Answer:
Step-by-step explanation:
Because this problem is not easily solvable through factoring, we must use long division to find the answer.
_______________ x+7 | x3 + kx2 - 34x + 56
When performing long division on polynomials, we should try to cancel out the term with the greatest power first. So, we must figure out how many x's go into x3, because x is the first term of the first polynomial and x3 is the first term of the second polynomial. x*x2 = x3, so:
x2
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
Then, we see how many x's go into (k-14)x2. x*(k-14)x = (k-14)x2, so:
x2 + (k-14)x
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
-7kx - 132x + 56= (-7k-132)x + 56
x*(-7k-132) = (-7k-132)x, so:
x2 + (k-14)x + (-7k-132)
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
(-7k-132)x + 56
(-) (-7k-132)x - 7k - 924
-7k - 868
The answer is x2 + (k-14)x + (-7k-132) - [(7k-868)/(x+7)]
PLEASE HELP Area of Cross Sections
Thus, the area of cross section perpendicular to the base area will be in form of rectangle : Area = 130.32 cm².
Explain about the Area of Cross Section?The area of a sliced piece of a 3D object, such a pipe, is known as the cross sectional area. The cross sectional area of a pipe when cut perpendicular to it's own longest axis is determined for the circle-shaped top portion of the sliced component.
Given data:
Base area of cylinder = 12.96 π cm²
height of cylinder = 18.1 cm.
Let the radius of the cylinder be 'r'.
Base area of cylinder = π*r².
π*r² = 12.96 π
r² = 12.96
r = 3.6 cm
now, the area of cross section perpendicular to the base area will be in form of rectangle with.;
Base = 2*r = 2*3.6 = 7.2 cm
height = 18.1 cm.
Area = base * height
Area = 7.2 * 18.1
Area = 130.32 cm²
Thus, the area of cross section perpendicular to the base area will be in form of rectangle : Area = 130.32 cm².
Know more about the Area of Cross Section
https://brainly.com/question/13029309
#SPJ1
A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nall
Number
of Nails
67
18
10
Abundance
(%)
[7]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
Med Nail % Abund.
Enter
According to the question the percent abundance of the medium nails in the sample is approximately 18.95%.
Explain medium?Whenever the set of data is presented from least to largest, the median is indeed the number in the middle. For instance, since 8 is in the middle, this would represent the median value here.
To find the percent abundance of the medium nails in the sample, we first need to calculate the total number of nails in the sample:
Total number of nails = 67 + 18 + 10 = 95
Next, we can calculate the percent abundance of the medium nails using the formula:
Percent abundance = (number of medium nails / total number of nails) x 100%
Using the values from of the table as inputs, we obtain:
Percent abundance of medium nails = (18 / 95) x 100% ≈ 18.95%
As a result, the sample's average percentage of medium nails is roughly 18.95%.
To know more about medium visit:
https://brainly.com/question/16408033
#SPJ1
Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Select three options. x + 15 + 35 = 155 35 x + 15 = 155 35 x = 155 minus 15 It will take 8 months to pay off the debt. It will take 4 months to pay off the debt.
Answer: 3. 35x + 15 = 155
Step-by-step explanation:
35 x 4 = 140
140 + 15 = 155
1 The table below shows the cost of an attorney as a function of the number o
hours worked.
A C=355h
3 C= _—_h+355°
Number of
Hours, h
1
255
4
7
8
Based on the table, which function models this situation?
Total Cost, C
с
$355
$1120
$1885
$2140
D
C=255h+100
C=765h-410
All three data points are compatible with this set of equations, leading us to the conclusion that C = -195h + 550 is the function that best describes the scenario.
What does a function look like in math?A function connects an input with an output. It works like a machine that has an input and an output. The traditional manner of writing a function is "f(x) = 5".
The following function represents this circumstance:
C = -195h + 550
The first two data points can be used to create two equations:
355 = -195(1) + C
1120 = -195(3) + C
When we solve for C in each equation, we obtain:
C = 550
C = 550 + 585 = 1135
We can try utilising the first and third data points as the second equation doesn't quite match the third data point:
355 = -195(1) + C
1885 = -195(4) + C
Solving for C in each equation, we get:
C = 550
C = 550 + 975
= 1525
To know more about function visit:-
https://brainly.com/question/12431044
#SPJ1
You want to create a simulation of the following scenario:
In country x 50% of people have blood type O, 25% have blood type A, 12.5% have blood type B, and 12.5% have blood type AB.
In country y, 60% have blood type O, 20% have type A, 10% have type B and 10% have type AB.
What is the best way to assign values for a simulation using random digits table?
