The salary is $55100 when [tex]a_n=55100[/tex].
[tex]55100=41900+1100n\\\\13200=1100n\\\\12=n[/tex]
So, her salary will be $55,100 after 12 years.
The salary is $55100 after 12 years.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that construction worker's starting salary is $43,000. Each year she receives a $1100 raise.
Therefore, an = 41,900 + 1100n
An explicit formula of the form an = bn + c to model this situation.
When n = 10,
= 41,900 + 1100n
= 41,900 + 1100(10)
= 41,900 + 11000
= 52,900
when an = 55,100
Then an = 41,900 + 1100n
55,100 = 41,900 + 1100n
1100n = 55,100 - 41,900
1100n = 13200
n = 13200/ 1100
n = 12
So, her salary will be $55,100 after 12 years.
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From a research paper, it is known that the number of soldiers who died annually
by being kicked by a horse followed a Poisson distribution with an average of 0.61
death in an army corps each year.
(a) Find the standard deviation of death in an army corps each year.
The standard deviation of death in an army corps each year is 0.78
How to determine the standard deviation?From the question, we have the following parameters that can be used in our computation:
Distribution type = Poisson distribution
Average of the distribution = 0.61
The standard deviation of the distribution is calculated as:
Standard deviation = √Average of the distribution
Substitute the known values in the above equation, so, we have the following representation
Standard deviation = √0.61
Evaluate the square root expression
So, we have
Standard deviation = 0.78
Hence, the standard deviation is 0.78
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What is the probability that the random variable has a value greater than 7
The probability that the random variable has a value greater than 7 is undetermined.
What is Probability?The formula to calculate the probability of occurrence of an event 'A' can be written as -
P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have a random variable having a value greater than 7
Now -
Number of outcomes favorable to event A = (-∞, + ∞) - (- ∞, 7)
Total number of outcomes for event A = (-∞, + ∞)
P(A) = (-∞, + ∞) - (- ∞, 7) / (-∞, + ∞)
P(A) = ∞/∞
P(A) = undetermined
Therefore, the probability that the random variable has a value greater than 7 is undetermined.
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Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (10,5) (-8,9)
Line 2: (2,-4) (11,-6)
The slope of line 1 is
.
The slope of line 2 is
.
Answer:
The lines through the given points are parallel
Step-by-step explanation:
The given lines can be evaluated as follows
The first step is to calculate the slope [tex]m_{1}[/tex] of the first line using the slope formula as follows
[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Take two coordinates on the first line
[tex](10,5)~\text{and}~(-8,9)[/tex]
Substitute [tex]9[/tex] for [tex]y_{2}[/tex], [tex]-8[/tex] for [tex]x_{2}[/tex] , [tex]5[/tex] for [tex]y_{1}[/tex] , [tex]10[/tex] for [tex]x_{1}[/tex] in the slope formula
[tex]m_{1}=\frac{9-5}{-8-10}[/tex]
Simplify the numerator and the denominator at the right side of the equation
[tex]m_{1}=\frac{4}{-18}[/tex]
Simplify the fraction at the right side of the equation
[tex]m_{1}=-\frac{2}{9}[/tex]
The slope of the first line is [tex]-\frac{2}{9}[/tex]
Take two coordinates on the second line
[tex](2,-4)~\text{and}~(11,-6)[/tex]
Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]11[/tex] for [tex]x_{2}[/tex] , [tex]-4[/tex] for [tex]y_{1}[/tex] , [tex]2[/tex] for [tex]x_{1}[/tex] in the slope formula
[tex]m_{2}=\frac{-6-(-4)}{11-2}[/tex]
Take out the brackets in the numerator at the right side of the equation
[tex]m_{2}=\frac{-6+4}{11-2}[/tex]
Simplify the numerator and the denominator at the right side of the equation
[tex]m_{2}=\frac{-2}{9}[/tex]
The slope of the second line is [tex]-\frac{2}{9}[/tex]
Since the slope of both lines are equal, then the lines through the given points are parallel
Hence the lines through the given points are parallel
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The exchange rate for US dollars to Canadian dollars is 0.77. What is value of 200 US dollars?
The value of 200 US dollars into canadian dollars is 259.74
What is an example of a unitary method?
A single or unique unit is referenced to using the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
Given That:
1 Canadian dollar is = 0.77 US dollar
So 1 US dollar is = 1/0.77 canadian dollar
So 200 US dollar is = 1/0.77 * 200 = 259.74 canadian dollar
Hence the answer is 259.74 dollar
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Please I need help asap. Please explain how you got the answer
The image of F after a counterclockwise rotation of 180° about G is F(2,7).
