Answers
The evaluation of the function gives:
f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3
How to evaluate f(-4) based on the given functions?
A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
The evaluation is as follow:
For f(-4):
since x = -4. This means x ≤ -4. Thus, we use the function |2x + 7|. That is:
f(-4) = |2*(-4) + 7|
f(-4) = |-8 + 7|
f(-4) = | -1 |
f(-4) = 1
For f(1):
x = 1. Thus, -4< x ≤ 1. Use 1 + x²
f(1) = 1 + x²
f(1) = 1 + 1²
f(1) = 2
For f(2):
x = 2. Thus, 1< x < 3. Use the value 6
f(2) = 6
For f(5):
x = 5. Thus, x ≥ 3. Use (1/3)x + 8.
f(5) = (1/3)*5 + 8
f(5) = 29/3
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Evaluating the function at various values of x over different intervals,
f(-4) = 1, f(1) = 2, f(2) = 6, f(5) = 29/3
What is the value of the functionTo evaluate the function f(x) at various values of x, we need to use the definition of the function for each interval of x.
For x ≤ -4:
f(x) = |2x + 7|
f(-4) = |2(-4) + 7| = |-1| = 1
For -4 < x ≤ 1:
f(x) = 1 + x²
f(1) = 1 + 1² = 2
For 1 < x < 3:
f(x) = 6
f(2) = 6
For x ≥ 3:
f(x) = (1/3)x + 8
f(5) lies in the interval x ≥ 3, so we use the definition of f(x) for this interval:
f(5) = (1/3)(5) + 8 = 29/3
Therefore,
f(-4) = 1
f(1) = 2
f(2) = 6
f(5) = 29/3
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Related Questions
two ice cream machines make a total of 320 gallons in a certain amount of time. working together for the same length of time, how many gallons of ice cream can each number of machines make? 3 ice cream machines
Answers
3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.
For the quantity 3 ice cream machines will make.
2 ice cream machines produce a total of 320 gallons in a certain amount of time.
If 2 ice cream machines can make a total of 320 gallons. Then,
3 ice cream machines will produce a total of x gallons in the same amount of time
x = (320 × 3)/2
x = 480 gallons
Hence, 3 ice cream machines will produce a total of 480 gallons.
For the quantity 4 ice cream machines will make.
If 2 ice cream machines can make a total of 320 gallons. Then,
4 ice cream machines will produce a total of y gallons in the same amount of time
y = (320 × 4)/2
y = 640 gallons
Hence, 4 ice cream machines will produce a total of 640 gallons.
--The given question is incomplete, the complete question is
"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?
3 ice cream machines
4 ice cream machines"--
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a group of fish is called a school . there are twenty-five in the small school.there are one hundered twelve fish in the big school. how many fewer fish are in the small school
Answers
There are 87 fewer fish in small school compared to big school.
We solve addition and subtraction problems by focusing on either the action (joining or separating) or the relationship in the problem. Many problems involve monetary relationships.
This week, we looked at COMPARISON problems, which involve determining the similarities and differences between sets.
Difference Unknown: One type of compare problem entails determining how many more items are in one set than another. James, for example, has six mice. Joy has eleven mice. Joy has how many more mice than James?
Given,
Number of fish in small school = 25
Number of fish in big school = 112
then,
Number of fewer fish does small school have 112 -25 = 87
Thus, there are 87 fewer fish in school than big school.
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Use the graphical method to solve the following Linear Programming model.
max = x1 + 3x2
s.t.
5x1 + 2x2 ≤ 10
x1 + x2 ≥ 2
x2 ≥ 1
x1, x2 ≥ 0
Answers
The given linear programming model needs to be solved using the graphical method. The objective function is to maximize the expression x1 + 3x2, subject to three constraints. The first constraint is 5x1 + 2x2 ≤ 10, the second constraint is x1 + x2 ≥ 2, and the third constraint is x2 ≥ 1. The decision variables x1 and x2 must be non-negative.