Choose answer from photo below! A, B, C, or D : this is the answer I want, not just an explanation please, thank you so much! 100 points!
Thank you :)
Answer: click thanks if you like my answer. have a good day <:
The best way to assign values for a simulation using a random digits table is to first identify the possible outcomes and assign a number or range of numbers to each outcome. Then, using the random digits table, randomly select digits and match them to the assigned outcomes.
For example, in the given scenarios for blood types in different countries, each blood type is assigned a specific number or range of numbers. Using the random digits table, the assigned numbers can be matched to the digits in the table to simulate the occurrence of each blood type in the population.
To answer the questions:
1.What is the purpose of assigning values for a simulation using a random digits table?
The purpose of assigning values for a simulation using a random digits table is to create a simulated scenario that reflects the likelihood of different outcomes based on assigned probabilities. This can help in making predictions and decisions in various fields such as medicine, finance, and social sciences.
2.In which scenario are blood types represented with the fewest number of digits?
Blood types are represented with the fewest number of digits in the third scenario for both Country X and Country Y. Blood type O is represented with 0, blood type A with 1, blood type B with 3, and blood type AB with 4, while all other digits are ignored.
3.In which scenario are blood types represented with the most number of digits?
Blood types are represented with the most number of digits in the first scenario for Country X, where blood type O is represented with 0, 1, 2, 3, 4, and 5, blood type A with 6 and 7, blood type B with 8, and blood type AB with 9. The same applies to Country Y in the first scenario.
Step-by-step explanation:
hope its help <:
PLEASE HELP NOW PLEASE!!!!!!
Answer:
[tex]\frac{2}{3} ^{7}[/tex]
Step-by-step explanation:
1) Count how many [tex]\frac{2}{3}[/tex] there are.
[tex]\frac{2}{3} ^{7}[/tex]
Write the solution in the interval notation x=1
Answer:
I'm too stressed rn like be so foreal
Answer:
x < 2 O R x > 1 ⇔ ( − ∞ , ∞ )
Explanation:
x < 2 means x can take any value less than two and interval notation, this means ( − ∞ , 2 ) , meaning that all numbers between − ∞ and 1 are included and as − ∞ and 2 are not included we have use small brackets. This forms one set of numbers, say P . x > 1 means x can take any value greater than one and interval notation tis means ( 1 , ∞ ) , meaning that all numbers between 1 and ∞ are included, but not 13 and ∞ . This forms another set of numbers, say Q . Hence x < 2 O R x > 1 represents the union of two sets P and Q i.e P ∪ Q or in other words ( − ∞ , 2 ) ∪ ( 1 , ∞ ) . Observe that P ∪ Q includes all the numbers from − ∞ to ∞ and hence x < 2 O R x > 1 ⇔ ( − ∞ , ∞ )
20 points!! please help!!
To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.
What is area?Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure
Area of rectangle = length x width
= 20 ft x 8 ft
= 160 sq. ft
Area of triangle = 1/2 xbase xheight
= 1/2 x 8 ft x 10 ft
= 40 sq. ft
To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).
Using the Pythagorean theorem, we have:
12² = 10² + b²
144 = 100 + b²
44 = b²
b = √44
b ≈ 6.63 ft
Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:
Area of total figure = area of rectangle + area of triangle
= 160 sq. ft + 40 sq. ft
= 200 sq. ft
To know more about Pythagorean theorem visit:
https://brainly.com/question/15169173
#SPJ1
f(x) = 2x - 1 g(x) = 7x + 8 find (gof) (x)
Answer:
(gof)(x) = 14x + 1
Step-by-step explanation:
We can think of (gof)(x) as g(f(x)). Writing it in this form shows that we must start with the inner function and work our way to the outer function.
Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.
f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1
Now, this output becomes the input for g(x):
g(2x-1) = 7(2x - 1) + 8
14x -7 + 8
(gof)(x) = 14x + 1
Maria and Ming start at the same point and rive in opposite directions. Maria drives 36 mph and Ming drives 32 mph. How far apart will they be in 2 hours
Maria and Ming will be 136 miles apart after 2 hours.
What is Distance?
Distance is the total length of a path an item or person takes to get from one place to another, ignoring the direction of motion. Given that it is a scalar number, it has only a magnitude and no direction. The most common units used to determine distance are meters, kilometers, miles, and feet. (ft).
The distance between Maria and Ming will grow at a rate that is equal to the sum of their speeds because they are traveling in opposite directions:
distance between them = (Maria's speed + Ming's speed) x time
= (36 mph + 32 mph) x 2 hours
= 68 mph x 2 hours
= 136 miles
Therefore, Maria and Ming will be 136 miles apart after 2 hours.
