Answers
The domain, ranges and piecewise functions are;
10. D = (-∞, 3], R = [-2, ∞)
11. D = (-∞, -1), R = (-∞, 3)
12. [tex]f(x) =\begin{cases}\frac{2}{5}\cdot x + 4 & \text{ if } x\leq 0 \\x-5 & \text{ if } x > 0 \end{cases}[/tex]
13. [tex]f(x) =\begin{cases}-x-2 & \text{ if } x < -1 \\5 & \text{ if } -1 < x < 3\\ -2\cdot x + 5& \text{ if } 3 \leq x < \infty\end{cases}[/tex]
14. [tex]f(x) = \begin{cases}-2 & \text{ if } x < 4 \\\frac{1}{2} \cdot x + 4 & \text{ if } -4 < x \leq 2 \\-x& \text{ if} 2 < x < \infty\end{cases}[/tex]
What is a piecewise function?A piecewise function comprises of two or more functions that set the definition or rule of the function based on the specified interval.
10. The piecewise function indicates;
p(x) = -3·x + 7 if x ≤ 3
When x = 3, p(x) = -3 × 3 + 7 = -2
When x approaches -∞, p(x) → ∞
The domain and range in the interval x ≤ 3 are;
Domain = (-∞, 3]
Range = [-2, ∞)
P(x) = x if 3 < x < 5
The domain and range in the interval 3 < x < 5 are;
Domain; (3, 5)
Range; (3, 5)
P(x) = -1 if x ≥ 5
The domain and range in the interval x ≥ 5 are;
Domain; [5, ∞)
Range; -1
Therefore;
D = (-∞, ∞)
R = [-2, ∞)
11. k(x) = x + 4 if x < -1
k(x) = 5 if -1 < x < 2
k(x) = -(1/2)·x + 1 if x ≥ 2
The domain and range in the interval x < -1 are;
Domain; (-∞, -1)
Range; (-∞, 3)
The domain and range in the interval -1 < x < 2 are;
Domain; (-1, 2)
Range; 5
The domain and range in the interval x ≥ 2 are;
Domain; [2, ∞)
Range; (-∞, 0]
The function is undefined for x = -1
The domain and range of the piecewise function is therefore;
D; (-∞, -1) ∪ (-1, ∞)
R; (-∞, 3) ∪ [5, 5]
12. The points on the graph where x ≤ 0 are; (0, 2), and (-5, 0)
The slope is; 2/5
The y-intercept is; (0, 4)
The equation is therefore; y = (2/5)·x + 4
Therefore; f(x) = (2/5)·x + 4 if x ≤ 0
The points on the graph when x > 0 are; (0, -5), and (5, 0)
The slope is; 5/5 = 1, the y-intercept is; (0, -5)
The equation is therefore; y = x - 5
Therefore; f(x) = x - 5 if x > 0
The piecewise function is therefore;
[tex]f(x) =\begin{cases} \frac{2}{5}\cdot x +4 & \text{ if } x\leq 0 \\x -5 & \text{ if } x > 0 \end{cases}[/tex]
13. The points on the graph when x < -1 are; (-1, -1), and (-2, 0)
The slope is; 1/-1 = -1
The equation is; y - 0 = -1×(x - (-2)) = -x - 2
y = -x - 2
Therefore, f(x) = -x - 2 if x < -1
The points on the graph when -1 < x < 3 are; (-1, 5), and (3, 5)
The slope is; 0, the equation is; y = 5
Therefore; f(x) = 5 if -1 < x < 3
The points on the graph when 3 ≤ x < ∞ are; (3, -1), and (5, -5)
The slope is; -4/2 = -2
The equation is; y - (-1) = -2×(x - 3) = -2·x + 6
y = -2·x + 6 - 1 = -2·x + 5
y = -2·x + 5
Therefore; f(x) = -2·x + 5 if 3 ≤ x < ∞
The piecewise function is therefore;
[tex]f(x) =\begin{cases} -x -2 & \text{ if } x < -1 \\5 & \text{ if } -1 < x < 3\\-2\cdot x + 5 & \text{ if } 3 \leq x < \infty \end{cases}[/tex]
14. The functions in the piecewise function graph are;
f(x) = -2 if x < -4
The points in the interval -4 < x ≤ 2 are; (-4, 2), (0, 4)and (2, 5)
The slope is; 3/6 = 1/2
The y-intercept is; (0, 4)
The function is therefore; f(x) = (1/2)·x + 4
The points in the interval 2 < x < ∞ are; (2, -2), and (4, -5)
The slope is; -3/2 = -1.5
The equation is; y - (-2) = (-3/2) × (x - 2) = -x + 2
y = -x + 2 - 2 = -x
y = -x
The function is therefore; f(x) = -x
The piecewise function is therefore;
[tex]f(x) =\begin{cases} -2 & \text{ if } x < -4 \\\frac{1}{2}\cdot x + 4 & \text{ if } -4 < x \leq 2\\-x & \text{ if } 2 < x < \infty \end{cases}[/tex]
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Related Questions
in order to be correct, a line graph of the number of marriages per year in the united states must have group of answer choices number of marriages on the horizontal scale. years on the horizontal scale. either marriages or years on the horizontal scale, as long as equal intervals are used. bars of equal width.
