Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = x^2 - x + 1 text( on ) [1,8]; M = 21 c =
Answers
Answer:
\(c = 5\)
Step-by-step explanation:
Given
\(f(c) = M\)
\(f(x) = x^2 - x + 1\)
\(Interval: [1,8]\)
\(M = 21\)
Required
Find c using Intermediate Value theorem
First, check if the value of M is within the given range:
\(f(x) = x^2 - x + 1\)
\(f(1) = 1^2 - 1 + 1\)
\(f(1) = 1\)
\(f(x) = 8^2 - 8 + 1\)
\(f(x) = 57\)
\(1 \le M \le 57\)
\(1 \le 21 \le 57\)
M is within range.
Solving further:
We have:
\(f(c) = f(x) = M\)
\(f(x) = 21\)
Substitute 21 for f(x) in \(f(x) = x^2 - x + 1\)
\(21 = x^2 - x + 1\)
Express as quadratic function
\(x^2 - x + 1 - 21 = 0\)
\(x^2 - x - 20 = 0\)
Expand
\(x^2 + 4x - 5x - 20\)
\(x(x+4)-5(x+4)=0\)
\((x - 5)(x+4) = 0\)
\(x - 5 = 0\) or \(x + 4= 0\)
\(x = 5\) or \(x = -4\)
The value of \(x = -4\) is outside the \(Interval: [1,8]\)
So:
\(x = 5\)
\(f(c) = f(x) = M\)
\(f(c) = f(5) = 21\)
By comparison:
\(c = 5\)
Related Questions
Help pldssssssss………………..
Answers
The missing value for the quadratic function is given as follows:
y = -3.
How to obtain the quadratic function?As a function of it's roots x* and x**, the quadratic function is defined as follows:
y = a(x - x*)(x - x**)
In which a is the leading coefficient.
The roots of the function are the values of x when y = 0, hence:
x* = -4, x** = -2.
Thus:
y = a(x + 4)(x + 2)
y = a(x² + 6x + 8).
When x = 0, y = -8, hence the leading coefficient a of the function is given as follows:
8a = -8
a = -1.
Hence:
y = -x² - 6x - 8;
The missing value is the value of y when x = -1, hence:
y = -(-1)² - 6(-1) - 8
y = -3.
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On a certain hot summer's day, 321 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $634.25. How many children and how many adults swam at the public pool that day?
Answers
Answer:
31 children and 290 adults
Step-by-step explanation:
Let a = number of adults and c = number of children.
a + c = 321
2a + 1.75c = 634.25
Multiply both sides of the the first equation by -2 and add it to the second equation.
-2a - 2c = -642
(+) 2a + 1.75c = 634.25
--------------------------------------
-0.25c = -7.75
Divide both sides by -0.25
c = 31
Use the first equation to find a.
a + c = 321
Substitute 31 for c.
a + 31 = 321
Subtract 31 from both sides.
a = 290
Answer: 31 children and 290 adults
Explanation:
Create two simultanous equations:
Let c stand for the number of children that bought a ticket, and a stand for the number of adults that bought a ticket, you get your first equation, being
c
+
a
=
508
then, you now create a second equation for the prices of the tickets.
(price of childrens tickets)(number of children that swam)+(price of adults tickets)(number of adults that swam) = total money collected
so:
1.75
c
+
2.25
a
=
1083.00
now we still know, that
a
=
508
−
c
so we can substitute it into the second formula
1.75
c
+
2.25
(
508
−
c
)
=
1083
now its just simple algebra
1.75
c
+
1143
−
2.25
c
=
1083
60
=
0.5
c
so:
c
=
120
now we know, that 120 children went to the swimming pool.
and we still have the formula from before:
a
=
508
−
c
so
a
=
388
Which value of x makes this inequality true? x+9<4x
A.4
B.1
C.3
D.2
Answers
Answer:
A. 4
Step-by-step explanation:
Given inequality:
\(x+9 < 4x\)
Rearrange the inequality to isolate x.
Subtract x from both sides of the inequality:
\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)
Divide both sides of the inequality by 3:
\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)
So the values of x that make the inequality true are:
Any value of x that is greater than 3.Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.
To check this, substitute x = 4 into the inequality:
\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)
As 13 is less than 16, the inequality is true when x = 4.
5 8 10 11 12 15 19 20 20 24 25 what is the median
Answers
Answer:
15 is the median by using the formula
hope this helps you a lot
i dont understand this
Answers
We can Add 7 black beads to make ratio 3 : 1.
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black)b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3
Both sides divisible by 3; reduce ratio
= 3 : 1
Which is Correct ratio
Hence, There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore , we need to add 7 black beads.
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Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box
Answers
Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)
How to determine the key features?Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:
Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).
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What is the solution to this system of linear equations 2x y 1 3x y 6 1 3?
Answers
Although part of your question is missing, you might be referring to this full question: What is the solution to this system of linear equations 2x + y = 1 and 3x – y = –6. So, the solution to the linear equation 2x + y = 1 and 3x – y = –6 is (-1, 3).
2x + y = 1 (1)
3x – y = –6 (2)
To solve the linear equations in two variables is by adding both the equation.
2x + 3x + y – y = 1 – 6
5x = –5
x = –1
Then, substitute the value of x in equation (1).
2x + y = 1
2 (-1) + y = 1
-2 + y = 1
y = 1 + 2
y = 3
Hence, the solution to the linear equation is (-1, 3).
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what is inequalities
Answers
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.
The most common symbols used in inequalities are:
">" (greater than): indicates that the value on the left side is larger than the value on the right side.
"<" (less than): indicates that the value on the left side is smaller than the value on the right side.
"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.
"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.
"≠" (not equal to): indicates that the values on both sides are not equal.
Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.
Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.
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Write a variable expression for the length of the bottom black bar with a being the length of the orange bar:
Answers
Answer:
orange divide by 3?
Step-by-step explanation:
looking at the graph, it looks like orange is 3x the length of black,
so black will be Orange/3
After Siddhartha Gautama death what happened to the Buddhists movement?
Answers
Answer:
after Siddhartha Gautama death the Buddhist moved all over the world
Find the value of x in the isosceles triangle
Answers
Does (2, 3) make the inequality 2x + 5y < 20 true?
yes
no
Answers
Answer:
Yes
Step-by-step explanation:
The left side 19 is less than the right side 20 , which means that the given statement is always true.
first to help gets brainliest
Answers
Find each value for the geometry triangles below
Answers
Answer:
14. x=18
Step-by-step explanation:
For 14 you can see that all the angles must add up to 180.
Setup the equation 5x+2x+x=180 and solve for x
For 15 do the same thing, add up all of the lengths and substitute the missing one as W. Set them equal to 360 and you should get your answer.
an airplane flew for one hour and landed 100 miles north and 80 miles east from its origin. what was the distance traveled, speed and angle of direction from its origin?
Answers
The distance traveled by airplane is 180 miles.
The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°
The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.
Then, the total distance traveled by airplane will be:
= 100 miles + 80 miles = 180 miles.
The speed can be defined as the distance traveled by the total time taken.
Speed = distance/time
Speed = 180 miles/ 1 hour
Speed = 180 miles/60 minutes
Speed = 3 miles per minute
The angle of direction from its origin will be:
tan (x) = 100 miles/80 miles
x = tan⁻¹ ( 100/80)
x = tan⁻¹ ( 10/8) = tan⁻¹ ( 5/4)
x = 51.34°
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if you know the length of sides a and c of a right triangle, which equation represents the length of side b, according to the pythagorean theorem?
(answer choices in picture)
Answers
Answer:
b = √( c² - a² )
Step-by-step explanation:
Equation to find the length of a right angle using pythagorean theoram is,
a ² + b² = c²
According to the question you have find the length of b side.
For that, you have to make b as the subject in this equation.
Let us solve now.
a ² + b² = c²
b² = c² - a²
b = √( c² - a² )
Therefore,
3rd Answer is correct.
Hope this helps you :-)
Let me know if you have any other questions :-)
2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answers
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
What type of angle is a 9 degree angle?
Answers
Answer:
An acute angle
Is there any answer choices??
Simplify the expression. Write the answer without using negative exponents. Assume that the variable is restricted to those numbers for which the expression is defined.
−m−8m9
Answers
The simplified expression is m^1 or simply m.
To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.
First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.
Now, we can simplify the expression further: 1/m^8 * m^9.
When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.
Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.
Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.
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A computer is used to generate passwords made up of numbers 0 through 9 and lower case letters the computer generated 400 passwords one character at a time a uniform probability model is used to predict the character in the password what is the prediction of the number of passwords in each the first character is a vow round your answer to the nearest whole number 56 passwords 77 passwords 111 passwords 233 passwords
Answers
Answer:
56
hope it helpes if you could give me brainliest so i could level up
PLEASE HELP ILL GIVE BRAINLIAST
CD is the perpendicular bisector of AB.
AD = 6x – 2 and DB = 2x + 18.
Determine the value of x.
x = [ ? ]
A.
D
B.
Enter
Answers
Answer:
Step-by-step explanation:
48-5+ 2x -7 -54 ABE 39. - x=2. 66 - 12 = 54. BC, 15. AB=5 =BC. 6x = 66. - They are. XH. Not. 2) Find the coordinates of the midpoint of the segment with the given endpoints. ... j) Concurrency of Perpendicular Bisectors of a Triangle Theorem: ... Find AE. 40. Find AD. 76. 76. Sy + 20. Find BC. 54. Find AC. 80. Find CD. 76.
What is the value of x ?
Answers
Answer:
x= - square root 141 or x= square root 141
Consider the function y = √4-x.
What are the domain and range of this function?
Answers
Answer:
For the function y = √4-x, we know that the value inside the square root must be non-negative. Therefore, we have the inequality:
4 - x ≥ 0
Solving for x, we get:
x ≤ 4
So the domain of the function is all real numbers less than or equal to 4.
For the range, we know that the square root of any non-negative number is always non-negative. Therefore, the smallest value that y can take is 0, which occurs when x = 4. As x decreases, y increases without bound. So the range of the function is [0,∞).
Step-by-step explanation:
Please help identify the slope for the graph thank you
Answers
Answer:
Undefined or y = 3
Step-by-step explanation:
I think it's Undefined. But if it asks for rise/run it is (0,3)
23/7y state restrictions
Answers
The restrictions on the variable of the given rational fraction is y ≠ 0.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbers: these include 1, 2, 3, 4, 5, 6, .....114, ....560.Whole numbers: these comprises all natural numbers and 0.Integers: these are whole numbers that may either be positive, negative, or zero such as ....-560, ...... -114, ..... -4, -3, -2, -1, 0, 1, 2, 3, 4, .....114, ....560.Irrational numbers: these comprises non-terminating or non-repeating decimals.Real numbers: these comprises both rational numbers and irrational numbers.Rational numbers: these comprises fractions, integers, and terminating (repeating) decimals such as ....-560, ...... -114, ..... -4, -3, -2, -1, -1/2, 0, 1, 1/2, 2, 3, 4, .....114, ....560.This ultimately implies that, a rational fraction simply comprises a real number and it can be defined as a quotient which consist of two integers x and y.
What are restrictions?In Mathematics, restrictions can be defined as all the real numbers that are not part of the domain because they produces a value of 0 in the denominator of a rational fraction.
In order to determine the restrictions for this rational fraction, we would equate the denominator to 0 and then solve:
23/7y;
7y = 0
y = 0/7
y ≠ 0.
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Complete Question:
State any restrictions on the variables 23/7y
The surface of the triangle shown in the picture 15.1 is:
A) 6 B) 21 C) 14 D) 12
I'm not sure I've solved it right.
Answers
Answer:
The coreect answer o
is 14
Instructions: Graph by hand or using a calculator to determine the solution to the given system. Put in slope-intercept form first if necessary.
Answers
ANSWER:
Solution: (-1, -1)
STEP-BY-STEP EXPLANATION:
The solution of a system by means of the graphical method is the intersection between the graph of each equation of the corresponding straight line.
Therefore, we graph each equation using a graphing calculator and determine the intercept, like this:
Therefore, the solution of the system is (-1, -1)
Find all values of m for which the equation has two real solutions.
3x² + 7x- (m + 1) = 0
Answers
Which graph appears to have an X intercept of -5 and a y intercept of 3?
A. Graph F
B. Graph G
C. Graph H
D. Graph J
Answers
Answer:
B) Graph G
Step-by-step explanation:
B) Graph G
G croses the X axis at -5 and the Y axis at 3
What is the value of y in the equation 4x +3 y= 23 when x=2 , x=6
Answers
Answer:
5, -⅓
Step-by-step explanation:
x = 2:
4x + 3y = 23
3y = 23 - 4(2)
3y = 15
y = 5
x = 6:
4x + 3y = 23
3y = 23 - 4(6)
3y = -1
y = -⅓