An equivalent expression for 18c+144 is 18(c+8), by factoring out the greatest common factor of the terms 18 and 144.
In the original expression 18c + 144, we have two terms that do not have any common factors other than 1. However, we can see that both terms are multiples of 18, with 18 as the greatest common factor. So, we can factor out the 18 to simplify the expression.
To factor out 18, we divide each term by 18, which gives us:
18c/18 + 144/18
The first term simplifies to c, and the second term simplifies to 8, so we have:
c + 8
This expression represents the sum of c and 8, and it is equivalent to 18c + 144. However, we can still simplify this expression further by factoring out the common factor of c + 8, which gives us:
c + 8 = 18(c + 8)
So, we have the equivalent expression 18(c + 8), which is the original expression 18c + 144 after factoring out the greatest common factor of 18.
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take your time in 2-6
How do you find the slope intercept in a table
Answer:
To find a slope intercept in a table look what x is like this. ( 2,9) 2 is the x-intercept and 9 is the y-intercept. Furthermore, if you get a slope like 0,0 which is the origin put a dot on there.
Answer:
Step-by-step explanation:
use this equation
(y1-y2)/(x1-x2)
Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 204 square meters. Solve for the dimensions (length and width) of the field
The dimension of rectangular piece of land is 17 x 12 square units in size.
The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.
The space occupied by a flat shape or an object's surface can be referred to as the area.
What is the rectangular area formula?
Rectangle area equals length x width
Let the rectangle plot's length and breadth be x and y, respectively.
Juliet has a 58-meter fence.
The rectangular piece of land's perimeter is 58 meters.
2(length + width) = 58
x + y = 58\2
⇒ x + y = 29
Moreover, the plot's total area is 204 square units.
x × y = 204
⇒ x × (29 - x) = 204
[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]
(x-12) (x-17) = 0
x = 12, x = 17
When, x= 17
y = 29 - 17 = 12m
when x = 12
y = 29 - 12 = 17m
As a result, the rectangular land parcel has dimensions of 17 x 12 square units.
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what can we conclude from the five number summary about the location of the 20th percentile? the 90th percentile?
By knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
The five number summary is a way to summarize the distribution of a set of data by providing information about its minimum, first quartile (25th percentile), median (50th percentile), third quartile (75th percentile), and maximum. Using this summary, we can infer information about the location of specific percentiles.
For the 20th percentile, we can conclude that it lies between the minimum and the first quartile. The 20th percentile represents the value below which 20% of the data falls, so it must be less than or equal to the first quartile, which is the value below which 25% of the data falls. It must also be greater than or equal to the minimum.
For the 90th percentile, we can conclude that it lies between the third quartile and the maximum. The 90th percentile represents the value below which 90% of the data falls, so it must be less than or equal to the maximum, which is the largest value in the data set. It must also be greater than or equal to the third quartile, which is the value below which 75% of the data falls.
In conclusion, by knowing the five number summary of a data set, we can make inferences about the location of specific percentiles within the data.
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The "hang time" of a football is the amount of time the football stays in the air after being kicked. Zara kicks a football, and the height (in meters) of the football above the ground at t seconds is shown in the graph below.
The completed statements with regards to the projectile motion of the football are presented as follows;
This graph is a nonlinear function
The hang time of the football is 3 seconds
The football reaches its maximum height when t = 1.5 seconds
The maximum height is about 11 meters
For t between t = 0 and t = 1.5, the height is increasing
What is a projectile motion?The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.
The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;
The x-intercept of the graph are; (0, 0), and (3, 0)
Therefore;
The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;
Hang time = 3 - 0 = 3
The hang time of the football is 3 secondsThe graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;
The football reaches the maximum height when t = 1.5 second(s)The maximum height reached, obtained from the coordinate of the maximum height is 11 metersThe height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds
For t between t = 0 and t = 1.5, the height is increasing
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Answer:
Nonlinear
3
1.5
11
increasing
Step-by-step explanation:
Select the correct answer. Newspaper Advertisement on Front Page ABC 89. 4% JKL 86. 3% PQR 80. 5% TUV 88. 7% XYZ 89. 1% Total 82. 4% The probabilities of different newspapers having an advertisement on the front page are given in the table. What is the chance of seeing an advertisement on the front page if the newspaper is JKL? A. 82. 4% B. 86. 3% C. 88. 7% D. Insufficient data
The chance of seeing an advertisement on the front page if the newspaper is JKL is 86.3%.
