Answer:1) An operator is missing in your statement. Most likely the right expression is:
Step-by-step explanation:
2x
f(x) = -------------
3x^2 - 3
So, I will work with it and find the result of each one of the statements given to determine their validiy.
2) Statement 1: The graph approaches 0 as x approaches infinity.
Find the limit of the function as x approaches infinity:
2x
Limit when x →∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
3 - 3/∞ 3 - 0 3
Therefore the statement is TRUE.
3) Statement 2: The graph approaches 0 as x approaches negative infinity.
Find the limit of the function as x approaches negative infinity:
2x
Limit when x → - ∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
3 - 3/(-∞) 3 - 0 3
Therefore, the statement is TRUE.
4) Statement 3: The graph approaches 2/3 as x approaches infinity.
FALSE, as we already found that the graph approaches 0 when x approaches infinity.
5) Statement 4: The graph approaches –1 as x approaches negative infinity.
FALSE, as we already found the graph approaches 0 when x approaches negative infinity.
25 ft
2 ft
24 ft
Is it impossible?
By applying the criterion of the law of cosine, the triangle presented in the picture is possible.
Is this triangle possible?
Herein we find an hypothetical triangles with all side lengths known. A criterion is using the law of cosine, a possible triangle has cosine values between - 1 and 1. Then, we proceed to check for each side:
cos A = - (a² - b² - c²) / (2 · b · c)
cos A = - (25² - 2² - 24²) / (2 · 2 · 24)
cos A = - 0.469
cos B = - (b² - a² - c²) / (2 · a · c)
cos B = - (2² - 25² - 24²) / (2 · 25 · 24)
cos B = 0.998
cos C = - (c² - a² - b²) / (2 · a · b)
cos C = - (24² - 25² - 2²) / (2 · 25 · 2)
cos C = 0.53
Since the law of cosine gives realistic results, then the triangle presented in the picture is possible.
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5 1-3a
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma
($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal
places, show both decimal places (5.06).
The variance of a distribution is 195. What is the standard deviation, rounded to the nearest thousandth?
Applying the square root of the variance, the standard deviation of the distribution is of 13.964.
What is the standard deviation of a distribution?The standard deviation of a distribution is given by the square root of the variance of the distribution.
For this problem, the variance of the distribution is of 195, hence the standard deviation is:
s = sqrt(195) = 13.964.
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The mean exam score for the first group of twenty examinees applying for a security
job is 35.3 with a standard deviation of 3.6.
The mean exam score for the second group of twenty examinees is 34.1 with a
standard deviation of 0.5. Both distributions are close to symmetric in shape.
a. Use the mean and standard deviation to compare the scores of the two groups.
b. The minimum score required to get an in-person interview is 33. Which group
do you think has more people get in-person interviews?
The mean exam score of the first group is [tex]35.3[/tex]
The mean exam score for the second group is [tex]34.1[/tex]
but [tex]35.3[/tex] is greater than [tex]34.1[/tex]
Standard deviation of the first group is [tex]3.6[/tex]
Standard deviation of the second group is [tex]0.5[/tex]
but [tex]3.6[/tex] is greater than [tex]0.5[/tex].
(a) We can draw a conclusion that the score of the second group is more evenly distributed.
(b) The second group has more people get in - person interviews because [tex]3.6\geq 0.6[/tex], so the scores of the exam for the second group are all close to 34.1. On the contrary, the score of exams for the first group is extreme polarization.
Mean: The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.Standard deviation: The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a database is in relation to its mean.To learn more about mean and standard deviation, click on the link given below:
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15, 10, 20/3
Find the 9th term.
Answer:
15*2/3=10
10*2/3=20/3
20/3*2/3=40/9
40/9*2/3=80/27
80/27*2/3=160/81
160/81*2/3=480/243
480/243*2/3=960/729
960/729*2/3=1920/2187.
=1920/2187
The 9th term of the geometric sequence will be 1280 / 2187.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The sequence is given below.
