Answer:
[tex]f(4)=e^{4}-3[/tex] or [tex]f(4)\approx51.5981500331...[/tex]
Step-by-step explanation:
The following is a general explanation of functions, what they mean, and how to evaluate them. The simplifications and calculations at the end are based on the clarification from your comments that [tex]f(x)=e^{x}-3[/tex] . If [tex]f(x)[/tex] is equal to something else, the simplifications/calculation will obviously be a little different, and the answer will likely be different, but the general process will be the same.
Understanding function notation
In the equation [tex]f(x)=e^{x}-3[/tex] , the left side of the equation is saying several things at once.
Names
The first character, "f", is the name of the function.
The name of a function tells you which set of directions you should look for to apply to an input. Some functions have names that are more than one letter, and even might give a hint as to what they do, for instance I might name a certain function [tex]squareroot[/tex], and based on the name, you might guess what the equation for [tex]squareroot(x)[/tex] might look like.
Mathematicians often use "f" as a function name between different problems over and over and over again, unless they come up with a special function that is worth giving a special name to.
Input
The rest of the characters after the name of the function, are "(x)" which is a pair of parentheses to contain the input, and the input itself.
Again, mathematicians often use "x" as a generic input over and over and over again, until we actually know which number we want to put into the function.
Output
Even though we've already discussed every character in the notation on the left, there is actually one more thing that the left side of the equation is saying: Altogether, "f(x)" is the output of the function, when the input "x" is put in. I feel it's worth stating, because it's often glossed over.
The equation itself
Next in the equation is the equals sign, which means that the left side of the equation, which is the output "f(x)", is equal to the stuff on the right.
The right side of the equation is the rule to follow describing what f(x) does to an input, and can help you calculate the output.
For instance, if I asked what p(4) was, it is clear that there is an input of 4, but without knowing what the function "p" does, there's no way to know what the function will give as an output when one inputs "4". This is why the right-hand side of the equation for a function is important.
Evaluating functions
To evaluate any function, we take an input, apply the function, and simplify/calculate the output.
In this case, the question asks for [tex]f(4)[/tex], meaning that the "input" is "4".
In this case, the question gives an explanation of what the function does through a rule given in equation form.
Given your clarification of the given function, [tex]f(x)=e^{x}-3[/tex] , meaning a generic input (in this case "x") is put into the function "f" and the output is found by doing the arithmetic on the right side of the equation (exponentiating the number by "e", and then subtracting 4)
Notice that in the expression [tex]f(4)[/tex], the "x" was replaced with "4". So, we need to substitute "4" where we see an "x" in the rule on the right hand side of the equation rule, and simplify and/or calculate (calculate, like with a calculator)
So, to evaluate the expression [tex]f(4)[/tex], simply substitute, and simplify/calculate.
Simplifying (no calculator)
To simplify without a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
As it turns out, this is as much as we could simplify things here (without a calculator). So, if an exact answer is needed, this would be it.
Calculating (with a calculator)
To calculate with a calculator, we substitute "4". Any time you make a substitution, use parentheses. Then, try to simplify.
[tex]f(4)=e^{(4)}-3[/tex]
[tex]f(4)=e^{4}-3[/tex]
[tex]f(4)=54.5981500331...-3[/tex]
[tex]f(4)=51.5981500331...[/tex]
So calculating with a calculator, the output of the function "f", for an input of "4", is approximately 51.598.
solve the compound inequality -5<4x+3<=8
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a< b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
We are given
-5 < 4x+3 ≤ 8
⇒ (add -3 to all sides to get ) -5+(-3) < 4x+3+(-3) ≤8+(-3)
⇒-8 < 4x ≤ 5
⇒[tex]\frac{-8}{4} < x \leq \frac{5}{4}[/tex]
⇒-2<x<5/4
Hence, the solution is -2<x<5/4.
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Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
Answer:
k(magnitude of vector a).vector a
Step-by-step explanation:
Given question is based on vectors so,
vectors :- Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication.
