The two lines, X and Y, are graphed below:
Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8
Determine the solution and the reasoning that justifies the solution to the systems of equations.
(2, 7), because this point is true for both the equations
(4, −6), because this point lies only on one of the two lines
(4, −6), because this point makes both the equations true
(2, 7), because the lines intersect the x-axis at these points
Answers
(-3, 12), (7, -16) are 21 points on this line, so by the 2-point form of the equation of a line, the equation of X is given as follows:
[tex] \frac{12-(-16)}{-3-7}= \frac{y-12}{x-(-3)} [/tex]
[tex]\frac{28}{-10}= \frac{y-12}{x+3} [/tex]
[tex]28(x+3)=-10(y-12)[/tex]
[tex]28x+84=-10y+120[/tex]
[tex]28x+10y-36=0[/tex], divide by 2 to simplify:
[tex]14x+5y-18=0[/tex]
similarly, the equation of Y is found using the points (0, -14) and (11, 8):
[tex] \frac{-14-8}{0-11}= \frac{y-(-14)}{x-0} [/tex]
[tex] \frac{-22}{-11}= \frac{y+14}{x} [/tex]
[tex]2= \frac{y+14}{x} [/tex]
[tex]2x-y-14=0[/tex]
so y=2x-14,
substitute y=2x-14 in 14x+5y-18=0:
14x+5y-18=0
14x+5(2x-14)-18=0
14x+10x-70-18=0
24x=88
x=3.667, then y=2x-14=2*3.667-14=-6.66
the intersection point is (3.667, -6.66), it is the only point which satisfies the equations of the lines, that were found.
Answer: (4, −6), because this point makes both the equations true
Answer:c
Step-by-step explanation:
(4,-6), because this point makes both the equations true.
Related Questions
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true? Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent. Both plans cost the same when 22 texts are sent. Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent. Both plans cost the same when 50 texts are sent
Answers
[tex] \left \{ {{y=0.05x+20} \atop {y=0.25x+10}} \right. [/tex]
Set the equations equal to each other and solve:
[tex]$0.05x+20=0.25x+10$[/tex]
[tex]$0.2x=10$[/tex]
[tex]$x=50$[/tex]
We then plug in to get [tex]$y$[/tex]:
[tex]$0.25(50)+10=22.5$[/tex]
The solution to the system is [tex] \left \{ {{x=50} \atop {y=22.5}} \right. [/tex].
Now, let's turn our attention to the statements.
The first one is false: Emilia's rate is higher, and the two plans cost the same at 50 texts, after which point Hiroto's plan becomes cheaper!
The second one is also false: we already figured out that the lines intersect at [tex]$x=50$[/tex].
The third statement is also false: as above, the lines intersect at [tex]$x=50$[/tex].
The fourth statement is true: the lines intersect at [tex]$x=50$[/tex].
In conclusion, the fourth statement - "Both plans cost the same when 50 texts are sent" - is true.
Answer:
d
Step-by-step explanation:
took the test yahoot
Find the value of each determinant
Answers
so, let's use the last column, 2,0,4, because it has a zero there, and we can use that as a cofactor to simply get a 0 as a product with the minor.
[tex]\bf \begin{bmatrix} 4&-1&\boxed{2}\\ 6&-1&\boxed{0}\\ 1&-3&\boxed{4} \end{bmatrix}\impliedby \textit{let's use the 3rd column for our cofactors}\\\\ -------------------------------\\\\ \begin{bmatrix} &&\boxed{2}\\ 6&-1&\\ 1&-3& \end{bmatrix}\implies +2 \begin{bmatrix} 6&-1\\1&-3 \end{bmatrix}\implies +2[(-18)-(-1)] \\\\\\ +2(-17)\implies -34\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{bmatrix} 4&-1&\\ &&\boxed{0}\\ 1&-3& \end{bmatrix}\implies -0 \begin{bmatrix} 4&-1\\1&-3 \end{bmatrix}\implies -0[(-12)-(-1)]\implies 0\\\\ -------------------------------\\\\ \begin{bmatrix} 4&-1&\\ 6&-1&\\ &&\boxed{4} \end{bmatrix}\implies +4 \begin{bmatrix} 4&-1\\6&-1 \end{bmatrix}\implies +4[(-4)-(-6)] \\\\\\ +4[2]\implies 8\\\\ -------------------------------\\\\[/tex]
so our determinant comes down to the sum of those three products... so -34 -0 + 8.
and surely you know how much that is.