To learn more about Distance
https://brainly.com/question/26046491
#SPJ9
a) Construct a probability distribution
b) Graph the probability distribution using a histogram and describe its shape
c) Find the probability that a randomly selected student is less than 20 years old.
d) Find the probability that a randomly selected student's age is more than 18 years
old but no more than 21 years old.
LOOK AT SCREENSHOT FOR FULL QUESTION
The probability that a randomly selected student's age is more than 18 years old but no more than 21 years old is 0.57.
What is a continuous random variable's probability?
Continuous random variables are defined as having an infinite number of possible values. A continuous random variable hence has no probability of having an accurate value.
a) In order to create a probability distribution, all potential values of the random variable must be listed along with the related probabilities. We may get the relative frequency (or probability) for each value of the random variable from the above frequency distribution:
Age Frequency Probability
16 3 0.03
17 5 0.05
18 10 0.10
19 15 0.15
20 20 0.20
21 22 0.22
22 17 0.17
Total 92 1.00
b) We can use a histogram to see the probability distribution. The likelihood is represented by the vertical axis, while the age is represented by the horizontal axis. The height of each bar in the histogram should represent the likelihood for that age, with bars for each age value.
With a peak at age 20, the distribution's shape looks to be roughly symmetrical.
c) To get the likelihood that a student chosen at random is under 20 years old, we must add the probabilities for the ages 16, 17, 18, and 19:
P(age < 20) = P(age = 16) + P(age = 17) + P(age = 18) + P(age = 19)
= 0.03+0.05+0.10+0.15
= 0.33
Consequently, there is a 0.33 percent chance that a randomly chosen student is under 20 years old.
d) To determine the likelihood that a randomly chosen student is older than 18 but not older than 21, we must add the probabilities for the ages 19, 20, and 21:
P(18 < age ≤ 21) = P(age = 19) + P(age = 20) + P(age = 21)
= 0.15 + 0.20 + 0.22
= 0.57
As a result, there is a 0.57 percent chance that a randomly chosen student will be older than 18 but not older than 21.
To know more about probability visit:
https://brainly.com/question/30719832
#SPJ1
during last nights basketball game the number of points scored by the hornets was triple the number of points scored by the raiders the raiders scored 6 points how many points did the hornets score?
2
9
12
18?
Answer:
18
Step-by-step explanation:
siz times three is eighteen
58 points please urgent super urgent
4x=16
what is x
Answer:4? Think
Step-by-step explanation:
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below.
Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
The maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
Using quadratic regression, [tex]y = ax^2 + bx + c[/tex]
where a, b and c are constants and x is the independent variable we can determine the equation of the curve that best fits the data. The equation will be in the form of[tex]y = ax^2 + bx + c[/tex], where y is the revenue, x is the number of photos sold, and a, b, and c are constants. The constants can be determined by solving the system of equations formed by the three data points.
After solving for the constants, we can determine the maximum revenue by finding the vertex of the curve. The vertex is located at x = -b/2a, and the corresponding revenue is[tex]y = ax^2 + bx + c[/tex]. Plugging in the values for a, b, and c, we can calculate that the maximum revenue is achieved when she sells 33 photos at a price of 25 per photo.
Learn more about quadratic regression here:
https://brainly.com/question/17018837
#SPJ1
Complete question
Darlena has started taking photos at amateur dog racing events, later offering the photos for sale to the dog owners by email. The prices she has charged per photo at each of her first three events, and the corresponding number of photos sold and total revenue raised, appear in the table below. Treating revenue as a function of the number of photos sold, a graph of the three data points is also shown. If she uses quadratic regression to fit a curve to the data, what number of photos sold and what price per photo will maximize her revenue?
You have been asked to build a scale model of your school out of toothpicks. Imagine your school is 30 feet tall. Your scale is 1 ft:1.68 cm.
If a toothpick is 6.3 cm tall, how many toothpicks tall will your model be?
The model will be
toothpicks tall.
Your mother is out of toothpicks, and suggests you use cotton swabs instead. You measure them, and they are 7.6 cm tall. How many cotton swabs tall will your model be? If necessary, round your answer to the nearest whole number.
The model will be approximately
cotton swabs tall.
