Option 1, {x | x = –4, –1, 3, 5, 6} is the domain of the given function.
For any function, domain is the set of all input values that are accepted by the given function. For example, if there is a function, say f(x) = x + 2, then all the values of x will make up the domain of f(x).
Here, we are given a function {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
In this case, all the input values = all the x values
and all the output values = all the y values
Thus, the domain of the given function will be a set containing the following x values-
3, 6, -1, 5, -4
Arranging these values in the ascending order we get,
-4, -1, 3, 5, 6
Therefore, the domain of the function can be represented as {x | x = –4, –1, 3, 5, 6}.
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(a-b)(a+b)-c(c-2b) help me guys
Answer:
a^2-b^2+2bc-c^2
Step-by-step explanation:
We multiply a with a and negative b with b. Then multiply negative c with c and multiply negative c with negative 2b. After all add/ subtract like terms
The figure below shows an image of Pac-Man from the classic video game. The "mouth" of Pac-Man forms a central angle of 55.0° in a circle with radius 4.00 millimeters.
Using the length of the perimeter of the Pacman is: 29.29 mm.
How to Find the Length of an Arc?Length of an arc = ∅/360 × 2πr
The length of the perimeter of the Pacman = length of the larger arc formed + 2r
∅ = 360 - 55 = 305°
r = 4.00 mm
The length of the perimeter of the Pacman = ∅/360 × 2πr + 2r
Substitute
The length of the perimeter of the Pacman = 305/360 × 2π(4.00) + 2(4.00)
The length of the perimeter of the Pacman = 21.29 + 8.00
The length of the perimeter of the Pacman = 29.29 mm
Therefore, using the length of the perimeter of the Pacman is: 29.29 mm.
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A television uses 1 unit of electricity every 10 hours.
A unit of electricity costs 9.8 p.
Calculate the cost of having a television turned on for 24 hours.
Answer:
Step-by-step explanation:
9.8 p = 10 hours
24 hours = ?
= 24 hours (9.8p)
10 hours
=23.92p
which value is an irrational number? a. 4/19 b. the square root of 200 c. the square root of seven over the square root of seven d. -0.58 repeated
Answer:
B. √200
Step-by-step explanation:
An irrational number is a number that excludes single-point decimals but includes integers and fractions. A square root is a repeating decimal(Most of the time), therefore, this is an irrational number.
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
Using exponent properties, the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
What is the equivalent expression?The original expression is:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2}[/tex]
When two terms that are divided have the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\left[\frac{y^{-3}z^5}{z^{-4}y^6}\right]^{-2} = [y^{-3 - 6}z^{5 - (-4)}]^{-2} = [y^{-9}z^9]^{-2}[/tex]
The negative exponent at the numerator goes to the denominator, hence:
[tex][y^{-9}z^9]^{-2} = \left[\frac{z^9}{y^9}\right]^{-2}[/tex]
The negative outer exponent means that we have to exchange the numerator and denominator, hence:
[tex]\left[\frac{z^9}{y^9}\right]^{-2} = \left[\frac{y^9}{z^9}\right]^{2}[/tex]
Then both numerator and denominator exponents multiply by 2, hence the equivalent expression is:
[tex]\frac{y^{18}}{z^{18}}[/tex]
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Answer:
y^18/x^18
Step-by-step explanation:
A truck can be rented from Company A for $90 a day plus $0.40 per mile. Company B charges $60 a day plus $0.70 per mile to rent the same truck.
Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
The number of miles in a day at which the rental costs for Company A and Company B are the same will be 10 miles.
How to calculate the value?Let the number of miles be represented by x.
Therefore the equation for the first company will be 90 + 0.4m
The equation for the second company will be 60 + 0.7m
Therefore, we will equate them. This will be:
90 + 0.4m = 60 + 0.7m
Collect like terms
90 - 60 = 0.7m - 0.4m
0.3m = 30
m = 30/0.3
m = 10
The number of miles will be 10 miles.
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If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?
Answer: Answer is 16 new releases and 22 classic movies.
Step-by-step explanation:
He'll buy 16 new releases and 22 classic movies.
Let x = number of new releases
Let y = number of classics.
The equation to solve the question will be:
20x + 8y = 500
When x= 16 and y = 22, thus will be:
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, since this is the number closest to $500, therefore this will be the appropriate number of movies that he can buy.
In conclusion, he'll buy 16 new releases and 22 classic movies.
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Evan invested $2500 in the stock market.
Four months later, the value of the
investment dropped to $2248. Find the
average monthly change in the value of
the investment.
Answer:
63
Step-by-step explanation:
Value dropped = 2500 - 2248 = 252
divide 252 across 4 months
252/4 = 63
The average monthly change in the value of the investment is $63.
Given that, Evan invested $2500 in the stock market. Four months later, the value of the investment dropped to $2248.
What is the investment?Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation. Investment meaning is primarily to obtain an additional source of income or gain profit from the investment over a specific period of time.
Now, change in investment is
2500-2248 = 252
The average monthly change
= 252/4
= 63
Hence, the average monthly change in the value of the investment is $63.