To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector from a given vector.
as its clear from the graph given in the question that only the magnitude of vector a is increased to produce another vector b
hence we multiply any constant ('k') with the magnitude of vector a to increase its magnitude.
and finally multiply the increased magnitude with the vector 'a' itself.
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Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Select one:
a. (-2, 11)
b. (5.5, -1)
c. (11, -2)
d. (-1, 5.5)
[tex]\left(\frac{-2+13}{2}, \frac{5-7}{2} \right)=\boxed{\left(5.5, -1)}[/tex]
9. What is the exact circumference of a circle that has a radius of 5 cm?
25ncm
5псм
10Kcm
100псм
Answer:
10π cm
Step-by-step explanation:
c = 2πr
c = (2*5) * π
c = 10π
a supermarket display consists of boxes of cereal. the bottom row has 23 boxes. each row has three fewer boxes than the row below it. the display has six rows.
Answer:
93 boxes
Step-by-step explanation:
sixth row has 23 boxes
fifth row has 20 boxes
fourth row has 17 boxes
third row has 14 boxes
second row has 11 boxes
first row has 8 boxes
the total is thus 23+20+17+14+11+8=93
A trapezoid is a quadrilateral with one or more pairs of parallel sides.
O A. True
OB. False
Select all the correct graphs.
Choose the graphs that indicate equations with no solution.
Solve this for me please
Answer:
30.5
Step-by-step explanation:
here :
n represents the number of trials
p represents the probability of success
In a binomial distribution, The mean
is equal to the product of those two values.
In other words,
The mean = n × p
= 122 × 0.25
= 30.5
Difference between y and 23 is 12
Answer:
[tex]y=11[/tex]
Step-by-step explanation:
⇒ [tex]23 - y[/tex] (Difference means subtraction)
⇒ [tex]23 - y = 12[/tex] (Subtract 12 from 23)
⇒ [tex]y = 11[/tex] (The difference from 23 - 12)
Hii!
___________________________________________________________
Answer:
y=11
Step-by-step explanation:
Let's set up an equation.
"difference between y and 23" tells us to subtract y from 23, so we'll do just that.
23-y=12
Now subtract 23 from both sides
-y=-11
Divide both sides by -1
y=11 "We solved for the variable"
--
Hope that this helped! Best wishes.
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Suppose that we agree to pay you 7¢ for every problem in this chapter that you solve correctly and fine you 6¢ for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly?
Answer:
I solved 26 problems correctly.
Match each equation below with its solution(s).
1. x² =4
2.x² = -4
3.x² +2=0
4.x²-2=0
5.x² = -18
6.x²=18
8.x+2=0
7.x-2=0
+2i +3i√√2 +√√2 2 ±2 -2 ±i√√2 +3√√2
Drag each solution above to the matching equation below.
1.
2.
3.
4.
5.
6.
7.
8.
[tex]1) \pm 2 \\\\2) \pm 2i\\\\3) \pm i\sqrt{2}\\\\4) \pm \sqrt{2}\\\\5) \pm 3i\sqrt{2}\\\\6) \pm 3\sqrt{2}\\\\7) 2\\\\8) -2[/tex]
For the regions bounded by y = 6cosx and y = one fourth x squared minus 7.
Part A: Find the limits of integration. (10 points)
Part B: Write the expression representing the total area. (10 points)
Part C: Solve for the total area. (10 points)
For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as
A=27.03squnit
What are the limits of integration, the expression representing the total area, and the total area.?
Generally, the equation for expression is mathematically given as
y = 6cosx
y=(1/4)x^2-7
therefore
[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]
The limits are
a=0 b=2\pi
Hence
[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]
A=27.03squnit
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A class of 32 students contains 15 boys.
Twenty of the students walk to school each
day. Eight of the girls do not walk to school.
How many boys walk to school each day?
Answer:
11 boys walk to school each day
Step-by-step explanation:
*The following will be assumed: the only genders of students in the class are male or female; the only options for getting to school are walking or not walking
If there are 32 students in the class total, and there are 15 boys,
32 - 15 = 17
there are 17 girls.