What is a line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we
Rotate FG through 180° about the origin O in an anticlockwise direction, the new position of points F and G are:
F (-2, -7) = F' (2, 7)
G (-4, -2) = G' (4, 2)
Thus, the new position of line segment FG is F'G'.
Hence, the image of F after a counterclockwise rotation of 180° about G is F(2,7).
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Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x^4+3x^3−2x^2+48x−288
The factoring of the polynomial f(x) = x^4 + 3x³ - 2x² + 48x - 288 is given as follows:
f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).
How to factor the polynomial?The polynomial is factored by it's linear factors, given as follows:
f(x) = (x - x')(x - x'')(x - x''')(x - x'''').
In which x', x'', x''' and x'''' are the roots of the polynomial f(x).
In this problem, we have that -4i is a root, hence, by the Conjugate Roots Theorem, 4i is also a root and hence:
f(x) = (x - 4i)(x + 4i)(x - x''')(x - x'''').
f(x) = (x² + 16)(x - x''')(x - x'''').
As a fourth order polynomial can be the product of two second order polynomials, hence:
x^4 + 3x³ - 2x² + 48x - 288 = (x² + 16)(ax² + bx + c)
x^4 + 3x³ - 2x² + 48x - 288 = ax^4 + bx³ + (c + 16)x² + 16bx + 16c.
Hence the coefficients are given as follows:
a = 1.b = 3.16c = -288 -> c = -18.Then the equation for the final two factors is:
x² + 3x - 18 = 0.
Which is simplified as follows:
x² + 3x - 18 = (x + 6)(x - 3).
Hence the simplified polynomial is:
f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).
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Which number line below shows the range of values that satisfy the inequality?
The number line that satisfies the inequality is option (B).
What are number lines?
Number lines are horizontal straight lines in mathematics where numbers are arranged in equal intervals. A numeric line can be used to represent every number in a sequence. The endpoints of this line go on infinitely. In other terms, it is an image of numbers on a straight line. It functions as a guide for distinguishing and organizing numbers. It can be used to represent any real number, including all whole numbers and natural numbers.
Solution Explained:
- (a+5) < 4/-2 <= -3-a
[tex]\left \{ {{- (a+5) < 4/-2} \atop { 4/-2 < -3-a}} \right.[/tex]
[tex]\left \{ {{-a - 5 < -2} \atop {-2 < = -a -3}} \right.[/tex]
[tex]\left \{ {{-a-5) +5 < -2+5} \atop {-2+3 < = (-a-3)+3}} \right.[/tex]
[tex]\left \{ {{-a- 5 +5 < 3} \atop {1 < = -a-3+3}} \right.[/tex]
[tex]\left \{ {{-a < 3} \atop {1 < = -a}} \right.[/tex]
[tex]\left \{ {a > -3} \atop {-a > = 1}} \right.[/tex]
[tex]\left \{ {{a > -3} \atop {a < = -1}} \right.[/tex]
[tex]-3 < a < = -1[/tex]
a ∈ (-3, -1]
Hence, the number line that satisfies the inequality -(a+5) < b/-2 <= -3-a is in option (B).
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The Ruffins are negotiating with two banks for a mortgage to buy a house selling for $190,000. The terms at bank A are a $25% down payment, an interest rate of 11%, a 25 -year conventional mortgage, and 2 points to be paid at the time of closing. The terms at bank B are a 15% down payment, an interest rate of 10.0%, a 30 -year conventional mortgage, and no points. Which loan should the Ruffins select in order for the total cost of the house to be less?
Click the icon to view the table of monthly payments.
From which bank should the Ruffins take the loan?
Bank B
Bank A
Bank A grants a shorter payment period and is the least costly, so the Ruffins should take the loan from Bank A.
How the payment period influences the cost of a loan?In finance literature and practice, the loan interest (cost) increases with a more extended payment period.
In other words, a shorter payment period reduces the interest cost of a loan. The loan cost is also influenced by the amount of the principal and the interest rate.