Probabilities:
In science, the probability of an event is a number representing the probability that an event will occur. It is expressed as a number ranging from 0 to 1, or as a number ranging from 0% to 100% using percentage display. The more likely an event is to happen, the more likely it is to happen. The probability of an impossible event is zero. The probability of an event that must happen is 1. The probabilities of two complementary events A and B (A or B) add up to 1.
A simple example is a fair (unbiased) coin toss. When the coin is fair, the two possible outcomes (heads and tails) are equally likely. Since the two outcomes are complementary and the probability of heads is equal to the probability of tails, the probability of each of the two outcomes is 1/2.
Therefore,
After looking at the table, the percentage that represents JKL and a front page advertisement is 86.3%.
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HELPPPPPPPPPPPPPPPPPPPPP
Answer: look at the image for the answer and solution
Step-by-step explanation:
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.
The scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
For this problem, we have that the original and the dilated figures are given as follows:
Original: right triangle on the left.Dilated: right triangle on the right.Hence the scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the scale factor was presented.
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college gpa and salary. do students with higher college grade point averages (gpas) earn more than those graduates with lower gpas (civicscience)? consider the college gpa and salary data (10 years after graduation) provided in the file gpasalary. a. develop a scatter diagram for these data with college gpa as the independent variable. what does the scatter diagram indicate about the relationship between the two variables? b. use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college gpa. c. at the .05 level of significance, does there appear to be a significant statistical relationship between the two variables?
The scatter diagram for the data with college GPA as the independent variable is illustrated as follows.
In this case, we have a dataset that includes the GPA and salary of graduates ten years after graduation. We can use GPA as the independent variable (or x-axis) and salary as the dependent variable (or y-axis). We can then plot each data point on the graph, where the x-coordinate represents the GPA and the y-coordinate represents the salary.
To create the scatter plot, we first need to organize the data into pairs of GPA and salary values. For example, the first pair is (2.22, 72,000), where 2.22 is the GPA and 72,000 is the salary. We can then plot this point on the graph by locating 2.22 on the x-axis and 72,000 on the y-axis.
We repeat this process for each data point, and then connect the points with a line or a curve. The resulting scatter plot shows us the overall pattern of the relationship between GPA and salary. If there is a positive relationship between the two variables, we would expect to see the points cluster around a line that slopes upwards from left to right.
Overall, the scatter plot provides a useful visual tool for exploring the relationship between college GPA and salary. While it suggests that there is a positive relationship between the two variables, it also reminds us that there are many other factors that contribute to earnings.
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Complete Question:
Do students with higher college grade point averages (GPs) earn more than those graduates with lower GPAs?
Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary (S)
72,000 2.22
48,000 2.29
72,000 2.57
64,000 2.59
86,000 2.77
98,000 3.12
133,000 3.35
130,000 2.85
157,000 3.66
162,000 3.68
Develop a scatter diagram for these data with college GPA as the independent variable
Convert milligrams per liter to micrograms per (fluid ounce)
To convert milligrams per liter (mg/L) to micrograms per fluid ounce (µg/fl oz), we can use the conversion factor of 29.5735.
This conversion factor takes into account the difference in volume between a liter and a fluid ounce.
1 fl oz = 29.5735 mL
1 L = 1000 mL
So, to convert from milligrams per liter to micrograms per fluid ounce, we divide by 29.5735 and multiply by 1000:
(mg/L) * 1000 / 29.5735 = (µg/fl oz)
Therefore, to convert a value x from milligrams per liter to micrograms per fluid ounce:
x (µg/fl oz) = x (mg/L) * 1000 / 29.5735
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The price of a car increased from £10,506
to £11,288. Calculate the percentage
change (to 1dp where needed).
In the data set below, what are the lower quartile, the median, and the upper quartile?
1235588
lower quartile =
median = 5
upper quartile =
The lower quartile is 2, the median is 5 and the upper quartile is 8.
What are quartiles?
The values that divide a list of numerical data into three quarters are known as quartiles.
We are given a data set as 1, 2, 3, 5, 5, 8, 8
From this, we get the median as 5 as median is the middle number of the data set.
We know that lower quartile is the median of the lower half of the data.
So, lower quartile is 2.
Upper quartile is the median of the upper half of the data.
So, upper quartile is 8.
Hence, the lower quartile is 2, the median is 5 and the upper quartile is 8.
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Suppose Q and R are independent events. Find P(Q and R).
P(Q) = 0.37, P(R) = 0.24
Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.
What is meant by probability?Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes.Statistics is the study of events subject to probability. The probability is typically expressed as a ratio between the number of positive outcomes and all of the outcomes in the sample space. It is written as follows: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the discipline of mathematics that deals with the occurrence of a random event.Therefore,
Events Q and R are not mutually exclusive, thus we are given two probabilities, P(Q) = 0.41 and P(R) = 0.44.. In this instance, the likelihood of Q and R is equal to P(Q) × P(R), which is 0.1804. The solution to this issue is this.
The complete question is:
Suppose Q and R are independent events. Find the probability of Q and R when P(Q)=0.41 Ans P(R)=0.44.
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6. 56% of
_ is 3.92 *
Answer:
60
Step-by-step explanation:
3.92 = (6.56/100) * _
To solve for _, we can multiply both sides by 100:
100 * 3.92 = (6.56/100) * _
100 * 3.92 = 6.56 * _
_ = (100 * 3.92) / 6.56
Therefore, _ = 60.
Answer: 60
Step-by-step explanation:
a college student is preparing a course schedule of four classes for the next semester. the student can choose from the open sections shown in the table. (a) find the number of possible schedules that the student can create from the offerings. (b) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed. (c) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the english 105 sections are closed.
(a) The number of possible schedules that the student can create from the offerings is 96.
(b) the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed is 48.
(c) the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the English 105 sections are closed is 4.
(a) To find the total number of possible schedules, we need to multiply the number of choices for each class:
Number of schedules = 4 x 2 x 3 x 4 = 96
So, there are 96 possible schedules that the student can create from the offerings.
(b) If two of the math 100 sections are closed, then there are only two choices for that class. So, we have:
Number of schedules = 2 x 2 x 3 x 4 = 48
So, there are 48 possible schedules that the student can create from the offerings with two of the math 100 sections closed.
(c) If two of the math 100 sections and four of the English 105 sections are closed, then there are only two choices for math 100 and one choice for English 105. So, we have:
Number of schedules = 2 x 2 x 1 x 1 = 4
So, there are 4 possible schedules that the student can create from the offerings with two of the math 100 sections and four of the English 105 sections closed.
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Given ƒ (z) — 5(x − 6)³ + 4, classify each statement about ƒ-¹ (z) as true or false. The point of symmetry on f-¹(x) is (4,6). The domain of f-¹(x) is (-∞,4). The graphs of f¹(x) and f(x) are reflections across the x axis. The range of f¹(x) is (-∞,∞). True False OO O
The correct classification of the statements is: False, True, False, True.
What is Function ?
Function can be defined in which it relates an input to output.
The point of symmetry on f-¹(x) is (4,6).
False. The point (4,6) is not on the graph of f-¹(x), so it cannot be the point of symmetry. We can verify that the function is not symmetric with respect to any vertical or horizontal line.
The domain of f-¹(x) is (-∞,4).
True. The cube root function is defined for all real numbers, so the expression inside the cube root must be nonnegative. Therefore, (z - 4) / 5 ≥ 0, which implies that z ≥ 4. This means that the domain of f-¹(x) is (-∞,4].
The graphs of f¹(x) and f(x) are reflections across the x-axis.
False. The graphs of f¹(x) and f(x) are not reflections across the x-axis. We can plot the functions to see that they have different shapes and are not symmetric with respect to the x-axis.
The range of f¹(x) is (-∞,∞).
True. The cube root function is defined for all real numbers, so f-¹(z) can take any real value. This means that the range of f¹(x) is (-∞,∞).
Therefore, the correct classification of the statements is: False, True, False, True.
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PLEASE HELP!!!
Write a linear equation given slop is -1/3 and the point (-9,-1)
The equation of a line is y = -1/3x - 4
How to determine the equation of the lineThe general formula for the equation of a line is expressed as;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the linex is a point on the x-axis of the linec is the intercept of the line on the y -axisFrom the information given, we have that;
Slope, m = -1/3
Substitute the values
-1 = -1/3(-9) + c
expand the bracket
-1 = 3 + c
collect like terms
= -4
Hence, the equation is y = -1/3x - 4
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See had some cherries. Every day he ate 10 cherries and gave 5 away. After he gave that last 5 cherries away he had eaten 40 cherries altogether. How many cherries did Seb have at the start?
50 must have been his starting number of cherries.
Seb had 50 cherries at the start. This can be determined by solving the equation 10x + 5 = 40, where x is the number of days he ate 10 cherries and gave 5 away. When you solve the equation, you get x = 5, meaning he did this 5 times. Since 10x is 50, and 5 is added to that, the total is 50. Therefore, Seb had 50 cherries at the start.
To solve the equation, you first need to subtract 5 from both sides to get 10x = 35. Then, divide both sides by 10 to get x = 3.5. Since Seb could not have eaten 3.5 days worth of cherries, it means that he did the 10 and 5 activity 4 times, giving him 40 cherries before giving away the last 5. So 40 + 5 = 45 and 10x = 50, so 50 must have been his starting number of cherries.
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A 7meter flog poce costs a shadow of 5meter. Calculate height of an electric pole that will cost a shadow of 10m under the same condition
The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.
The flog poce cast a shadow of 5 metre and itself as a height of 7 m.
Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.
The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,
Tan A = perpendicular/base
Tan A will be equal for both.
Tan A = 7/5
Tan A = H/10
H is the height of the electric pole.
7/5 = H/10
H = 14m
The height of the electric pole will be 14 m.
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The distance between two towns is 600km,correct to the nearest 10km
A car takes 8 hours 40minute, correct to the nearest 10 minute, to travel this distance
Calculate the lower bound for the average speed of the car in km/h
Answer:
Below
Step-by-step explanation:
rate X time = distance
rate = distance / time <=====we want minimum of this so make denominator as large as possible and numerator as small as possible
distance = 595 KM ( rounds up to 600 km)
time = 8 hr 44 min rounds down to 8 :40 you could make it 8:44.99)
595 km / (8 + 44.99/60) hr = 68 km/hr
a standard pair of six-sided dice is rolled. what is the probability of rolling a sum less than or equal to 6 ? express your answer as a fraction or a decimal number rounded to four decimal places.
The probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778.
To calculate the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice, we need to find the number of ways the dice can be rolled to get a sum less than or equal to 6 and divide it by the total number of possible outcomes.
There are 6 x 6 = 36 possible outcomes when rolling a pair of dice, since there are 6 possible outcomes for each die. To get a sum less than or equal to 6, the only possible outcomes are:
1+1 = 2
1+2 = 3
1+3 = 4
1+4 = 5
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
4+1 = 5
There are 10 possible outcomes that result in a sum less than or equal to 6. Therefore, the probability of rolling a sum less than or equal to 6 is:
P(sum less than or equal to 6) = number of favorable outcomes / total number of possible outcomes
P(sum less than or equal to 6) = 10 / 36
Simplifying this fraction, we get:
P(sum less than or equal to 6) = 5 / 18
Therefore, the probability of rolling a sum less than or equal to 6 when rolling a pair of six-sided dice is 5/18 or approximately 0.2778 when rounded to four decimal places.
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The isosceles right triangle reflection to prove ASA congruence
A line of reflection in a triangle can be any line that acts as a mirror image, such that the reflected image of the triangle is congruent to the original triangle.
This line is perpendicular to the plane of the triangle and bisects the angle between the two sides that are being reflected.
How we used the reflection ruleTo be sure that each point was reflected across this line, we apply the reflection rule.
The reflection rule states that the distance from a point to the line of reflection is equal to the distance from its reflection to the line of reflection. This ensures that the reflected image of the triangle is congruent to the original triangle.
In an isosceles right triangle, two of its sides are congruent. This means that it satisfies the Angle-Side-Angle (ASA) congruence theorem. The ASA theorem states that if two triangles have two congruent angles and a congruent side between them, then the two triangles are congruent.
In addition to satisfying the ASA congruence theorem, an isosceles right triangle also satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Finally, the reflection of a triangle is considered a rigid motion, as it preserves the size and shape of the triangle.
Rigid motions do not change the lengths of the sides or the angles between them. They only change the position of the triangle in space. In the case of reflection, the triangle is flipped over the line of reflection, but its size and shape remain unchanged
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Isosceles Right Triangle Reflection to prove ASA Congruence
Answer the following questions:
What line of reflection did you choose for your transformation?
How are you sure that each point was reflected across this line?
What reflection rule did you apply to your triangle?
What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.
Did your triangle undergo rigid motion? Explain why.
Estimate the depth d of the crater to the nearest tenth.
The depth d of the crater is 714 m. The solution has been obtained by using trigonometry.
What is trigonometry?
The area of mathematics known as trigonometry is concerned with the study of the sides, angles, and connections of the right-angle triangle.
We are given a figure which shows that the sun's rays are falling at an angle of 55° and the base is given as 500 m.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan θ = d/500
Here, θ = 55°
So,
⇒tan 55° = d/500
⇒x = 500 tan 55°
⇒x = 500 * 1.428148
⇒x ≈ 714.074
⇒x ≈ 714 m
Hence, the depth d of the crater is 714 m.
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If you borrow $1,100 for 9 years at an annual interest rate of 4% , what is the total amount of money you will pay back?
A researcher found that for the years 2011 to 2017, the equation y = -0. 25(x - 2)^2 + 16, models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. During what year was the average of couches sold in Germany the greatest?
The vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
The equation y = -0.25(x - 2)² + 16 models the average of couches sold in Germany, where x is the number of years since 2011 and y is the number of couches sold. We can find the year when the average of couches sold in Germany was the greatest by finding the maximum value of the equation.
To find the maximum value, we can first rewrite the equation in vertex form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
y = -0.25(x - 2)² + 16
y = -0.25(x² - 4x + 4) + 16
y = -0.25x² + x + 15
To find the vertex of the parabola, we can use the formula h = -b/2a and k = f(h), where f(h) is the value of y at the vertex.
h = -b/2a = -1/(2*(-0.25)) = 2
k = f(h) = -0.25(2)² + 2 + 15 = 16
Therefore, the vertex of the parabola is (2, 16). This means that the average of couches sold in Germany was the greatest in the year 2013, which is 2 years after 2011.
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What shape do u expect the graph of the function described by 3x + 7y =8
Answer: A linear function with a line heading toward negative infinity as x approaches infinity and with a y-int at (0,8/7)
Step-by-step explanation:
The line will be linear as you rearrange the function to be y=
You would do this by moving the 3x over to the right side by subtracting both sides by 3x, giving you 7y=-3x+8. From here, you get y by itself by dividing both sides by 7. Giving a final function of [tex]y=-\frac{3}{7} x+\frac{8}{7}[/tex]
A large cheese pizza costs
$
18
$18dollar sign, 18. Each topping you add on costs
$
1.50 dollar sign, 1, point, 50.
How much would it cost to get a large cheese pizza with
cc toppings added?
Write your answer as an expression.
Answer:
A
=
1.50c + 18
where
A
is amount and
c
is toppings added
Step-by-step explanation:
The constant price is
18
dollars, which never changes and for every topping you get, it costs
$
1.50
. If you got no toppings, sub in
0
for
c
to get
$
18
.
Hello guys. If you could help me with this one question you shall get 80 whole points!
The solution to the given problem is 25/88. The solution has been obtained by applying BODMAS rule.
What is the BODMAS rule?
The letters BODMAS stand for Bracket, Of, Division, Multiplication, Addition, and Subtraction. An explanation of a mathematical expression's execution sequence is provided by the BODMAS. According to the BODMAS rule, brackets must be answered first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction.
We are given an expression as (3/11 + 2/11) * 5/8
Now, as per the BODMAS rule, we will first solve the brackets.
On solving the brackets, we get
5/11 * 5/8
Now, on solving it further, we get
5/11 * 5/8 = 25/88
Hence, the solution to the given problem is 25/88.
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Question
You work with a carpenter who asks you to cut 4 boards to the following lengths: 7½ inches, 10½ inches, 9 inches, and 5½ inches. What is the total length, in inches, of the cut boards?
The total length, in inches, of the four cut boards is 130 inches.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.
We have to find the total length of the board.
Total length of the board is found by adding each length.
Total length = 7½ + 10½ + 9 + 5½
Mixed fraction can be converted to improper fraction by cross multiplication.
7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2
Total length = 15/2 + 21/2 + 9 + 11/2
= (15/2 + 21/2 + 11/2) + 9
= 47/2 + 9
= 65/2
Again improper fraction can be converted to mixed fraction.
Total length of a board = 32 1/2 inches
But there are 4 boards.
Total length of the 4 boards = 4 × 65/2 = 130 inches
Hence the total length is 130 inches.
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What is the average rate of change of the function -4≤x≤-3
Check the picture below.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}[/tex]
Answer:
-2
[tex]\hrulefill[/tex]
Step-by-step explanation:
The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:
[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]
The given interval is -4 ≤ x ≤ -3, so:
[tex]a=-4[/tex][tex]b=-3[/tex]From observation of the given graph, the values of f(a) and f(b) are:
[tex]f(a)=f(-4)=-4[/tex]
[tex]f(b)=f(-3)=-6[/tex]
Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:
[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}[/tex]
Therefore, the average rate of change of the function f(x) on the given interval is -2.
