Use the Intermediate Value Theorem to show that the given function has a zero in the interval [0, 2].
![Use The Intermediate Value Theorem To Show That The Given Function Has A Zero In The Interval [0, 2].](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/hBvblt3Em8aJJPW6zAO2VuDN0VjThpIo.jpeg)
Answers
Answer:
See below for answer and explanation
Step-by-step explanation:
The Intermediate Value Theorem (IVT) states that there is a value [tex]c[/tex] in [tex][a,b][/tex] such that [tex]f(c)=0[/tex]. Because [tex]f(0)=0^2+5(0)-4=-4[/tex] and [tex]f(2)=2^2+5(2)-4=10[/tex], this must mean that 0 is in between -4 and 10, which concludes that there is a zero over the interval [0,2] for the given function by IVT.
Related Questions
What is the intermediate step in the form
(x+a)^2=b as a result of completing the square for the following question
Answers
The intermediate step in completing the square is[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex]
To complete the square for the equation [tex]$(x+a)^2=b$[/tex], we can follow these steps:
1. Expand the left side of the equation: [tex]$(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$[/tex].
2. Rewrite the equation by isolating the squared term and the linear term: [tex]$x^2 + 2ax = b - a^2$[/tex].
3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:
[tex]$x^2 + 2ax + (a^2) = b - a^2 + (a^2)$[/tex].
4. Simplify the right side of the equation: [tex]$x^2 + 2ax + (a^2) = b$[/tex].
This step can be represented as: [tex]\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\][/tex]
This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.
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A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 156 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (13, 2014), and decreases through about (31, 0). Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points) Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points) Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)
Answers
The maximum daily profit the company can earn is $2,350.
It is a set of points in a coordinate plane that represents the values of the function for different inputs.
The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.
Therefore, the maximum daily profit the company can earn is $2,350.
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1.
Find the surface area of the right cone.
Round your answer to the nearest
hundredth.
22 ft
8 ft
Answers
Answer:
789.40 square feet (to nearest hundredth)
Step-by-step explanation:
surface area = area of circular base + curved surface area
= πr² + πrL, where L is length of sloped edge.
using Pythagoras' Theorem, L² = 22² + 8² = 548.
L = 2√137 (do not round the answer yet, keep it in this form).
surface area = πr² + πrL
= π(8)² + π(8)(2√137)
= 789.40 square feet (to nearest hundredth)
Fill in the missing digit to make the least number that satisfies the condition (makes it
a true statement).
234.... is divisible by 3.
TYSM 4 UR HELP
(If you get it right I will give you Brainiest )
Answers
Adding up the digits of the number that we have so far, we get:
2 + 3 + 4 = 9
The missing digit should be a number that, when added to 9, results in a multiple of 3. Because 9 is already a multiple of 3, the smallest such number would be 0.
So, the missing digit is 0, and the least number that satisfies the condition is 2340.
if a circle has a radius of 10 cm and the measure of arc AB is 45 degrees, find the length of the arc AB
Answers
Answer:
[tex]\huge\boxed{\sf S= 7.85 \ cm}[/tex]
Step-by-step explanation:
Given:arc AB = θ = 45 degrees
Radius = r = 10 cm
π = 3.14
Required:Length = S = ?
Formula:[tex]\displaystyle S= \frac{\theta}{360} \times 2 \pi r[/tex]
Solution:Put the given data in the formula.
Finding arc length.
[tex]\displaystyle S = \frac{45}{360} \times 2(3.14)(10)\\\\S = 0.125 \times 62.8\\\\S= 7.85 \ cm\\\\\rule[225]{225}{2}[/tex]
Please, someone help me with this answer, I really would appreciate it so much. Show all work. Recall the formula: A = P(1 + 2)² nt Mark invests $7,938 in a retirement account with a fixed annual interest rate of 2% compounded semiannually. What will the account balance be after 19 years
Answers
The account balance will be approximately $11,390 after 19 years.
In this case, Mark invests $7,938 with an annual interest rate of 2% compounded semiannually. Therefore:
P = $7,938
r = 2% = 0.02 (as a decimal)
n = 2 (compounded semiannually)
t = 19 years
Plugging these values into the formula, we have:
[tex]A = \$7,938(1 + 0.02/2)^{(2*19)[/tex]
Calculating the expression inside the parentheses:
(1 + 0.02/2) = 1.01
Raising this to the power of (2*19):
[tex](1.01)^{(2*19)} = 1.43[/tex]
Multiplying this by the principal amount:
A ≈ $7,938 * 1.43
A ≈ $11,390
Therefore, the account balance will be approximately $11,390 after 19 years.
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Triangles MNO and JKL below are congruent. If m<M =40c, m<N =120c, and m<O =20c, whats m<L? a. 120° b. 20° c. 40° d. 70°
Answers
Answer: b, 20°
Step-by-step explanation: Since triangles MNO and JKL are congruent, we know that all of their corresponding angles are congruent. This means that m<L = m<O = 20°
Show that the equations x+y+z = 4, 2x+5y-2z =3, x+7y-7z =5 are not consistent
Answers
Answer:
We can start by using the second equation to eliminate x:
2x + 5y - 2z = 3
2x = -5y + 2z + 3
x = (-5/2)y + z + 3/2
Now we can substitute this expression for x into the first and third equations:
x + y + z = 4
(-5/2)y + z + 3/2 + y + z = 4
(-5/2)y + 2z = 5/2
x + 7y - 7z = 5
(-5/2)y + z + 3/2 + 7y - 7z = 5
(9/2)y - 6z = 7/2
Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.
Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:
(-45/2)y + 18z = 45/2
(45/2)y - 30z = 35/2
Adding these two equations, we get:
-12z = 40/2
-12z = 20
z = -5/3
Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:
(-5/2)y + 2(-5/3) = 5/2
(-5/2)y - 10/3 = 5/2
(-5/2)y = 25/6
y = -5/12
Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:
x + y + z = 4
x - 5/12 - 5/3 = 4
x = 29/12
Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:
2x + 5y - 2z = 3
2(29/12) + 5(-5/12) - 2(-5/3) = 3
29/6 - 5/2 + 5/3 ≠ 3
Since there is no solution that satisfies all three equations, the system is inconsistent.
Step-by-step explanation:
Answer:
See below for proof.
Step-by-step explanation:
A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.
Given system of equations:
[tex]\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}[/tex]
Rearrange the first equation to isolate x:
[tex]x=4-y-z[/tex]
Substitute this into the second equation to eliminate the term in x:
[tex]\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}[/tex]
Subtract the first equation from the third equation to eliminate x:
[tex]\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}[/tex]
Now we have two equations in terms of the variables y and z:
[tex]\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}[/tex]
Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:
[tex]\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}[/tex]
Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.
For example, if we subtract the second equation from the first equation we get:
[tex]\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}[/tex]
Zero does not equal negative 11.
Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.
find the diameter of the crcle with the gven circmfence . use 3.14
c=31cm
Answers
The diameter of the given circle is 9.87 cm.
Given.
Circumference = 31 cm
Now,
Circumference of circle = 2×π×r
r = Radius of Circle
Substitute the value of circumference in the formula,
31 = 2×π×r
31 = 2× 3.14 × r
r = 4.935 cm
Diameter of circle is double the radius of circle,
D = 2r
D = 2(4.935)
D = 9.87 cm
Hence diameter of the circle is 9.87 cm.
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I’m confused on this, help. Thanks you all. : )
Answers
Answer: There is no solution to this problem.
Step-by-step explanation:
The goal test score pints are 150, 103, and 41. Let's check to see if each statement is true
A. The total points for the tests are:
Type A - 156
Type B - 98
Type C - 40
None of these matches the total points.
B. The total points for the tests are:
Type A - 39
Type B - 98
Type C - 160
None of these matches the total points.
C.
Type A - 156
Type B - 2,352
Type C - 40
None of these matches the total points.
Since none of these statements match this data, there is no solution to this chart. Hope this helps!
-From a 5th Grade Honors Student
The number 84 can be expressed as the sum of 54 + 30. Which shows how to use the distributive property to rewrite that sum as a multiple of a sum whose addends have no common factors greater than 1?
A. 2(27 + 15)
B. 3(18 + 10)
C. 5(11 + 6)
D. 6(9 + 5)
Answers
The answer of the sum is D. 6(9 + 5).
To rewrite the sum 54 + 30 using the distributive property as a multiple of a sum whose addends have no common factors greater than 1, we need to factor out the greatest common factor from both numbers.
The greatest common factor of 54 and 30 is 6. By factoring out 6, we can rewrite the sum as:
54 + 30 = 6 * (9 + 5)
Now, let's examine the options given:
A. 2(27 + 15) does not have a common factor of 6.
B. 3(18 + 10) does not have a common factor of 6.
C. 5(11 + 6) does not have a common factor of 6.
D. 6(9 + 5) is the correct answer because it has a common factor of 6, which is the greatest common factor of 54 and 30.
Therefore, the answer is D. 6(9 + 5).
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I need help!!!!!!!!!!!!!!!!!!
Answers
p+T+S+S=5+5 it is our answer it is write
What would be the Prefix notation for the given equation?
(a+(b/c)*(d^e)-f)
a.
-+a*b/c^def
b.
-a+*/bc^def
c.
-+a*/^bcdef
d.
-+a*/bc^def
Answers
The Prefix notation for the given equation is "[tex]\pm a \times /bc^{de}^f[/tex]". d.
The Prefix notation for the given equation "[tex](a+(b/c) \times (d^e)-f)[/tex]" would be:
[tex]\pm a \times /bc^{de}^f[/tex]
In Prefix notation, also known as Polish notation, the operators come before their operands.
Here's a step-by-step breakdown of converting the given equation to Prefix notation:
Start with the given equation: (a+(b/c)*(d^e)-f)
Replace the arithmetic operators with their corresponding symbols in Prefix notation:
Addition (+) becomes +
Division (/) becomes /
Exponentiation (^) becomes ^
Subtraction (-) becomes -
Rearrange the equation to move the operators before their operands:
Replace [tex](a+(b/c)(d^e)-f)[/tex] with [tex](\pm a/bc^{de}^f)[/tex]
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The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closet to the length of this rectangle in feet?
Answers
The length of the rectangle is about 12.37 feet.
We are given that;
Width= 4 feet
Diagonal length= 13feet
Now,
The width and length of the rectangle are the legs and the diagonal is the hypotenuse. We can label them as:
w = 4 (width) l = ? (length) d = 13 (diagonal)
Plugging these values into the Pythagorean theorem, we get:
w^2 + l^2 = d^2 4^2 + l^2
= 13^2 16 + l^2 = 169
l^2 = 169 - 16
l^2 = 153
l = √(153)
l ≈ 12.37
Therefore, by Pythagoras theorem the answer will be 12.37 feet.
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what is the following term of -3;0;3;6.
Answers
Step-by-step explanation:
Start at -3 then begin adding 3's to get the next terms
-3 0 3 6 9 .....
Kathy had of a pepperoni pizza in
her refrigerator. She gave her friend
a slice that was of the original pizza.
How much pizza does Kathy have left?
Answers
The answer is she has 7/8 (or seven slices) of the pizza left. Based on the information given, we can calculate that Kathy ate 1/8 (or one slice) of the original pepperoni pizza.
It is important to note that the size of the original pizza is unknown, so we cannot accurately determine the exact amount of pizza Kathy has left in terms of square inches or centimeters.
However, we do know that she has the majority of the pizza remaining, and could potentially have enough for multiple meals or leftovers. Additionally, if Kathy is tracking her caloric intake, she can calculate the number of calories consumed from the slice she ate and adjust her diet accordingly.
Overall, it seems like Kathy has a decent amount of pizza left to enjoy
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solve for x solution will be in decimal form
Answers
Answer:
x = -0.25
Step-by-step explanation:
You want to solve for x when corresponding sides of the similar triangles have lengths 6 and 15, and (2x -3) and (3x -8).
ProportionCorresponding sides are proportional in similar triangles, so we have ...
(2x -3)/6 = (3x -8)/15
5(2x -3) = 2(3x -8) . . . . . . multiply by 30
10x -15 = 6x -16 . . . . . . simplify
4x = -1 . . . . . . . . . . . . add 15-6x
x = -0.25
The value of x is -0.25.
__
Additional comment
This negative value of x gives side length ratios in the two triangles of -7/12. Negative side lengths of -3.50 and -8.75 make no sense geometrically. The proportion is satisfied, but the figure cannot be drawn with a negative side length.
<95141404393>
Which equation gives the number of 13
inches that are in 56
inch?
CLEAR CHECK
13÷56=25
56÷13=518
13÷56=185
56÷13=52
Answers
Step-by-step explanation:
The answer is 5/6 ÷ 1/3 = 5/18
because
5/6 × 1/3 = 5/18 and it's true
y is inversely proportional to the square root of x. y=5 when x=36. find a formula linking x and y.
Answers
Answer:
y = 30/√x
Step-by-step explanation:
y = k/√x (where k is a constant).
5 = k/√36
5 = k/6
5 X 6 = k
k = 5 X 6 = 30.
y = 30/√x
Sandra is traveling 15 mph on her bicycle. After 4 hours, how far will she have traveled?
Answers
Answer:
→ 15m/hr * 4hr = 60! ←
Hope This Helps On You're Quiz/Assignment
Speed/DistancexTime
the length of arc AB is 6pi and the measure of arc AB=60 degrees. What is the diameter of the circle?
Answers
Answer:
36
Step-by-step explanation:
Arc = rad * radius
radius = arc/rad
given, arc = 6π
rad = 60 * π/180 = π/3 rad
radius = 6π / (π/3)
= 6π * 3/π
= 18
Diameter = 2 * radius
= 2*18
= 36
Can anyone help me solve this question?
x = e^y
Answers
Step-by-step explanation:
Pick any point on the graph below for a solution:
Please help i need help on pre-calc
Answers
Answer:
32.5 square units
Step-by-step explanation:
Area of triangle = ½ ab sin C
where a and b are to sides that meet at angle C.
Area of triangle = ½ (13)(10) sin 150
= 32.5 square units.
please see attachment for a visual
factorise fully
1) x²y - 5yx - 6y
2) w² (a - b) - 9 (a - b)
please help
Answers
1) x²y - 5yx - 6y
To factorise this expression, we can first look for the greatest common factor (GCF) among the terms. We can see that they all have a common factor of 'y'. So, we can factor out 'y' from each term:
y(x² - 5x - 6)
Now, we need to factorise the quadratic expression inside the parenthesis. We can do this by finding two numbers that multiply to -6 and add to -5. These numbers are -6 and 1:
y(x - 6)(x + 1)
So, the fully factorised form of the given expression is:
y(x - 6)(x + 1)
2) w² (a - b) - 9 (a - b)
In this expression, we can notice that both terms have a common factor of (a - b). So, we can factor out (a - b) from each term:
(a - b)(w² - 9)
Now, we can see that the expression inside the parenthesis is a difference of two squares. We can factorise it further as (w + 3)(w - 3):
(a - b)(w + 3)(w - 3)
So, the fully factorised form of the given expression is:
(a - b)(w + 3)(w - 3)
By factorising expressions fully, we can simplify them and make them easier to understand or use in further calculations. It is an essential skill in algebra and helps in solving equations, graphing functions, and finding solutions to various mathematical problems.
Can someone find x and y pls
Answers
Answer: x = 101, y = 20
From corresponding angles, as both pairs of lines are parallel, we know that 79 is the supplement of x. That means 79 + x = 180.
From this we have x = 101 degrees.
From corresponding angles, x is the supplement of ( 4y - 1 )
Since we know x = 101, we can plug it into our equation:
4y - 1 + 101 = 180
Simplifying:
4y + 100 = 180
Subtracting 100 from both sides of the equation:
4y = 80
Dividing by 4:
y = 20
Hope this helps!
Question Number 16 of 20 - Geometry
In square ABCD, AC = 32-4 and BE = x + 6, where E is the intersection of the diagonals.
What is the length of AC?
16
11
D
44
22
Answers
The length of AC is 28. so none of the given options is correct.
In square ABCD, AC represents the length of one side of the square. The given information states that AC is equal to 32-4.
To calculate AC, we subtract 4 from 32:
AC = 32 - 4
AC = 28
Therefore, the length of AC is 28. None of the provided options match this result, so none of the given options is correct.
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please look at the picture
Answers
6x-7y=-10
12x-5=16
2xay=10
-10+16+x=10
10=-10+16+x=6x
6x+10=16x
ay=16x
15% will last how long when the battery discharge rate is 0.12% in 30 seconds
Answers
37.5 seconds is equivalent to 0.625 minutes for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To calculate how long a battery will last when it discharges at a rate of 0.12% per 30 seconds, we can set up a proportion based on the given information.
Let's assume the battery has a total charge of 100%. We want to find out how long it takes for the battery to discharge from 15% to 0%, given a discharge rate of 0.12% every 30 seconds.
First, let's determine the proportion:
(0.12% / 30 seconds) = (15% / x sec
To solve for x (the time it takes for the battery to discharge from 15% to 0%), we can cross-multiply:
0.12% × x = 30 seconds × 15%
Now, let's solve for x:
0.0012 × x = 0.3 × 15%
0.0012 × x = 0.045
Divide both sides by 0.0012:
x = 0.045 / 0.0012
x ≈ 37.5
Therefore, it would take approximately 37.5 seconds for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To convert 37.5 seconds into minutes, we divide the number of seconds by 60 (since there are 60 seconds in a minute).
37.5 seconds / 60 = 0.625 minutes
Therefore, 37.5 seconds is equivalent to 0.625 minutes.
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A 500g packet of beans costs £1.55. A 125g packet of the same beans costs £0.36. Which packet is better value for money?
Answers
Step-by-step explanation:
Find unit cost per gram for each packet....lower unit cost is better value
L 1.55 / 500 g = .0031 L/g
L .36 / 125 g = .0029 L/g <=======best value 125 g packet
5) El precio del petróleo en los dos últimos días tuvo las siguientes fluctuaciones: aumentó un 3,5% en
el primer día y luego bajó un 2% en el último día. Si el valor final es de U$S 68, ¿cuál era el valor
inicial?
Answers
Answer:
5) El precio del petróleo en los dos últimos días tuvo las siguientes fluctuaciones: aumentó un 3,5% en el primer día y luego bajó un 2% en el último día. Si el valor final es de U$S 68, ¿cuál era el valor inicial?
La solución al problema matemático es la siguiente:
Supongamos que el valor inicial del petróleo es x. En el primer día, el precio aumentó en un 3,5%, por lo que el nuevo precio es x + 0.035x = 1.035x. En el segundo día, el precio disminuyó en un 2%, por lo que el precio final es 1.035x - 0.02(1.035x) = 0.98(1.035x) = 1.0143x.
Dado que sabemos que el precio final es de U$S 68, podemos establecer una ecuación para resolver x: 1.0143x = 68.
Resolviendo para x, obtenemos x = 68/1.0143 ≈ U$S 67.04.
Entonces, el valor inicial del petróleo era aproximadamente U$S 67.04.
MARCA COMO CEREBRO!!!