The surface area of the pyramid is approximately 74.24 square inches.
What is a pyramid?
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.
The area of each triangular face can be found using the formula:
Area = (1/2) * base * height
where the base is one of the sides of the square base and the height is the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
slant height² = height² + (1/2 * base)²
where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.
height = 7 in.
base = 4 in.
slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53
slant height = √53 ≈ 7.28 in.
Now we can find the area of each triangular face:
Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 14.56 = 58.24 in²
The area of the square base is:
Area = side² = 4² = 16 in²
Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:
Surface Area = 58.24 + 16 = 74.24 in²
Therefore, the surface area of the pyramid is approximately 74.24 square inches.
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What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size
The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.
In the confidence interval formula p ± z, the circled portion represents the Margin of Error.
The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.
It indicates the range within which the true population parameter is likely to fall based on the sample data.
The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.
The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.
The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.
It reflects the trade-off between the desired level of confidence and the width of the interval.
A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.
Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
a. x² - 4x-2x+8
Answer:
(x -2)(x -4)
Step-by-step explanation:
You want to factor x² - 4x -2x +8.
Factor by groupingWe recognize that the product of the coefficients of the two linear terms is equal to the contant, so this is more easily factored by not combining like terms prior to factoring.
Grouping the terms in pairs, we find we can factor each pair:
(x² -4x) + (-2x +8)
= x(x -4) -2(x -4) . . . . . these terms have a common factor of (x -4)
= (x -2)(x -4) . . . . . . . factored form of the expression
On a sample tray, 3 out of 6 cake samples are chocolate.
What is the probability that a randomly selected piece of cake will be chocolate?
Write your answer as a fraction or whole number.
The probability that a randomly decided piece of cake maybe chocolate is 1/2 or half of or 0.
The proportion of chocolate cakes to all other cakes can be used to calculate the probability that a person will pick a chocolate cake from the pattern tray.
In this case, there are 3 chocolate cakes out of a total of 6 cakes.
So the probability of selecting a chocolate cake is:
3/6 = 1/2 (Dividing the numerator and denominator by their greatest common factor, in this case, 3 will simplify the fraction 3/6.)
Therefore, the probability of selecting a chocolate cake is 1/2 or 0.5 when expressed as a decimal.
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PLSSS HELP AND PLEASE SHOW WORK ASWELL
Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.
Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.
Part B.) To have the largest possible area for the pen, which pen should Collin build?
Answer:
A.
circular: ≈ 795.77 square feet
square: 625
Step-by-step explanation:
the circular pen would have a larger area.
Solving for the radius, we have:
r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)
Therefore, the area of the circular pen would be:
Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet
For a square pen with side length s, the perimeter is given by:
4s = 100
s = 25
The area of a square pen with side length s is given by:
A = s^2 = 25^2 = 625
Find each of the following probabilities for a normal distribution.
a. p(z > 1.25)
b. p(z > –0.60)
c. p(z < 0.70)
d. p(z < –1.30)
The solution is: the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
Here, we have,
Explanation:
To find each probability we need to use the normal distribution table that is accumulated to the left, so each probability is equal to
P(-1.80 < z < 0.20) = P( z < 0.20) - P( z < -1.80)
P(-1.80 < z < 0.20) = 0.5793 - 0.0359
P(-1.80 < z < 0.20) = 0.5434
P(-0.40 < z < 1.40) = P( z < 1.40) - P( z < -0.40)
P(-0.40 < z < 1.40) = 0.9192 - 0.3446
P(-0.40 < z < 1.40) = 0.5746
P(0.25 < z < 1.25) = P(z < 1.25) - P(z < 0.25)
P(0.25 < z < 1.25) = 0.8944 - 0.5987
P(0.25 < z < 1.25) = 0.2957
P(-0.90 < z < -0.60) = P(z < -0.60) - P(z < -0.90)
P(-0.90 < z < -0.60) = 0.2743 - 0.1841
P(-0.90 < z < -0.60) = 0.0902
Therefore, the answers are, the following probabilities for a normal distribution is:
a. 0.5434
b. 0.5746
c. 0.2957
d. 0.0902
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Factor Completely
n^4 − 4n^3 − 17n^2 − 36n + 108
Answer:
It can't be factor
Step-by-step explanation:
n^4 − 4n^3 − 17n^2 − 36n + 108
The GCF of this is 1, so the equation can't be factor.
y= +- 3/5 is equivalent to?
