Answers
Answer:
AC = 3 + 2√15
Step-by-step explanation:
Call the center of the circle O.
(OB)² = 2² + 3²
(OB)² = 13
OD = OB
(OD)² + (DC)² = (CO)²
13 + 51 = (CO)²
(CO)² = 64
(CX)² + 2² = (CO)²
(CX)² = 64 - 4
(CX)² = 60
CX = √60 = 2√15
AX = BX = 3
AC = AX + CX
AC = 3 + 2√15
Related Questions
Use synthetic division to evaluate for the indicated x value.
x³ + x²-3x +9; ƒ (-4)
f(-4)=
Answers
The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:
Column 1 | Column 2-4 | 11 -3 91 -3 9 -63 |The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.
How to calculate synthetic division?We must reduce the first coefficient, which is 1. Then we multiply -4 by 1 to get -4 and write that in the next coefficient, which is 1. We add the two numbers to get -3 , which we write under the next coefficient , which is -3. We multiply -4 by -3 to get 12 and write that under the last coefficient, which is 9. We add the two numbers together to get -51, which is the remainder.Therefore, we find ƒ(-4) = -51.
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1. When solving the equation: 8n -2 = 1 +n + 5 + 6, Response area could NOT be the first step that would yield a solution
Answers
Answer:
n = 2
Step-by-step explanation:
Which of the following represents the transformation of abc
Answers
Answer:
option (3) and (4)
Step-by-step explanation:
A population of rare birds in town is currently listed at 2,000. It is declining at a rate of 2% per year. How many birds will be left after 20 years? Round your answer to the nearest whole number.
A. 1,335 birds
B. 1,980 birds
C. 2,972 birds
D. 23 birds
Answers
Option(A) is the correct answer is A. 1,335 birds.
To calculate the number of birds that will be left after 20 years, we need to consider the annual decline rate of 2%.
We can use the formula for exponential decay:
N = N₀ * (1 - r/100)^t
Where:
N is the final number of birds after t years
N₀ is the initial number of birds (2,000 in this case)
r is the annual decline rate (2% or 0.02)
t is the number of years (20 in this case)
Plugging in the values, we get:
N = 2,000 * (1 - 0.02)^20
N = 2,000 * (0.98)^20
N ≈ 2,000 * 0.672749
N ≈ 1,345.498
Rounded to the nearest whole number, the number of birds that will be left after 20 years is 1,345.
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Which statements about the reflection are true? Check all that apply.
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will remain in the same location as C because it is on the line of reflection.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Answers
The statements that are true are:
Clayton could use the relationship (x, y) right-arrow (y, x) to find the points of the image.
Clayton could negate both the x and y values in the points to find the points of the image.
C’ will move because all points move in a reflection.
The image and the pre-image will be congruent triangles.
The image and pre-image will not have the same orientation because reflections flip figures.
Options A, B, D, E, and F.
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
Clayton could use the relationship (x, y) → (y, x) to find the points of the image.
This is the y = x reflection rule.
This is true.
Clayton could negate both the x and y values in the points to find the points of the image.
Reflection of (x, y) along the x-axis and y-axis consecutively will give us
(-x, -y).
This is true.
C’ will remain in the same location as C because it is on the line of reflection.
This is not true.
C’ will move because all points move in a reflection.
This is true.
The image and the pre-image will be congruent triangles.
This is true.
The image and pre-image will not have the same orientation because reflections flip figures.
This is true.
Thus,
All statements are true except the statement:
C’ will remain in the same location as C because it is on the line of reflection.
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through (2,2) parallel to y=x+4
in slope intercept form.
Answers
Answer:
y = x
Step-by-step explanation:
slope of y=x+4 is 1
parallel means same slope = 1
so y - 2 = 1*(x - 2)
y = x
4) A music shop purchases a guitar for $105. They then markup the price
60% before selling it in their shop. What is the retail price of the guitar? *
Plz help
Answers
Answer:
$168
Step-by-step explanation:
The markup amount is ...
60% × $105 = $63
When that is added to the store's cost, the retail price is ...
selling price = cost price + markup
selling price = $105 +63 = $168
The retail price of the guitar is $168.
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
Answers
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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For the attached graph two questions:
1. What does the slope of the line represent, in context of the problem?
2. What does the y intercept represent, in context of the problem?
Answers
The slope of the line represents the speed in miles per hour
The y intercept represents the initial distance
What does the slope of the line representfrom the question, we have the following parameters that can be used in our computation:
The graph
Where, we have
x = time in hours
y = distance in miles
The slope is
slope = change in y/x
So, we can conclude that the slope is the speed
What does the y intercept representBy definition, the y intercept is the initial value of the graph
In this case;
y intercept = initial distance
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. The table below shows the cost of making a long distance call based on the length of the call. Long Distance Rates Time (minutes) Cost 5 $0.55 6 $0.62 7 $0.69 8 $0.76 9 $0.83 10 $0.90 Refer to the above table of long distance rates. Write an expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes.
Answers
An expression that can be used to find the cost of an n-minute long distance call, where n is at least 5 minutes is (0.55 + (n - 5) x 0.07) dollars.
Given:
Long Distance Rates Time (minutes) Cost5 $0.556 $0.627 $0.698 $0.769 $0.8310 $0.90We need to find an expression that can be used to find the cost of an n-minute long-distance call, where n is at least 5 minutes.
The cost of making a long-distance call is given for 5 minutes, 6 minutes, 7 minutes, 8 minutes, 9 minutes, and 10 minutes.
We can observe from the above table that for every increase of 1 minute, the cost increases by $0.07.
We can conclude that the cost of n minutes long-distance call is given by: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes.
Therefore, the required expression is: (0.55 + (n - 5) x 0.07) dollars when n is at least 5 minutes. The above expression is based on the pattern in the table provided for long-distance call rates. We can use this expression for values of n greater than or equal to 5.
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Manny buys 16 apples at the market and 8 oranges. what are the ratios of apples to oranges ?
Answers
Answer:
2:1 or 16:8
Step-by-step explanation:
Answer:
2:1
Apple: orange
Step-by-step explanation:
Divide the number of apples by the number of oranges
A rectangular swimming pool is surrounded by a cement walkway with the dimensions shown.
Length: 22 ft
Width: 3 ft
Height: 5x ft
Write an expression, in factored form, that represents the area of the cement walkway.
Answers
The expression that represents the area of the cement walkway is 11 ( 12 + 32x)
How to determine the area
The formula for area of a rectangular prism is given as;
Area = 2 ( wl + hw + h )
Where;
width, w = 3ftheight, h = 5x ftlength, l = 22ftNow, let's substitute into the formula for area;
Area = 2 {3(22) + 5x(3) + 22(5x) }
expand the bracket
Area = 2 { 66 + 15x + 110x }
collect like terms
Area = 2{66 + 176x}
Area = 132 + 352x
Area = 11 ( 12 + 32x)
Thus, the expression that represents the area of the cement walkway is 11 ( 12 + 32x)
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A movie membership costs $10 a month plus an additional $5 for each movie purchased. If you have only budgeted to spend a maximum of $25 this month, how many movies can you purchase?
Answers
Answer:
3
Step-by-step explanation:
25-10/3=3
Answer:
3 movies
Step-by-step explanation:
You can pay for 3 movies because
5*3=15 and you have to pay for the membership which is 10 so
10+15=25
Joel had 200 coins,
which were dimes and quarters. The total value is $32.
Answers
Answer:
Joel had 120 dimes and 80 quarters.
Step-by-step explanation:
Given that Joel had 200 coins, which were dimes and quarters, and the total value was $ 32, to determine how many coins of each type he had, the following calculation must be performed:
0.25 - 0.10 = 0.15
200 x 0.10 = 20
32 - 20 = 12
12 / 0.15 = 80
200 - 80 = 120
(80 x 0.25) + (120 x 0.1) = X
20 + 12 = X
32 = X
Thus, Joel had 120 dimes and 80 quarters.