To solve the linear programming model using the graphical method, we start by graphing the feasible region determined by the constraints. Each constraint is represented by a linear inequality, and the feasible region is the area where all constraints are satisfied. By plotting the feasible region on a graph, we can identify the region where the optimal solution lies.
Next, we evaluate the objective function, which is to maximize the expression x1 + 3x2. We identify the corner points or vertices of the feasible region and calculate the objective function value at each vertex. The vertex that yields the highest objective function value represents the optimal solution.
In this case, without having specific values and the graphical representation, it is not possible to provide the exact coordinates of the corner points or the optimal solution. To obtain the precise solution, you would need to plot the feasible region, determine the vertices, and evaluate the objective function at each vertex.
It's important to note that the graphical method is suitable for problems with two decision variables, allowing for easy visualization of the feasible region and identification of the optimal solution.
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Calculate the slope of a line that passes through the following two points.
(5,-2) and (4, -8)
help please it’s due tonight
Answers
Answer:
the slope is 6 (6/1)
Step-by-step explanation:
Use the slope formula: y2-y1/x2-x1 ( i did the one that was further to the right ats the second pair rather than the order that you put it in)
Answer:
Yo, the slope of the line is 6 yo!
Step-by-step explanation:
You see, to find the slope of 2 points, Here's what ya do little fella: Pick any y-coordinate point(-2) or (-8). When you do, subtract -2 and -8 so in this case, -y - (-x) = -y + x. So, when done correctly, you get 6 because -2 - (-8) is equal to -2 + 8. Ya go to the x-coordinate. If you subtracted -8 from -2, you have to subtract 4 from 5. If you also subtracted -2 from 8, you have to subtract 5 from 4. So, it has to be in order. 5 - 4 = 1. So then, you divide your answer 6/1 = 6. So 6 is the slope people. NA YOU PEOPLE EHN, YA BETTER GO AND START LEARNING ALGEBRA.
What is the value of tan(60°)? One-half StartRoot 3 EndRoot StartFraction StartRoot 3 EndRoot Over 2 EndFraction StartFraction 1 Over StartRoot 3 EndRoot EndFraction
Answers
Answer:
\(\sqrt3\)
Step-by-step explanation:
To find:
The value of \(tan60^\circ\) = ?
Solution:
Kindly consider the equilateral \(\triangle ABC\) as attached in the answer area.
Let the side of triangle = \(a\) units
Let us draw the perpendicular from vertex A to side BC.
It will divide the side BC in two equal parts.
i.e. BD = DC = \(\frac{a}{2}\)
Using Pythagorean Theorem in \(\triangle ABD\):
\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\)
Side AD = \(\frac{\sqrt3}{2}a\)
Using Trigonometric ratio:
\(tan\theta = \dfrac{Perpendicular}{Base}\)
\(tanB = \dfrac{AD}{BD}\)
Putting the values of AD and BD:
\(tan60^\circ=\dfrac{\frac{\sqrt3}{2}a}{\frac{1}{2}a}\\\Rightarrow tan60^\circ = \bold{\sqrt3}\)
15
A shop sells small chocolate bars and large chocolate bars.
There are
small chocolate bars are sold in packs of 4
large chocolate bars are sold in packs of 9
On one day
the number of packs of
small chocolate bars sold
the number of packs of
large chocolate bars sold
A total of 95 chocolate bars were sold.
Work out the number of small chocolate bars sold.
= 5:2
Answers
Answer:
Step-by-step explanation:
i think the answer is 380 but i am not sure
Probability
Boy Percentage = 55%
Left-handed = 12%
Right-handed = 88%
Girl Percentage = 45%
Left-handed = 9%
Right-handed = 91%
Only need C
C) "What's the probability of a newborn baby being left handed?"