The equivalent value of the expression is y = + 3/5 and y = -3/5
Given data ,
Let the expression be represented as A
Now , the value of A is
y = ±3/5
On simplifying the equation , we get
y = +3/5
And, y = -3/5
Now , the decimal values of y are
y = ±0.6
Hence , the expression is y = ±0.6
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For the functions f and g find a. (f+g)(x), b. (f-g)(x), c. (f
The value of the given functions are:
(a) (f + g)(x) = (x -8 + 14) = x + 6
(b) (f-g)(x) = (x -8 - 14) = x - 22
(c) (f • g)(x) = (x - 8 (14)) = 14x - 112
(d) (f/g)(x) = (x - 8)/ 14
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have the functions are as follows:
f(x)=x - 8,
g(x)=5 + 9
To solve :
a. (f + g)(x),
b. (f-g)(x),
c. (f • g)(x), and
d. (f/g)(x)
Now,
(a) (f + g)(x) = (x -8 + 14) = x + 6
(b) (f-g)(x) = (x -8 - 14) = x - 22
(c) (f • g)(x) = (x - 8 (14)) = 14x - 112
(d) (f/g)(x) = (x - 8)/ 14
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The given question is incomplete, complete question is:
For the functions f and g find a. (f+ g)(x), b. (f-g)(x), c. (f• g)(x), and d. (f/g)(x) f(x)=x - 8, g(x)=5 + 9
Find cos B. a. Cosine B = StartFraction 41 Over 40 EndFraction c. Cosine B = StartFraction 40 Over 41 EndFraction b. Cosine B = StartFraction 9 Over 41 EndFraction d. Cosine B = StartFraction 9 Over 40 EndFraction
The answer choice which correctly represents the value of cos B as required is; Cosine B = StartFraction 40 Over 41 EndFraction.
Therefore Choice B is correct
What is the cosine rule?The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles and it states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
we know that from the trigonometric ratios that the cosine of an angle is the ratio of its opposite and hypothenuse.
Hence, we can say that:
cos B = 80 / 82
cos B = 40 / 41.
Inn conclusion, the cosine of angle B following from trigonometric ratios as requested is; cos B = 40 / 41.
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#complete question:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
Triangle A B C. Angle C is 90 degrees. Hypotenuse A B is 82, adjacent B C is 18, opposite A C is 80.
Find cos B.
a.
Cosine B = StartFraction 9 Over 41 EndFraction
c.
Cosine B = StartFraction 9 Over 40 EndFraction
b.
Cosine B = StartFraction 40 Over 41 EndFraction
d.
Cosine B = StartFraction 41 Over 40 EndFraction
Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.
Answer: y = (9/5)x + 5.
Step-by-step explanation:
The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.
In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.
what is the surface area of 11cn and 14cm
The surface area of the shape will be 46 yards².
What is the surface area?Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.
The formula for the surface area of the 2 bases is just b*h
12*8=96 yd²
Finding the lateral area:
(10*10)+(10*10)+(12*10)=
100+100+120=
320 yd²
Add the lateral surface area and the surface area of the 2 bases for the total surface area:
320+96=416 yd²
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Solve for p.
p − 4
2
= 3
The value of p in the expression is 45
What is additive inverse?Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
For example a+5 = 2 , by solving this we add the additive inverse of 5 to both sides. The additive inverse of 5 is -5
this means,
a+5-5 = 2-5
a = 2-5
a = -3
Similarly, p-42 = 3 is solved in the same way. we add the additive inverse of -42 which is +42 to both sides,
p-42+42 = 3+42
p = 3+42
p = 45
therefore the value of p is 45
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Hi can someone please help me? Look in the picture. I’ll give brainly if you explain :)
Miguel is 3 years older than Katrice. In 9 years the sum of their ages will be 51. How old is Miguel now?
At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?
b) How far from Town X did each vehicle travel when they passed each other?
Answer:
a) 2:15 pm
b) 240 km
Step-by-step explanation:
You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.
Head startThe van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.
Closing speedThe speed at which that distance is reduced is the difference between the car speed and the van speed:
80 km/h -64 km/h = 16 km/h
Closing timeThe time it takes for the head-start distance to be reduced to zero is ...
time = distance/speed
time = (48 km)/(16 km/h) = 3 h
a) Meeting timeThree hours after the car leaves, it will catch up with the van. That time is ... 11:15 +3:00 = 14:15 = 2:15 p.m.
b) Meeting distanceIn 3 hours, the car travels (3 h)(80 km/h) = 240 km.
Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.
__
Additional comment
The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.
PLEASE SOMEONE HELP ME DO THIS MATH PROBLEM
i am having a mental breakdown rnn :(.