The question is about finding the value of a determinant for matrices, a fundamental concept in Mathematics, especially linear algebra. For 2 × 2 matrices, the determinant calculation is straightforward and essential for various applications.
Explanation:The subject of this question is clearly Mathematics, specifically it pertains to linear algebra and the concept of determinants. The task involves finding the value of a determinant for a given matrix. For a 2 × 2 matrix, the determinant is found using a simple formula: if the matrix is given by
\[\begin{pmatrix} a & b \\ c & d \end{pmatrix}\]
then the determinant is calculated as \(ad - bc\). Additionally, the determinant provides important information about the matrix, such as whether the matrix is invertible and the product of its eigenvalues.
To understand determinants for larger matrices, a recursive approach is often used, breaking down the determinant into smaller matrices until 2 × 2 matrices are reached, where the simple formula can be applied. Also of note is that the determinant of the product of two matrices is equal to the product of their determinants (det(AB) = det(A)det(B)).
This fundamental concept is crucial for many applications in mathematics, including solving systems of linear equations, finding eigenvalues, and understanding linear transformations.
Use the half-angle identities to find the exact value of cos 15 degrees.
This is what I have so far:
cos15 degrees = cos1/2(30 degree) = sqrt (1+cos30)/2 = sqrt (1+ sqrt3/2)/ 2
But.. I don't understand how the cos30 turns into sqrt 3/2??
Answers
Let's start by considering the equilateral triangle ABC in the diagram below. An equilateral triangle has equal size of angles, 60°, 60°, and 60°. Let's say the length of each side to be 2 units.
If we split this triangle into two congruent right-angled triangle, we will have the measurement of the perpendicular height to be √3 by Pythagoras theorem.
By trigonometry ratio we then have [tex]cos(30) = \frac{ \sqrt{3} }{2} [/tex]
This ratio will always work for any right angle triangle with angles 90°, 60° and 30°
Going back to the original question:
cos(15°) = cos(30°) which is cos([tex] \frac{30}{2} [/tex])
let θ be 30° then cos(15°)=cos(θ/2)
by the trigonometry formula for half angle identity
cos(θ/2) = √(1+cosθ)/2
cos(15) = √(1+cos(30))/2
cos(15) = √(1+[tex] \frac{ \sqrt{3}} {2} [/tex]) / 2
cos(15) = [tex] \frac{ \sqrt{2+ \sqrt{3} } }{2} [/tex]
The cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
The trigonometry identity of half angles is given as:
cos([tex]\theta[/tex]/2) = [tex]\sqrt{[/tex](1 + cos([tex]\theta[/tex]))/2
Substitute 30 for [tex]\theta[/tex]
So, the equation becomes
cos(30/2) = [tex]\sqrt[/tex](1 + cos(30))/2
In trigonometry, we have:
cos(30) = [tex]\sqrt[/tex]3/2
So, we have:
cos(30/2) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Divide 30 by 2
cos(15) = [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Hence, the cosine value of cos(15) is [tex]\sqrt[/tex](1 + [tex]\sqrt[/tex]3/2)/2
Read more about trigonometry identities at:
https://brainly.com/question/7331447
Two perpendicular lines intersect at the origin. If the slope of the first line is .5, what is the equation of the second line?. .
Answers
Consider the equation ay'' + by' + cy = d, where a, b, c, and d are constants. (a) find all equilibrium, or constant, solutions of this differential equation. (enter your answers as a comma-separated list of equations.)
Answers
The constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
The equilibrium solutions of the given differential equation [tex]\(ay'' + by' + cy = d\)[/tex] are found by setting the derivatives equal to zero.
1. Setting [tex]\(y'' = 0\)[/tex]: When [tex]\(y'' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Solving for y, we get [tex]\(cy = d\)[/tex], and therefore, [tex]\(y = \frac{d}{c}\)[/tex].
2. Setting [tex]\(y' = 0\)[/tex]: When [tex]\(y' = 0\)[/tex], the equation becomes [tex]\(a \cdot 0 + b \cdot 0 + c \cdot y = d\)[/tex]. Again, solving for y, we obtain [tex]\(cy = d\)[/tex], and hence, [tex]\(y = \frac{d}{c}\)[/tex].
So, the constant solutions are [tex]\(y = \frac{d}{c}\)[/tex], and this is the equilibrium solution for the given differential equation.
Therefore, the constant solutions are given by [tex]\(y'' = 0\) and \(y' = 0\)[/tex].
What is 1/4 of 268 ?
Answers
Answer: 67
To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.
Explanation:Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.
The calculation is as follows:
Divide the number 268 by 4.268 ÷ 4 equals 67.This means that 1/4 of 268 is 67.
Learn more about Mathematical Division here:https://brainly.com/question/32582499
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Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)
Answers
As n->inf, o(log(n+1)) -> o(log(n)) since the 1 is insignificant compared with n.
We can similarly drop the "1" as n-> inf, the expression becomes log(n^2+1) ->
log(n^2)=2log(n) which is still o(log(n)).
So yes, both are o(log(n)).
Note: you may have more offers of answers if you post similar questions in the computer and technology section.
Both functions log(n + 1) and log(n^2 + 1) are not o(log n). For large values of n, log(n + 1) is approximately equal to log n, and log(n^2 + 1) behaves like 2*log n, none of which grows strictly slower than log n.
To determine whether the functions log(n + 1) and log(n2 + 1) are o(log n), we'll use the definition of little-o notation. A function f(n) is said to be o(g(n)) if for any positive constant c > 0, there exists a threshold n0 such that for all n > n0, f(n) < c * g(n). In other words, f(n) grows slower than any constant multiple of g(n) as n approaches infinity.
Analysis for log(n + 1)
When n is very large, the +1 becomes negligible, and log(n + 1) behaves similarly to log n. Therefore,
log(n + 1) ≈ log n when n is large.
This implies that log(n + 1) is not o(log n) because it does not grow strictly slower than any multiple of log n.
Analysis for log(n2 + 1)
Using logarithm properties:
log(n2 + 1) < log(n2 + n2) = log(2n2) = log 2 + 2*log n.
As n grows, the constant term (log 2) becomes insignificant, and the function approaches the behavior of 2*log n. However, since there is a multiple of log n (which is 2*log n), this still means that log(n2 + 1) is not o(log n) because it grows faster, not slower, than log n.
What is the value of b2 - 4ac for the following equation? x(x + 8) = 9 28 64 100
Answers
Answer:
C) 100
Step-by-step explanation:
The given equation is x(x + 8) = 9
Distributing x insides, we get
x^2 + 8x = 9
Now set the equation equal to zero.
x^2 + 8x - 9 =0
Here a = 1, b = 8, and c = -9
b^2 - 4ac = (8)^2 - 4*1*-9
= 64 + 36
= 100
Therefore, b^2 - 4ac = 100.
Answer: C) 100
Hope this will helpful.
Thank you.
Answer:
C. 100
Step-by-step explanation:
how much larger is 1 ft in one cubic inch
Answers
Mark deposited $9,000 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 8% while the other rate is 7%. If the total interest earned after one year is $700, find the amount deposited into each of the accounts
Answers
Solve for x
0.07x+720-0.08x=700
0.07x-0.08x=700-720
-0.01x=-20
X=20÷0.01
X=2,000 invested at 7%
9000-2000=7000 invested at 8%
If you earn $3500 per month and you expect your earnings to increase by 2.3% per year, how much do you think you will be making in 10 years? (Express your answer rounded correctly to the nearest cent!)
Answers
Final answer:
Your expected monthly earnings in 10 years, with a 2.3% annual increase, would be $4424.10, rounded to the nearest cent.
Explanation:
To calculate your expected monthly earnings in 10 years, taking into account a 2.3% annual increase, we will use the formula for compound interest: P(1 + r)^n, where:
P is the principal amount (your current earnings)
r is the annual raise rate
n is the number of years
Your current monthly earnings are $3500. The annual raise rate is 2.3%, so r is 0.023 when expressed as a decimal. The number of years, n, is 10.
Plugging the values into the formula, we get:
Earnings in 10 years = $3500 * (1 + 0.023)^10
Calculating the result, we find that your expected monthly earnings in 10 years are:
$4424.10
What is the step by step process of solving for the GCF from a list of terms.
Ex. (see picture)
Answers
Explain the place value relationship when the same two digits are next to each other in a multi-digit number.
Answers
Partitioning this value,
5664 = 5000 + 600 + 60 + 4
Notice that one digit of 6 worth 100 and the other worth 10
Take another example, 78869 where there are two digits of '8'
Partitioning this value, we have
78869 = 70000 + 8000 + 800 + 60 + 9
Notice that one digit of '8' worth 8000 and the other worth 800
One other characteristic that we can tell from both example, is that when two same digits are placed next to each other in a value, one digit's value is always worth ten times than the other digit.
for example, the value 600 and 60 from the first example, 600 = 10 × 60
Round 241,639 to the nearest thousand
Answers
The thousandths place is the fourth digit to the left of the decimal.
241,639
Look to the right of the 1.
Since 6 is greater than 4, we round up.
242,000
The answer is 242,000
Hope this helps! :)
A rectangular yard measuring 26ft by 40ft is bordered (and surrounded) by a fence. Inside, a walk that is 2ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
Answers
The area of the yard (minus the walk) is simple to find. Just multiply 26 and 40, and you'd get 1,040 ft squared.
The area of the yard including the walk is a bit more complicated. You have to include add measurement of the walk to the measurements of the length and width of the yard. However, you must add it twice, considering it goes all the way around the yard. So, since the walk is 2 feet wide, you add it (twice) to 26 (26 + 4 = 30) and twice to 40 (40 + 4 = 44). Now, multiply the two new measurements. You now have 1,320 feet squared.
So now you have the combined area of the walk and yard, and the area of the yard without the walk. To find the area of the walk, you just subtract the area of the yard from the entire measurement of both. 1,320 square feet - 1,040 square feet is 280 square feet.
The price of 1 lb of potatoes is $ 1.65. if all the potatoes sold today at the store bring in $ 1220, how many kilograms of potatoes did grocery shoppers buy?
Answers
1220/1.65 = 739.39 pounds of potatoes were sold
1 pound = 0.453592 kilograms
739.39 x 0.453592 = 335.38 kilograms
Final answer:
By dividing the total sales of $1220 by the price per pound ($1.65), we find that approximately 739.39 pounds were sold, which converts to roughly 335.38 kilograms of potatoes purchased by grocery shoppers.
Explanation:
To calculate the number of kilograms of potatoes grocery shoppers bought, we need to use the given prices and total sales. Since the price of 1 lb of potatoes is $1.65, we can find the total weight of the potatoes sold by dividing the total sales amount by the price per pound:
Total weight in pounds = Total sales
= $1220
= $1220 / $1.65
= 739.39 pounds approximately
Next, we need to convert pounds to kilograms. There are approximately 2.20462 pounds in 1 kilogram. The conversion is:
Total weight in kilograms = Total weight in pounds / 2.20462
= 739.39 / 2.20462
= 335.38 kilograms approximately
Therefore, grocery shoppers bought approximately 335.38 kilograms of potatoes.
how to solve this linear equation step by step please
Answers
[tex]\bf \cfrac{3}{c(c-4)}-\cfrac{9}{c(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{3(2c+3)-9(c-4)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-(9c-36)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-9c+36}{1}=\cfrac{2[c(c-4)(2c+3)]}{(2c+3)(c-4)} \\\\\\ -3c+45=2c\implies 45=5c\implies \cfrac{45}{5}=c\implies 9=c[/tex]
Round 65.85 to the nearest whole number
Answers
Since the value after the decimal place is above 5, it rounds to 66 and not 65
How do you write 314,207 in word form
Answers
write 103,727,495 in word form and expanded
Answers
One hundred three million, seven hundred twenty seven thousand, four hundred ninety five
Expanded Form:
100,000,000 + 3,000,000 + 700,000 + 20,000 + 7,000 + 400 + 90 + 5
Hope this helped
HELP? The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.
Answers
48-16=32
ive completed that lesson
Answer : The volume blue prism in Model 1 is, [tex]32in^3[/tex]
Step-by-step explanation :
As we are given that:
Volume of Model 1 = Volume of Model 2
Given:
Volume of blue prism in Model 2 = [tex]36in^3[/tex]
Volume of orange prism in Model 2 = [tex]12in^3[/tex]
Volume of orange prism in Model 1 = [tex]16in^3[/tex]
Now we have to calculate the total volume of Model 2.
Total volume of Model 2 = [tex]36in^3+12in^3[/tex] = [tex]48in^3[/tex]
Now we have to calculate the volume blue prism in Model 1.
Volume of Model 1 = Volume of Model 2
Volume of orange prism in Model 1 + Volume blue prism in Model 1 = Total volume of Model 2
[tex]16in^3[/tex] + Volume blue prism in Model 1 = [tex]48in^3[/tex]
Volume blue prism in Model 1 = [tex]48in^3-16in^3[/tex]
Volume blue prism in Model 1 = [tex]32in^3[/tex]
Thus, the volume blue prism in Model 1 is, [tex]32in^3[/tex]
What is the slope intercept equation of the line below
Answers
so you already have the slope=-6/5 and the intercept is 3
y=-(6/5)x+3
What's the correct answer for this?
Answers
[tex]\bf \textit{\underline{N} is inversely proportional to \underline{A}}\qquad N=\cfrac{k}{A} \\\\\\ \textit{we also know that } \begin{cases} A=3\\ N=16 \end{cases}\implies 16=\cfrac{k}{3}\implies 16\cdot 3=k \\\\\\ 48=k\qquad thus\qquad \boxed{N=\cfrac{48}{A}}\\\\ -------------------------------\\\\ \textit{if \underline{A} is 4, what is \underline{N}?}\qquad N=\cfrac{48}{4}[/tex]
If the rate of inflation is 3.7% per year, the future price pt (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. =pt400( 1.037)t Find the current price of the item and the price 8 years from today. Round your answers to the nearest dollar as necessary.
Answers
[tex]\bf p(t)=400(1.037)^0\implies p(t)=400\cdot 1\implies \boxed{p(t)=400}[/tex]
now, 8 years from now, well, 8 years would had passed by then, t = 8
[tex]\bf p(t)=400(1.037)^8\implies p(t)\approx 400\cdot 1.3373037\implies \boxed{p(t)\approx 535}[/tex]
The current price is 400
The price 8 years from today is
P (8)=400×(1.037)^(8)=534.9 round your answer to get 535
A dozen eggs cost $1.10 in Dover. In Ensley, the eggs cost 10% more than in Dover. Find the price of a dozen eggs in Ensley.
Answers
1.10 + .11 = 1.21
In Ensley, the price of a dozen eggs costs $1.21.
Hope this helps.
Final answer:
The price of a dozen eggs in Ensley is $1.21.
Explanation:
To find the price of a dozen eggs in Ensley, we need to consider that the eggs in Ensley cost 10% more than in Dover. If a dozen eggs in Dover cost $1.10, we can calculate the 10% increase by multiplying $1.10 by 1.10:
$1.10 x 1.10 = $1.21
Therefore, a dozen eggs in Ensley cost $1.21.
Solve 2x2 + 26 = 0 to identify the roots.
Answers
Answer:
[tex]x=+/-i\sqrt{13}[/tex]
Step-by-step explanation:
To find the roots, factor and set equal to 0 or use the quadratic formula. This quadratic equation does not factor and must be solved using the quadratic formula.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
where a = 2, b=0, and c=26
[tex]x=\frac{0+/-\sqrt{0^2-4(2)(26)} }{2(2)} \\x=\frac{+/-\sqrt{-208)} }{4} \\x=\frac{+/-i\sqrt{16*13)} }{4}\\x=\frac{+/4i\sqrt{13} }{4}\\x=+/-i\sqrt{13}[/tex]
Answer:
Step-by-step explanation:
X=-i√13,x=i√13
A single batch of cookies requires two cups of sugar and three cups of flour. if more than one batch or a partial batch was made, the unit rate of sugar to flour would remain the same. match the correct amount of sugar to the correct amount of flour to keep the same unit rate of sugar and flour in a single batch. 11.5 cups of flour 4.5 cups of sugar 6.75 cups of flour 12 cups of flour 5 cups of sugar 11.25 cups of flour 7.5 cups of sugar 7.5 cups of flour 8 cups of sugar 4 cups of sugar
Answers
First write down the amounts of flour (in cups)
11.5
6.75
12
11.25
7.5
then write down two-third of the values of flour on the right to represent the number of cups of sugar
11.5 7.67
6.75 4.5
12 8
11.25 7.5
7.5 5
Then check if all the amounts of sugar are on the list.
It seems that 6 cups of flour (to match 4 cups of sugar) and 7.67 cups of sugar (to match 11.5 cups of flour) are missing.
Please check for typos.
Answer:11.5
Step-by-step explanation: 11.5
There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two carriers is 4178 feet, while the difference of their lengths is only 14 feet.
Answers
Answer:
Length of carrier A = 2096 feet Length of carrier B=2082 feet.Step-by-step explanation:
Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.
Total length of two carriers =4178 feet
Difference of two carriers = 14 feet
Let
Length of carrier A =x feet
And
Legth of carrier B =y feet
According to question
The I equation is
x+y=4178
The II equation is
x-y= 14
Substitution method: In this method step I : we find value of x or y from the equation I
Step II: put the value of x or y in II equation then we get the value of another varaiable x or y
Step : Again put the obatined value of variable x or y from step II in equation I then we get value of other variable x or y .
By using substitution method ,
we find value of x from equation I
x= 4178-y
Now, put the value of x in equation II then we get
4178-y-y=14
4178-2y=14
4178-14=2y
4164=2y
[tex]y=\frac{4164}{2}[/tex]
y= 2082
Again , put the value of y in equation I
2082 +x=4178
x= 4178-2082
x=2096
Hence, the length of carrier A = 2096 feet
The length of carrier B= 2082 feet
Final answer:
To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.
Explanation:
The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:
Equation 1: A + B = 4178
Equation 2: A - B = 14
To solve for A and B, we can add the two equations together to eliminate B.
This gives us 2A = 4192, hence A = 2096 feet.
Substituting A back into one of the equations, we find B = 2082 feet.
Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.
7^-2 without exponent
Answers
Ex: (7x)^-1 ----> 1 over 7x or 1/7x
Ex: (5/8x)^-1 ------> 8x over 5 or 8x/5
The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x , where x is his monthly income. f^-1x . The variable x represents in the inverse function. If John's spending limit is $60,000, his monthly income is .
Answers
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
[tex]x= \frac{y-15,000}{1.5} [/tex]
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
[tex]x=g(y)=\frac{y-15,000}{1.5} [/tex]
since we generally use the letter x for the variable of a function, we write g again as:
[tex]g(x)=\frac{x-15,000}{1.5} [/tex]
for example :
[tex]g(50,000)=\frac{50,000-15,000}{1.5}= \frac{35,000}{1.5}= 23,333 [/tex]
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
[tex]g(60,000)=\frac{60,000-15,000}{1.5}= \frac{45,000}{1.5}=30,000 [/tex]
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation [tex]f ^{-1}(x) [/tex]