Answer:
8 toothpicks
7 cotton swabs
Step-by-step explanation:
Since the school is 30 feet tall and the scale is 1 ft : 1.68 cm, 30 feet will require a scale model of 1.68 x 30 = 50.4 cm
Since each toothpick is 6.3 cm tall, the total number of toothpicks required for 50.4 cm = 50.4/6.3 = 8 toothpicks
If using cotton swabs each 7.6 cm tall, the number of cotton swabs would be 50.4/7.6 = 6.63
Rounding this to the nearest number means you will need 7 cotton swabs
the cost for3.8 pounds of shrimp is 18.05 . find the unit price in dollars per pound. if necessary round it to the nearest cent
The unit price in dollars per pound is $4.75 (rounded to the nearest cent).
What is profit and loss?
Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every commodity. We can determine the profit made or loss suffered for a specific commodity based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are discussed in this article.
To find the unit price in dollars per pound, we need to divide the total cost by the total weight:
Unit price = Total cost / Total weight
In this case, the total weight is 3.8 pounds and the total cost is $18.05.
Unit price = $18.05 / 3.8 pounds
Unit price = $4.75 per pound (rounded to the nearest cent)
Therefore, the unit price in dollars per pound is $4.75 (rounded to the nearest cent).
Learn more about cost on:
https://brainly.com/question/19104371
#SPJ9
Zoe is saving money to go on a trip to Mexico. She earns 16.75 for mowing the lawn . If Zoe mows the lawn 28 times how much money will she earn
469
do 16.75 x 28 which will equal to 469
Jaylen estimates the side of the square to be 8.5 inches long. The actual length of the side of the square is 8.3 inches long. What is the percent error of the area of the two squares?
Answer:
4.88%
Step-by-step explanation:
All sides of a square are equal
let x = length of a side
Area = x·x = x²
Estimated area = (8.5)² = 72.25 in²
Actual area = (8.3)² = 68.89 in²
percent error = (actual area - estimated area) / (estimated area) x 100
% error = (68.89 - 72.25) / (68.89) x 100 = -4.88% the negative sign means the estimate was higher than the actual.
Find d/dx (cos(x) + e^5x) using derivative rules.
O-sin(x) +5e^5x
O-sin(x) + 5xe^(5x-1)
O-sin(x) +e^5x
None of the answers listed is correct.
O sin(x) +e^5x
Answer:
1st one.-sin(X)+5e^5x
It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
mentum
Copyright© 2022 Edmentum, Inc. All Rights Reserved
Privacy Policy California Priv
Mar 10
11:
Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
What is the volume of this cone?
The volume of the cone is 2119. 5 cubic centimeters
How to determine the volume of the coneThe formula used for calculating the volume of a cone is expressed as;
V = πr² h/3
Given that the parameters are namely;
V is the volume of the cone.π takes the constant value of 3.14h is the height of the cone.r is the radius of the cone.Now, substitute the values, we have;
Volume , V = 3.14 × 15² × 9/3
Divide the values, we have;
Volume = 3.14 × 225 × 3
Multiply the values, we get;
Volume, V = 2119. 5 cubic centimeters
Learn about volume at: https://brainly.com/question/1972490
#SPJ1
An image of a rhombus is shown.
A rhombus with a base of 17 inches and a height of 14 inches.
What is the area of the rhombus?
62 in2
119 in2
124 in2
238 in2
Answer: The area of a rhombus can be calculated using the formula:
A = (base x height) / 2
Substituting the given values, we get:
A = (17 in x 14 in) / 2
A = 119 sq in
Therefore, the area of the rhombus is 119 square inches.
Hence, the answer is option B, 119 in2.
Step-by-step explanation:
The area of the rhombus is 238 square inches.
Explanation:To find the area of a rhombus, you can use the formula: Area = base * height.
In this case, the base of the rhombus is 17 inches and the height is 14 inches. Plugging these values into the formula, we get Area = 17 * 14 = 238 square inches.
Therefore, the area of the rhombus is 238 square inches.
Learn more about Area of a Rhombus here:https://brainly.com/question/33943232
#SPJ2
the front of a tent has the shape of an isosceles triangle with equal sides of 163 cm long. the measure of the angle at the peak of the tent is 103 degrees. determine the height of the tent to the nearest centimetre.
To find the height of the tent, we need to use trigonometry. Let's draw a diagram to help visualize the problem
/|\
/ | \
h / | \ h
/ | \
/ | \
/ | \
/ | \
/_ _|_ __\
b 81.5 b
We can see that the height of the tent (h) forms one leg of a right triangle, with the base (b) being half of one of the equal sides of the isosceles triangle. We can use the angle at the peak of the tent (103 degrees) to find the height using the tangent function:
tan(103) = h/b
To find b, we can use the fact that the equal sides of the isosceles triangle are 163 cm long, so b = 163/2 = 81.5 cm.