Check the picture below.
uppose that you are told that the Taylor series of f(x)=x3ex2
about x=0
is
x3+x5+x72!+x93!+x114!+⋯.
Find each of the following:
ddx(x3ex2)∣∣∣x=0=
d7dx7(x3ex2)∣∣∣x=
a. Using Taylor series d(x³eˣ²)/dx about x = 0 is x⁴.
b. Using Taylor series d⁷(x³eˣ²)/dx⁷ about x = 0 is x¹⁰.
What is a Taylor series expansion?A Taylor series is a polynomial expansion of a function about a given point. It is given by f(x - a) = ∑(x - a)ⁿfⁿ(x - a)/n! where
a = point where f(x) is evaluated fⁿ(a) = nth derivative of f(x) about a and n is a positive integerGiven that the Taylor series of the function f(x) = x³eˣ² about x = 0 is
f(x) = x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4!, (1) we proceed to find the given variables
a. To find d( x³eˣ²)/dx about x = 0, the Taylor series expansion about x = 0 is given by
f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!
f(x - 0) = ∑(x - 0)ⁿf(0)/n!
f(x) = ∑xⁿf(0)/n!
f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....
f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + ....(2)
Since fⁿ(x) is the nth derivative of f(x), and we desire f¹(x) which is the first derivative of f(x). Comparing equations (1) and (2), we have that
x⁵ = xf¹(x)
f¹(x) = x⁵/x
= x⁴
So, d( x³eˣ²)/dx about x = 0 is x⁴.
b. To find d⁷( x³eˣ²)/dx⁷ about x = 0, the Taylor series expansion about x = 0 is given by
f(x - a) = ∑(x - a)ⁿfⁿ(a)/n!
f(x - 0) = ∑(x - 0)ⁿf(0)/n!
f(x) = ∑xⁿf(0)/n!
f(x) = x⁰f(x)/0! + xf(x)/1! + x²f(x)/2! + x³f(x)/3! + ....
Expanding it up to the 8 th term, we have that
f(x) = f(x) + xf¹(x) + x²f²(x)/2! + x³f³(x)/3! + x⁴f⁴(x)/4! + x⁵f⁵(x)/5! + x⁶f⁶(x)/6! + x⁷f⁷(x)/7!.....(3)
Now expanding equation (1) above to the 8th term by following the pattern, we have that
f(x) = x³ + x⁵ + x⁷/2! + x⁹/3! + x¹¹/4! + x¹³/5! + x¹⁵/6! + x¹⁷/7!.....(4)
Since fⁿ(x) is the nth derivative of f(x), and we desire f⁷(x) which is the seventh derivative of f(x). Comparing equations (3) and (4), we have that
x⁷f⁷(x)/7! = x¹⁷/7!
f⁷(x) = x¹⁷/x⁷
= x¹⁰
So, d⁷( x³eˣ²)/dx⁷ about x = 0 is x¹⁰.
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A bug crawls 5 1/2 feet in 28.6 seconds. At that pace, how many seconds does it take the bug to crawl one foot?
Answer:
5.2 seconds
Step-by-step explanation:
To get one foot, we need to divide by 5.5
Set up a proportion:
[tex]\frac{5.5}{5.5}=\frac{28.6}{5.5}[/tex]
Solve:
[tex]1ft.=5.2secs.[/tex]
a group of students were asked if they are in the math club and if they are in the literature club. Partial results are shown in the table. What is the value of x+y?
Hence Option A. 22 is correct.
How to solveOf the students in the maths club , 67% are not in the literature club.
So the number of students in Maths club =
[ ( Number of students in maths club but not in the literature club) / 67 ] * 100 % = [ 16 / 67 ] * 100% = 24 (Rounded)
Hence, Number of students in maths club and in the literature club =
x = Total Number of students in Maths club - Number of students in maths club but not in the literature club
x = 24 - 16 = 8
Of the students not in the maths club , 78% are not in the in the literature club.
So, Of the students not in the maths club , 100% - 78% = 22% are in the literature club.
So the number of students not in the Maths club =
[ ( Number of students not in the maths club and in the literature club) / 22 ] * 100 %
= [ 4 / 22 ] * 100% = 18.18 = 18 (Rounded)
Hence, Number of students not in the maths club and not in the literature club =
y = Total Number of students not in the Maths club - Number of students not in the maths club and in the literature club
y = 18 - 4 = 14
So, x + y = 8 + 14 = 22.
Hence Option A. 22 is correct.
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help me solve this please 2x+5y
Answer:
35
Step-by-step explanation:
Simply plug in the value of your 'x' and 'y':
x = 4.5
y = 5.2
[tex]2(4.5)+5(5.2)=9+26=35[/tex]
need help please
here is the picture is about Row Ops
The result of adding -3 (row 1) to row 2 is determined as (0 10) |-14.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 -4] | 8
To multiply row1 by -3, we will multiply each entity by 3 as shown below;
= -3(1 -4) | 8
= (-3 12) | -24
To add the result to 3;
(-3 12) | -24 + (3 -2)|10
= (0 10) |-14
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.
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A card is drawn from a deck of 52 cards. What is the probability that it is a 3 or a spade?
Answer:
P = 4/13 = 0.308
Step-by-step explanation:
3 cards 3
13 spade cards (includes the card 3 of spades)
[tex]P=(3+13)/52= 16/52 = 4/13=0.308[/tex]
Hope this helps.
Andy has $100 in an account. The interest rate is 6% compounded annually.
To the nearest cent, how much will he have in 2 years?
The amount that will be in Andy's account in 2 years after the addition of interest is $112.36
How to calculate the amount in Andy's account after 2 years ?Andy has $100 in an account
An interest rate of 6% is compounded annually
The amount that will be present in the account after 2 years can be calculated as follows
= 100(1+ 6/100)²
= 100(1 + 0.06)²
= 100(1.06)²
= 100(1.1236)
= 112.36
Hence the amount that will be present in the account after 2 years with the addition of interest is $112.36
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Please help!!!!!!!!!
Answer: I did not do the math, I just tell people how to do it
Hope I helped.
Step-by-step explanation:
Multiply the number of triangles you created by 180.
Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these?
Spinner B is the spinner that has a probability of 1/3 of spinning orange.
How to find the he probability of spinning orange is more than 40%a) For one of the spinners, the probability of spinning orange is 1/3. To identify which spinner this is, we need to find the spinner that has exactly one orange sector out of three total sectors.
From the given spinners, Spinner B is the only spinner that has one orange sector out of three, so Spinner B is the spinner that has a probability of 1/3 of spinning orange.
b) For two of the spinners, the probability of spinning orange is more than 40%. To find these spinners, we need to look for the spinners that have at least three orange sectors out of a total of eight sectors (since 3/8 is greater than 40%).
From the given spinners, Spinner A and Spinner C both have three orange sectors out of eight total sectors, so they are the two spinners for which the probability of spinning orange is more than 40%.
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Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: C {m | m > 2}
Step-by-step explanation:
write the number in exponential form with the base of 2
2^3m-4 > 2^2
compare the exponents = 3m-4 >2
move the constant to the right and then change the sign
3m> 2+4 add
3m>6 divide
m>2
Find the measure of EB
The measure of angle subtended by the arc EB is 96 ⁰.
What is the measure of arc angle EB?The measure of angle subtended by the arc EB is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, the theory states that, the angle formed by the intersection of two chords at the circumference of a circle is equal to half of the difference between the arc angles of the two chords.
We will have the following equation;
m∠ECB = ¹/₂( 7x + 6 - (4x + 16))
25 x 2 = 7x + 6 - 4x - 16
50 = 3x - 10
60 = 3x
x = 60/3
x = 20
The measure of arc angle EB is calculated as follows;
m∠EB = 4x + 16
m∠EB = 4(20) + 16
m∠EB = 96 ⁰
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b/8 < 8 help me please I also need the graphic
The solution of the inequality given is b < 64
the graph is attached
How to solve for bIn the equation, let us replace b with x
To solve the inequality x/8 < 8 for x, we need to isolate x on one side of the inequality.
We can do this by multiplying both sides of the inequality by 8, which will cancel out the 8 in the denominator on the left side:
Therefore, the solution to the inequality x/8 < 8 is x < 64.
This means that any value of x that is less than 64 will make the inequality true.
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For the function value f(−9)=6, write a corresponding ordered pair.
Answer:
(-9, 6) This ordered pair is used to find the function value f(-9)=6
or the given function value, write a corresponding ordered pair.
Step-by-step explanation:
For the given function value, write a corresponding ordered pair.
f(-9) = 6
The ordered pair of each function can be written as (x,y).
For any function, for example, g(x)= 10x, the input is x, and the output y is 10x. So ordered pair is (x,10x)
The given function value is: f(-9) = 6
Here input x=-9 and y value is 6
So, he corresponding ordered pair is (-9, 6)