1) f(x)-3
[tex]\begin{gathered} f(x)=2x-4 \\ \Rightarrow f(x)-3=2x-4-3 \end{gathered}[/tex]Therefore, f(x)-3=2x-4-3
2) f(x-3)
[tex]\Rightarrow f(x-3)=2(x-3)-4[/tex]Thus, f(x-3)=2(x-3)-4
3) f(-3x)
[tex]f(-3x)=2(-3x)-4[/tex]Then, f(-3x)=2(-3x)-4
4) -3f(x)
[tex]-3f(x)=-3(2x-4)[/tex]Hence, -3f(x)=-3(2x-4)
Let f(-1)=16 and f(5) = -8Write the equation of the line in slope intercept form that passes throughthese two points
6. Taylor lost 5 chips to Minnie while playing a card game. Taylor then lost 20 chips toSally in the second round. Taylor won 10 chips from Paul in the 3rd round. Howmany chips did Taylor make or lose during these 3 rounds?
Step 1
[tex]\begin{gathered} \text{Given; } \\ \text{Taylor lost 5 chips to Minnie in round 1} \\ \text{Taylor lost 20 chips to Sally in round 2} \\ \text{Taylor won 10 chips from Paul in the 3rd round.} \end{gathered}[/tex]Step 2
Find how many chips Taylor made or lost during these 3 rounds.
[tex]\begin{gathered} \text{Taylor made 10 chips} \\ \text{Taylor lost (20+5) chips} \end{gathered}[/tex][tex]\begin{gathered} \text{Total chips made or lost= 10+(-25)} \\ \text{Total chips made or lost}=10-25=-15 \\ \text{The negative sign means he lost chips} \end{gathered}[/tex]
Since the total number of chips made or lost = -15, then Taylor lost 15 chips during the 3 rounds. If it where to be positive, then it woud have ment Taylor won some chips.
Therefore, Taylor lost 15 chips in the 3 rounds
1/6 of a number r decreased by 24 what is the algebraic expression
Max's bedroom is rectangular shaped and has a total area
of 140 square feet. If the short wall is at 10 feet long,
what is the length of the longer wall?
Answer:
14 ft
Step-by-step explanation:
Area is length times width. So, you need to find something times 10 that equals 140. Or, you could just do 140 divided by 10. 140/10=14.
60 is 24% of what number?
Explanation
Question
60 is 24% of what number?
Let the number be n.
is represent = in mathematics
of represent x
60 is 20% of what number?
60 = 20% x n
[tex]undefined[/tex]Calculate the population growth rate for Brazil:
r = (CBR + Immi) - (CDR + Emigr)
CBR = 2.6%, Immi = 2%, CDR = 2.3%,
Emig = 2%
(Portions of the numeric data are factual.)
0.3% is the population growth rate for Brazil.
How to find the population growth rate?CBR = 2.6%
Immi = 2%
CDR = 2.3%
Emig = 2%
Solution:
r = (CBR + Immi) - (CDR + Emigr)
r = (2.6 + 2) - (2.3 + 2)
r = 4.6 - 4.3
r = 0.3%
0.3% is the population growth rate for Brazil.
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Write the equation of the function shown below. Identify domain and range.
The function can be split in 2 straight lines: the first one from x = 2 to the left, and the other one from the same point to the right.
Now, a straight line equation is of the form
[tex]ax+m[/tex]Where a is the slope and m is the y-intercept.
"Left" line:
- m (y-intercept):
To find it we need to see where the line cross (intercepts) the y-axis. From the figure we can see that m = -2.
- a (slope):
To calculate the slope, we can use the following equation:
[tex]a=\frac{\Delta y}{\Delta x}[/tex]Where, chossing 2 points in the line, we have:
[tex]\begin{gathered} \Delta y=how\text{ much do we move up or down between the 2 points} \\ \Delta x=\text{ how much do we move to the right betw}en\text{ the 2 points} \end{gathered}[/tex]Look that for x we have to move to the right. Let's see a drawing:
In our case, we can take the points (0, -2) and (2, 4), so, we have:
[tex]a=\frac{\Delta y}{\Delta x}=\frac{4-(-2)}{2-0}=\frac{6}{2}=3[/tex]So, we have the equation for the "left" line:
[tex]3x-2[/tex]-"Right" line:
- m (y-intercept):
In this case we can not see where the line cross (intercepts) the y-axis. Let's leave this for latter.
