Answer:one million one hundred and twenty-seven thousand three hundred and twenty-six
Step-by-step explanation:
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 8^x and y = 2^x + 2 intersect are the solutions of the equation 8^x = 2^x + 2. (4 points)
Part B: Make tables to find the solution to 8^x = 2^x + 2. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 8^x = 2^x + 2 graphically? (2 points)
Answer + Step-by-step explanation:
Part A :
Let M(a , b) be a point where the graphs
of the equations y = 8ˣ and y = 2ˣ⁺² intersect.
M lies on both graphs
Then
the coordinates of M verify both equations (equation of graph1 and equation of graph 2)
Then
[tex]b=8^{a}\ \text{on the other hand} \ b=2^{a+2}[/tex]
Then
[tex]8^{a}=2^{a+2}[/tex]
Therefore ‘a’ (the x-coordinates of the points M where the two graphs intersect) is a solution to the equation :
[tex]8^{x}=2^{x+2}[/tex]
Part B : check the attached table.
Part C :
Graphically, we try to spot the points of intersection of the two graphs ,the x-coordinates of those points are the solution to our equation.
In our case , obviously the two graphs intersect at only one point M(1 ,8)
Therefore 1 is the only solution to 8ˣ = 2ˣ⁺².
Also ,Check the attached graph.
Find the distance between 4 (7,-7) and B (13,0). Write your answer as a radical and as a decimal rounded to the nearest tenth.
The distance between the two points is_____,
or about_____.
Answer:
Distance is [tex]\sqrt{85}[/tex] or 9.2195...
Hope this helps!
Step-by-step explanation:
d = [tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]
d = [tex]\sqrt{(13 - 7 )^{2} + (0-(-7)^{2} }[/tex]
d = [tex]\sqrt{(6)^{2} +(7)^{2} }[/tex]
d = [tex]\sqrt{36 + 49}[/tex]
d = [tex]\sqrt{85}[/tex]
d = 9.2195444...
Use Table 12-2 to solve.
Ron Sample is the grand prize winner in a college tuition essay contest awarded through a local organization's scholarship fund. The winner receives $8,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 6% interest compounded annually to award the prize? (Round your answer to the nearest cent.)
$
Based on the amount that Ron Sample gets at the beginning of each year, the number of years, and the interest compounded annually, the amount that should be invested to award the price is $35,720.80.
How to find the invested amount?The value of $8,000 is constant which makes it an annuity. However, it comes at the beginning of each year which makes it an annuity due.
The amount to be invested to gain this $8,000 every year is therefore the present value of this annuity due based on the interest rate.
Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)
= 8,000 x 4.4651
= $35,720.80
Find out more on annuity due at https://brainly.com/question/24245699
#SPJ1
Ahmed has L.E. 15 He went to the market and spent 725 piastres. find a The ratio between the money he spent and the total sum he had b The ratio between the money left and the total sum he had. The ratio between the money left and the money he spent.
The ratio between the money he spent and the total sum he had , the ratio between the money left and the total sum he had, the ratio between the money left and the money he spent. are 29:60, 31:60 and 31:29 respectively.
Ahmed has L.E. 15 which when converted in piastres, it is 1500 piastres
He spent 725 piasters and the money left with Ahmed is 1500-725 which is 775 piastres
The ratio between the money spent and the total sum is 725:1500 which is simplified to 29: 60 by dividing both with anything which is common in both that is 25
The ratio between the money left and the total sum he had is 775:1500 which is simplified to 31:60 by dividing both with anything which is common in both that is 25
The ratio between the money left and money spent is 775:725 which is simplified to 31:29 by dividing both with anything which is common in both that is 25
To know more about Ratios - https://brainly.com/question/13419413
#SPJ9
Movie tickets at the local theater cost $9 for matinee showings and $13.50 for prime-time
showings. If the total number of tickets the theater sold on a particular day was 1,411 and $17,149.50
was collected, how many matinee and how many prime-time movie tickets were sold that day?
The number of many matinee and prime-time movie tickets were sold that day are
What is defined as the linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers and also the coefficients of x and y, i.e. a and b, are not equal to zero.
If there is only one solution, the given lines are intersecting; if no solution is possible, the given equations have been of parallel lines. If there are an infinite number of solutions, it means that given equations form coincident lines.For the given question.
Let 'x' be the number of matinee showings.
Let 'y' be the number of prime-time showings.
Then. the total ticket sold are 1,411.
Thus, x + y = 1,411.
or, x = 1,411 - y
The cost of one matinee showings is $9.
The cost of one prime-time showings is $13.50.
Now, the total cost earned is $17,149.50.
So,
9x + 13.5y = 17,149.50
Put the value of the 'x' in the above equation.
9(1,411 - y) + 13.5y = 17,149.50
Simplifying;
12699 - 9y + 13.5y = 17,149.50
4.5y = 4450.5
y = 989.
Calculate x;
x = 1,411 - 989
x = 422
Therefore, the number of matinee and prime-time movie tickets were sold that day are 422 and 989.
To know more about linear equation in two variables, here
https://brainly.com/question/13951177
#SPJ9
WORTH 75 POINTS Find an equation of the perpendicular bisector of the segment "AB" which has end points points A(1, –2.5) and B(5, 5.5).
Answer:
Step-by-step explanation:
Question
To save for a down payment on a home, suppose you decide to invest in an annuity that pays 7.0% annual interest,
compounded annually. If you contribute $8,000 every year for 5 years, how much interest would you earn during the
5 years? Enter your answer, rounded to the nearest cent, without the dollar sign or comma ($21,678.1235 should be
entered as 21678.12.)
If you contribute $8,000 every year for 5 years, the interest would you would earn during the 5 years is:6005.91
What is future value of annuity?
The future value of the annuity means the future worth of 5 annual contributions of $8000 every year, based on the fact that the deposits would earn 7.0% interest rate every year, in short, the worth of the savings in 5 years can be determined using the future value of an ordinary annuity as shown below:
FV=PMT*(1+r)^N-1/r
FV=accumulate balance after 5 years=unknown
PMT=annual savings=$8,000
r=interest rate per year=7.0%
N=number of annual payments over 5 years=5
FV=$8000*(1+7.0%)^5-1/7.0%
FV=$46,005.91
Total deposits in 5 years=$8000*5=$40,000
Interest =FV-total deposits
interest=$46,005.91-$40,000
interest=$6,005.91
Find out more about annuity future value on:https://brainly.com/question/25718498
#SPJ1
−2(3n+ 8) = −6(n − 2)
Answer:
Step-by-step explanation:
0
On a long hike Lucy drank 6 pints of water. How much is this in quarts?
On a long hike Lucy drank 6 pints of water, which is equal to 3 quarts.
What is quarts?An English measurement of volume equal to one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system. One liter is roughly equivalent to each. It is divided into four cups or two pints (in the US). The precise dimensions of the quart have historically changed in line with shifting values of gallons over time and in relation to various commodities.
A measure of liquid capacity that is equal to two pints or a quarter of a gallon, or roughly 0.94 liter in the US and 1.13 liter in the UK.
Since, 1 quart = 2 pints
Therefore by unitary method we can say,
2pint= 1 quart
6pint= 3quarts
To know more about quarts visit: https://brainly.in/question/13601478
#SPJ9
Drake Kennedy's regular-time pay rate is $12.73 an hour. Last week he was paid for 37.5 hours at his
regular rate and for 5 hours at a time-and-a-half overtime rate. Find Drake's gross pay for week?
Answer:First, determine the total number of hours worked by multiplying the hours per week by the number of weeks in a year (52). Next, divide this number from the annual salary.if an employee has a salary of $50,000 and works 40 hours per week, the hourly rate is $50,000/2,080 (40 x 52) = $24.04.
Step-by-step explanation:
Divide the gross pay by the wage hours worked. For example, if your records show that the employee was paid $4,000 for the total month, divide 4,000 by 172 to reach $23.26. This is an accurate representation of an hourly rate for that employee's monthly work.
Use this image to classify each pair of lines.
Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD. The lines CD and GH cannot be defined. The lines AB and GH cannot be defined. Lines IJ and CD are perpendicular
What are Parallel and perpendicular lines in terms of slope of lines?Two lines are said to be parallel if : m(1) = m(2).
Two lines are perpendicular to each other if : m(1) x m(2) = -1.
We have to classify the set of these lines as; Parallel, Perpendicular or Cannot Be Determined.
1. Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD.
2. The lines CD and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.
3. The lines AB and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.
4. Lines IJ and CD are perpendicular; because they intersect each other at right angle.
Hence, the solutions to the table are shown above as options.
To solve more questions on Parallel and Perpendicular lines, visit the link below :-
brainly.com/question/10850077
#SPJ1
Can someone please help
Answer: 40
Step-by-step explanation:
when x=0, y=0
when x=2.5, y=100
(y2-y1)/(x2-x1)=
(100-0)/(2.5-0)=
100/2.5=40
Answer:
40
Step-by-step explanation:
the point on the graph is (1,40). The ordered pair is in the form (x,y) The constant of proportionality is the y/x or 40/1 which equals 40.
What are the coordinates of G after it is ROTATED 90 DEGREES CLOCKWISE?
The coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).
What is a translation?
The process of changing the location of the image on the coordinate system will be known as the translation.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, and make y-negative.
Given that point, G is translated to 90 degrees. The translated coordinates of point G will be calculated as:-
( -x, y ) = ( y, x )
( -4 , 3 ) = ( 3 , 4)
Therefore, the coordinates of G after it is rotated by 90 degrees will be ( 3, 4 ).
To know more about translation follow
https://brainly.com/question/12861087
#SPJ1
The sum of four and eight times a number is -76.
Answer: x = -10
▬▬▬▬▬▬▬▬▬▬
Given problem,[tex]4 + 8 \times x = -76[/tex]
Find x▬▬▬▬▬▬▬▬▬▬
[tex]4+8(x)-4=-76-4\\8(x)=-80\\\frac{8(x)}{8}=\frac{-80}{8}\\= -10\\x = -10[/tex]
▬▬▬▬▬▬▬▬▬▬
Answer Explained:
Given the keywords sum(add), times(multiply), as well as a number(variable), we can make an equation out of this, which was 4 + 8 * x = -76. We subtracted the sides by 4, then divided both of the sides by the next factor, 8, to get -10.
Thus,
4 + 8 × -10 = -76
Hope this helped you. :)
LA Fitness charges $50 to be a member and $2 each
time you attend the gym. 24 Hour Fitness charges $4
each time you attend the gym and $30 to be a
member.
After how many visits to the gym will the cost be the
same?
10 visits
9 visits
6 visits
7 visits
8 visits
Answer:
10 visits
Step-by-step explanation:
Let's model the expressions:
LA Fitness = 50 + 2x24 Hour Fitness = 30 + 4xNow set them to equal each other to find x, the number of visits
50 + 2x = 30 + 4x Subtract 2x
50 = 30 + 2x Subtract 30
20 = 2x Divide by 2
10 = x
After 10 visits to the gym, the cost will be the same.
Which funcation has an inverse that is a function b(x)=x^2 +3 d(x)=-9
Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
Steps of Finding the inverse of a function f(x):
1. First, replace f(x) with y. This is done to make the rest of the process easier.
2. Replace every x with a y and replace every y with an x.
3. Solve the equation from Step 2 for y. This is the step where mistakes are most often made so be careful with this step.
4. Replace y with In other words, you’ve managed to find the inverse.
5. Remember: the domain of f is the range of and the range of f is the domain of [tex]f^{-1}(x)[/tex].
Using this algorithm, you can find the inverse of non.
for f(x) = x^2 +3
y = x^2 + 3
x = y^2 + 3
y = √x-3
[tex]f^{-1}(x)[/tex] = √x-3
The domain and the range of f'(x) :
domain : [3,∞]
Range : [3,∞]
The domain and the range of f(x) :
Domain: x ∈ R (all real number)
Range: y ≥ 3
Functions b(x) is not one-to-one functions as the domain of there inverse is not the range of function then you can't find an inverse function. Function d(x) doesn't include x, then you can't also find an inverse function.
Therefore, for both the given function we cannot find the inverse.
To learn more on inverse of a function click:
https://brainly.com/question/12040579
#SPJ1
Ling is a camp counselor at a local summer camp. She is in charge of the weekly craft activity
for 40 campers. She plans to make fabric-covered frames that each require 1/6 yard of fabric.
The camp director gave her 6 2/3 yards of fabric remnants for this project. Does Ling have
enough fabric for her craft activity?
She has the exact amount of fabric that she needs for this project.
Does Ling have enough fabric for her craft activity?
We know that she is in charge of 40 campers, and she wants to make fabric-covered frames, such that each one needs 1/6 yards of fabric.
We know that he has a total of 6 + 2/3 yards to do this, and we need to see if that is enough.
Now, for each one of the 40 campers she needs 1/6 yards, so the total amount she needs is given by the product:
T = 40*(1/6 yards) = 40/6 yards = (36 + 4)/6 yards = (6 + 4/6) yards
T = (6 + 2/3) yards
So she has the exact amount of fabric that she needs for this project.
If you want to learn more about products:
https://brainly.com/question/10873737
#SPJ1
Need help with this please
Answer:
Step-by-step explanation:
185miles / 75mph = 2.5 hours
NEED ALL ANSWERS PLEASE NUMBER THEM PLEASE:)))
Answer:
6. B
7. C
8. C
Step-by-step explanation:
6.
3x
------- = 1.5 (x + 1)
x + 1 (x + 1)
3x = 1.5 (x + 1)
3x = 1.5x + 1.5
-1.5x -1.5x
1.5x = 1.5
x = 1
7.
2x + 3y = 15
(x + y = 3)-2
2x + 3y = 15
-2x - 2y = -6
----------------------
y = 9
x + y = 3
x + 9 = 3
-9 -9
----------------
x = -6
(x, y) = (-6, 9)
8.
(-4x + y = 4) -2
-8x + 2y = -2
8x - 2y = -8
-8x + 2y = -2
--------------------
-10
No Solution
I hope this helps!
Which type of sampling is being used in this scenario: a school
administrator gets the alphabetical list of students and chooses every
third one to survey.
A:Cluster
B:Convenience
C:Stratified
D:Systematic
The given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.
In the question, we are asked to identify the type of sampling used in the scenario: "a school administrator gets the alphabetical list of students and chooses every third one to survey", among cluster, convenience, stratified, and systematic.
First, we will understand all these types of sampling:-
Cluster Sampling: By segmenting the population into clusters, usually, geographically, cluster sampling is performed. These units are referred to as blocks or clusters. The clusters are chosen at random, and each component in the chosen clusters is used.Convenience Sampling: Convenience sampling is the most straightforward method, but it should never be used. Convenient data are utilized in convenience sampling. These are the first individuals the surveyor encounters.Stratified Sampling: The population is also divided into groups known as strata via stratified sampling. This time, though, it is based on a characteristic rather than a location.Systematic Sampling: In systematic sampling, the elements are "counted off" from the list. Every kth element is thus taken. Comparable to having everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc." All those numbered 4 would be used once the list had been completed.In the given scenario, the school administrator is getting the list of students in alphabetical order, similar to taking everyone in a line and counting off "1,2,3,4; 1,2,3,4; etc. And then he is choosing every third student, similar to choosing all those numbered 4.
Thus, the given scenario, "A school administrator gets the alphabetical list of students and chooses every third one to survey", is Systematic Sampling.
Learn more about sampling at
https://brainly.com/question/28202337
#SPJ9
Suppose we have a bottomless bag of 3 different kinds of balls: blue, green, and red. How many possibilities are there to choose 3 balls and arrange them in a line.
The number of possibilities that are there to choose 3 balls is 6.
How to illustrate the information?From the information, we have a bottomless bag of 3 different kinds of balls: blue, green, and red.
The number of possibilities that are there to choose 3 balls will be:
= 3!
= 3 × 2 × 1
= 6 possibilities.
Therefore, the number of possibilities that are there to choose 3 balls is 6.
Learn more about permutations on:
brainly.com/question/4658834
#SPJ1
Algebraic fraction equations
Solving question
Answer:
10x-11 over 4
Step-by-step explanation:
step1:find common denominator
step 2:apply the distributive property
step3: remove the parentheses for addition or subtraction
step4: reorder and gather like terms
step5: collect co-efficients of the like terms
step6: calculate the sum or difference
Which of the following sets does the number 0.1453 belong to
Answer: The number 0.1453 belong to rational numbers and real numbers.
Step-by-step explanation:
The whole numbers are 0,1,2,3,..., so 0.1453¯¯¯¯¯ (repeat bar on 53)does not belong to the set of whole numbers. The integers are the whole numbers and their opposites, so 0.1453¯¯¯¯¯(repeat bar on 53) does not belong to the set of integers. Rational numbers include decimals that repeat or stop.The integers are the whole numbers and their opposites, so 0.1453¯¯¯¯¯(repeat bar on 53) does not belong to the set of integers.Rational numbers include decimals that repeat or stop. Because 0.1453¯¯¯¯¯(repeat bar on 53) is a repeating decimal number, it belongs to the set of rational numbers. Because 0.1453¯¯¯¯¯(repeat bar on 53) is a rational number, it does not belong to the set of irrational numbers.Because 0.1453¯¯¯¯¯(repeat bar on 53) is a rational number, it does not belong to the set of irrational numbers.All rational numbers are real numbers, so 0.1453¯¯¯¯¯ (repeat bar on 53) belongs to the set of real numbers. In summary, 0.1453¯¯¯¯¯(repeat bar on 53) belongs to the following sets: rational numbers and real numbers.Therefore,
The number 0.1453 belong to rational numbers and real numbers.
Learn more about event correlation here: brainly.com/question/14004767
#SPJ9
A line has a slope of 1/10 and passes through the point (-10, 4). What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form.
[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{10} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ \cfrac{1}{10}}(x-\stackrel{x_1}{(-10)}) \implies y -4= \cfrac{1}{10} (x +10) \\\\\\ y-4=\cfrac{1}{10}x+1\implies {\LARGE \begin{array}{llll} y-\cfrac{1}{10}x+5 \end{array}}[/tex]
find negative 2 and 2/5 + 4/5
Answer:
[tex] - \frac{8}{5} [/tex]
Step-by-step explanation:
[tex] - 2 \frac{ \\ 2}{5} + \frac{4}{5} = - \frac{8}{5 \\ } [/tex]
Please help me I’ll mark brainly
Answer: -3
Step-by-step explanation:
( 19+ 4 x ( 20 - 18 ) ÷9
Answer:
do u want me to graph or solve it
Step-by-step explanation:
Answer:
97
Step-by-step explanation:
I believe that is your answer
Given f(x) = x^2- 3x + 5, what is f(-2)?
Step-by-step explanation:
f(x) = x² - 3x + 5
f(-2) = (-2)² - 3.(-2) + 5
f(-2) = 4 + 6 + 5
f(-2) = 15
Answer:
Step-by-step explanation:
Comment
In general, f(x) can be thought of as being y. So the equation could read as "Let x = - 2" when y = x^2 - 3x + 5.
Another way of thinking of it is by saying f(-2), wherever you see an x on the right hand side, substitute the value given on the left side (in this case x = - 2
Solution
f(-2) = (-2)^2 - 3x + 5
f(-2) = 4 - 3(-2) + 5 Combine
f(-2) = 4 + 6 + 5 Add
f(-2) = 15
Simplify the following equation:
Answer:
The answer is 4!
for the function f(x) = 4x+2, evaluate and simplify the difference quotient
The difference quotient of the function f(x) = 4x + 2 is 4.
What is a function?Functions were originally the idealization of how a varying quantity depends on another quantity.
The given function is,
f(x) = 4x + 2
For a given function f(x), we define the difference quotient as:
[tex]\frac{f(x+ h)-f(x)}{h}[/tex]
Thus, for the given function, difference quotient is given as,
[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4(x+h)+2-(4x+2)}{h}[/tex]
expanding the brackets we get,
[tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4x+4h+2-4x-2}{h}[/tex]
Solving we get,
⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = [tex]\frac{4h}{h}[/tex]
Thus,we get
⇒ [tex]\frac{f(x+ h)-f(x)}{h}[/tex] = 4
Thus, the difference quotient of the function f(x) = 4x + 2 is 4.
To learn more about difference quotient :
https://brainly.com/question/18270597
#SPJ1
