplified as follows:
(7 − 3) = 4
Therefore, the value of the expression (7 − 3) is 4.
Answer:
Step-by-step explanation:
For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or
Assignment Scoring
Your last submission is used for your score.
8. [0/1 Points) DETAILS PREVIOUS ANSWERS
TANFIN12 5.3.033.
Andrea, a self-employed individual, wishes to accumulate a retirement fund of $500,000. How much should she deposit each month into her retirement account, which pays interest at a rate of
2.5%/year compounded monthly, to reach her goal upon retirement 45 years from now? (Round your answer to the nearest cent.)
Answers
The density of the metal is determined as 6.1 g / cm³.
We have,
The density of the metal is defined as the ratio of the mass per unit volume of the metal.
Mathematically, the formula for density is given as;
ρ = m / V
where;
m is the mass of the metal
V is the volume of the metal
The density of the metal is calculated as follows;
ρ = ( 0.47 kg x 1000 g/kg ) / ( 77 cm³ )
ρ = 6.1 g / cm³
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complete question:
Or this assignment, you submit answers by question parts. The number of submissions remaining for each
ssignment Scoring
our last submission is used for your score.
DETAILS
………….
Compute the density in g/cm³ of a piece of metal that has a mass of 0.470 kg and a volume of 77 cm³.
X g/cm³
Enter a number.
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Submit Answer
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45°F
Mostly cloud
SHIPPS15 1.6.E.019.
Read It
the correct answer.
Which inequality represents the values of that ensure triangle ABC exists?
A
2x+4
B
O D.
18
OA.
<< 1
OB. -< < ¹
O c. 1 < x < 5
6x
2 < < 6
Answers
Using the triangular inequalities we can get:
7/4 < x < 11/2
The image of the triangle is in the image at the end.
Which inequality represents the values of that ensure triangle ABC exists?A triangle with sides A, B, and C must meet the triangular inequality, it says that the sum of any two sides is larger than the other side.
Now, see the triangle attached at the end, the triangular inequalities say that:
18 + 6x > 2x + 4
18 + 2x + 4 > 6x
6x + 2x + 4 > 18
Now simplify these, for each one we will get:
4x > -14 -----> x > -7/2
22 > 4x -----> 11/2 > x
8x > 14 -----> x > 7/4
Using the second two we can get:
7/4 < x < 11/2
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Find the domain of the function represented by the list of ordered pairs below. {(6,7),(−5,−11),(−7,−10),(−2,8)}.
Answers
Let’s take a look
The domain of a function is the set of all possible input values (usually x-values) for which the function is defined.
In this case, we have four ordered pairs: {(6,7),(-5,-11),(-7,-10),(-2,8)}.
The x-values in these ordered pairs are 6, -5, -7, and -2. Therefore, the domain of the function is:
Domain = {6, -5, -7, -2}
So the domain of the function represented by the given list of ordered pairs is {6, -5, -7, -2}.
Use the compound interest formula to determine the final value of the given amount
Answers
The final value of the given amount compounded is $1518.69
Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
[tex]A=P(1+r/n)^n^t[/tex]
where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year & t = time in years.
The given principal is $800 for 11 years & annual interest rate is 6%.
To find the amount compounded annually at 6% for 11 years substituting the given values in the above formula i.e.
Amount = [tex]800(1+0.06)^1^1[/tex]
Amount = $1518.69
Hence, the Amount is equal to $1518.69.