- a (slope):
As we did before, we can pick to points on the line, like (3, 1) and (2, 4).
[tex]a=\frac{\Delta y}{\Delta x}=\frac{1-4}{3-2}=\frac{-3}{1}=-3[/tex]- m (y-intercept) continues:
We now know that the equation for this line is:
[tex]-3x+m[/tex]To find m, we can pick one single point and solve for that variable. For example, taking the point (2,4), we have:
[tex]\begin{gathered} y=ax+m \\ y=-3x+m \\ 4=-3\cdot(2)+m \\ 4=-6+m \\ 4+6=m \\ 10=m \end{gathered}[/tex]And so, for the right line, we have:
[tex]-3x+10[/tex]Finally, the equation of the function can be written as:
[tex]f(x)=\begin{cases}3x-2\text{ if x }\leq\text{ 2} \\ -3x+10\text{ if x }\ge\text{ 2}\end{cases}[/tex]Now, the domain of the function is the set of points (or numbers) for which the function has values. The set of departure. In this case, all the numbers can be "trasnformed" or mapped with this function, so the domain is all the numbers, the set of real numbers, R:
[tex]\begin{gathered} -\inftyLastly, the range of the function is the complete set of all possible resulting values after aplying the function. We can see that the function can takes, as maximum, a value of 4, then the range is:[tex]\begin{gathered} (\infty;\text{ 4}\rbrack \\ or \\ y\leq4 \end{gathered}[/tex]"How can an understanding of thenumber properties help you to solveequations that represent real-worldsituations?"
Undersatanding number properties helps you to solve equation because we can transfom ans simplify any equation in a way we just have to add or rest numbers. for example when you go shopping and there is a sale or a promotion, knowing this properties would help you to get the best price.
Whats 5 and 6/4 ×8 and 9/6
Given that 5 6/4 x 8 9/6
Firstly, we need to convert the mixed fraction into improper fractions
[tex]undefined[/tex]The number of bacteria present after t hours is given by the function B = 100e^0.563t. How many bacteria will there be after 4 hours? Round to the nearest whole number and label your answer.
Answer;
[tex]B\text{ = 951}[/tex]Explanation;
Here, we want to get the number of bacteria that will be present after 4 hours
What we have to do here is to substitute 4 for t in the equation of the model given
Mathematically, we have this as;
[tex]\begin{gathered} B=100e^{0.563t} \\ B=100e^{(0.563\times4)} \\ B\text{ =950.67 = 951} \end{gathered}[/tex]There are eight turtles 15 fish and 17 pelicans what percent of the animals are pelicans
The number of animals are given as;
[tex]\begin{gathered} \text{Turtles}=8 \\ \text{Fish}=15 \\ \text{Pelicans}=17 \\ \text{Total animals}=40 \end{gathered}[/tex]The percentage that are pelicans would be calculated as follows;
[tex]\begin{gathered} \text{Percentage Pelicans}=\frac{17}{40}\times\frac{100}{1} \\ \text{Percentage Pelicans}=\frac{1700}{40} \\ P\text{ercentage Pelicans}=42.5\text{ } \end{gathered}[/tex]ANSWER:
The percentage of the animals that are Pelicans is 42.5%
1. Brian's math test scorés: 86, 90, 93, 85, 79, 92, 20, 84Mean:Median:
Answer:
[tex]\begin{gathered} \text{ Mean=78.625} \\ \text{Median}=84 \end{gathered}[/tex]Step-by-step explanation:
The mean is the sum of all the values in a set of data, divided by the number of values on the list.
Hence, the mean of Brian's math test scores:
[tex]\begin{gathered} \text{ Mean= }\frac{86+90+93+85+79+92+20+84}{8} \\ \text{ Mean=}\frac{629}{8} \\ \text{ Mean=78.625} \end{gathered}[/tex]The median is the middle number in a sorted, ascending or descending, list of numbers:
Arrange the data set from smallest to largest, if the number of data set is even, the median is the average of the two middle data points in the list.
[tex]20,79,84,82,86,90,92,93[/tex]Hence, the median is the average of 82 and 86:
[tex]\begin{gathered} \text{Median}=\frac{82+86}{2} \\ \text{Median}=84 \end{gathered}[/tex]6 3 2 1 -6 -5 4 22 10 2 3 6 13 What kind of transformation does the graph show? A) flip B) rotation 9 slide D) translation
Student did not provided any picture and became unresponsive.
In a two digit number, the tens digit s twice the ones digit. the diffrence of the ones digit and half the tens digit is 0. An equation created to find the digit in the ones place will have:No solutionOne soulutionMany solutions
let
the two digit = xy
x= tens digit
y = ones digit
2x = y
[tex]\begin{gathered} y-\frac{1}{2}(2x)=0 \\ y-x=0 \end{gathered}[/tex]2x - x =0
x = 0
What is the correct answer there are more selective choices I’ll show you later
6. Three formulas for calculating present value are shown below.Formula #1Formula #2Formula #311PV =FV(1 + i)PVOA = CG--)PVAD = CG--T) +0Ci(1 + i)nti(1+i)nt-1Part 1: Using complete sentences, explain how each of these formulas is used.Part 2: Create an example scenario for at least one of the formulas.(3
SOLUTION:
Case: Present Value
Present Value is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential.
Part 1
[tex]PV=\frac{FV}{(1+i)^{nt}}[/tex]Sentence:
The Present Value is the Future Value divided by 1 is added to the rate of returns(i), raised to the number of periods(nt).
Part 2:
Present Value of Ordinary Annuity
[tex]PVOA=C[\frac{1}{i}-\frac{1}{i(1+i)^{nt}}][/tex]C is the annuity payment deposited or received at the end of each period.
i= discount or interest rate per period
n= number of periods.
The factor with interest rate and the number of periods is multiplied by annuity payments
Part 3:
Present value of Annuity due
[tex]PVAD=C[\frac{1}{i}-\frac{1}{i(1+i)^{nt-1}}]+C[/tex]C is the annuity payment deposited or received at the end of each period.
i= discount or interest rate per period
n= number of periods.
The factor with interest rate and the number of periods less 1 is multiplied by annuity payments and then added again to the annuity payments
Example of Part 1 (Present Value)
What is $56000 in 5 years time worth now, at an interest rate of 10%?
what is the volume of the object in cubic centimeters? i think its 20, but i just want to double check to see if im right.
Given,
The measure of edge of the cube is 4 cm.
The total number of cubes are 5.
Required
The volume of the soid.
The volume of the solid is calculated as,
[tex]volume\text{ = side}\times side\times side[/tex]Substituting the values then,
[tex]\begin{gathered} Volume\text{ =4}\times4\times4 \\ =64\text{ cm}^3 \end{gathered}[/tex]The volume of the solid is,
[tex]\begin{gathered} Volume=5\times64 \\ =320\text{ cm}^3 \end{gathered}[/tex]Hence, the volume of the solid is 320 cm^3.
david borrowed $4 from his mother each of the last tree months how much money does he owe his mother?
Answer:
12$
Step-by-step explanation:
He borrowed 4$ for three months.
4 x 3 = 12.
Answer = 12.
Hope this helps!
(Brainliest would mean a lot to me, thanks!)
The sum of three numbers is 107. the second number is 7 less than the first. The third number is 2 times the second. What are the numbers?
a. What is the dependent variable?b. What is the independent variable?c. What is the slope (rate of change) of the line?d. What does this number mean for the circus?e. What is the y-intercept (initial condition) of the line? Why?
Part (a)
The dependent variable should be y for a function y=f(x).
Therefore, in this case dependent variable is profit
Part (b)
The independent variable is number of tickets sold.
Part (c)
Consider two coordinates in the graph (40,60) and (20,30).
Then, the slope will be,
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ =\frac{60-30}{40-20} \\ =1.5 \end{gathered}[/tex]Therefore, the avlue of slope is 1.5.
Part (d)
The slope is the rate of change profif with repect to the number of tickets sold for a circus.
Part (e)
From the graph, it can be noted that the y intersept is 0. Because intitial point is (0,0).
Which represents the equation 6x+3y= 12 whO y=-2x+4O y = 2x+4Oy=-2x-4O y=2x-4
Given the equation:
6x + 3y = 12
We need to solve for y. Dividing by 3:
2x + y = 4
Subtracting 2x:
y = -2x + 4
First choice
help me pleaseeeeeeeeeeeeeeeeeeeeeeeee !!!
Answer:
f(x) = 5/6x +21
Step-by-step explanation:
You want the equation of the line with slope 5/6 through point (-18, 6) written using function notation.
Point-slope formGiven a slope and a point, it can be useful to write the equation of the line in point-slope form:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
The line of interest has slope m = 5/6 through point (h, k) = (-18, 6), so its equation can be written as ...
y -6 = 5/6(x -(-18))
y = 5/6x +15 +6 . . . . . eliminate parentheses, add 6
y = 5/6x +21
Function notationFunction notation gives a name to the relation, and identifies the independent variable. We want to call this f(x), meaning the name of the relation is "f", and the independent variable is "x". Essentially, "f(x)" replaces "y" in the above equation:
f(x) = 5/6x +21
Select all correct solutions for the equation.
15(2x - 10) + 4x = -2(15x + 4)
A. x = 2.21875
B. x = 14264x = 14264
C. x = 35.5
D. x = 7132x = 7132
E. x = 39.5
F. x = 792x = 792
G. x = 714
Answer:
Step-by-step explanation:
We can rewrite:
15(2x-10) + 4x = -2(15x+4)
gives
30x - 150 + 4x = -30x -8
Adding 30x on both sides and adding 150 on both sides gives us:
30x + 4x - 150 + 30x + 150 = -30x - 8 + 150 + 30x
which gives us: 64x = 142
We can now divide both sides by 64, which gives us:
x = 142 / 64 = 2.21875
So the only right answer is A
You can fill in all the other options into the starting equation if you want too see this is indeed true
going to send u a pic of the q
we have the phrase
fifteen occupant or less
[tex]\begin{gathered} n\leq15 \\ n\ge0 \end{gathered}[/tex]Remember that the occupants can not be negative numbers
so
n=0,1,2,3,.....,15we have
seventy stadiums or more
the algebraic expression is
[tex]n\ge70[/tex]so
n=70,71,72,73,...
option Abecause the number of stadiums must be a whole number be awhat is 7754-(9x34)+667
Answer:
the answer is 8115
Step-by-step explanation:
you do 9 times 34 which is 306. then u do 7754 minus 306 which is 7448. then u add 667 to that which is 8115.
Between which steps does Morgan use the subtraction property of equality to justify her work?
Morgan uses the subtraction property of equality in step 5.
What is the subtraction property of equality?The subtraction property of equality describes the balancing of an equation by subtracting the same value on both sides of the equality.
There is also the addition property of equality which states adding the same number to both sides of the equality also balances an equation.
Given Morgan's work Step 1 - 6(x+5) = 25.
Step 2 - 6(x) + 6(5) = 25 . (Distributive property).
Step 3 - 6x + 30 = 25.
Step 4 - 6x + 30 - 30 = 25 - 30 (Subtraction property of equality)
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Help! Help! 9261 divided by 57
162.4736842 is 9261 divided by 57
Cody's rent is increasing by $51 per month starting next year. That is an increase of 15% from his current rent. Let r represent Cody's current rent. Set up an equation and solve it to fibd the value of r.
Given :
Cody's rent is increasing by $51 per month starting next year.
That is an increase of 15% from his current rent.
Let the current rent = r
so, the increase = 15% of r = 0.15r
So, the equation that represent the situation is :
[tex]0.15\cdot r=51[/tex]Solve for r :
[tex]r=\frac{51}{0.15}=340[/tex]So, the current rent = $340
The rent for the next year = 340 + 51 = $391
3z - 8xyz + 4x^2y^2z please solve this
Answer:
z(3-8xy+4x^2y^2)