15, 10, 20/3
The first term is 15. And the common ratio is given as,
r = 10 / 15
r = 2 / 3
The 9th term of the geometric sequence is given as,
a₉ = 15 · (2/3)⁹⁻¹
a₉ = 15 · (2/3)⁸
a₉ = 15 · 256/6561
a₉ = 1280 / 2187
The 9th term of the geometric sequence will be 1280 / 2187.
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if h(x)=4-6x, find each of the following
h(-1)
h(10)
h(5)
Answer:
(-1)=10
(10)= -54
(5)= -26
Step-by-step explanation:
h(-1)=4-6(-1)
h(-1)=4 (-6*-1)
h(-1)=4+6
h(-1)=10
h(10)=4-6(10)
h(10)=4 (-6*10)
h(10)=4-60
h(10)=-54
h(5)=4-6(5)
h(5)=4 (-6*5)
h(5)=4-30
h(5)=-26
Hope this helps.
A straight line has a gradient of 4 and passes through the point (2,9).
Work out the equation of the line.
Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
The equation of the given line passes through the point (2,9) y = 4x + 1.
What exactly is the slope of a line?The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
A line equation is defined as:The conventional form of a line equation is ax + by + c = 0. Here, the coefficients are a and b, the variables are x and y, and the constant term is c. It is a one-degree equation with variables x and y. The coordinates of both the point on the line that appears in the coordinate plane are represented by the values of x and y.
According to the given data:m = 4
equation of the line = y = mx + c
substituting the value of m = 4
y = 4x + c
the point (2,9):
putting the points in the line of the equation:
x = 2
y = 9
So,
y = mx + c
9 = 4 * 2 + c
9 = 8 + c
c = 1
The equation of the given line y = 4x + 1.
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Answer:
y=4x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-9=4(x-2)
y=4x-8+9
y=4x+1
Given y = x² + 3x - 2, find y when x = -2
Answer: - 10
Step-by-step explanation: -2 to the 2nd power is - 4. And 3 * - 2 is -6. So -4 + -6 = - 10.
I hope I have helped and I hope you have a wonderful day!
A man owns 50 shares of stock worth $30 each. The corporation declared a dividend of 6% payable in stock. How many shares did he then own?
Answer:53 shares
Step-by-step explanation:
If we assume the price remained constant, then the number of shares increased by 6%.
(50 shares)(1 +6%) = 53 shares
The man then owned 53 shares
f(x) = x²
What is f(x) + f(x) + f(x)?
The result of the given expression f(x) + f(x) + f(x) = 3x².
What is defined as the quadratic function?A quadratic function is one of the following: f(x) = ax² + bx + c, where a, b, and c are positive integers and an is not equal to zero.
A parabola is a curve that represents the graph of a quadratic function. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all share the identical basic "U" shape.A quadratic equation is defined in mathematics as an equation of degree 2, which means that the highest exponent of the this function is 2.As per the given question;
f(x) = x²
Now, we have to estimate the value of the function;
= f(x) + f(x) + f(x)
Substitute the value of f(x).
= x² + x² + x²
= 3x²
Thus, the value of the given function is found as 3x².
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Find the equation of a line parallel to 3x + 3y = 21 that passes through the point
(8,-2).
Answer:
awsome
Step-by-step explanation:
565
which is the midpoint of AB?
Please help I’ll give Brainliest answer to whoever is correct
Andrea, Roberto, Charlene, Maria, and Nguyen volunteer their time as computer science tutors after school. Due to their
schedules, though, they are only able to tutor on certain school days:
Andrea is able to tutor every second school day (every other school day).
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
If all five people are tutoring together today, how many school days from today will be the next time all five tutor together again?
From today 36 days later, all five will be tutoring again.
As we have given that,
Andrea is able to tutor every second school day
Roberto is able to tutor every third school day.
Charlene is able to tutor every fourth school day.
Maria is able to tutor every sixth school day.
Nguyen is able to tutor every ninth school day.
So, as a result, our working days are 2, 3, 4, 6, and 9 days.
Today's tutoring session will involve all five participants.
Next time, all five tutors will work together = LCM (2, 3, 4, 6, 9) = 36
Therefore, from today 36 days later, all five will be tutoring again.
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find two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm.
Two possible lengths for CD if C, D, and E are collinear, CE 17.9 cm, and DE = 8.2 cm is 12.3cm and 19.3cm.
In space, a point is a precise position or location. It is possible to depict it in relation to a coordinate system and its origin. It has no length and is a zero-dimensional entity.
A line is made up of an unlimited number of points that form a straight line. One-dimensional objects like lines lack both thickness and width. It stretches forever in both directions. An endpoint and a beginning point define a line segment, which is a component of a line. A linear equation can be used to depict a line.
D is between C and E
_ _ _
C D E
CD =CE-DE
CD=15.8-3.5cm
CD=12.3 cm
E is between D and C
_ _ _
D E C
CD=CE+DE
CD=15.8+3.5cm
=19.3cm
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Dwayne can spend no more than $12 at the grocery store buying loaves of bread and eggs. Each egg costs $0.20 and each loaf of
needs at least 6 eggs and 3 loaves of bread.
Let x represent the loaves of bread and y represent the number of eggs. Select all the inequalities that represent constraints for the situation.
OA 2x+0.2y>_ 9
OB. 2x+0.2y≤ 12
O C. x>_3
OD. x+y ≤ 12
O E x ≤ 3
OF. y ≤ 6
OG y>_6
The inequalities that represent constraints for the situation will be:
x+y ≤ 12
x >= 3
y >= 6
How to calculate the value?Let x represent the loaves of bread
Let y represent the number of eggs.
From the information, Each egg costs $0.20 and each loaf of needs at least 6 eggs and 3 loaves of bread.
Therefore,
x >= 3
>= 3y >= 6
Also, Dwayne can spend no more than $12 at the grocery store buying loaves of bread and eggs. This will be x+y ≤ 12.
The correct options are C, D, and F.
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7. Kevin can run a lap around the field in 4-6 minutes. If he has 30 minutes to run, how
many laps is he able to finish?
The number of laps that Kevin can run is 5 laps.
How to calculate the number of laps?From the information, Kevin can run a lap around the field in 4-6 minutes and he has 30 minutes to run.
Therefore, the number of laps that he can run will be:
= Total minutes / Time taken for each lap
= 30 minutes / 6
= 5 laps.
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Evaluate the expression when a = 7 and c= -3.
-a+4c
Hello,
[tex] - a + 4c = - 7 + 4 \times ( - 3) = - 7 - 12 =- 19[/tex]
Answer:
-19
Step-by-step explanation:
-7 + 4(-3)
-7 - 12= -19
andrew took a handful of change out of his picket adn noticed taht he was only holding dimes adn quarters in his hand. he counted that he had 22 coins that ammounted to $4. how many quarters and how many dimes does andrew have?
Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
What is a system of linear equations?A system of linear equations is a set of two or more linear equations. Linear equations refer to the equations that involve two or more variables in the form of "ax + b".
Given:
Number of coins = 22; only dimes and quarters.Amount of coins = $4To find: Number of dimes and quarters.
Finding:
Now, 1 dime = 10 cents and 1 Quarter = 25 centsAlso, 100 cents = $1=> By unitary method, $4 = 4(100) = 400 cents
Let the number of dimes be d and number of quarters be q.Now, According to question, a system of linear equations follows:d + q = 22 (Number of coins) => d = 22 - q (eqn1)
and 10d + 25q = 400 (amount of coins)
=> 10 ( 22 - q ) + 25q = 400
=> 220 - 10q + 25q = 400
=> 15q = 400 - 220 = 180
=> q = 12, i.e., number of quarters = 22 upon the solving of this system of linear equations.
On substituting the value of q in eqn1, we get: d = 22 - 15 = 7, i.e., number of dimes = 7.
Hence, Andrew has 7 dimes and 15 quarters, as obtained from the system of linear equations so formed.
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For this exponential
function,
what is the output value (y),
when the input value (x) is O?
y = 10•5x
(0,[?])
The output value of (y) will be 1 .
In mathematics, an exponential function is a function of the form f(x) = ax. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. Exponential functions, as the name suggests, involve exponents. But note that the base of the exponential function has a constant and the exponent has a variable, not vice versa.We have given an exponential function [tex]y=10.5^x[/tex] ......(1)
It is given that input value is 0 which means that replace the x with the input value in the given function.
Putting x = 0 in the equation (1) , we get
[tex]y=10.5^0[/tex]
Value of any number raised to power zero is always one .
[tex]y=1[/tex]
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aaliyah compares the heights of two plants to see which plant grows more per day. The table shows the height of Plant 1, in centimeters, over 5 days. The graph shows the height of Plant 2, in centimeters, over 10 days. aaliyah says that since Plant 1 grows 4cm per day and Plant 2 grows 6cm per day, plant 2 grows more per day. Do you agree with aaliyah? Explain your response.
A. I agree that plant 2 grows more per day than plant 1, but I disagree with aaliyahs's reasoning.
B.
I think that plant 1 grows more per day than plant 2, but I agree with aaliyah's reasoning.
C.
I think that plant 1 grows more per day than plant 2, and I disagree with aaliyahs's reasoning.
D.
I agree that plant 2 grows more per day than plant 1, and I agree with aaliyah's reasoning.
The table that shows the growth rate of Plant 1 which is 4 cm/week, and the graph that gives the growth rate of Plant 2 as 2 cm/week gives the correct option as C;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
What is a proportional relationship?A proportional relationship between two variables is one in which one variable is a multiple of the other.
The possible table in the question is presented as follows;
Plant 1
Week; 2, 3, 4, 5Height; 8, 12, 16, 20The values on the graph are;
Plant 2
Week; 2, 4, 6, 8, 10Height; 4, 8, 12, 16, 20The rate, r1, of growth of Plant 1 is therefore;
r1 = 8 cm/(2 weeks) = 4 cm/week
The rate, of growth, r2, of plant 2 is found as follows;
r2 = 4 cm/(2 weeks) = 2 cm/week
Given that Plant 1 grows faster at 4 cm/week, than Plant 2, that grows at 2 cm/week, the correct statement is since Plant 1 grows 4 cm/week and Plant 2 grows 2 cm/week, Plant 1 grows more per day.
The correct option is therefore;
C. I think that plant 1 grows more per day and I disagree with Aaliyah's reasoning
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Round 2798.01 to 2 significant figure
The approximation of 2798.01 to 2 significant figures is 2800
How to round the expression to 2 significant figures?The expression is given as
2798.01
The approximation is given as
2 significant figures
The above means that we approximate the given expression such that only 2 significant figures are left
In this case, the 2 significant figures in the expression 2798.01 are 2 and 7
So, we start the approximation from 9
When 9 is approximated, the expression becomes
2798.01 = 2800
Hence, the approximation of 2798.01 to 2 significant figures is 2800
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1. f(3)=2x-5 (show work)
Answer:
The answer is 1
Step-by-step explanation:
On a graph, it would be at the plot point (3,1)
Simplify this algebraic expression completely.
10y - 3(y + 5)
O A. 7y+2
O B. 7y+ 5
© C. 7y- 15
• D. 7y- 5
The answer for the following algebraic expression [tex]10y-3(y+5)[/tex] is Option C [tex]7y-15[/tex].
According to the given question statement, We are supposed to simplify the given algebraic expression [tex]10y - 3(y + 5)[/tex]
Solution is as follows:
[tex]10y - 3(y + 5)\\= 10y-3(y)-3(5)\\\[/tex]
[tex]=10y-3y-15[/tex]
[tex]=7y-15[/tex]
Hence [tex]7y-15[/tex] is our final answer.