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3x+y=1/3
2x-3y=8/3
Solve the system of linear equation using any method. EXPLAIN your choice of method. PLEASEE
Answers
Answer:
x = 1/3; y = -2/3
Step-by-step explanation:
We can solve using substitution by isolating y in the first equation and plug in this y for y in the second equation. I chose this method because it's very simply to isolate the y and only requires a simple subtraction:
[tex]3x+y=1/3\\y=-3x+1/3\\\\2x-3(-3x+1/3)=8/3\\2x+9x-1=8/3\\11x-1=8/3\\11x=11/3\\x=1/3[/tex]
Now, we can plug in 1/3 for x in any of the two equations. Let's try the first original equation:
[tex]3(1/3)+y=1/3\\1+y=1/3\\y=-2/3[/tex]
Finally, we can check our answers by plugging in 1/3 for x and -2/3 for y into to both equations and see that we get 1/3 and 8/3 respectively:;
First equation:
[tex]3(1/3)-2/3=1/3\\1-2/3=1/3\\1/3=1/3[/tex]
Second equation:
[tex]2(1/3)-3(-2/3)=8/3\\2/3+2=8/3\\8/3=8/3[/tex]
please help will mark brainlist!!!!!!
Answers
The transformed equation of the given function is y = x²+5.
Given that a transformed graph of the function y = x², we need to find the equation of the transformed graph,
We see that the y-intercept is (0, 5) so the graph has been translated 5 units up.
Therefore the equation can be written as y = x²+5.
Hence, the transformed equation of the given function is y = x²+5.
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No calculator Explanation please. Will choose brainliest. Pre-Calc. Lim as x approaches 9
Answers
The limit of the expression is determined as 0.
What is the limit of the expression?The limit of the expression is calculated as follows;
The given expression = lim (x ---> 9) [ ( x - 9 ) / √x - 3)
For the given limit in the expression, we have x maps to 9 or x tends to 9.
When x tends to 9, we will have;
x ---->9 = (9 - 9 ) / (√9 - 3)
= (0)/(-3 - 3)
note: since √x can be negative or positive, we will choose negative so that our solution will not be undefined.
= 0/-6
= 0
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[tex]\sf \longrightarrow \: \: \lim_{x\to \: 9} \: \: \: \frac{x \: - \: 9}{ \sqrt{x} - 3 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ({ \sqrt{x} \: )}^{2} \: - \: {(3)}^{2} }{ \sqrt{x} - 3 } \\ [/tex]
Now , by using Identity:-
a² - b² = ( a+b ) ( a-b )[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)( \sqrt{x} - 3)}{ \sqrt{x} - 3 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3) \cancel{( \sqrt{x} - 3)}}{ \cancel{ \sqrt{x} - 3} } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \frac{ ( \sqrt{x} + 3)(1)}{1 } \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)(1) \\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{x} + 3)\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: ( \sqrt{9} + 3)\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: \sqrt{9} + 3\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 3 + 3\\ [/tex]
[tex]\sf \longrightarrow \: \: \lim_{ x\to \: 9} \: \: \: 6\\ [/tex]
Match the exact value of
hypotenuse to its triangle.
Hypotenuse is 29 meters
Hypotenuse is 13 meters
Hypotenuse is 15 meters
Hypotenuse is 17 meters
A right angle triangle, having one side as 12 meters and other side as 9 meters.
A right angle triangle, having one side as 5 meters and other side as 12 meters.
A right angle triangle, having one side as 8 meters and other side as 15 meters.
A right angle triangle, having one side as 20 meters and other side as 21 meters.
Answers
Answer: 1. 15 2. 13 3. 17 4. 29
Step-by-step explanation:
12^2 + 9^2 = 15^2, 5^2 + 12^2 = 13^2, 8^2 + 15^2 = 17^2, 20^2 + 21^2 = 29^2.
Emmitt party supply is known for their long lasting helium balloons Emmitt kept track of the number of balloons in each order he received yesterday
Answers
Answer: It's kind of hard to answer a question you don't have all the parts too. :(
Step-by-step explanation:
if lauras account balance has gone from -30 to -45, what has hapened to her debt
Answers
A negative balance in an account indicates that the account holder owes money, or has a debt. In this case, Laura's account balance has become more negative, going from -30 to -45. This means that she now owes more money than before, and her debt has increased by 15 units.