Answers
Answer:
25%
Step-by-step explanation:
55 + 12 + 88 + 45 + 9 + 91=300/12=25=25%
Two functions are shown in the table below:
Complete the table, then select the value that is a solution to f(x) = g(x).
Function x = 1 x = 2 x = 3 x = 4 x = 5 x = 6
f(x) = −x2 + 4x + 12
g(x) = x + 8
Answers
The value that is a solution to f(x) = g(x) is x = 4.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: f(x) = −x² + 4x + 12
g(x) = x + 8, x = 1 x = 2 x = 3 x = 4 x = 5 x = 6
We have to find the value that is a solution to f(x) = g(x).
When x = 1
f(1) = −(1)² + 4(1) + 12
f(1) = -1 + 4 + 12
f(1) = 15
g(1) = 1 + 8
g(1) = 9
f(1) ≠ g(1)
When x = 2
f(2) = −(2)² + 4(2) + 12
f(2) = -4 + 8 + 12
f(2) = 16
g(2) = 2 + 8
g(2) = 10
f(2) ≠ g(2)
When x =3
f(3) = −(3)² + 4(3) + 12
f(3) = -9 + 12 + 12
f(3) = 15
g(3) = 3 + 8
g(3) = 11
f(3) ≠ g(3)
When x = 4
f(4) = −(4)² + 4(4) + 12
f(4) = -16 + 16 + 12
f(4) = 12
g(4) = 4 + 8
g(4) = 12
f(4) = g(4)
When x = 5
f(5) = −(5)² + 4(5) + 12
f(5) = -25 + 20 + 12
f(5) = -5 + 12
f(5) = 7
g(5) = 5 + 8
g(5) = 13
f(5) ≠ g(5)
When x = 6
f(6) = −(6)² + 4(6) + 12
f(6) = -36 + 24 + 12
f(6) = 0
g(6) = 6 + 8
g(6) = 14
f(6) ≠ g(6)
Hence, the value that is a solution to f(x) = g(x) is x = 4.
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How many 3/5's are in 4?
Answers
Answer:
6.6
Step-by-step explanation:
Answer:
6.6
Step-by-step explanation:
Solve the inequality: −34 < −2(4x − 1)
Answers
\( - 34 < - 2(4x - 1) \\ - 34 < - 8x + 2 \\ - 34 - 2 < - 8x \\ - 36 < - 8x \\ 36 > 8x \\ \frac{36}{8} > x \\ x < \frac{9}{2} \)
which type of analysis involves three or more variables?group of answer choicesunivariate statistical analysisbivariate statistical analysismultivariate statistical analysispolyvariate statistical analysis
Answers
The type of analysis that involves three or more variables is called multivariate statistical analysis. The correct option is multivariate statistical analysis.
This type of analysis is used to identify relationships between multiple variables in a dataset, and to determine how these variables interact with each other to affect an outcome. Multivariate analysis is a powerful tool for data analysis because it allows researchers to examine complex relationships between variables, and to identify patterns that might not be visible through simpler analyses.
Examples of multivariate statistical analysis include regression analysis, factor analysis, and principal component analysis. These methods allow researchers to examine the relationships between multiple variables, to identify the most important variables in a dataset, and to create models that can be used to predict future outcomes. Multivariate analysis is used in a wide range of fields, including psychology, economics, biology, and social sciences, and is an essential tool for anyone who needs to analyze large, complex datasets. The correct option is multivariate statistical analysis.
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(4x² − 3x² + 7x + 2) ÷ (x-1/2)
Answers
By performing divsion in (4x² − 3x² + 7x + 2) ÷ (x-1/2), the resultant answer is x² + 7x + 2 ÷ (x-1/2) respectively.
What is division?The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.
Multiplication, addition, and subtraction make up the remaining operations.
The following formula can be used to determine the division of two numbers: Quotient plus the remainder is the dividend divisor.
The dividend in this situation refers to the number that is being divided.