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if [tex]i = \sqrt{-1}, what is i^3[/tex]i^3 equal to?
If the radius of a circle is 16 inches find the diameter area and circumference
diamater:
[tex]d=2r \\\\d=2 \cdot 16 \\\\d=32[/tex]
circumference:
[tex]C=2 \pi r \\\\C=2 \cdot \p \cdot 16 \\\\C=32 \cdot \pi \\\\C \approx 100.48[/tex]
Hope that I helped you!
Which factor provides the basis for the grading of newly diagnosed malignant tumors? size of the tumor x number of metastases degree of differentiation of the cells number of lymph nodes involved
The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.
What is the degree of differentiation?The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.
The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.
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The records of four baseball teams are shown below. Which team had the greatest percent of wins?
Rattlers won 95 and lost 65. Cobras Won 92 and lost 58. Boas Won 94 and lost 66. Pythons won 96 and lost 64.
the Boas
the Cobras
the Pythons
the Rattlers
Answer:
The Cobras
Step-by-step explanation:
I just took the test
Answer:the Cobras
Step-by-step explanation:
Select the correct answer.
Simplify the following expression.
4 -11/3 divided by 4 -2/3
A 12
B. 1/64
C. 64
D. 12
The correct value of the expression is 4/5.
How to calculate the fraction?The question is about simplifying 4 -11/3 divided by 4 -2/3.
It should be noted that 4 - 1 1/3 = 2 2/3
Also, 4 - 2/3 = 3 1/3
We will divide
2 2/3 ÷ 3 1/3
= 8/3 ÷ 10/3
= 8/3 × 3/10
= 4/5
Note that the correct option wasn't given.
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Answer: The correct value of the expression is 4/5.
How to calculate the fraction?
The question is about simplifying 4 -11/3 divided by 4 -2/3.
It should be noted that 4 - 1 1/3 = 2 2/3
Also, 4 - 2/3 = 3 1/3
We will divide
2 2/3 ÷ 3 1/3
= 8/3 ÷ 10/3
= 8/3 × 3/10
= 4/5
Note that the correct option wasn't given.
Step-by-step explanation:
What is the standard deviation and its meaning given this population of customer ages? 45, 76, 30, 22, 51, 40, 63, 66, 41
The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}[/tex]
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
N is the number of observations in the data set.
It is given that:
The data set:
45, 76, 30, 22, 51, 40, 63, 66, 41
From the formula:
∑(x(i) - X)² = 2463.55
N = 9
SD = √(2463.55/9)
SD = 16.54
Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
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select the correct answer. what is the slope of the line that goes through the points (-4,2) and (8,5)?
A. "-4"
B. "-1/4"
C. 1/4
D. 4
Answer: The slope of the line that goes through the points is = ¼
Step-by-step explanation:
Define Slope:
The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points.
The slope of the line that goes through the points (-4,2) and (8,5).
Let, X1=-4
Y1=2
X2=8
Y2=5
We can use m=(y2-y1) / (x2-x1)
replace with x1, y1 and x2, y2 values in this equation
We can write: m=[(5-2) / (8-(-4))]
Solve it: M= 3/12
M=1/4
So, the slope of the line that goes through the points is = ¼.
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Find the GCF 1.16,60 2.52,84 3.32,89,144 4.48,96,108 5.144,176,1
Answer:
The GCF is 1.
Step-by-step explanation:
The factors of 1 are: 1
The factors of 1 are: 1
The factors of 2 are: 1, 2
The factors of 3 are: 1, 3
The factors of 4 are: 1, 2, 4
The factors of 5 are: 1, 5
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 89 are: 1, 89
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The factors of 176 are: 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
Then the greatest common factor is 1.
Evaluate the expression for X=6 y= -1 4x + 5y
We know the value of x and y,
x = 6 and y = -1 [Given]
Substitute the value,
4x + 5y4(6) + 5(-1)24 + (-5)24 - 519 Ans.Find the area of the shaded region. All angles are right angles.
5m
30 m
20m
5m
What is the least common multiple of 10 and 11 ?
Answer:
Step-by-step explanation:
The answer is 110
hope this helps :)
what is the MAD for 3,4,5,5,5,6,6,6,7,8
Answer:
1.1
Step-by-step explanation:
Find the mean of the data:(3+4+5+5+5+6+6+6+7+8)/10 = 5.5Step 2: Find the difference between each data and mean:Difference between 3 and 5.5 is 2.5Difference between 4 and 5.5 is 1.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 5 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 6 and 5.5 is 0.5Difference between 7 and 5.5 is 1.5Difference between 8 and 5.5 is 2.5Step 3: Add all the differences:2.5+1.5+0.5+0.5+0.5+0.5+0.5+0.5+1.5+2.5 = 11Step 4: Divide it by the number of data:11/10 = 1.1So, the MAD = 1.1
Miguel is asked to solve the problem below and wants to convert the values to the same form. Which form would you encourage Miguel to choose?
-0.6(⅚)
Group of answer choices
No answer text provided.
Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions.
Since 5/6 is a repeating decimal, Miguel should convert the fraction 5/6 to a decimal and multiply decimals.
Since 5/6 is a terminating decimal, Miguel should convert 5/6 to a decimal and multiply the decimals.
the correct option is:
"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."
Which form would you encourage Miguel to choose?
Miguel wants to do the product below:
-0.6*(5/6)
And he know that to do it, he should convert both numbers to the same form, only that he does not know if he should transform the decimal number into a fraction or the fraction into a decimal.
It is always easier to work with fractions, so the blind answer is to go with the fraction, but let's see why this is the best option.
5/6 written as a decimal will give:
5/6 = 0.833....
It is a repeating decimal number, so taking the exact product would be impossible to do by hand if we used both numbers in decimal form.
While -0.6 written as a fraction is really trivial, just multiply it and divide it by 10, it becomes:
-0.6 = -6/10
Then the product is:
(-6/10)*(5/6) = -5/10 = -1/2
Then the correct option is:
"Since 5/6 is a repeating decimal, Miguel should convert the decimal -0.6 to a fraction and multiply the fractions."
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Pls help me im not that smart !!
Work Shown:
5 times 2 = 10
5 times 13 = 65
5 times 2.13 = 10.65
This rounds to 10.7 when rounding to the nearest tenth, i.e. one decimal place.
the number of triangles is 1/3 the number of sides
Answer:
y=(1/3) or y=1/3x
Step-by-step explanation:
Without the parenthesis, your equation can be interpreted as Y = one over 3x
The equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
Let's denote the number of sides of a polygon as "s" and the number of triangles that can be formed within the polygon as "t."
The equation for the number of triangles being 1/3 the number of sides is:
t = (1/3) × s
This equation states that the number of triangles (t) is equal to one-third of the number of sides (s) in a given polygon.
Hence, the equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
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Complete question:
Write an equation for the number of triangles is 1/3 the number of sides.
The parent graph for a linear function and an absolute value function are shown below. Compare and contrast the two functions. Please include information about the characteristics of each graph, including, but not limited to domain/range, shape of the graph, etc.
From the left, the first graph's characteristics is as follows
v shaped representing two straight line graphIt has two slopes, one is negative the other is positive slopeThe intercept is 0The domain is - 10 to 10The range is - 10 to 10The graph passed through the originThe second graph characteristics is as follows
The shape represents a single straight line graphThe graph has one positive slopeThe intercept is zeroThe domain is - 10 to 10The range is - 10 to 10This graph passed through the originWhat is a graph?A graph is a pictorial representation of values used in data presentation. A graph is very useful in research as the values can help show the relationship between the data obtained. Graphs can also be used to predict events and can have multiple other uses depending on the type of graph and the nature of data plotted.
A graph has so many features that varies by the type of graph and the information it is representing. The graph treated here is a straight line graph and the equation is: y = mx + c
where m is the slope , and c is the intercept
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Write 0.8
as a fraction.
thank youuu
Answer:
8/9
Step-by-step explanation:
The other answer is wrong because the problem is asking for the fraction form of 0.8 repeating, not just 0.8.
25 points plus brainliest
Answer: y-3 = 3(x+4)
Step-by-step explanation:
See attached
sam is 6 years older than mia. mia is 3 years younger than alice. if sam is 19 years old, how old is alice?
a) 17
b) 16
c) 10
d)18
e) 15
The cost of pumpkins is shown in the table. Determine whether the cost of a pumpkin is proportional to the number bought by graphing the relationship on the coordinate
plane. Explain.
Number of Pumpkins: 0 1 2 3 4
Cost: ($) 0 4 8 12 16
Cost of pumpkins
y
16
12
8
4
0 2 4 6 8 x
Pumpkins
Yes, it is true the cost of a pumpkin is proportional to the number bought.
What is the Proportional Relationship?
We are given the table showing cost of each number of pumpkins. Now, let us analyze the table values;
1) When number of pumpkins is 1, then cost is $4. Thus;
Cost per pumpkin = 4/1 = $4 per pumpkin
2) When number of pumpkins is 2, then cost is $8. Thus;
Cost per pumpkin = 8/2 = $4 per pumpkin
3) When number of pumpkins is 3, then cost is $12. Thus;
Cost per pumpkin = 12/3 = $4 per pumpkin
4) When number of pumpkins is 4, then cost is $16. Thus;
Cost per pumpkin = 16/4 = $4 per pumpkin
In all these rates, we see that the cost rate for pumpkins remains the same. Thus, we can conclude that it is true the cost of a pumpkin is proportional to the number bought.
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(a) Write an expression for a number that is
three more than r.
.
Answer:
r+3
Step-by-step explanation:
r is an expression. To get an expression that is 3 more, just add 3
r+3
If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
The different ways can a student check off one answer to each question is 1024.
It is required to find the different ways can a student check off one answer to each question.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
If a multiple choice test consists of 5 questions each with 4 possible answers of which only one is correct,
,To find how many different ways can a student check off one answer to each question we have,
: 4^5 = 2^10
= 1024
Therefore, the different ways can a student check off one answer to each question is 1024.
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