Bill Ding plans to build a new hardware store. He buys a rectangular lot that is 50 ft by 200 ft, the 50-ft dimension being along the street. The store is to have 4000 ft2 of floor space. Construction costs $100 per linear foot for the part of the store along the street and only $80 per linear foot for the parts along the sides and back. To what dimensions should Bill build the store to minimize construction costs
Answers
Answer:
Length a = 59.62
Width b = 67.09
Cost = $10,734.4
Step-by-step explanation:
Solution:
Let a be the length and b be the width.
Area of the rectangle = a x b
a x b = 4000
Cost of the construction:
Cost = 100a + 80(a + 2b)
Cost = 100a + 80a + 160b
Cost = 180a + 160b Equation of the Cost of the construction.
Now, we need a and b to calculate the minimum cost required to build a lot.
From the area = a x b
we have,
a x b = 4000
b = 4000/a
Putting this equation into the cost of the construction.
We get:
Cost = 180a + 160 x (4000/a)
Cost = 180a + 640000/a
Differentiating with respect to a, we get
\(C^{'}\) = 180 - 640000/\(a^{2}\)
Putting \(C^{'}\) = 0
180 - 640000/\(a^{2}\) = 0
Taking LCM
180\(a^{2}\) - 640000 = 0
Solving for a
180\(a^{2}\) = 640000
\(a^{2}\) = 640000/180
\(a^{2}\) = 3555.55
Taking square root
a = 59.62
As we know,
b = 4000/a
putting the minimum value of a = 59.62
b = 4000/59.62
b = 67.09
So, now we have both the dimensions a and b
Putting the values of a and b we will get the cost of the construction.
Cost = 180a + 160b
Cost = 180(59.62) + 160(67.09)
Cost = $10,734.4
Hence, $10,734.4 will be the minimum cost of the construction for Bill Ding.
given: ab=bc, ae=fc
prove m
rsm problem pls help
Answers
The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem
How to determine the proof of the trianglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two triangles are congruent by SAS,
Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
The proof is given as:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given2. AC ≅ AC 2. Reflexive property of congruence3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC4. ∆AEC ≅ ∆AFC. 4. SAS5. <AEC ≅ <AFC. 5. CPCTCRead more about congruence proof at:
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Match the expressions to their solutions or equivalents. Solution of 0.5 x = 0
Answers
\(\huge\text{Hey there!}\)
\(\huge\textbf{Assuming that your expression is:}\)
\(\textsf{0.5x = 0}\)
\(\huge\textbf{If so, let's solve for the given expression:}\)
\(\textsf{0.5x = 0}\)
\(\huge\textbf{Divide 0.5 to both of the sides you have:}\)
\(\mathsf{\dfrac{0.5x}{0.5} = \dfrac{0}{0.5}}\)
\(\huge\textbf{You have to simplify the equation above:}\)
\(\mathsf{x = \dfrac{0}{0.5}}\)
\(\mathsf{x = 0}\)
\(\huge\textbf{Therefore, your answer should be:}\)
\(\huge\boxed{\mathsf{x = }\frak{0}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
Need Help
Answers
Answer: -27
Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
We can start by looking at the differences between consecutive terms in the list:
9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12
Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:
-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21
Therefore, we predict that the most probable next number in the list is -27.
234,143 rounded to the nearest hundred
Answers
Answer:
234,100
anything that is below 50 will go down.
Step-by-step explanation:
Answer:
234,100
Step-by-step explanation:
4 below let him go
5 and above bump him up
if youre looking in the hundreds place (the 1) you look to the right to see what number you have, if you follow the saying ^^ then 4 is let go so you just keep 100.
or if you want to look at it on a number line, 143 is closer to 100 than 200 :)
Write this ratio as a fraction in lowest terms 40 minutes to 90 minutes
Answers
Answer:
your answer should be 4/9
Step-by-step explanation:
Hope this helps!
The ratio as a fraction in lowest terms is 4/9
How to express the ratio as fraction?The ratio is given as:
Ratio = 40 minutes to 90 minutes
Remove the units
Ratio = 40 to 90
Express as fraction
Fraction = 40/90
Simplify
Fraction = 4/9
Hence, the ratio as a fraction in lowest terms is 4/9
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Rusty's hair grows at the rate of 1 over 4 inch per month.
How many months will it take Rusty's hair to grow 5 over 8 inch?
Explain your answer using words, and show your work using division of fractions
Answers
Answer:
5 months
Step-by-step explanation:
because 1,1,1,1,1 = 5 4,4=8 5/8
Answer:
I got the answer 0.388888... by divided 7 by 18. (1) I added a zero to 7. (2)I times 3 to 18 to make 54 and subtracted my dividend by this. (3)The answer was 160 which I subtracted by 18x8 which equals 144. The answer of the was 160 and I could go on and on repeating step 3.
Step-by-step explanation:
I got the answer 0.388888... by divided 7 by 18. (1) I added a zero to 7. (2)I times 3 to 18 to make 54 and subtracted my dividend by this. (3)The answer was 160 which I subtracted by 18x8 which equals 144. The answer of the was 160 and I could go on and on repeating step 3.
Which set of numbers includes only integers?
Group of answer choices
12,23,67,0
−3,−2,2,3
−6,−4,−2,−12
−5,−314,1,18
Answers
Answer:
12, 23, 67, 0 is the answer
Answer:
a or b
Step-by-step explanation:
we have you find the answer and an integer in a set of number or its opposites
Round these numbers to the hundred- 6,232 490- 23,058
Answers
Answer:
6,200 500 23,000
Hoped this helped:)
Step-by-step explanation:
Answer:
6,232 rounded is 6,200
490 rounded is 500
23,058 rounded is 23,100
Please I need an answer
Answers
Answer:
D. No x-intercept, y-intercept 9
Step-by-step explanation:
The line intercepts at (0, 9)
You lease a car at $23,495 for 3 years at $429.95 a month with a $500 down payment. The interest is 30% of the payments and $4,643.46 in interest is paid over 3 years. What is the remaining balance when the lease ends? How did you arrive at $12,160.26?
Answers
Answer:
Step-by-step explanation:
total interest paid is given as $4,643.46.
total payments = $429.95 x 36 months = $15,478.20
total lease payments = total payments - total interest
total lease payments = $15,478.20 - $4,643.46 = $10,834.74
Remaining balance = Total cost of the lease - Total lease payments
$23,495 - $10,834.74 = $12,660.26
PLEASE ANSWER - PLEASE ANSWER
The diagram shows triangle ABC. ABC and BED are straight lines. AB = 12.2cm, CD = 5.8cm, BE:ED = 3:1, Angle ADB = 90°, Angle ABD = 38°.
Work out the size of angle DCE, correct to 1 decimal place. SHOW ALL WORKING IN TEXT FORM, NO IMAGES.
Answers
The measure of angle DCE in this problem is given as follows:
m < DCE = 22.5º.
How to obtain the measure of angle DCE?The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:
cos(38º) = DB/12.2
DB = 12.2 x cosine of 38 degrees
DB = 9.6 cm.
BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:
DE = 1/4 x 9.6
DE = 2.4 cm.
Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:
tan(x) = 2.4/5.8
x = arctan(2.4/5.8)
x = 22.5º
m < DCE = 22.5º.
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Answer:
x = 22.5°
Step-by-step explanation:
BD = cos(38)*12.2 = 9.61DE = 9.61*¼ = 2.4∠DCE = tan(2.4/5.8) = 22.5°According to a salad recipe each serving require 6 teaspoons of vegetable oil and 9 teaspoons of vinegar and 24 teaspoons of vegetable oil were used how many teaspoons of vinegar should be used
Answers
Therefore, if 24 teaspoons of vegetable oil were used, we would need 16 teaspoons of vinegar to make the recipe correctly.
According to a salad recipe, each serving requires 6 teaspoons of vegetable oil and 9 teaspoons of vinegar. If 24 teaspoons of vegetable oil were used, we can determine the amount of vinegar needed for the recipe to be correct as follows:
First, we must determine the ratio of vinegar to oil in the recipe. To do this, we divide the amount of vinegar needed per serving (9 teaspoons) by the amount of oil needed per serving (6 teaspoons):
9 ÷ 6 = 1.5
This means that for every 1.5 teaspoons of oil used, we need 1 teaspoon of vinegar. Next, we use this ratio to determine the amount of vinegar needed when 24 teaspoons of oil are used:
1.5 ÷ 1 = 1.5
(teaspoons of oil per 1 teaspoon of vinegar)
24 ÷ 1.5 = 16
(teaspoons of vinegar needed)
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Please give steps and explanation!
Answers
\(f(x)=\cfrac{e^x+1}{e^{x^2} + 1}\implies \cfrac{df}{dx}=\stackrel{\textit{\large quotient rule}}{\cfrac{e^x(e^{x^2}+1)~~ - ~~(e^x+1)\stackrel{chain~rule}{(e^{x^2}\cdot 2x)}}{(e^{x^2} + 1)^2}} \\\\\\ \left. \cfrac{df}{dx} \right|_{x=0}\implies \cfrac{e^0(e^{0^2}+1)~~ - ~~(e^0+1)(e^{0^2}\cdot 2(0))}{(e^{0^2} + 1)^2}\implies \cfrac{2~~ - ~~0}{4}\implies \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ f(0)=\cfrac{e^0 + 1}{e^{0^2} + 1}\implies f(0)=\cfrac{2}{2}\implies f(0)=1\)
now, let's simply plug all those guys in the point-slope form for that tangent line at x = 0.
\((\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{0})\implies y=\cfrac{1}{2}x+1\)
1. Use precise mathematical language to justify and explain each mathematical process.
Use the rectangle with side lengths 5.22 – 8x + 9 and x + 5 for the following two questions.
1. What is the perimeter of the rectangle? Write a summary of the process used to determine the expression.
2. What is the area of the rectangle? Write a summary of the process used to determine the expression.
Answers
Mathematical processes are the steps used to determine the result of operations
The perimeter of the rectangle is \(10x^2 - 14x + 28\)The area of the rectangle is \(5x^3 +17x^2 -31x + 45\)The dimension of the rectangle is given as:
\(Length = 5x^2 - 8x + 9\)
\(Width = x + 5\)
(1) The perimeter of the triangle
This is the sum of the side lengths of the rectangle.
So, we have:
\(Perimeter = 2 \times (Length + Width)\)
This gives
\(Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)\)
Collect like terms
\(Perimeter = 2 \times (5x^2 - 7x + 14)\)
Open brackets
\(Perimeter = 10x^2 - 14x + 28\)
Hence, the perimeter of the rectangle is \(10x^2 - 14x + 28\)
(2) The area of the triangle
This is the product of the dimensions of the rectangle.
So, we have:
\(Area = Length \times Width\)
This gives
\(Area = (5x^2 - 8x + 9) \times (x + 5)\)
Open brackets
\(Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45\)
Collect like terms
\(Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45\)
\(Area = 5x^3 +17x^2 -31x + 45\)
Hence, the area of the rectangle is \(5x^3 +17x^2 -31x + 45\)
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Answers
An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.
An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or \(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\)
Where:
m represent the slope.x and y represent the points.At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
\(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)\)
y + 3 = 2(x + 1)
y = 2x + 2 - 3
y = 2x - 1
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
2 × m₂ = -1
m₂ = -1/2.
At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x + 4)
y = -x/2 - 2 + 5
y = -x/2 + 3
Read more on point-slope here: brainly.com/question/24907633
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