Answer:
Laura's debt has increased by $15, as her account balance has gone from -$30 to -$45. This means that she owes $15 more than what she owed before. A negative account balance indicates that Laura owes money to someone or a company, and the increase in the negative balance implies that her debt has become more significant. It is essential for Laura to keep track of her account and try to improve her financial situation to avoid accumulating debt further.
A motorized scooter rental company has a linear pricing plan. The total cost in dollars, C, to rent scooter for 2, 4, 5, or 8 hours h, is shown. Hours (h) Total cost (C) 2 $39 4 $53 5 $60 8 $81 What is the cost of each additional hour? Complete the equation to represent the pricing plan. C = h +
Answers
So the cost of each additional hour depends on the time interval. To calculate the cost of each additional hour, we can divide the change in cost by the change in time.
From 2 to 4 hours, the cost increases by $14 for an additional 2 hours, so the cost of each additional hour is:
$14 ÷ 2 hours = $7 per hour
From 4 to 5 hours, the cost increases by $7 for an additional 1 hour, so the cost of each additional hour is:
$7 ÷ 1 hour = $7 per hour
From 5 to 8 hours, the cost increases by $21 for an additional 3 hours, so the cost of each additional hour is:
$21 ÷ 3 hours = $7 per hour
We can see that in each case, the cost of each additional hour is $7.
Therefore, the equation to represent the pricing plan is:
C = 7h + 25
Elephant and Piggy have 56 books to give away to different
schools across America. Each school will get 7 books. Which of the
following equations will help them figure out how many schools, s,
they can give books to?
A. s ÷ 7 = 56
B. 56 + 7 = s
C. 56 x 7 = s
D.
7 xs = 56
Answers
The number of schools that can get the book is obtained using the formula
s = 56 ÷ 7
How to find the number of schoolsInformation form the problem
Elephant and Piggy have 56 books to give away to differentschools across
Each school will get 7 booksTo find the number of schools, s; that will get the book we use the formula
s = number of books / how many books each school will get
substituting into the formula
s = 56 / 7
s = 56 ÷ 7
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It takes 10 hours to type for reports how long will it take to type of 15 reports
Answers
Time to type one report = 10 / 4 = 2.5 hours
Therefore, it would take 2.5 hours to type one report.
To find how long it would take to type 15 reports, we can multiply the time to type one report by the number of reports:
Time to type 15 reports = 2.5 hours/report x 15 reports = 37.5 hours
Therefore, it would take 37.5 hours to type 15 reports.
What is the equation, in point-slope form, of the line
that is perpendicular to the given line and passes
through the point (-4,-3)?
Oy+3=-4(x+4)
Oy+3= (x+4)
Oy+ 3 = (x+4)
Oy+3=4(x+4)
Answers
A line that is perpendicular to this line will have a slope that is the negative reciprocal of -4, which is 1/4.
So, the equation of the line that is perpendicular to the given line and passes through the point (-4,-3) can be written in point-slope form as:
y - (-3) = 1/4(x - (-4))
Simplifying this equation gives:
y + 3 = 1/4(x + 4)
Therefore, the answer is "y + 3 = 1/4(x + 4)".
The equation of the line in point-slope form is y + 3 = 1/4(x + 4).
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The given line passes through the points (-1,1) and (0,-3).
The slope of the line passing through these points can be calculated as:
slope = (y2 - y1) / (x2 - x1)
= (-3 - 1) / (0 - (-1))
= -4 / 1
= -4
Since we are looking for a line that is perpendicular to this line, the slope of the new line will be the negative reciprocal of -4, which is 1/4.
Using the point-slope form of a linear equation, we can write the equation of the new line as:
y - y1 = m(x - x1)
where (x1, y1) is the point (-4,-3) and m is the slope 1/4.
Plugging in the values.
y - (-3) = 1/4(x - (-4))
Simplifying and rearranging.
y + 3 = 1/4(x + 4)
Therefore,
The equation of the line in point-slope form is y + 3 = 1/4(x + 4).
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