The divisor is the number that divides the number (dividend) into equal parts.
So, we have:
(4x² − 3x² + 7x + 2) ÷ (x-1/2)
Now, divide as follows:
(4x² − 3x² + 7x + 2) ÷ (x-1/2)
(1x² + 7x + 2) ÷ (x-1/2)
x² + 7x + 2 ÷ (x-1/2)
Therefore, by performing divsion in (4x² − 3x² + 7x + 2) ÷ (x-1/2), the resultant answer is x² + 7x + 2 ÷ (x-1/2) respectively.
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Correct question:
Compute the division:
(4x² − 3x² + 7x + 2) ÷ (x-1/2)
add the following polynomial of x3+3xy-2×y2+y3,2×3-5x2y-3xy2-2y3
Answers
The addition of the polynomial \(x^{3}+3xy-2xy^{2} +y^{3}\) with \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).
What is a polynomial?
⇒ A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
⇒ In the addition of polynomials, the like terms are added while in subtraction, the like terms are subtracted.
Calculation;
We have been given two polynomial which we have to add \(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\)
The sign after addition or subtraction will always be of the variable having more value.
\((x^{3}+3xy-2xy^{2} +y^{3} )+(2x^{3}-5x^{2} y-3xy^{2}-2y^{3})\)
On adding like terms with each other
⇒ \((x^{3} +2x^{3})+ 3xy-5x^{2} y-(2xy^{2}+3xy^{2})+(y^{3}-2x^{3})\)
⇒ \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\)
Hence the addition of the polynomial\(x^{3}+3xy-2xy^{2} +y^{3}\) and \(2x^{3}-5x^{2} y-3xy^{2}-2y^{3}\) is \(3x^{3}+3xy-5x^{2} y-5xy^{2}-y^{3}\).
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a bike path is 12.5 miles. Dominic is 70% of the way to the end how far is Dominic on the path
Answers
Dominic is on the 8.75 mile of the bike path
How to determine how far on the path is the distance?From the question, the given parameters are:
Proportion of distance = 70% of the bike path Bike path = 12.5 milesThe above parameters implies that
Dominic's position = 70% of the total distance
Represent the total distance with x
So, we have the following representation
Dominic's position = 70% * x
Where
x = 12.5
So, we have
Dominic's position = 70% * 12.5
Evaluate the products
Dominic's position = 8,75
Hence, Dominic's position is 8,75 miles
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Indicate the level of measurement for the data set described. Number of classes taken in a semester by each student at a college Answer :a. Nominal b. Ordinal c. Interval d. Ratio
Answers
The correct answer is option c. Interval. The level of measurement for the data set described is Interval.
This is so because the data set calculates each student's enrollment in classes during the course of a semester at a particular college.
Numerical information that is measured on a scale with evenly spaced intervals but lacks an absolute zero point is called interval data.
The numerical values themselves do not reflect quantities or have any absolute value, but the intervals between them all have the same size.
The interval between 3 classes and 4 classes, for instance, would be the same as the interval between 8 classes and 9 classes if the data set were measuring the number of classes each student took in a semester, but 3 classes and 8 classes do not have any such absolute value.
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Mr. Jones eats out at his favorite buffet restaurant every Friday night. If the cost is $9 and he budgets $42 for the month, how many times will he be able to eat at this restaurant?
Answers
Mr. Jones will be able to eat at the buffet restaurant approximately 4 times in a month.
To determine how many times Mr. Jones will be able to eat at the buffet restaurant based on his budget, we need to divide his monthly budget by the cost per visit.
Mr. Jones budgets $42 for the month, and the cost per visit is $9.