If 8 of these girls do not walk to school,
17 - 8 = 9
9 girls walk to school
So, if 20 total students walk to school, and 9 of those are girls
20 - 9 = 11
11 boys walk to school each day.
Answer:
11
Step-by-step explanation:
a single card is drawn from a standard 52-card deck calculate the probability and odds for the following event a jack or club is drawn
17/52
Step-by-step explanation: There are 13 clubs in a deck of fifty-two cards and there are four jacks in a fifty-two deck. So adding that up it's 17 out of 52 = 17/52. And you can not reduce it.
Please help !!! I will give 20 points to the correct answer !!! Thanks so much
Answer:
x=-4,8
Step-by-step explanation:
To solve this, we can take the absolute value sign off -4x+8 and make the right side ±24. This makes the equation -4x+8=±24.
Simplifying, we have
[tex]-4x=\pm24-8\\x=\frac{\pm24-8}{-4} \\x=\frac{+24-8}{-4}, \frac{-24-8}{-4} \\x=-4, 8[/tex]
14. The probability my daughter will eat her dinner without complaining is 5/7. The probability she will eat
her dinner and do her homework all without complaining is 2/7. What is the probability she will do her
homework without complaining given that she ate her dinner without complaining?
Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Let eating dinner without complaining be A, and doing homework without complaining be B.
Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,
P(A) = 5/7
Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,
P(A∩B) = 2/7
Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,
[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]
Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.
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Question 1 of 10
Solve the rational equation:
2x/ x - 3 = 3x/ x - 2
A hostel has food for 60 days if after 15 days 500 more students joined th hostel and the food lasted for 40days only. How many students were there in hostel
Answer:
625
Step-by-step explanation:
here we are in an inverse proportion situation :
As the number of days increases
when the number of students decreases and vice versa.
__________________
Say n is the original number of students.
___________________________________________
After 15 days, the rest of food is enough for n students for 45 days,
or enough for n+500 students for 25 days.
Then
45n = 25×(n + 500)
Then
45n = 25n + 25×500
Then
45n - 25n = 25×500
Then
20n = 12500
Then
n = 12500÷20
= 625
and thus , there were 625 students in the hostel.
Use the graph or table to find the equation that represents the relationship.
please HELP!!!!!!
100 points and a Brainliest if your answer is clear and correct
#1
(5,-10)(10,-25)Find slope
m=-25+10/10-5m=-15/5m=-3y=-3x+5 is the equation as there is no other having slope -3
#2
(7,3)(1,-3)slope
m=-3-3/1-7m=-6/-6m=1y=x-4 as no other have slope m
#3
(0,-1)y intercept is -1
y=2x-1 is the equation as it has y intercept -1
#4
(0,-4)y intercept is -4
y=4/5x-4find the first 4 terms and the 10th term from 3n+4
Answer:
16 and 34
Step-by-step explanation:
The general form = 3n+4
The 4th term = 3(4)+4 = 12+4 = 16
The 10th term = 3(10)+4= 30+4= 34
How to solve this one
Please step by step
Answer: 1/2
Step-by-step explanation:
Dividing the numerator and denominator by x, we get the limit is equal to:
[tex]\lim_{x \to -\infty} \frac{-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3}{4+\frac{7}{x}}\\\\=\frac{\lim_{x \to -\infty} \left(-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3 \right)}{\lim_{x \to -\infty} \left(4+\frac{7}{x} \right)}\\\\=\frac{2}{4}=\boxed{1/2}[/tex]
prove that ABC is a right triangle. Select the correct answer from each drop down menu.
All the blanks have been filled , which proves ultimately that Triangle ABC is a right angled Triangle.
What is Right Angled Triangle ?A triangle in which one angle is 90 degree is called a Right Angled Triangle.
AB is congruent to DB because segment DE was constructed so that DE = AB , BC is congruent to EF , because segment EF was constructed so that EF = BC , Since Triangle DEF is a right angled triangle .