Now we can plug in b and the angle measure into the tangent equation and solve for h:
tan(103) = h/81.5
h = 81.5 * tan(103)
h ≈ 370.5 cm
Therefore, the height of the tent is approximately 370.5 cm or 371 cm to the nearest centimeter.
Answer the questions about the graph shown below.
Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.
what is inequality ?An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A relationship between two values, where one value is larger than, less than, or not equal to the other, is expressed by an inequality. The inequality marks "" (less than), ">" (greater than), "=" (less than or equal to), ">=" (greater than or equal to), and "" can be used to denote an inequality (not equal to).
given
The disparity is as follows:
-3x + 2 ≥ 11
By subtracting 2 from both sides of the inequality and then dividing the result by -3, we can separate x on one side of the inequality .
-3x + 2 - 2 ≥ 11 - 2
-3x ≥ 9
x ≤ -3
Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
Whats the the sum of x and 2
The sum of x and 2 is equal to x + 2.
What is value?Value in math is the numerical representation of a quantity or expression. It can also be defined as an amount or a numerical representation of a quantity that is assigned to a variable or a constant in a mathematical expression. Value can be expressed in various forms, such as decimal, fraction, and scientific notation. Value is also used to calculate the result of an equation or a problem. Value is a fundamental concept in mathematics, and it is used to measure and compare different quantities.
This equation can be used to calculate the sum of any two numbers, x and 2. For example, if x is equal to 5, then the sum of x and 2 is equal to 5 + 2, which is equal to 7. Similarly, if x is equal to 10, then the sum of x and 2 is equal to 10 + 2, which is equal to 12. Therefore, the sum of x and 2 depends on the value of x.
To know more about value click-
https://brainly.com/question/843074
#SPJ1
Please helpppppppp!!!!
The 3rd graph is the correct one representing the open sentence.
What is an Inequality?Inequalities is defined as the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values or data. The equal sign in between can be replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
-5≤n-2≤2
First you need to get n by itself, so add 2 to all 3 terms:
-5 +2 ≤ n-2+2 ≤ 2+2
Simplify:
-3 ≤ n ≤ 4
The less than or equal to signs (≤) mean the dots on the line graph are solid.
And n is between -3 and positive 4, the 3rd graph is the correct one.
to know more about line, visit:
https://brainly.com/question/30003330
#SPJ1
How do you write y = 6 in slope intercept form
examine each equation and determine if it represents a
linear or nonlinear function. Explain your reasoning please.
7 y = ²³/x+7
8 y = x³ + 2
Using function concepts, we have that:1. Non-linear2.B)x y0 11 22 53 103. Linear4.: Linear: Linear: Non-Linear: Linear5. LinearIn a linear function, the rate of change is constant.A linear function is also of the first degree.Item 1:From -3 to -1, the rate of change is of From -1 to 1, the rate of change is of .Different rates of change, so non-linear.Item 2:At function b, from 0 to 1, the rate of change is of 1, from 1 to 2 of 3, different rates of change, so non-linear.Item 3:Highest degree of x is 1, so first degree, and thus linear.Item 4:The only non-linear is , which is of the second degree. is a constant function, with a rate of change of 0, so linear.The last function is written as:Highest degree of x is 1, so also linear.Item 5:In all cases, the rate of change is constant, so linear.
I will mark you brainiest!
What is the value of x in the figure below
A) 4.5
B) 10
C) 5
D) None of the choices are correct
Answer:
I will not show you the process it is easy the answer is 4.5 or 6 ≈
HELPPPPPP PLEASE PLEASEEEEEE
Determine a function type that
could represent the values in the
table.
x f(x)
0 −18
1 −15
2 −12
3 −9
4 −6
◻ linear
◻ quadratic
◻ exponential
Answer: Linear
Step-by-step explanation:
Since the difference between consecutive values of f(x) is constant, this suggests that the function could be linear. To confirm this, we can calculate the differences between consecutive values:f(1) - f(0) = -15 - (-18) = 3
f(2) - f(1) = -12 - (-15) = 3
f(3) - f(2) = -9 - (-12) = 3
f(4) - f(3) = -6 - (-9) = 3
Since the differences are constant and equal to 3, this confirms that the function is linear.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation:
y = mx + bwhere m is the slope and b is the y-intercept.
We can use the first two points (0, -18) and (1, -15) to find the slope:
m = (change in y) / (change in x) = (-15 - (-18)) / (1 - 0) = 3
Now we can use the slope and one of the points to find the y-intercept:
y = mx + b
-18 = 3(0) + b
b = -18
Therefore, the equation of the linear function is:
f(x) = 3x - 18
So the function type that could represent the values in the table is linear.