Bank A Terms:Down payment = 25%
Interest rate = 11%
Mortgage period = 25 years
2 points at closing
N (# of periods) = 300 months (25 years x 12)
I/Y (Interest per year) = 11%
PV (Present Value) = $142,500 ($190,000 - $47,500)
FV (Future Value) = $0
Results:
Period Payments (PMT) = $1,396.66
Sum of all periodic payments = $418,998
Total Interest = $276,498
Total Costs:Down payment = $47,500 ($190,000 x 25%)
2 points = $2,850 ($142,500 x 2%)
Sum of periodic payments = $418,998
Total costs = $469,348 ($47,500 + $2,850 + $418,998)
Bank B Terms:Down payment = 15%
Interest rate = 10%
Mortgage period = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 10%
PV (Present Value) = $161,500
FV (Future Value) = $0
Results:
Period Payments (PMT) = $1,417.28
Sum of all periodic payments = $510,220.08
Total Interest = $348,720.08
Total Costs:Down payment = $28,500 ($190,000 x 15%)
Sum of periodic payments = $510,220.80
Total costs = $538,720.80 ($28,500 + $510,220.80)
Thus, we can recommend the Ruffins should go for a Bank A loan that costs less than Bank B's.
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Which
angle is an adjacent interior angle?
3 is an adjacent interior angle which is both adjacent and interior angle, this angle lie inside a triangle.
What is an adjacent angle of a triangle ?The two angles are said to be adjacent angles when they share the common vertex and side.
What is interior angle of a triangle?An interior angle is an angle inside a triangle.
What is exterior angle of a triangle?The angle between the extended side and the side next to it is called an exterior angle.
Since we know that any two interior angles that share a common side are called the "adjacent interior angles" of the polygon, or just "adjacent angles".
Therefore,
In the diagram the adjacent angles are 3 and 4.
The interior angles from the diagram are 1, 2, and 3.
and the exterior angle is 4.
Hence , 3 is the only angle which is both adjacent and interior angle .
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PPEASE HELPPPPPPPPP!!!!
Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of
the price. How much shipping and handling will Elizabeth pay?
According to the given percentage, the shipping and handling fee that Elizabeth will pay is $16.6
Percentage:
Percentage refers one-hundredth (1/100) of something. And it refers to the rate or proportion of that one hundred.
Given,
Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of the price.
Here we need to find the shipping and handling will Elizabeth paid.
We know that, the price of the product is $83.
And the charges for the shipping and handling is 20%.
So, it can be written as the following form,
=> Additional charges = 20% of 83
=> Additional charges = 20/100 x 83
=> Additional charges = 20 x 0.83
=> Additional charges = 16.6
Therefore, the shipping and handling charges is $16.6
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Solve 2/3c - 1 = 1+2/3c
No solution
Infinite Solution
c = 6/4
c = 2/3
The variable 'c' in the given expression has No Solution.
Given, that
2/3c - 1 = 1 + 2/3c
Now, as we have same coefficient of the variable c i.e. 2/3
So, On subtracting 2/3c from both the sides, we get
2/3c - 2/3c - 1 = 1 +2/3c - 2/3c
-1 ≠ 1
Hence, we got no solutions that can satisfy the given expression.
So, the variable 'c' in the given expression has No Solution.
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The function f(x) is graphed below. How many points on the graph represent a relative minimum? PLEASE need help i don't understand. Need by TONIGHT!!!
Answer:
b and d are relative minimums (minima)
Step-by-step explanation:
An "absolute" minimum is the very lowest point on a graph. This graph doesn't have an "absolute" minimum because the end points both go to negative infinity (they go down forever)
But, this graph DOES have points that are "relative" minimums, which means the points are the minimum (lowest) in their neighborhood. In the immediate vicinity of the point, it is the lowest point.
In case there are further questions with this graph:
relative max: a and c
absolute max: f
x-intercepts: a,c,e,g
probably a 6th degree function,
multiplicity 2 at a and c
multiplicity 1 at e, g
leading coeffient is negative.
Which statements are true about exponential decay functions? Check all that apply.
O The domain is all real numbers.
O As the input increases, the output increases.
O The graph is the same as that of an exponential growth function.
The base must be less than 1 and greater than 0.
O The function has a constant multiplicative rate of change.
The correct options are:
The domain is all real numbers.The base must be less than 1 and greater than 0.The function has a constant multiplicative rate of change.Given,
In the question:
Which statements are true about exponential decay functions?
Now, According to the question;
We know that the exponential function is given by:
[tex]f(x) = ab^x[/tex]
where a>0 and b are constants.
Also, it represents a growth function if b>1
and a decay function if 0<b<1
where b is the base.
x belongs to whole of the real numbers( since the exponential function is well defined for all the real values of x.Hence, the domain of the function is all the real numbers )
Also, the graph of a decay function decreases continuously i.e. with the increasing input value the output value decreases.The exponential decay function always have a constant multiplicative rate of change i.e. b.Learn more about Exponential Function at:
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Question 7
Complete the equation so that it has no solution.
-15x + 4x + 2 - x =
x+3
Answer:
x=-1/13
Step-by-step explanation:
HELP ASAP THANKS 50 PNTS
Answer:
um well fierst da answer is proberly yes and no
Step-by-step explanation:
i tried to do da work
Please explain your answer. Thank you. :)
An equation of the line that began with a y-intercept of (0, 4), shifted up 3 units, and is perpendicular to y = 3/4(x) - 2 is: A. y = -4/3(x) + 7.
How to interpret the linear equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.In Mathematics, the condition for perpendicularity of two lines is given by m₁ × m₂ = -1. Next, we would determine the slope of this equation that began with a y-intercept of (0, 4):
3/4 × m₂ = -1
3m₂/4 = -1
3m₂ = -4
m₂ = -4/3
In order to determine the new y-intercept, we would translate the equation by shifting it 3 units up:
Translation = y + 3 = 4 + 3 = 7.
Now, we can write this equation in slope-intercept form as follows:
y = mx + c
y = -4x/3 + 7 or y = -4/3(x) + 7.
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Complete Question:
What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?
answer choices:
A. y = -4/3(x) + 7
B. y=-3/4(x)+7
C. y=-3/4(x)+4
D. y =-4/3(x)+4
Please help due tomorrow!!
Answer: 63
Step-by-step explanation:
When there are two lines intercepting the two angles opposite each other are the same
and GHK and IHF are opposite of each other so there for are equal
A man has $460,000 invested in three rental properties. One property earns 6.5% per year on the investment, the second earns 7%, and the third earns 9%. The total annual earnings from the three properties is $36,350, and the amount invested at 9% equals the sum of the first two investments. Let x equal the investment at 6.5%, y equal the investment at 7%, and z represent the investment at 9%. Complete parts (a) through (d) below.
The system of equations representing the amount invested are;
(a) x + y + z = 460,000
(b) 0.065·x + 0.07·y + 0.09·z = 36,350
(c) z = x + y
(d) There is one solution. The man invested $90,000 at 6.5%, $140,000 at 7% and $230,000 at 9%
What is a system of equations?A system of equations are two or more equations that have variables that are common to the equations in the system.
The questions in the parts (a) to (d) obtained from a similar question are;
(a) An equation stating the sum of the three investments
(b) The equation that states that of the sum of the return is 36,350
(c) The equation that states that the amount invested at 9% equals the sum of the other two investments
(d) Solve the derived system of equations
(a) The amount the man invests in the three rental properties = $460,000
Amount invested in the property that earns 6.5% = x
Amount invested in the property that earns 7% = y
The amount invested in the property that earns 9% = z
The equation that represents the sum of the three investments is therefore;
x + y + z = 460,000...(1)
(b) The equation that represents the sum of the returns from the three investment is found as follows;
6.5% = 0.065, 7% = 0.07, 9% = 0.09
0.65·x + 0.07·y + 0.09·z = 36,350...(2)(c) The equation stating the amount invested at 9% equals the sum of the other two investment is; z = x + y...(3)
(d) The system of equations is solved as follows;
From equation (1) and (2), we get;
x + y + z = 460,000
z + z = 460,000
2·z = 460000
· = 460,000 ÷ 2 = 230,000
The amount invested in the property that earns 9% per year is $230,000
Equation (3) indicates;
0.65·x + 0.07·y + 0.09 × 230,000 = 36,350
0.65·x + 0.07·y = 36,350 - 0.09 × 230,000 = 15650
The interest earned in the properties that earn 6.5% and 7% = $15650
0.65·x + 0.07·y = 15650...(4)
x + y = 230000...(5)
Equation (4) and (5) indicates;
y = 230,000 - x
0.065·x + 0.07×(230,000 - x) = 15650
16100 - 0.005·x = 15650
0.005·x = 16,100 - 15,650 = 450
x = 450 ÷ 0.005 = 90,000
The amount invested in the property that yields 6.5% per year = $90,000
Therefore;
The amount invested in the property that earns 7% per year = $230,000 - $90,000 = $140,000
There is one solution, the man invested $90,000 at 6.5%, $230,000 at 7%, and $230,000 at 9%
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Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.
f(x)=
The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9
How to determine the equation of the parabola?The equation of the function is given as
f(x) = 3x²
Also, we have
Vertex = (5, 9)
The form of the equation is given as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
This means that
Vertex = (h, k) = (5, 9)
Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 5)² + 9
This also means that
f(x) = -3(x - 5)² + 9
The -3 is gotten from f(x) = -3x²
Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9
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When Ada got to the store, she found that they only had 330 eggs. What is the largest number of egg tarts she can make with this amount of eggs?
Answer:
120
Egg. Egg tarts
2.75 = 1
330 = 1 x 330 divided by 2.75 = 120
Andrew is riding his bike. He biked a distance of 14 miles at a rate of 7 miles per hour. Using the distance formula, d = rt, solve for Andrew's time in minutes.
Answer:
120 minutes
Step-by-step explanation:
d=rt
D-distance
r-unit rate
T- time
14=7t
/7. /7
2=t
2 hours
2 x60=120
120 minutes
Hopes this helps please mark brainliest
IXL Please Help Fast I Still Have A Few More... :(
Answer:
x=3
Step-by-step explanation:
I’m pretty sure these 2 angles are equivalent
64-4x=58-2x
6-4x=-2x
6=2x
3=x
Hopes this helps please mark brainliest
The half-life of Radium-228 is 5.75 years. What is the annual decay rate? Express the result to four decimal places.
Express the annual decay rate as a percentage to two decimal places.
The required rate of annual decay rate is given as 11.70%.
Given that,
The half-life of Radium-228 is 5.75 years. What is the annual decay rate is to be determined.
The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.
Here,
According to the question,
[tex]1/2 = (1 - r)^{5.57}\\(1/2)^{1/5.57} = (1 -r)\\r = 0.1170\\r = 11.70%[/tex]
Thus, the required rate of annual decay rate is given as 11.70%.
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Simplify the following expression by combining like terms. Select the most simplified expression:
Option (A) is the correct option and on simplifying the expression by combining like terms we get,
24 - 3p.
Given, the expression 6(4 - 2p) + 9p
On simplifying, we get
24 - 12p + 9p
24 - 3p
So, on simplifying the given expression, we get
24 - 3p
Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,
24 - 3p
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f(x)=3x-6 draw the graph
Find the derivative of [tex](\sqrt{3x+x^2}+3sin(3x))^2[/tex] and evaluate the derivative at x=1. Round to 1 decimal place. Make sure that the calculator is in radians mode.
The first derivative of the function f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x], whose value at x = 1 is - 35.909.
How to find the derivative of a given function
Herein we find a function whose first derivative has to be found. This can be done by using the following derivative rules:
Derivative of a power
f(x) = c · xⁿ → f'(x) = n · c · xⁿ ⁻ ¹
Chain rule
f[g(x)] = (df / dg) · (dg / dx)
Derivative of a sum of functions
d / dx [f(x) + g(x)] = df / dx + dg /dx
Derivative of the sine
d / dx [sin x] = cos x
Now we proceed to find the derivative of the function:
f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x]
And we evaluate the derivative at x = 1:
f'(1) = 2 · [√(1 + 1²) + 3 · sin 3]² · [(1 + 2) / [2 · √(1 + 1²)] + 9 · cos 3]
f'(1) = 2 · (√2 + 0.423)² · (3 / 2 - 8.910)
f'(1) = - 35.909
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Find the exact value of x.
x= √ {type your answer...} Do the side lengths form a Pythagorean triple? {choose answer, yes no}
The value of x is .[tex]\sqrt{170}[/tex]
What is Pythagorean Theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.
Here, the two sides of the triangle are, 7 and 11.
By Pythagorean theorem,
[tex]7^2 + 11^2 = x^2\\49 + 121 =x^2 \\170 = x^2\\x = \sqrt{170} \\[/tex]
Hence, the value of x is [tex]\sqrt{170}[/tex].
Here, the sum of two sides of triangle is not a perfect square.
Therefore, the side lengths is not a Pythagorean triple.
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Wanda is designing a label for a can that is 7 centimeters tall and has a 14-centimeter diameter. the label wraps around the can, and there must be one centimeter for overlap. what should be the label dimensions? Please help...
Answer:
Step-by-step explanation:
it is 2
The line 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5. True or False?
Answer:
this is Ture
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
By changing both equations to slope-intercept, it is easier to determine whether two lines are perpendicular.
Since [tex]y = \frac{5}{2} x+ 5[/tex] is already in slope-intercept form, we just need to change the first given equation.
2x + 5y + 3 = 0
2x + 5y = -3
5y = -2x -3
[tex]y=\frac{-2}{5}x-\frac{3}{5}[/tex]
Two lines are perpendicular when the slope of the lines (coefficient of x) are negative reciprocals (opposite sign of the inverse of a number).
Comparing the two slopes [tex]\frac{5}{2}[/tex] and [tex]\frac{-2}{5}[/tex], we can see they they both fit the criteria of being opposite signs and inverses of each other.
So 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5.
