Which set of ordered pairs is a
function?
A. (-2,4), (0, 4), (2, 4), (2,6)}
B. {(-10, 4), (-8, 3), (-8, 2), (-4,1))
C. {(1, 5), (1, 6), (2,7), (3, 8))
D. Of(-1, 1), (0, 0), (1, 1), (2, 2))
Answers
A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function.
The set of ordered pairs is a function exists {(1, 5), (1, 6), (2,7), (3, 8)}.
What is meant by function?A set of ordered pairs that contain only unique ordered pairs with unique x coordinates exists directed to as a function. A function is defined by an equation that generates a set of ordered pairs. Each x value in a relation must have a unique value for the y value for it to be a function. if there are multiple y-values associated with an x-value.
Because no two ordered pairs have the same first coordinates with the same second coordinates, the initial set of ordered pairs is a function.
A relationship and a function vary in that a relationship can have multiple outputs for a single input, whereas a function only needs one input to produce one outcome. This is the fundamental criterion used to distinguish between relation and function. These model concepts are created through the usage of relations.
Therefore, the correct answer is option C. {(1, 5), (1, 6), (2,7), (3, 8)}.
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Related Questions
3.21. a causal lti system has the following system function:(2(a) what is the roc for h(z)? (b) determine if the system is stable or not. (e) determine the difference equation that is satisfied by the input x[n) and the output yin. (d) use a partial fraction expansion to determine the impulse response h[n].
Answers
The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge.
What is meant by the roc for h(z)?When applying the z-transform on the sequence h, the ROC concept is applied to the function H(z) (n). The ROC essentially specifies the parameters under which the system's impulse response, h(n), will converge. Neither X(z), the input, nor Y(z), the output, are involved in the ROC.
The region (regions) where the z-transform converges is known as the region of convergence (ROC). We can uniquely determine the inverse z-transform thanks to ROC. Let's first think about some examples. The unit sample δ(n)has z-transform 1 , hence ROC exists all the z plane .
The Registrar of Companies assigns the company registration number, or CIN number as it is known in India (ROC). The Ministry of Corporate Affairs oversees the ROC, which is present in several Indian states. It is utilized to locate the essential information for every firm that is registered in India.
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Avery is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. The labor and materials cost $100 for each phone manufactured, and the total cost of producing 3 phones in a day would be $600. Write an equation for C, in terms of p, representing total cost, in dollars, of producing pp phones in a given day.
Answers
If Avery is in the business of manufacturing phones. The equation for C, in terms of p, representing total cost, in dollars, of producing pp phones in a given day is: 100p + 300.
Determining the equation for total costGiven data:
Labor and materials cost = $100
Numbers of phones = 3
Total cost = $600
Where,
P = Total cost
The equation for C in terms of p is:
100p + 300
Now let determine the total cost
Total cost = $600 + ( 3 × $100)
Total cost = $600 $300
Total cost =$600
Therefore 100p + 300 is the equation.
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Prealgebra- Write an equation of the line that passes through the points(Question in photo) (Can only attach one photo at time, so for graphing part of question, i will send the photo)
Answers
Given:
Point 1 → (-5, 0.6)
Point 2 → (5, -2.4)
Find: the equation of the line and its graph
Solution:
To help us determine the equation of the line passing through the given points, let's use the Two-Point Form formula.
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let's plug into the formula above the coordinates of the two points.
[tex]y-0.6=\frac{-2.4-0.6}{5-(-5)}(x-(-5))[/tex]Then, solve.
[tex]y-0.6=\frac{-3}{10}(x+5)[/tex]Multiply -3/10 by the terms inside the parenthesis.
[tex]y-0.6=-\frac{3}{10}x-1.5[/tex]Add 0.6 on both sides of the equation.
[tex]y-0.6+0.6=-\frac{3}{10}x-1.5+0.6[/tex][tex]\begin{gathered} y=-\frac{3}{10}x-0.9 \\ or \\ y=-0.3x-0.9 \end{gathered}[/tex]Hence, the equation of the line passing through the given points in slope-intercept form is y = -0.3x - 0.9.
In the equation, the slope is -3/10 while the y-intercept is -0.9.
Since the slope is negative, the line must be leaning to the left. Since the y-intercept is -0.9, the line must cross the y-axis or the vertical line at -0.9. Hence, the graph of the equation is:
The cost of entering a carnival and riding rides is given by the linear equation, c(r) = 1.25r + 6.00, where c(r) is the total cost of attending the carnival and r is the number of rides. the slope of the linear equation represents the response area .
Answers
Answer: Cost per rides
Step-by-step explanation:
For the polynomial function f(x)=x^3 - 2x^2 - 5x + 6, we have f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0. Rewrite f(x) as a product of linear factors.
Answers
The given polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)
In the above question, a polynomial function is given
f(x)=x^3 - 2x^2 - 5x + 6
However, we know that, zero of a polynomial means all the x-values that bring a polynomial, p(x), to zero are referred to as its zeros, which means putting any value of x in the function we should get value of f(x) as zero
And, in the question, it is given as
f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0
We can clearly see that, f(-2) = 0, f(3) = 0, f(1) =0
=> (x+2), (x-3), (x-1) are the linear factors of the given polynomial
Hence, we can write the given polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)
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during an election, a group of 4 council members must be selected from a group of 18 people running for these positions. how many such selections are possible?
Answers
The possible number of ways of selection by using combination formula is 3060.
What is combination?
A grouping of items where the order in which they were chosen is irrelevant is known as combination.
Given that the number of people in the group is 18. Only 4 people will be member of the council.
The formula of combination is [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex] , where r number of objects are selected from n objects.
In the given question the value of n is 18 and the value of r is 2.
Substitute the value of n and r in [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex].
[tex]^{18}C_{4}=\frac{18!}{4!(18-4)!}[/tex]
Solve the above expression:
18^C_4 = 18x17x16x15x14/4x14
18^C_4 = 18x17x16x15/4x3x2x1
3060 18^C_4 = 3060
The number of ways such selection is 3060.
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A small square has an area of 40 inches squared. A large square has sides that are 8 times longer than the small square. What is the area of the large square?
Answers
Solution
Given that
Area f small square = 40 inches squared.
[tex]\begin{gathered} a=40 \\ \\ \text{ since a}=l^2 \\ \\ \Rightarrow40=l^2 \\ \\ \Rightarrow l=\sqrt{40} \end{gathered}[/tex]Let the side of the large square be L
Since the large square has sides that are 8 times longer than the small square
=> L = 8l
[tex]\begin{gathered} \Rightarrow L=8l \\ \\ \Rightarrow L=8(\sqrt{40}) \end{gathered}[/tex]Hence, the area of Large square is;
[tex]A=L^2=(8\sqrt{40})^2=64\times40=256[/tex]Hence, the area of the large square is: 256 inches squared.
In anatomy, a student learned that the average resting heart rate is between 60 and 100 beats per minute. The student decided to record the heart rate of people over five minutes while waiting in line at the pharmacy. The dot plot shows the results.
Answers
The correct option regarding the symmetry of the distribution is given as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
How to find the symmetry of the distribution?To find the symmetry of the distribution, the mean and the median need to be calculated and compared, if they are equal or which is greater.
A dot plot shows the number of times that each observation appears in the data-set, hence the complete data-set of heart beats per minute is given as follows:
62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.
The mean is the sum of all these observations divided by the number of observations, which is of 20, hence:
Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.
The median is the middle value of the data-set, the value which 50% of the observations are less than and 50% are greater than. The cardinality of 20 in this data-set is an even number, hence the median is the mean of the 10th and of the 11th element, as follows:
Median = (72 + 75)/2 = 73.55.
When the mean is greater than the median, as is the case in this problem, the distribution is right skewed, which is the reason for the correct option.
Missing InformationThe problem is given by the image at the end of the answer.
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HELPPppppp PLS AOUHF
Answers
As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.
Area of triangle:
In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,
Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}
As the area is always positive.
Given,
Here we have the triangle VWX,
And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).
Now we have to find the area of the triangle.
To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).
Now, we have to apply the values on the formula, in order to get the area of the triangle,
=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|
When we expand the terms, then we get,
=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|
Further simplify the expression will gives you the following,
=> A = 1/2 |27 - 20 + 12|
=> A = 1/2 |19|
Therefore, the area of the triangle is 9.5 square units.
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HELP ME PLEASE ASAP!!!
2. Use the space provide to respond to each statement concerning the given graph of a radical function.
a.) State the domain of the function.
b.) State the range of the function.
c.) Identify the end behavior of the function.
d.) Identify the y – intercept. Write as an ordered pair.
e.) Explain how you know this function is increasing?
Answers
Part a
The domain is the set of x-values, which is [tex](-\infty, \infty)[/tex].
Part b
The range is the set of y-values, which is [tex](-\infty, \infty)[/tex].
Part c
As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex], and as [tex]x \to -\infty[/tex], [tex]y \to -\infty[/tex].
Part d
The y-intercept is when x=0, which is [tex](0, 1)[/tex].
Part e
The function is increasing when y increases as x increases, which is true for this function.
find angle x giving your answer to one decimal place
Answers
⇒I will use the trig ratios to find the value x.
[tex]\frac{sin(x)}{11cm}=\frac{sin( 38)}{8} \\[/tex]
⇒Moving on solving I will use the cross multiplication
[tex]8sin(x)=11sin(38)\\sin(x)=\frac{11sin(38)}{8} \\x=sin^{-1} (\frac{11sin(38)}{8} )\\x=57,8[/tex]
∴ x=57,8°
Goodluck!!
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
y = −0.5x2 + 1.5x − 5
y = −0.5x2 + 1.5x + 5
y = 0.5x2 + 1.5x − 5
y = 0.5x2 + 1.5x + 5
Answers
Answer:
y = 0.5x^2 + 1.5x − 5
Step-by-step explanation:
See attached graph
Dog food comes in two different sized bags. The 40 lb bag sells for $24 while the 10 lb
bag sells for $7. Which is cheaper and by how much? (compare unit rates)
Answers
Answer:
The 40 lb bag is cheaper by $4
Step-by-step explanation:
10 x 4 = 40
7 x 4 = 28
If you bought the 10 lb bag 4 times, you'd spend more money than just buying the 40 lb bag once.
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Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Point B is the midpoint of segment TY. What are the coordinates of point Y?
Answers
Using the midpoint, the coordinates of point Y in the line segment TY is (-18, -9).
How to use midpoint to find coordinates?Point T is located at (2, 5). Point A is located at (-3, 1.5). Point A is the midpoint of segment TB.
Therefore, the mid point formula can be represented as follows:
(xₙ, yₙ) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
Hence, let's find the coordinates of point B.
(-3, 1.5) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 3
cross multiply
2 + x₂ = -6
x₂ = -6 -2
x₂ = - 8
1.5 = 5 + y₂ / 2
3 = 5 + y₂
y₂ = 3 - 5
y₂ = -2
Therefore, the coordinates of B is (-8, -2)
Hence, let's find the coordinate of point Y. The coordinates of point B is the mid point of segment TY.
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
(-8, -2) = (2 + x₂ / 2 , 5 + y₂ / 2)
2 + x₂ / 2 = - 8
-16 = 2 + x₂
x₂ = -18
-2 = 5 + y₂ / 2
-4 = 5 + y₂
-4 - 5 = y₂
y₂ = -9
Therefore, the coordinates of y is (-18, -9)
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8/13 x 3 =
SHOW YOUR WORKl
Answers
13 x 3 = 39
Answer: 24/39
8/13 x 3/1 = 24/13
24 - 13 =11
So, simplified answer is 1 11/13 or 24/13
Hope this helps!
Hattie drew a box plot of annual rainfall in some cities in the world. Select all the statements that are true about the data in the box plot.
Answers
Rainfall anually table data
Then
Option A)
Half of the data are between 6 and 18
TRUE , because there are 8/2 = 4 data in the box plot
Option B)
Data point 27 ,could be an outlier
FALSE, because 27 is a black point. It means it belongs, is not out
Option C)
More points between 6,9 that between 9,18
FALSe,. Area between 6,9. Is smaller than area between 9,18
Option D)
Data are less spread out to the left
TRUE, because box plot is ubicated at left
Option E)
Only one data point is less than 6
TRUE, is data point 3
How can you show two figures are congruent?
O Use the Third Angles Theorem.
O Use rigid transformations.
O Confirm they have the same symmetries.
Answers
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
What in mathematics is the congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Use the Third Angles Theorem for two figures are congruent.
When two of a triangle's angles match up with two of another triangle's angles, the third angle must likewise match up.
If at least two sides and one angle of two triangles are similar, then the triangles are congruent.
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i need help with the image below
Answers
Answer:
A. k ≥ 8.14
Step-by-step explanation:
Hope this helps! :))
how many 1/5 inch pieces can be cut from a piece of ribbon 7/20 of an inch long.
Answers
1) Gathering the data
1/5 inch
7/20 inches long
2) Let's them divide, 7/20 by 1/5 inches
When divide fractions, we multiply the reciprocal of the second fraction
and if possible we can simplify
How is 6 divided by (-3) equals -2
Answers
Since a positive number divide or multiplies a negative number
Then the answer will be a negative number
So:
6 / -3 = -2
6 is a positive number and it's being divide by -3 which is a negative number
So the answer is -2
suppose that 3 j of work is needed to stretch a spring from its natural length of 34 cm to a length of 40 cm. (a) how much work is needed to stretch the spring from 36 cm to 38 cm? (round your answer to two decimal places.)
Answers
Work done in stretching spring from 36 cm to 38 cm is 0.333J.
The work needed to stretch a spring is given by the formula mentioned below:
[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]
Here, k is spring constant and x is the elongation.
So, x = [tex]x_{f} - x_{i}[/tex]
When spring is stretched from 40 cm to 34 cm
x = 40 - 34 = 6cm = 0.06 m
We need to know the spring constant so that we can calculate work.
3 = (1/2) K × [tex](0.06)^{2}[/tex]
K = 1666.67
Now, when spring is stretched from 36 cm to 38 cm
x = 38 - 36 = 2 cm = 0.02 m
[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]
[tex]W_{s}[/tex] = 0.333J
So, 0.333J work is done in stretching spring from 36 cm to 38 cm.
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Please help ASAP starting to fall behind! This equation really confuses me and if someone could help that would be amazing!
Given the function:
f(x) = x² - 4x - 2
Find the following values.
a) f(2)
f(2)=
b) f(4)
f(4)=
c) f(-3)
f(-3)=
Answers
f(4) = 4^2 - 4*4 - 2 = 16 - 16 - 2 = -2
f(-3) = (-3)^2 - 4*-3 - 2 = 9 + 12 - 2 = 19
3. Jackson's soccer coach filled the teams' water container with 40 quarts of
water. Since 32 ounces equal 1 quart, how many times can a soccer player fill a
16-ounce water bottle before using all the water?
Answers
40 times 32 = 1280
40 quarts = 1280 ounces of water
1280 ounces of water divided by 16 ounce water bottle = 80 refills
RS =9y + 2, ST = 2y + 3, and RT = 60
Answers
Answer:
y=5
Step-by-step explanation:
RS + ST = RT
9y+2 + 2y+3 = 60
11y + 5 = 60
11y = 55
Y = 5
P(x) = -0.3x² + 75x - 2000, where x represents the selling price.
1. At what price should the stands be sold to earn the maximum profit?
2. According to the function given, what is the maximum profit that the company can make?
3. What are the break-even points (the selling prices for which the profit is 0)? Give the answer to the nearest cent.
Answers
Answer:
Below in bold.
Step-by-step explanation:
P(x) = -0.3x² + 75x - 2000
Convert this to vertex form:
p(x) = -0.3(x^2 - 250)^2 - 2000
= -0.3[(x - 125)^2 - 125^2] - 2000
= -0.3[(x - 125)^2 - 15625] - 2000
= -0.3(x - 125)^2 + 4687.5 - 2000
= -0.3(x - 125)^2 + 2687.5
2687.5 is the maximum value of the profit.
1. This corresponds to a selling price of $125 for the stands.
2. Maximum profit is $2687.5.
3. At the breaking points P(x) = 0:
-0.3(x - 125)^2 + 2687.5 = 0
(x - 125)^2 = 2687.5 / -0.3 = 8958.33
x - 125 = +/- sqrt( 8958.33)
x = 125 +/- sqrt( 8958.33)
x = 30.352, 219.648,
So, the breaking even points are $30.35 and $219.65 to nearest cent.
what is the value of x
Answers
Answer:
the value of x is 17
Step-by-step explanation:
7x-32+5x-27=9x-8{sum of 2 interior angles of a triangle is equal to the sum of exterior angle}
therefore x=17
Answer:
x = 17°
Step-by-step explanation:
Hello!
Angle KLM is an exterior angle of Triangle JKL. An exterior angle's measure is equal to the sum of the two remote interior angles.
The two remote interior angles are Angle K and Angle J. We can solve for x by setting up an equation: (7x - 32) + (5x - 27) = (9x - 8)
Solve for x (7x - 32) + (5x - 27) = (9x - 8)7x - 32 + 5x - 27 = 9x - 812x - 59 = 9x - 812x - 51 = 9x12x = 9x + 513x = 51x = 17The value of x is 17°.
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Evaluate.
7 x 5 + 4² − 2³ / 4
Answers
Follow PEMDAS
7 x 5 + 16 - 8 /4
35 + 16 - 2
51 -2
49
What is (3 x 10^7) (3 x 10^8)?
Answers
[tex] = 3 \times 3 \times {10}^{7} \times 10^{8} \\ = 9 \times {10}^{7 + 8} \\ = 9 \times {10}^{15} \\ [/tex]
NOTE YOU CAN WRITE IT IN FULL BUT I CHOSE NOT TO BECAUSE IT'S LARGE .
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7+3(p-1)=64 how to solve
Answers
Answer:
p = 20
Step-by-step explanation:
7 + 3(p - 1) = 64 ( subtract 7 from both sides )
3(p - 1) = 57 ( divide both sides by 3 )
p - 1 = 19 ( add 1 to both sides )
p = 20
An elevator in a skyscraper rises 240 feet in 15 minute. What is the
elevator’s rate in feet per minute?
Answers
Answer:
Step-by-step explanation:
answer is 16