According to the Mean Value Theorem:
[tex]f^{\prime}(c)\text{ = }\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex][tex]f^{\prime}(c)\text{ = }\frac{f(8)-f(0)}{8-0}[/tex]f(x) = x² - 6x + 8
f(0) = 0² - 6(0) + 8
f(0) = 8
f(8) = 8² - 6(8) + 8
f(8) = 64 - 48 + 8
f(8) = 24
f'(x) = 2x - 6
f'(c) = 2c - 6
[tex]\begin{gathered} 2c\text{ - 6 = }\frac{24-8}{8} \\ 2c\text{ - 6 = }\frac{16}{8} \\ 2c\text{ - 6 = 2} \\ 2c\text{ = 2 + 6} \\ 2c\text{ = 8} \\ c\text{ = }\frac{8}{2} \\ c\text{ = 4} \end{gathered}[/tex]how do I calculate the area of a partial circle?
A part of a circle is called an arc and an arc is named according to its angle.
F (x) +5 x-2 Someone pls help me I’m crying
Given the function:
[tex]f(x)=2x^2+5\sqrt[]{x-2}[/tex]to find f(3), we have to make x = 3 and substitute on the function, to get the following:
[tex]\begin{gathered} f(3)=2(3)^2+5\sqrt[]{3-2}=2(9)+5\sqrt[]{1}=18+5=23 \\ \end{gathered}[/tex]therefore, f(3)=23
im gonna send a photo of the problem
You have the following interval:
(-∞,-2]
the previous interval can be written as follow:
x ≤ -2 as an inequality
and on the number line you have:
I need help with my math
Given data:
The given points are (-2,-1) and (3, -1).
The slope of the line passing through the given points is,
[tex]\begin{gathered} m=\frac{-1-(-1)}{3-(-2)} \\ =\frac{0}{5} \\ =0 \end{gathered}[/tex]Thus, the slope of the line passing through the given points is 0.
g(0) 10 Cabin Rental Cost ($) У 70 60 50 + (0,57] ) 40 30 10 1 (0.15) 0 1 2 3 4 5 6 7 8 9 10 Number of Days
f(x) = x +57
g(x) =7x+15
The solution is (7,64). To rent the cabin for 7 days cost $64
1) Let's examine the graph. We can see two linear equations.
Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:
2) For f(t) , let's plug into the slope-intercept formula, plugging one point:
(0,57)
y=mx+b
57=0x +b
57= b
So the rule for the function is, in terms of f(x) = x +57
(0,15)
y=mx +b
15=0x +b
15 =b
So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15
Interpreting the solution:
The solution to this Linear System of Equations is the common point (7,64).
So filling in the blanks we have:
The solution is (7,64). To rent the cabin for 7 days cost $64
Given the diagram below, whereAB||CD, find the measure of xand y.
Notice that there are two triangles between the parallel lines.
Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.
[tex]160+y=180[/tex]We solve for y.
[tex]\begin{gathered} y=180-160 \\ y=20 \end{gathered}[/tex]On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.
[tex]x=30[/tex]Therefore, x = 30° and y = 20°.1. 2х^2 * 3x^3y * 3x^3y=1. 2х^2 * 3x^3*y * 3x^3*y=
Given the expressions
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y= \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}= \end{gathered}[/tex]First: we group and multiply the numbers
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y=(2\cdot3\cdot3)\cdot x^2\cdot x^3\cdot y\cdot x^3\cdot y=18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}=(2\cdot3\cdot3)x^2\cdot x^{3y}\cdot x^{3y}=18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Now we have the expressions
[tex]\begin{gathered} (A).18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Second: we multiply the expressionswith the same base adding its exponents
[tex]\begin{gathered} (A).18x^{2+3+3}\cdot y^{1+1}=18x^8y^2 \\ (B).18x^{2+3y+3y}=18x^{6y+2} \end{gathered}[/tex]At a New Car Dealership, a particularmodel comes in 4 different trim levels(CX, DX, EX, and Si). The same modelcomes in 5 different colors (Night Black,Pearl White, Evening Blue, Sandy Red,and Forest Green). The model of car alsohas 3 different interior options (GreyCloth, Tan Cloth, Black Leather). Howmany different versions of this model canbe created from these options?
solution
diferent trim levels = 4
different colors = 5
different interior options = 3
then:
[tex]4\cdot5\cdot3=60[/tex]answer: 60 different versions of this model
Use the given information to determine the lateral and surface areas of thesolid. Round your answer to the nearest unit.
Here, we want to use the given information to calculate the lateral and the total surface area
To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism
Now, we will make the shape lie on its side
This mean the triangles will represent the base
Mathematically, the perimeter of a triangle is the sum of its side
We need the last side of the triangle
We can get this by the use of Pythagoras' theorem
As we can see, the side measure 5 is the hypotenuse as it faces the right angle
The square of the hypotenuse equals the sum of the squares of the two other sides
3,4 and 5 are a Pythagorean triple
This means that, the measure 3 is the last side of the triangle
So the perimeter is;
[tex]3+4+5\text{ = 12 in}[/tex]The height is the measure 8 inches
Thus, the lateral area is;
[tex]12\text{ }\times8=96in^2[/tex]Now, we want the total surface area, but firstly, we need the area of the base
The area of the base is the area of the triangle
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\times b\times h \\ \\ B\text{ = }\frac{1}{2}\times4\times3=6in^2 \end{gathered}[/tex]two times this is 12 in^2
The total suface area is thus;
[tex]96in^2+12in^2=108in^2[/tex]Please help I only have the first given answer.
By the property of congruency of triangles, the following conclusions are taken from the figure
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
What is congruency of triangles?
Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.
There are five axioms of congruency
They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom
Here,
In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]
[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]
[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]
So,
[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]
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Can you help me solve this? And step by step please?
Given the sequence:
1/2, 3/4, 9/8, 27/16, ..........
We are to find the recursive formular
A recursive geometric formular has a pattern:
An = An - 1 * r
Where r is the common ratio. But before we write the formular, we need to look for the value of r.
This r value has to be the same between each consecutive number in the series.
Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:
x/2 = 3/4 where x/2 is the same as 1/2 x.
Cross multiply to get 4x = 6 and x = 3/2.
That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.
3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:
An = An - 1 * 3/2
Therefore, the crrect optio is B.
The table below shows the thickness of coins. Coin Thickness quarter i millimeters 12 millimeters dime nickel millimeters penny 13 millimeters Hailey stacks a dime on top of a penny. She estimates the thickness of the two coins to be less than 3 millimeters. Write a symbol (, or =) in the box to make the statement true. Then use the statement to tell whether Hailey's estimate is correct. 12 + 12 + 1 Is Hailey's estimate correct?
A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.
Stacking both coins, we will have :
[tex]1\frac{1}{2}+1\frac{7}{20}[/tex]and we have the inequality :
[tex]1\frac{1}{2}+1\frac{7}{20}\boxed{\text{ }}1\frac{1}{2}+1\frac{1}{2}[/tex]Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"
[tex]1\frac{1}{2}+1\frac{7}{20}<1\frac{1}{2}+1\frac{1}{2}[/tex]since 1 1/2 + 1 1/2 is equal to 3mm
Therefore, the thickness of stacking coins is less than 3mm
Hailey's estimate is correct (Yes)
-7>-10 true or false
To answer this question we need to see it on an axis.
-7> -10 , it is true. -7 it's more near to 0.
what is the mean? 66, 594, 69, or 74what is the median? 74, 66, 69, or 75what is the mode? 74, 90, 21, or 66what is the range? 69, 66, 74, or 594
We have the distribution;
74, 90, 21, 68, 62, 84, 34, 87,74.
Let's arrange this from ascending to descending order, we obtain;
[tex]21,34,62,68,74,74,84,87,90[/tex]i. The mean or average of this distribution is
[tex]\begin{gathered} \frac{21+34+62+68+74+74+84+87+90}{9}=\frac{594}{9} \\ \operatorname{mean}=66 \end{gathered}[/tex]ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.
[tex]\operatorname{median}=74[/tex]iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;
[tex]\text{mode}=74[/tex]iv. The range is the difference between the highest and lowest values, this is;
[tex]\begin{gathered} 90-21=69 \\ \text{Range}=69 \end{gathered}[/tex]
what are the coordinates of the vertex for x^2+ 5x - 24 = 0
Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
Can you please solve this equation and please explain to me ^step-by-step^ (this is my homework)
In the equation
[tex]0.07(6t-4)=0.42(t-1)+0.14[/tex]to solve for t, we first expand both sides of the equation.
[tex]0.42t-0.28=0.42t-0.42+0.14[/tex]We subtract 0.42t from both sides to get
[tex]-0.28=0.42+0.14[/tex]The right side does not equal the left side of the equation; therefore, this equation has no solution and choice C is correct.
the center of the circle is at O. determine the measure of angle ABC
If the center of the circle is at O.then the measure of angle ABC is 28 degree
The measure of angle ABC can be calculated by using central angle theorem
What is central angle theorem
The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.
The angle ABC = 1/2 angle AOC
the angle ABC = 1/2 x 56
the angle ABC is 28
Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree
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estimate the product by rounding to the nearest 10: 28×56×76
EXPLANATION
Given the operation:
28------> rounded to 30
56-------> rounded to 50
76 ------> rounded to 80
Now, we can mentally calculate that:
3x5= 15 so 30x50 = 1500 (two zeros)
15x8 = 120 so,
1500x80 = 120,000
The answer is 144,000.
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2
–9
–1
–1
0
9
1
21
2
35
1
9
11
22
The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
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Which of the numbers 12, 13, or 14 is the solution of 106 = 118 - x?
The given expression is
[tex]106=118-x[/tex]First, we add x on each side
[tex]\begin{gathered} 106+x=118-x+x \\ 106+x=118 \end{gathered}[/tex]Then, we subtract 106 from each side
[tex]\begin{gathered} 106-106+x=118-106 \\ x=12 \end{gathered}[/tex]Question #5The table shows four relations.RelationRelation 2Relation 3Rolation 4-2-5-3Y-4-4-2-1- 11312372Which relations represent functions?ARelation 1 and Relation 3BRelation 2 and Relation 4СRelation 3 and Relation 2DRelation 4 and Relation 1
The RELATION 1 and 3 represent a function
Rationale
There are no x value with several y values.
For a relation to be a function, there should only one y value fot each x
Which of the following transformations are used when transforming the graph of the parent function f(x) = log7x to the graph of g(x) = -log7(3x)+4? Select all that apply.
In this problem, we have the transformations
option B (shift the graph of f(x) 4 units up
option C reflect the graph of f(x) over the y-axis
what number do you need to add/subtract/multiply/divide each side by in order to solve the problem below?[tex] \frac{5}{6} = - \frac{2}{3} x[/tex]
The equation is,
[tex]\frac{5}{6}=-\frac{2}{3}\cdot x[/tex]The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,
[tex]\begin{gathered} \frac{5}{6}\cdot\frac{-3}{2}=-\frac{2}{3}x\cdot\frac{-3}{2} \\ x=-\frac{5}{4} \end{gathered}[/tex]So to eliminate -2/3
*Will mark brainiest* Rectangle ABCD is rotated 90° clockwise about the origin to produce Rectangle A'B'CD' What is the length, in units of line segment CD'?
When the given rectangle is rotated 90° around origin point, you obtain the same rectangle, but instead of a horizonatl rectangle as before, you get a vertical rectangle with height CD' and width A'D'.
The length of the segment CD' is 6 units
The local newspaper charges $34.80 for an 8-week subscription. Paige buys an 8-week subscription. How much does it cost her each week?
Answer:
$4.35
Step-by-step explanation:
8 weeks = $34.80
1 week = x
Cross-multiply
$34.80/8
=$4.35
So, for each week, Paige will pay $4.35
$(4.35 × 8 = 34.8)
i need to show work pls
Solve using substitution. y = 7x + 3 y = 6x + 4(_ , _)
We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
A physical education teacher divides the class into teams of 5 to play floor hockey. There are atotal of 4 teams. How many students, s, are in the class? Solve the equation 8 + 5 = 4 to find thenumber of students.
we know that
the number of students (s) is equal to the number of teams, multiplied by the number of students in each team
so
s=4*5
s=20
answer is 20 students
I really sure what to do for this question some help would be greatly appreciated
Given the Domain and the Range of the relation, you need to remember that the Domain is the set of all input values (x-values), and the Range is the set of all the output values (y-values).
Therefore, knowing the input values and the corresponding output values indicated in the Diagram, you can write the following ordered pairs:
[tex](1,9),(4,10),(10,3)[/tex]Notice that they have this form:
[tex](x,y)[/tex]Where "x" is the x-coordinate of the point, and "y" is the y-coordinate.
Therefore, you need to plot all the points on the Coordinate Plane in order to express the relation as a graph.
Hence, the answer is:
I need help checking to make sure my work is correct. Start with the basic function f(x) = 2x. If you have an initial value of 1, then you end up with the following iterations:f(1) = 2 x 1 = 2f^2 (1) = 2 x 2 x 1 = 4f^3 (1) = 2 x 2 x 2 x 1 = 8The question Part 1: If you continue the pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. I put: f^4 (1) = 2 x 2 x 2 x 2 x 1 = 16f^5 (1) = 2 x 2 x 2 x 2 x 2 x 1 = 32f^6 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 1 = 64f^7 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 128f^8 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 256f^9 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 512f^10 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 1024Part 2: Repeat the process with an initial value of -1. What happens as the number of iterations grows?
Given: The function below:
[tex]f(x)=2x[/tex]To Determine: The interation with initial value of 1
When the initial value is 1, it means that x = 1
If x =1, we can determine f(1) by the substituting for x in the function as shown below:
[tex]\begin{gathered} f(x)=2x \\ x=1 \\ f(1)=2(1)=2\times1=2 \end{gathered}[/tex][tex]f^2(1)=2^2\times1=2\times2\times1=4[/tex]Part 1:
It can be observed that as the number of iterations grow, the number increase in powers of 2
This can be modelled as
[tex]f^n=2^n\times1=2^n[/tex][tex]f^{10}=2^{10}\times1=1024[/tex]Part 2:
If we repeat the process with an initial value of -1. As the number of iterations grows, the number can be modelled as
[tex]\begin{gathered} f^{-n}=2^{-n}\times1 \\ f^{-1}=2^{-1}\times1=\frac{1}{2}\times1=\frac{1}{2} \\ \text{For initial value of -2, we would have} \\ f^{-2}=2^{-2}\times1=\frac{1}{2^2}\times1=\frac{1}{4} \end{gathered}[/tex]So, as the initial value decreases, it can be observed by the above calculations that the number would be decreasing by the the reciprocal of the power of 2.