Algebraic expression: The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We get to know how to express an unknown value using letters like x, y, and z in the basics of algebra. Here, we refer to these letters as variables. Variables and constants, both can be used in an algebraic expression. A coefficient is a value that is added before a variable and then multiplied by it. These letters are called as variables here. Both constants and variables may be employed in an algebraic expression. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.To learn more about Algebraic expression, click on the link given below:
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in a month, carlos can produce a maximum of either 60 bushels of pears or 30 bushels of apples, or any linear combination in between. similarly, diane can produce a maximum of either 20 bushels of pears or 5 bushels of apples, or any linear combination in between.
Thus 3 bushels of pears can be acceptable term of trade for bushels of pears.
Opportunity cost of 1bushel of apple for Carlos=2pears
Opp. Cost of 1 bushles of apple for Donna=4pears
Thus ,
Term of trade acceptable to both for one bushels of apple is 2-4 bushels of pears
Ryan bought 6 apples and 9 peaches for a total of $9.75. Madi bought 4 apples and 5 peaches for $5.75. How much are apples and peaches?Define the variables.▪ Write 2 equations that model the situation.▪ Solve the system by either graphing, substitution or linear combinations.▪ Answer the question that was asked.▪ Plug in both answers and check your worka. The required equations are 6a+9p = 9.75 and 4a+5p = 5.75 .
b. The solution is given in the attached picture.
c. Apples are 1/2 and Peaches are 0.75
d. Solving the equations by putting the values
Let's take equation 1
6a+9p = 9.75
6 (1/2) + 9 (0.75) = 9.75
So equation satisfies both sides
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. Tell whether (7,-4) is a solution of y ≥ 5 - x.
(7,-4) is not a solution of the inequality y ≥ 5 - x
How to tell whether (7,-4) is a solution of y ≥ 5 - x?The inequality expression is given as
y ≥ 5 - x
The solution is given as:
(7, -4)
This means that
(x, y) = (7, -4)
Substitute (x, y) = (7, -4) in the inequality y ≥ 5 - x
So, we have
-4 ≥ 5 - 7
Evaluate the difference
-4 ≥ -2
On the numbering system, -4 is less than -2
Hence, (7,-4) is not a solution of the inequality y ≥ 5 - x
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what is the answer to 3(x-2) = 6
[tex]3(x - 2) = 6 \\ x - 2 = \frac{6}{3} \\ x - 2 = 2 \\ x = 2 + 2 \\ x = 4[/tex]
Answer:
Step-by-step explanation:
x =4
8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables
Evaluate the expression with its given values. 5 x − 2 y ; x = 2 , y = − 1
The value of the given expression (5 x − 2 y) = 12.
What is substituting method:The substitution technique is an algebraic approach for solving simultaneous linear equations. In this procedure, the value of one variable through one equation is substituted in the second equation, as the name implies.
What is the substitution technique formula?Three phases are involved in the substitution method: Solve one equation for one of the variables. Substitute (plug-in) this expression in the other equation as well as solve. Replace the value in the original equation to obtain the equivalent variable.
According to the given data:5 x − 2 y
x = 2;
y = -1;
substituting the value in the given equation:
5 x − 2 y
5(2) - 2(-1)
5(2) - (-2)
5(2) +2
10+2
12
The value of the given expression (5 x − 2 y) = 12
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How many times greater is 70,000 than 7,000?
Answer
70.000 в 10 раз больше 7.000
Step-by-step explanation:
It takes Mike 18 minutes to finish reading 4 pages of a book. How
long does it take for him to finish reading 30 pages?
Answer:
135 minutes
Step-by-step explanation:
18 divided by 4
4.5 pages per minute
4.5 times 30 = 135
Answer: 135 minutes
Step-by-step explanation: 18 times 30, then divide by 4
What is the image point of (8, -3) after a translation right 5 units and down 5 units?