Answers
In order to be correct, a line graph of the number of marriages per year in the United States must have years on the
horizontal scale.
It is defined as the process of adding more instances of the same type to the existing pool of resources and not
increasing the capacity of existing resources like in vertical scaling. This kind of scaling also helps in decreasing the
load on the server. This is called Horizontal Scaling
This allows for a clear representation of the number of marriages over time. To create such a graph, follow these steps:
1. Label the horizontal axis with years, making sure to use equal intervals between each year.
2. Label the vertical axis with the number of marriages.
3. Plot the data points for each year, representing the number of marriages.
4. Connect the data points with a line to show the trend over time.
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What is the rule for the following geometric sequence? 64, -128, 256, -512…
A. an = 64(-1/2)n-1
B. an = 64(2)n-1
C. an = 64(-2)n-1
D. an = 64(1/2)n-1
Answers
Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.
what is sequence ?An structured of integers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. The name for each number or item in the sequence is. A series can be explicitly created or defined recursively, and it can be infinite or finite. A method or rule that directly expresses the n - th term of the series in terms of n defines an explicit sequence. For instance, the explicit sequence 2, 4, 6, 8, 10,... has the formula a = 2n, where n is the term's position inside the sequence. A starting value and recursive formula that determines the nth word of the series in terms of the preceding terms describe a recursive sequence.
given
The number sequence is as follows: 64, -128, 256, -512.
We must determine the common ratio between the following terms in order to get the rule for this sequence.
Any term can be divided by its previous term to obtain the common ratio (r). For instance, the result of subtracting the second term (-128) from the first term (64) is
r = (-128) / 64 = -2
The third term (256) divided by the second term (-128) results in:
r = 256 / (-128) = -2
And when the fourth term (-512) is divided by the third term (256), the result is
r = (-512) / 256 = -2
We can observe that for all pairings of following terms, the common ratio is -2.
Now we can apply the following formula to a geometric sequence's general term:
a = a1 * r^(n-1) (n-1)
where r is the common ratio and a1 is the first term.
In place of the values we hold:
[tex]a = 64 * (-2)^(n-1) (n-1)[/tex]
Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
Step-by-step explanation:
quit
Determine the equation of the circle with center ( 3 , 9 ) containing the point ( 8 , − 3 )
Answers
Answer:
see the answer in the picture
Step-by-step explanation:
I don't know which equation you want. but I put both the standard and general form. but the equation should be the stander form. the radius is 13 in this case
We will see that this circle is centered at the point (-5, -49) and has a radius of 1.
What is the general circle equation?For a circle of radius R centered at the point (a, b), the equation is:
(x - a)^2 + (y - b)^2 = R^2
In this case, we have:
given the equation of the circle is
x^2 + y^2 + 10x + 14y + 73 = 0
We can rewrite this as:
(x^2 + 10x) + (y^2 + 14y) + 73 = 0
(x^2 + 2*5*x + 25) + (y^2 + 2*7*y + 49) - 25 - 49 + 73 = 0
(x + 5)^2 + (y + 49)^2 -74 + 73 = 0
(x + 5)^2 + (y + 49)^2 = 1
So we have a circle centered at the point (-5, -49) with a radius equal to 1.
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complete question:
Determine the center and radius of the following circle equation
x^2 + y^2 + 10x + 14y + 73 = 0
need help with this question, im stuck on it
Answers
Answer:
120° and 60°
Step-by-step explanation:
5x - 10 + 3x - 18 = 180
8x = 180 + 10 + 18
8x = 208 / : 8
x = 26
.
(5x - 10)° = (5 × 26 - 10)° = 120°
(3x - 18)° = (3 × 26 - 18)° = 60°
Find the value of x. *
43⁰
99°
2x°
A.28
B22.5
C.19
D.71
Answers
You want to buy some noodles. A 6-ounce package costs $1.98. A 14-ounce package costs $4.90. A 22-ounce package costs $7.04. Which package is the best buy?
Answers
Answer:
22-ounce package is the best buy as it has the lowest price per ounce.
Step-by-step explanation:
To determine which package is the best buy, we need to calculate the price per ounce of each package:
Price per ounce of 6-ounce package = 1.98 / 6 = $0.33 per ounce
Price per ounce of 14-ounce package = 4.90 / 14 = $0.35 per ounce
Price per ounce of 22-ounce package = 7.04 / 22 = $0.32 per ounce
Therefore, the 22-ounce package is the best buy as it has the lowest price per ounce.
Q8g Chengbo Sold for 180000 (3 yaun. the amount for which he Sold the house is 24% more than the amount hepaid. for the house -work out the house. Give your 3 significant figure answer
Answers
x ≈ 145161.29
Step-by-step explanation:
Let's assume that the amount Chengbo paid for the house was x.
According to the problem, the amount for which he sold the house (180000) is 24% more than the amount he paid:
180000 = x + 0.24x
Simplifying this equation:
180000 = 1.24x
x = 180000 / 1.24
x ≈ 145161.29
Therefore, the amount Chengbo paid for the house was approximately 145161.29 yuan (to 3 significant figures).
Note: We rounded the answer to 3 significant figures because that is the level of precision given in the question (the sale price is given to the nearest 1000 yuan).
Step-by-step explanation:
he sold the house for 180000, which is 24% more than the amount he paid.
180000 = x + 0.24x
Simplifying this equation, we get:
1.24x = 180000
x = 180000 / 1.24
x ≈ 145161.29
Chengbo paid approximately 145161.29 yuan for the house.
suppose that three students are randomly selected from the student body. what is the probability that all three will possess a gpa in excess of 3.0?
Answers
The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.
To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:
P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336
Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial formula and the probabilities of success and failure:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
we get:
P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311
P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421
P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040
Therefore:
P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772
So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.
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--The given question is incomplete, the complete question is given
" The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--
Leslie has received 10 more instant messages than Anita, and Anita has received 2 more than Sondra. Together, these three individuals have received 83 instant messages (and that's just in one evening). How many instant messages has Sondra received?
Answers
Step-by-step explanation:
A = S + 2
L = A + 10 = S+2 + 10 = S + 12
S = S
Summed , they equal 83
S+2 + S+12 + S = 83
3S = 69
S = 23 messages
An Oblique prism has a square base and height of 3 centimeters (5, 5, 3)
A. 30 cm^3
B. 45 cm^3
C. 60 cm^3
D. 75 cm^3
the answer is 75 cm^3
Answers
The volume of the oblique prism is 75 cm³, which is option D.
Define Oblique prismAn oblique prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by parallelogram-shaped lateral faces. Unlike a right prism, the lateral faces of an oblique prism are not perpendicular to the base faces.
The formula for the volume of an oblique prism is given by:
Volume = Base Area × Height
Since the base of the prism is a square, its area is given by:
Base Area = Side × Side = 5 × 5 = 25 square centimeters
Substituting this and the height given as 3 cm in the formula for the volume, we get:
Volume = Base Area × Height
= 25 × 3
= 75 cubic centimeters
Therefore, the volume of the oblique prism is 75 cm³, which is option D.
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Answer the questions below. Write your answers in simplest form.
Answers
A = s^2
64 = s^2
s = √64
s = 8
Therefore, the length of each side of the square is 8 meters.
(b) The perimeter of a square is given by the formula P = 4s, where P is the perimeter and s is the length of each side. Given that the perimeter is 48 cm, we can solve for s as follows:
P = 4s
48 = 4s
s = 48/4
s = 12
Therefore, the length of each side of the square is 12 centimeters.
Answer:
(a.) 8m
(b.) 12 cm
Step-by-step explanation:
a:
given: area of square = 64m²
formula of area of a square A = s²
We will reverse the formula to find the sum of the sides:
S = √A
S =√64
S = 8
b:
Given: perimeter of a square is 48 cm
formula for a perimeter of a square: P = 4 · s
We will reverse the formula to find the sum of the sides:
S = P ÷ 4
S = 48 ÷ 4
S = 12
Lillian and Khadija are reading the same book. At the beginning of the
month, Lillian was on page 40 and Khadija was on page 10. Lillian will read
15 pages per day and Khadija will read 20 pages per day. Let L represent the
page of the book that Lillian is on at the end of t days into the month, and let
K represent the page of the book that Khadija is on at the end of t days into
the month. Graph each function and determine whether Lillian or Khadija is
farther along in the book after 4 days.
Answers
After solving the linear equation Lillian is farther along in the book than Khadija after 4 days.
What is a linear equation?A linear equation is an algebraic equation of the form:
y = mx + b
where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point at which the line intersects the y-axis.
According to the given informationAs we know, Lillian was on 40 pages and Khadija was on 10 pages. So, the equation is,
And Let L represent the page of the book that Lillian is on at the end of t days into the month, and let K represent the page of the book that Khadija is on at the end of t days into the month.
[tex]L(t) = 40 + 15t[/tex] Lillian's progress after t days
[tex]K(t) = 10 + 20t[/tex] Khadija's progress after t days
After solving the linear equation, we will get the rate of the reading page.
Let's say t=4,
[tex]L(4) = 40 + 15(4) = 100[/tex]
[tex]K(4) = 10 + 20(4) = 90[/tex]
Therefore, after 4 days, Lillian is farther along in the book than Khadija.
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Express the vector in component form given its magnitude is 41 and direction angle is 220 degrees
Answers
Answer:
What I myself would do is plug in the given values, and we get: x = 41 * cos(220 degrees) ≈ -22.59 y = 41 * sin(220 degrees) ≈ -33.73
Therefore, the component form of the vector is (-22.59, -33.73).
Step-by-step explanation:
Astronomers estimate that the diameter of the Andromeda galaxy is approximately 2.2 X 10^5 light-year. A light-year is the distance light travels in a vacuum in 1 year. One light-year is approximately 5.9 X 10^12 miles. What is the diameter of the Andromeda galaxy in miles? Write your answer in scientific notation.
Answers
Answer:
Step-by-step explanation:
To find the diameter of the Andromeda galaxy in miles, we can use the given information:
Diameter of Andromeda galaxy = 2.2 X 10^5 light-years
1 light-year = 5.9 X 10^12 miles
So, we can use dimensional analysis to convert light-years to miles:
2.2 X 10^5 light-years * 5.9 X 10^12 miles/light-year = 1.298 X 10^18 miles
Therefore, the diameter of the Andromeda galaxy in miles is approximately 1.298 X 10^18 miles.
a computer password consists of nine characters. replications are allowed. how many different passwords are possible if each character may be any lowercase letter or digit? enter your answer in scientific notation with two digit of accuracy after the decimal point.
Answers
To calculate the number of possible passwords, we need to find the total number of combinations of lowercase letters and digits for each character of the password.
Then raise that number to the power of 9 (since there are 9 characters in the password and replications are allowed). There are 26 lowercase letters and 10 digits (0 to 9), so the total number of options for each character is 26+10=36.
Therefore, the number of possible passwords is[tex]36^9[/tex], which is equal to 1.0333862 ×[tex]10^16[/tex] (rounded to two decimal places in scientific notation). In other words, there are over 10 quadrillion possible combinations of passwords, making it very difficult for someone to guess or hack into the system by trying different combinations.
This highlights the importance of choosing a strong and secure password that is difficult for others to guess or brute-force.
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a box contains a combination of solid-colored tickets: 1/10 of the tickets are green, 1/2 are red , 1/4 are blue, and the remaining 30 tickets are white. how many blue tickets are in the box?
Answers
There were 50 blue box at total in the box.
What is combination?In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.
In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.
The bοx will be represented as (x)
From the question, we form:
White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30
Blue tickets = 3/20 x = 30
Blue tickets = = 30 x 20 / 3 = 200
Blue tickets = 1/4 x 200 = 50
Thus, There were 50 blue box at total in the box
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8. True or False: A person only pays interest on the balance remaining at the end of the
billing cycle.
لامت 2 (
Answers
Answer: True.
Step-by-step explanation: A person only pays interest on the balance remaining at the end of the billing cycle. If you carry a balance beyond the grace period, your credit card issuer will charge interest. Each month you carry a balance over from the previous month, you’ll have a finance charge added to your balance.
The Area of a Rectangle is 40. The width is 2 less than 3
times the length. Find the width.
O 10
O 12
O 15
O 14
Answers
Answer:
Let Length= x, Width= y
A.t.c.
3x-2=y ...(1)
Area = length × width
= xy = 40
from (1)
[tex]x(3x - 2) = 40 \\ 3 {x}^{2} - 2x = 40 \\ 3 {x}^{2} - 2x - 40 = 0 \\ 3 {x}^{2} - 12x + 10x - 40 = 0 \\ 3x(x - 4) + 10(x - 4) = 0 \\ (3x + 10)(x - 4) = 0 \\ x = - \frac{10}{3} \: or \: 4[/tex]
neglecting -10/3
length = 4
width = 3(4)-2=12-2
= 10
A bowl contains 3 apples, 5 bananas, 4 oranges. Mary randomly selects one piece of fruit from the bowl. What is the probability that she selects and apple out of the bowl? Give the answer in the form of a decimal.
Answers
Answer:
Step-by-step explanation:
You have a little unclear question with "selects and apple out of the bowl?" I only chose apples (there are 3 of them)
[tex]\frac{3}{12} =\frac{1}{4}[/tex] answer
Step-by-step explanation:
Given,
n(S) = 12
n(A)=3
We have,
P(A) = n(A)/n(S)
= 3 /12
= 1 /4
A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. If the writer writes for one more day and comes up with 8 new comic strips, how will the skew be affected?
Answers
On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
The skew of a dataset refers to the degree to which the distribution of values is asymmetrical. A dataset is said to be skewed if the majority of the values lie on one side of the mean.
In this case, the dataset has a right skew because there are more values on the right side of the distribution (higher values) than on the left side. We can see this by noting that the median (middle value) is 3, while the mean (average value) is slightly higher at 3.375.
If the writer writes 8 more comic strips on the next day, it will increase the maximum value in the dataset from 7 to 8. This will slightly shift the distribution to the right, but the skew will remain right because the majority of the values are still clustered on the right side of the distribution.
However, the effect on the overall skew will depend on the number of comic strips the writer produces on the next day relative to the other values in the dataset. If the writer produces a large number of comic strips relative to the other values, it could shift the distribution to a more symmetrical shape.
Therefore, On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.
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a) determine an equation for the family of quartic functions with zeroes -5/2, -1, 7/2, 3.
b) write equations for two functions that belong to this family
c) determine an equation for the member of the family whose graph passes through the point (-2,25)
Answers
a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)
where "a" is a constant that determines the overall scaling of the function.
b) Two examples of functions that belong to this family are:
f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)
Note that these functions differ only in the value of the constant "a".
c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):
25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)
Simplifying this expression:
25 = a(5/2)(-1)(-11/2)(-5)
25 = a(6875/4)
a = 100/6875 = 4/275
Therefore, the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
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please answer fast will give brainliest ANSWER EVERYTHING
Answers
The given points can only be represented by an exponential function.
What is a linear function?
A linear function has the following form = y = f(x) = a bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is a constant term or y-intercept. This is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also called the slope and gives the rate of change of the dependent variable.
We can determine the type of function that can represent the given points by looking at the pattern of y values corresponding to the x values.
Linear Function: A linear function has a constant slope, which means that the difference between any two consecutive values of y must be the same as the difference between two consecutive values of x. The difference between two consecutive y values is 9/8, which is not the same as the difference between two consecutive x values (which is 1). Therefore, the given points cannot be represented by a linear function. Exponential function: an exponential function has a constant ratio between two consecutive y-values, meaning that the ratio of any two consecutive y-values must be the same as the ratio of any two consecutive x-values.
The ratio of two consecutive y values is 2, which is the same as the ratio of two consecutive x values (which is 1/2). Therefore, the given scores can be represented by an exponential function. Quadratic function: A quadratic function has a quadratic term, which means that the y-values should show an increasing or decreasing pattern of differences between successive x-values. The differences between successive y values are 9/8, 3/8, 1/2, and 9. There is no pattern of increasing or decreasing differences between successive x values, so the given points cannot be represented by a square. function
Therefore, the given scores can only be represented by an exponential function.
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which of the following is true of primary data? multiple choice primary data collection methods are unaffected by biases of the respondent. primary data are relatively less expensive than secondary data. primary data consists of two types: exploratory and descriptive. primary data are collected exclusively from academic journals. primary data are collected specifically for the research problem at hand.
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The following is true of primary data collection: primary data are collected specifically for the research problem at hand.Primary data collection refers to the process of collecting new data or original data that have not been collected before. Primary data are the first-hand data gathered by researchers from original sources.
The following is true of primary data: primary data are collected specifically for the research problem at hand. Primary data are collected to meet specific research objectives and to provide solutions to research problems.Primary data collection methods are affected by the biases of the respondent.
This is because the collection of primary data requires direct contact between the researcher and the respondents or participants. It is important to note that primary data collection methods are relatively more expensive than secondary data. Therefore, researchers should consider the cost implications of primary data collection methods before using them.
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the same answer 3 Question. I think by of a number multiply. and add 7. I if I multiply the number by 4 and subtract 12. find the number? Solve this in equation
Answers
The value of the number is 19
What are algebraic expressions?Algebraic expressions are defined as those expressions that are composed of terms, constants, variables, coefficients and factors.
These expressions are also made up of certain mathematical operation, such as;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have;
Let the number be x
Then,
3x + 7
4x - 12
Equate the expressions
3x + 7 = 4x - 12
collect the like terms
7 + 12 = 4x - 3x
add or subtract the values
x = 19
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The diameter of a circle is 10 centimeters. What is the angle measure of an arc bounding a sector with area 10 square centimeters?
Answers
Answer:
72 degrees
Step-by-step explanation:
Jamie was given the problem, "Find the result when the factors of 65 x 2 + 212 x − 313 65x 2 +212x−313 are multiplied together." Before she could answer, her sister, Lauren, said, "I know the answer without factoring or multiplying!" What was Lauren's answer and how did she know?
Answers
The product of the factors of [tex]65x^2 + 212x - 313[/tex] is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.
We can first simplify the expression [tex]65x^2 + 212x - 313[/tex] by factoring it:
[tex]65x^2 + 212x - 313 = (13x - 1)(5x + 313)[/tex]
(13x - 1)(5x + 313) = [tex]65x^2 + 212x - 313[/tex]
Therefore, the product of the factors is equal to the original expression.
To see this, we can rewrite the expression as:
[tex]65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 212x - 49[/tex]
= [tex](5x - 7)^2 - 1^2\cdot 49 - 212x[/tex]
= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49
= 5x(5x - 14) - 49
= 5x(5(x - 2) - 9)
= 5x(5x - 29)
Therefore, the factors of the expression are (5x - 7) and (5x - 29).
Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.
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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich
Answers
Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.
The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.
To assemble the sandwiches, Charlie can follow these simple steps:
1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.
2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.
3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.
4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.
5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.
6. Top the sandwich with the other slice of bread, condiment-side down.
7. If desired, cut the sandwich in half or quarters for easy sharing and eating.
Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.
In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.
Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?
complete the figure with 4-fold rotational symmetry. the point is the center of rotation.
Answers
By following these steps, we will have a figure with 4-fold rotational symmetry around the given center point.
To complete the figure with 4-fold rotational symmetry around the center point, follow these steps:
1. Identify the center of rotation:
As mentioned, the given point is the center of rotation.
2. Determine the existing shape or pattern:
Observe the figure and identify the existing shape or pattern to replicate.
3. Divide the circle around the center point into four equal sections (quadrants):
This can be done by drawing two lines that intersect at the center point, dividing the area around it into four equal parts (90 degrees each).
4. Replicate the existing shape or pattern in each quadrant:
Copy the shape or pattern in the first quadrant to the other three quadrants, keeping them equidistant from the center point.
5. Check for symmetry:
Ensure that when you rotate the figure 90 degrees, 180 degrees, or 270 degrees around the center point, it remains identical in appearance.
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What is the length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) ?
Answers
The length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) is 12.16 units.
What are distance formulae?If two points of coordinates are given then we calculate the distance between them by using the following formulae
To find the length of the line is nothing but the calculation of the distance between two points that are given in the question.
[tex]d = \sqrt{(x_{2} - x_{2} )^{2} +(y_{2} - y_{1} )^{2} }[/tex]
d is the distance between two points.
(x1, x2) and (y2, y1) are the two endpoints of the line.
We can put all the values into the distance formulae and find the length of the line segment.
x1 = -4 1/2 = -3.5, y1 = 5
x2 = 26/3 = 8.6667, y2 = 5
[tex]d = \sqrt{(8.6667-(-3.5))^{2} +(5 - 5)^{2}\\[/tex]
= 12.16
Therefore, the length of the line segment is approximately 12.16 units.
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