Number of visits = Monthly budget / Cost per visit
= $42 / $9
≈ 4.67
Since we cannot have a fractional number of visits, we round down to the nearest whole number because Mr. Jones cannot have a partial visit. Therefore,
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please help me find angle e
Answers
Answer:
e = 35
Step-by-step explanation:
The central angle VOU is twice the inscribed angle VTU , that is
70 = 2e ( divide both sides by 2 )
35 = e
Fill in the missing number in this sequence:
{ } 216, 36, 6, 1
Answers
Answer:
1296
Step-by-step explanation:
times each number by 6
example: 1x6=6 6x6=36 36x6=216 216x6=1296
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to fill in the missing number in the sequence
\(\star~\mathrm{(~~),216,36,6,1}\)
\(\triangle~\fbox{\bf{KEY:}}\)
Take a look at the common ratio.Since every number is divided by 6, we need to multiply 216 times the common ratio, 6:
\(\star~\mathrm{216\times6}\)
Simplify!
\(\star~\mathrm{1296}\)
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
explain in qualitative terms why the curve you chose has the shape it does
Answers
The shape of a curve is determined by the relationship between the variables it represents. For example, a linear curve has a constant rate of change between the two variables, while an exponential curve shows an increasing rate of change.
In general, curves can have various shapes depending on the specific data set and the underlying relationship between the variables. The shape of the curve can provide insights into the nature of the relationship between the variables, such as whether it is linear or nonlinear, whether it has a positive or negative correlation, and whether it is symmetrical or skewed.
Therefore, to explain the shape of a particular curve, we need to look at the data set and the relationship between the variables it represents. We can then use qualitative terms to describe the curve, such as whether it is concave or convex, whether it has inflection points or asymptotes, and whether it has a plateau or a steep slope. By analyzing the shape of the curve, we can gain a better understanding of the relationship between the variables and make informed decisions based on the data.
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PLEASE ANSWER THIS ILL GIVE BRAINLIEST
Use the quadratic formula to solve
x ^2 - 4x +3
. Show your work. Then describe the solution.
Answer:
Answers
LO
5
Select all the ways that zero can be
classified. select all that applied. (1 Point)
Whole number
Integer
rational number
Real number
none of the above
Answers
Answer:
?
Step-by-step explanation:
express 3.145 x 10^-6 in decimal notation
Answers
The number 3.145 x 10^-6 expressed in decimal notation is 0.000003145. To express 3.145 x 10^-6 in decimal notation, follow these steps:
Decimal notation is a system of writing numbers that uses the base 10 and decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent any quantity. In decimal notation, each digit to the left of the decimal point represents a multiple of a power of 10, starting with 10^0 (which is 1), and each digit to the right of the decimal point represents a fractional part of a power of 10, starting with 10^-1 (which is 0.1). Step 1: Understand the exponent. In this case, the exponent is -6, which means you'll be moving the decimal point 6 places to the left.
Step 2: Start with the given number, 3.145.
Step 3: Move the decimal point 6 places to the left. Add zeroes as needed to fill in the spaces.
The number 3.145 x 10^-6 expressed in decimal notation is 0.000003145.
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Subtract-3x - 8 from 4x² - 7x - 2.
Answers
\(( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.\)
3x-6y=-12
x-2y=-8
Is it:
Inconsistent
Not enough information
Coincident
Consistent Independent
Answers
Answer:
(a) Inconsistent
Step-by-step explanation:
Two linear equations can be compared by putting both of them in standard form. Here, that means removing a common factor from the coefficients of the first equation.
3x -6y = -12 . . . . given first equation
x -2y = -4 . . . . . . divide by 3
Compare this to the second equation:
x -2y = -8
The constants (-4, -8) are different, so there are no values of x and y that can satisfy both equations. The equations are described as inconsistent.
Answer:
InconsistentStep-by-step explanation:
Equation 1
3x - 6y = -12Divide throughout by 3 to simpliest formx - 2y = -4Equation 2
x - 2y = -8On comparison, it is seen that the slopes are same, but the y-intercepts are different.
This means this has no solution, or the graph is inconsistent.