DE² +EF² = DF² by the Pythagoras Theorem .
WE are given that AB² +BC² = AC²
Since DE = AB and EF = BC , DE² +EF² = AC² by the given data
Also DF² = AC² by the above equation .
Taking the square root on both the sides of the equation gives DF = AC .
So AC is congruent to DF by the definition of congruency .
Applying SSS Congruency , Triangle ABC is congruent to DEF .Therefore ABC is a right angled triangle.
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Including jose, there are 8 people in his family
If order matters, how many ways can he arrange his family members into a row of 5 seats if jose must sit in the first seat?
The number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The number of ways Jose can make his family sit is,
Number of ways = number of ways people can sit on the first sit × number of ways people can sit on the second sit × number of ways people can sit on the third sit × number of ways people can sit on the fourth sit × number of ways people can sit on the fifth sit
Since Jose wants to sit on the first seat there are only options for the first seat, therefore,
Number of ways = 1 × 7 × 6 × 5 × 4 = 840
Hence, the number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
83 ⁰
to
59°
The value of x is 38 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three sides .
The sum of all angles in a triangle is equal to 180 degree
The angles of the triangle given are
83 degree and 59 degree and x degree
83 + 59 + x = 180
x = 38 degree
Therefore the value of x is 38 degree.
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What is f(0)?
O 0 only
O -6 only
O -2, -1, 1, and 3 only
O -6, -2, -1, 1, and 3 only
A function assigns the values. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given graph, the value of f(0) means the value of function when the value of x is 0. Thus, when the graph intersect with the x-axis is the value of f(0), therefore,the values of f(0) are -2, -1, 1, and 3 only.
Hence, the correct option is C.
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(9x³+5)/(2x - 3)
How do I divide these using long division
(9x³+5)/(2x - 3)
split up (9x³+5)
9x³/2x-3 + 5/2x-3
attached solution.
Evaluate tan5π. 0 1 -1 undefined
Step-by-step explanation:
[tex] = \tan(5\pi) [/tex]
[tex] = \tan(\pi + 4\pi) [/tex]
[tex] = \tan(\pi) [/tex]
[tex] = \tan(180 \degree) [/tex]
[tex] = 0[/tex]
The answer is A.
In a certain Algebra 2 class of 26 students, 16 of them play basketball and 9 of them
play baseball. There are 5 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
Answer:
.7692307692 or 10/26
Step-by-step explanation:
You solve this problem by finding the total number of sports playing students and dividing it by the total, in this case 26. Since we know there are 5 students that play both sports, you subtract that 5 from the total number of basketball plyers and baseball players, so 16-5=11 and 9-5=4, then add those together, so 11+4=15. From there you add back in the students that play both which is 5, so 15+5=20. 20/26 is your answer.
Denise is designing the seating arrangement for a concert at an outdoor theater. To give everyone a good view, each row must have 6 more seats than the row before it, and the 1st row can only have 11 seats. Explain to Denise how to create an equation to predict the number of seats in any row. Then, using your equation, show your work to determine the number of seats in row 18.
As per the question each row must have 6 seats more than the row before it. And there are 11 seats in the first row.
So, the first row has 11 seats
2nd row has 11+6 seats
3rd row has 11+2*6=11+12=23
4th row has 11+3*6=11+18=29
and so on...
We know that the difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Arithmetic progression can be calculated as
aₙ = a₁ + (n - 1)d,
where aₙ is the nth and a₁ is the first term of this progression respectively and d is the common difference between terms.
So, we can observe the trend and develop the equation for the problem.
There are 11+(n-1)*6 seats in the n-th row.
So, there is 11+(18-1)*6=11+17*6=113 seats in the 18th row.
Therefore, there are 113 seats in the 18th row.
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What is the domain of the linear parent function?
Answer:
The parent function of linear functions is y=x and it passes through the origin.The domain and range of all linear functions are all real numbers.
Step-by-step explanation:
