Find the value of a and z: x5⋅x4=axz a = , z = Find the values of a and z: 6x20+5x20=axz a = , z = Find the value of a and z: (x5)4=axz a = , z = Find the value: x25−x25 = Find the values of a, b and z: 8x−9=abxz a = , b = , z =

Answers

Answer 1

Final answer:

To find the values of a and z, we need to solve the given equations. Without specific numerical values, we cannot determine the exact values of a and z.

Explanation:

To find the values of a and z, we need to solve the given equations. Let's go through each question:

1. For the equation x^5 * x^4 = axz, we can simplify it as x^9 = axz. Since there is no specific numerical value given, we cannot find the exact values of a and z.

2. Similarly, for the equation 6x^20 + 5x^20 = axz, we can simplify it as 11x^20 = axz. Again, without a specific value for x, we cannot determine the values of a and z.

3. In the equation (x^5)^4 = axz, we can simplify it as x^20 = axz. Without numerical values, we cannot find the exact values of a and z.

4. The equation x^25 - x^25 simplifies to 0. There are no variables to solve for.

5. Lastly, for 8x - 9 = abxz, we cannot determine the values of a, b, and z without additional information.

Related Questions

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

[tex]\bf \qquad \textit{Amount for Exponential Growth}\\\\ A=I(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &3500\\ r=rate\to 2.3\%\to \frac{2.3}{100}\to &0.023\\ t=\textit{elapsed time}\to &10\\ \end{cases} \\\\\\ A=3500(1+0.023)^{10}[/tex]

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

how much larger is 1 ft in one cubic inch

Answers

Simply plugging in the dimensions into Google's easy Volume converter I found a cubic foot is 1728 times bigger than a cubic inch. In other words 1728 cubic inches fit into a cubic foot.

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

Let's turn that into a linear system:
[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:

Step-by-step explanation:

took the test yahoot

Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)

Answers

Assuming the order required is as n-> inf.

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.

91284 the nearest ten thousand

Answers

91284 the nearest ten thousand is 9

91284 rounded to the nearest ten thousand is 91, 000
Its more closer to 91,000 then 92,000

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

0.07x+0.08 (9000-x)=700
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%

7^-2 without exponent

Answers

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ 7^{-2}\implies \cfrac{1}{7^2}\implies \cfrac{1}{49}[/tex]

in any negative exponent problem all you do is flip the number(s) and or variable(s).
Ex: (7x)^-1 ----> 1 over 7x or 1/7x
Ex: (5/8x)^-1 ------> 8x over 5 or 8x/5

After 5 years of earning interest at an annual rate of 3% an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment

Answers

[tex]\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$950\\ P=\textit{original amount deposited}\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ t=years\to &5 \end{cases} \\\\\\ 950=P\cdot 0.03\cdot 5[/tex]

solve for P.

In an inductive generalization, in order to achieve an error margin of plus or minus 3 percentage points at a confidence level of about 95 percent, whats the smallest random sample we can get away with, regardless of the size of the target population

Answers

Let n = required random sample size.

Assume that the population standard deviation is known as σ.
Let m = sample mean.
At the 95% confidence level, the expected range is
(m - k(σ/√n), m + k(σ/√n))
where k = 1.96.

Therefore the error margin is 1.96(σ/√n).
Because the error margin is specified as 3% or 0.03, therefore
(1.96σ)/√n = 0.03
√n = (1.96σ)/0.03
n = 128.05σ²

This means that the sample size is about 128 times the population variance.

Answer:
Smallest sample size = 128.05σ², where σ = population standard deviation.

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

The question is: how does cos(30) = [tex] \frac{ \sqrt{3} }{2} [/tex]

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

Round 241,639 to the nearest thousand

Answers

Hi!

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! :)

Find the value of each determinant

Answers

now, recall that, to get the determinant of a 3x3 or higher matrix, you pick a column or row to get the cofactors, also recall that the cofactors need to go witht the checkerboard pattern, so [tex]\bf \begin{bmatrix} +&-&+&-&+&...\\ -&+&-&+&...\\ +&-&+&-&+&... \end{bmatrix}[/tex] and so on.

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.

Final answer:

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.

Erika worked 14 hours last week and 20 hours this week. If she earns $9 per hour, how much did she earn during these two weeks? 4 of 60

Answers

309 Dollars were earned by Erika for both weeks

we know that

Erika earns [tex]\$9[/tex] per hour

By proportion

Find how much she earn during the total hours of two weeks

The total hours of two weeks is equal to

[tex]14+20=34\ hours[/tex]

[tex]\frac{9}{1} \frac{\$}{hour} =\frac{x}{34} \frac{\$}{hours} \\ \\x=34*9 \\ \\x=\$306[/tex]

therefore

the answer is

[tex]\$306[/tex]

What is the slope intercept equation of the line below

Answers

y=(m)(x)+b
so you already have the slope=-6/5 and the intercept is 3
y=-(6/5)x+3

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

well, for the current price today, let's see, not even one day has passed, to we don't have a "t" value that's greater than 0, so since today 0years and 0days and 0seconds have passed, t =0

[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]

P (t)=400 (1.037)^t
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

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:

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

The ratio of flour to sugar is 3:2, whatever the unit is.

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

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.

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

The origin is at the point (0,0). Therefore, the y-intercept will be 0. For two points to be perpendicular, the slopes must be opposite reciprocals of each other. .5 can be seen as 1/2, so the reciprocal is 2, and it is positive, making that 2 negative. Your equation would be y = -2x.

The average national basketball association player is over 6 feet tall. the average horse jockey is shorter than 5 1/2 feet tall. this is because height provides nba players with:

Answers

Final answer:

Height is crucial for NBA players due to its impact on their performance. Z-scores help compare player heights to the average. Taller stature offers basketball players notable advantages.

Explanation:

Height is a critical factor for NBA players as it can significantly impact their performance, especially in areas like rebounding, shot-blocking, and scoring.

Z-score calculations help determine how a player's height compares to the average, with values above the mean indicating taller heights, which are advantageous in basketball.

Being taller provides NBA players with advantages in terms of reaching high for shots, blocking opponents, and having a better field of vision on the court.

If you know out of 140 pounds, 60 pounds is muscle weight, what is the muscle weight of a 200 pound male?

Answers

you can cross multiply on this and then solve.

140 / 60 = 200 / x
140x = 12000
x= 85.7142857143
x= 85.7

How do you write 314,207 in word form

Answers

three hundred fourteen thousand and 207

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].

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 multiplied by .10 = .11
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.

Round 65.85 to the nearest whole number

Answers

66.

Since the value after the decimal place is above 5, it rounds to 66 and not 65

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

Tony plans to deposit $1,000 at the end of each of the next three years. if his funds earn 5% compounded annually, how much will he have at the end of three years?

Answers

Final answer:

Tony will have a total of $3,152.50 after depositing $1,000 annually for three years in an account with 5% interest compounded annually, by calculating the future value of each deposit and summing them up.

Explanation:

When Tony deposits $1,000 at the end of each year into an account that earns 5% interest compounded annually for three years, we need to calculate the future value of an annuity. Each deposit will earn interest for a different amount of time based on when it was deposited.

The first $1,000 will earn interest for two years.

The second $1,000 will earn interest for one year.

The third $1,000 will not earn interest, as it is deposited at the end of the third year.

The formula to calculate the future value of each deposit is:

Future Value = Principal × [tex](1 + Interest rate)^{number of years}[/tex]

Calculating each separately:

First deposit: $1,000 × [tex](1 + 0.05)^2[/tex] = $1,102.50

Second deposit: $1,000 × [tex](1 + 0.05)^1[/tex] = $1,050.00

Third deposit: $1,000 × [tex](1 + 0.05)^0[/tex] = $1,000 (as it earns no interest)

Adding them together gives us the total amount Tony will have at the end of three years:

Total amount = $1,102.50 + $1,050.00 + $1,000 = $3,152.50.

Therefore, at the end of three years, Tony will have $3,152.50 in his account.

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

Answers

In all triangles, inner angles add to 180 degrees.
In an isosceles triangle, the base angles are the same and the vertex angle is different from the rest.

b= (180-40)/2
b= 140/2
b=70

Final answer: 70 degrees

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

1.
"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]

HELP? The two models shown have the same volume. Complete the equation and expression below about the volume of each figure.

Answers

36+12=48

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]

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