In a hat, you have index cards with the numbers 1 through 10 written on them. Find how many of the 10 possible numbers you can pick match the described event, then drag and drop each of the numbers into the correct box to order the events from least likely to happen (1) to most likely to happen (8) when you pick one card at random.A. You pick a number greater than 0.B. You pick an even number.C. You pick a number that is at least 2.D. You pick a number that is at most 0.E. You pick a number divisible by 3.F. You pick a number divisible by 5.G. You pick a prime number.H. You pick a number less than the greatest prime number among the numbers 1 through 10.
Answers
The order of events from least likely to most likely are as follows:
D. You pick a number that is at most 0A. You pick a number greater than 0C. You pick a number that is at least 2B. You pick an even numberE. You pick a number divisible by 3F. You pick a number divisible by 5G. You pick a prime numberH. You pick a number less than the greatest prime number among the numbers 1 through 10The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.
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Determine the values of the following quantity.
x^2 0.05,5= _________
Answers
Thus, the value of the quantity x^2 0.05,5 is found to be 0.00001x^2.
The expression x^2 0.05,5 can be a bit confusing, but it essentially means that we need to multiply x^2 by the value of 0.05 repeated five times.
In other words, we need to find the value of x^2 multiplied by 0.05^5.
To do this, we can use our calculator or a scientific calculator. We can first calculate 0.05^5, which gives us the value of 0.00001.
Then, we can multiply this value by x^2 to get the final answer.
Therefore, the value of x^2 0.05,5 is 0.00001x^2. This means that if we know the value of x, we can substitute it into the expression to get our final answer.
In summary, to determine the value of x^2 0.05,5, we need to multiply x^2 by 0.05^5, which gives us the final result of 0.00001x^2.
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Kelly has a rectangular fish aquarium that measures 18 inches long, 8 inches wide, and 12 inches tall. If Kelly wanted to put a protective covering on the four glass walls of the aquarium, how big does the cover have to be
Answers
The protective covering should be 624 square inches. This will cover all four sides of the glass walls of the aquarium. It is the surface area of the aquarium.
Kelly has a rectangular fish aquarium that measures 18 inches long, 8 inches wide, and 12 inches tall.
If Kelly wanted to put a protective covering on the four glass walls of the aquarium, how big does the cover have to be?
A protective covering on the four glass walls of the aquarium can be equated to the surface area of the glass walls.
The aquarium is rectangular, and thus has two identical sides that are 12 inches tall and 8 inches wide each, and two identical sides that are 12 inches tall and 18 inches long each.
Hence, the surface area of the glass walls of the aquarium is
Area = 2 × (length × height) + 2 × (width × height)
= 2 × (18 × 12) + 2 × (8 × 12) = 432 + 192
= 624
Therefore, the protective covering should be 624 square inches.
This will cover all four sides of the glass walls of the aquarium. It is the surface area of the aquarium.
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Which phrase matches the algebraic expression below? 3(x - 7) + 10A. Three times the sun of x and seven plus tenB. Three times x minus plus tenC. Three times x minus the sun of seven and tenD. Three times the difference of x and seven plus ten
Answers
Step 1
Given:
\(3(x-7)+10\)Required; To pick the phrase that matches the algebraic
the sum of two numbers is 68. the larger number is 14 more than the smaller number. what are the numbers?
Answers
Answer:
The numbers are 27 and 41.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Answer:
The numbers would be 41 and 27
Step-by-step explanation:
It would be 41 and 27 because the number we know is 64 so if you divide that by 2 you have 34 (34+34=68) and if you then take half of 14 (14 comes from this part of the question "the larger number is 14 more than the smaller number".) (14/2=7) 7 from one side and add it to the other side you get 41+27=68
(we can also fact check this because your smaller number 27 plus 14 equal 41, then and 41 plus 27 equals 68)
Khan shennanigans ;(
Answers
Answer:
15
Step-by-step explanation: