The inverse of the function is 1/64x², for x≥0
What is a function?
Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the first documented treatment of the concept of function. Initially, functions expressed the idealized interaction of two changing quantities. A planet's location, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity). The realms of application of the idea of a function were substantially expanded at the conclusion of the 19th century when it was defined in terms of set theory.
The inverse of the function is given by option (D) 1/64x², for x≥0
To know more about function, click on the link
https://brainly.com/question/11624077
#SPJ9
Can i change the language to English
Answer:
Yeah you can change the language
Answer:
yes of course you can do it.
When value of y varies directly with x. When y = 3 1/3 , x = 1/3. What is the value of y when x is 2/3?
when y varies directly as x , the value of y when x = 2 / 3 is 6 2 / 3
How to find the value of y using direct variation?y varies directly with x.
Therefore,
y ∝ x
Hence,
y = kx
where
k = constant of proportionalitywhen
y = 3 1 / 3 = 10 / 3
x = 1 / 3
Therefore,
y = kx
10 / 3 = 1 / 3 × k
cross multiply
3k = 30
divide both sides by 3
k = 30 / 3
k = 10
Therefore, the value of y when x = 2 / 3 can be calculated as follows:
y = 10x
y = 10 × 2 / 3
y = 20 / 3 = 6 2 / 3
learn more on direct variation here: https://brainly.com/question/12378778
#SPJ1
I need to find the cost per table, the linear equation and the cost for making 15 tables
Explanation:
Let the cost of tables be C
Let the number of tables be"x"
If the cost of making 14 tables is $1,460 and the cost of making 17 tables is $1625, this can be expressed in the coordinate form of (C, x) to have two coordinates (14, 1460) and (17, 1625)
The general linear equation will be of the form C = mx + b
Get the rate of change "m"
[tex]\begin{gathered} m=\frac{C_2-C_1}{x_2-x_1} \\ m=\frac{1625-1460}{17-14} \\ m=\frac{165}{3} \\ m=55 \end{gathered}[/tex]Get the intercept "b" of the linear equation;
[tex]\begin{gathered} 1460=55(14)+b \\ 1460=770+b \\ b=1460-770 \\ b=690 \end{gathered}[/tex]Get the required linear equation:
[tex]C(x)=55x+690[/tex]Get the cost per table. When x = 1
[tex]\begin{gathered} C(1)=55(1)+690 \\ C(1)=745 \end{gathered}[/tex]Get the cost per for making 15 tables
[tex]\begin{gathered} C(15)=55(15)+690 \\ C(15)=825+690 \\ C(15)=\$1515 \end{gathered}[/tex]Hence the cost of making 15 tables is $1515
Given AB || DC and AC is the segment bisector of BD, complete the flowchartproof below. Note that the last statement and reason have both been filled in foryou. Triangle ABE is congruent to Triangle CDE, the reason is SAS.**there are also two 3 boxes that got cut off, they are the same as the first two.**
Solution
First, we have CD and AB
- 2 + {-3 - [7 + 4 (-2+5)]}-4
Answer:
-28
Step-by-step explanation:
- 2 + {-3 - [7 + 4 (-2+5)]}-4
-2 + {-3 - [7 + 4 * 3]}-4
-2 + {-3 - 19}-4
-2 + -22 -4
-28
Hello,I need help with the following question. 9. Find the domain and range of the function shown.y 4 (-2,2)(2,2) x -5 5-4 If the graph is that of a function, what are the domain and range of the function? Select the correct choice below and fill in any answer boxes within your choice.A. The domain is . The range is . (Type your answers in interval notation.)B. The graph is not a function.A screenshot is posted below
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.
A.
From the graph, we can conclude:
The domain is:
[tex](-\infty,\infty)[/tex]The range is:
[tex](-\infty,2\rbrack[/tex]B.
A function is a specific type of relation in which each input value has one and only one output value. Therefore, this graph represents a function
Iris claims that if we have two positive rational numbers, the one with the greater numerator is the greater. How do you respond?
If the denominators were the same for both fractions, then Iris would be correct.
Example: Compare 2/7 with 5/7
Since 2 < 5, this means 2/7 < 5/7
This works because a < b leads to a/c < b/c where c is some positive integer. The inequality sign doesn't flip when you divide both sides by a positive number. In the example above, I divided both sides by 7.
--------------------------
But what if we wanted to compare 2/7 with 5/1000?
2 < 5 is true but 2/7 < 5/1000 is not true.
We can use a calculator to get a decimal value for each fraction
2/7 = 0.2857 approximately5/1000 = 0.005We see that 2/7 is actually larger than 5/1000
Unfortunately the rule Iris came up with is incorrect.
If she mentioned the denominators being the same, then she would be correct. But overall in general, the claim is not correct.
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount c
gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams
The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold.
Determine the number of bracelets made and the number of necklaces made.
The jeweler made
Submit Answer
bracelets and
necklaces.
attempt 1 out of
The jeweler made 7 bracelets and 9 necklaces .
In the question ,
it is given that
amount of gold in each bracelet is [tex]=[/tex] 6 grams
amount of gold in each necklace is [tex]=[/tex] 24 grams .
let the number of bracelets [tex]=[/tex] "b" .
let the number of necklaces [tex]=[/tex] "n" .
since the total number of necklace and bracelet is 16 .
the equation is b + n = 16
so , b = 16 - n
also given that total gold used is 258 grams .
so the equation is 6b + 24n = 258
Substituting b= 16 - n in the equation ,
we get , 6*(16 - n) + 24n = 258
96 - 6n + 24n = 258
96 + 18n = 258
18n = 258 - 96
18n = 162
n = 162/18
n = 9
and b = 16 - 9 = 7
Therefore , The jeweler made 7 bracelets and 9 necklaces .
Learn more about Equations here
https://brainly.com/question/10994155
#SPJ1
What two perfect squares does 14 fall in
between?
Answer:
3 and 4
Step-by-step explanation:
3. Choose the type of variation that relates the variables in the table.хy512.14.23.57combined variationjoint variationdirect variationinverse variation
Answer:
Inverse variation
Step-by-step explanation:
An inverse variation is when y varies inversely as x if there is some nonzero constant k such that, xy=k or y=k/x.
For Inverse variation equations, you say that y varies inversely as x as we can see in the table above.
James and lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $82,000 How much does each of them earn per year?
James and lin got married and got new jobs. Lin earns $3100 more per year than James. Together they earn $82,000 How much does each of them earn per year?
Let
x ----> amount earned by James
y ----> amount earned by Lin
we have
x+y=82,000 -----> equation A
y=x+3,100 -----> equation B
solve the system
substitute equation B in equation A
x+(x+3,100)=82,000
2x+3,100=82,000
2x=82,000-3,100
2x=78,900
x=39,450
Find the value of y
y=39,450+3,100
y=42,550
therefore
amount earned by James is $39,450amount earned by Lin is $42,550anna has 4 apples, rickelle has 302 apples, anna gave all her apples to rickelle, rickelle gave four apples to each homeless person, how many homeless people were given apples
Answer:
76 homeless people were given apples.
Step-by-step explanation:
Anna has 4 apples, all of which she gave to Rickelle.
Rickelle had 302 apples, and after Anna gave the 4 to her, she had 302 + 4 = 306 apples.
Rickelle gave four apples to each homeless person, how many homeless people were given apples?
This can be solved using a rule of three.
One person got 4 apples. How many people were given 306 apples.
1 person - 4 apples
x people - 306 apples
Applying cross multiplication
4x = 306
x = 306/4
x = 76.5
We cannot give apples to half a person, so we take only the whole number.
76 homeless people were given apples.
Paint the Walls
The height of the bedroom is 9 feet. There are 4 rectangular windows in the room that are each 30 inches wide and 36 inches high. You will not paint the windows, the floor, or the ceiling. You will paint the rest of the room, including the door. Your client likes two colors, Light-at-Dawn and Cloudy Sunrise. Both colors are only available in 1-gallon cans. Light-at-Dawn: The regular price of a 1-gallon can is $24, but it is on sale for 25% off the regular price.
This type of paint requires 2 coats. Cloudy Sunrise: The price of a 1-gallon can is $28. This type of paint only requires 1 coat. Each gallon of paint will cover an area of about 350 square feet.
Your client has stated that if the cost for using Cloudy Sunrise is no more than 5% greater than the cost for using Light-at-Dawn, then you should use Cloudy Sunrise. Which paint color should you use? Explain or show your reasoning. You may use diagrams, drawings, or equations as well as words.
You should use cloudy Sunrise because the overall cost of the cloudy sunrise color seems to be less expensive than the total cost of light at dawn color.
Light-at-Dawn: A 1-gallon bottle ordinarily costs $24, but it is presently 25% off that price. This paint requires two coats.
A gallon of Cloudy Sunrise costs $28. This type of paint just requires one coat.
Each gallon will cover 350 square feet at a time.
The price of 1 gallon of light at dawn = 24 - 25/100(24) = 18
One gallon of cloudy sunrise color costs $28.
It seems cloudy. Sunrise color is more costly before accounting for the number of square feet that each color may cover.
Both cans are supposed to cover 350 square feet.
If everything else remains constant,
Dawn color lighting would cost:
⇒ 18 / 350 = 0.0514285714, per square foot.
However, the light at dawn color needs two coats.
The total cost per square foot for the light at-dawn color would be
⇒ 2×0.0514285714 = 0.1028571429.
A cloudy sunrise costs 28/350 = 0.08 per square foot.
Because overcast dawn only requires one coat, this is the total cost per square foot.
If the second coat of paint uses the same amount of paint as the first, the overall cost of the cloudy sunrise color seems to be less expensive than the total cost of light at dawn color.
As a result, cloudy Sunrise should be used.
Learn more about the Ratio here:
brainly.com/question/1504221
#SPJ1
How do you turn 8 1/3% into a proper fraction?
Answer:
multiply 3 with 8 and then add 1
25/3
Step-by-step explanation:
EASY PLEASE ANSWER
A flight from Toronto to Miami usually takes 3 hours and 5 minutes. Unfortunately, your plane takes off 45 minutes late. As your plane approaches Miami, it needs to circle the airport for another 12 minutes. How much longer than expected has your flight taken as a percentage?
The flight has taken 30.8 % longer as compared to the usual time.
Given that:-
Usual time taken by the flight from Toronto to Miami = 3 hours 5 minutes = 185 minutes
Time by which the plane is late for take off = 45 minutes
Time taken by plane to circle the airport = 12 minutes
We have to find by how much percentage the plane has taken more time as compared to the usual time.
Extra time taken by the flight = 45 minutes + 12 minutes = 57 minutes
Percentage by which the plane has taken more time as compared to the usual time = (57/185)*100 = 30.8 %
To learn more about Percentage, here:-
https://brainly.com/question/28269290
#SPJ1
30 POINTS
The given table of values represents a linear equation. What is the slope?
x 3 4 5 6
y 1 5 9 13
Responses
2,
3,
5,
4
Answer: The slope of the given values is 4.
Step-by-step explanation:
Slope is calculated by rise/run and by looking at the first two values of both the x and y we can conclude that the slope is 4. Furthermore, we can fact-check this answer by looking at other sets of coordinates.
The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.66 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.54 inches.
The probability of women is more from its z score.
What is a Z score?
A score's connection to the mean within a group of scores is statistically measured by a Z-Score.A Z-score can show a trader whether a value is normal for a given data collection or not.For instance, a Z-score below 1.8 indicates that a business may be on the verge of bankruptcy, while a number closer to 3 indicates that a business is in good financial standing.95% of the time, a score from -1.96 & +1.96 standard deviation and variance out from the mean will be chosen at random.This is considered a statistically meaningful result if the probability of a raw score being chosen at random is less than 5%.For men:
m=69.2, s=2.66
when x=6 feet 3 inches = 75 inches
z score, z=x-m/s=75-69.2/2.66=2.18
P(z<2.18)=0.98537
For women:
m=64.7, s=2.54
when x= 5 feet 11 inches =71 inches
z score, z=x-m/s=71-64.7/2.54=2.48
P(z>2.48)=0.99343
The probability of women is more from its z score.
To learn more about z-score visit:
https://brainly.com/question/25638875
#SPJ1
a gannet flies 24 1/2 ft above sea level. it increases its elevation by 5ft. then it dives and changes its elevation by - 47 2/3. after it dives, what is the gannets elevation relative to sea level? show your work.
A gannet initial elevation is 24 1/2 ft
it increases its elevation by 5ft then the elevation is 5 + 24 1/2 = 29 1/2 ft
now it dives 47 2/3 ft
so the final elevation is,
[tex]29\frac{1}{2}-47\frac{2}{3}[/tex][tex]=\frac{59}{2}-\frac{143}{3}[/tex][tex]=\frac{177-286}{6}=\frac{-109}{6}[/tex]so its elevation below to the sea level is -109/6 or -18 1/6 ft
Describe the complement of a given event77% of a persons credit card purchases are $50 a more
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sets
[tex]77\%\text{ of a person's credit card purchases are \$50 and more}[/tex]STEP 2: find the complement
The complement will be the percentage that cannot purchase $50 and more.
Since percentages equal 100, therefore the complement will be:
[tex]100\%-77\%=23\%[/tex]Hence, the answer in % is given as 23
Use the slope formula to find the slope of a line that passes through M(3, 7) and N(3,-1). m =
the formula of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a right point from (x1,y1)
on this case the points are the same distance, so we can use any order
[tex]\begin{gathered} m=\frac{-1-7}{3-3} \\ \\ m=\frac{-8}{0} \end{gathered}[/tex]the slope cannot be calculated because the division between 0 dosnt exist, and the line is a vertical line x=3
the line is
9. On your paper, solve the inequality & answer it below. For or 2 signs,
copy and paste into your answer. ENTER ANSWER WITH NO SPACES.
Format: x<5 If the answer is no solution, write NS. If the answer is infinitely
many solutions, write IMS.
4x + 2(x -
2(x - 12) and 6(x + 1) < 10(x + 7)
Jhry
Your answer
two added to the quotient of a number x and y
(translate to mathematical expression)
pls help
The mathematical expression for given condition is [tex]\frac{x}{y} +2[/tex] .
What is Quotient?The Quotient is the answer we get after dividing one number by another. For example, in [tex]\frac{10}{5}[/tex] = 2, the result of the division is 2, so the quotient is 2. The dividend is 10 and the divisor is 5. A division problem's quotient is found by dividing the dividend by the divisor. This can be accomplished by performing repeated subtraction or long division.
It is essentially the result of the division method. In arithmetic division, four main terms are used: divisor, dividend, quotient, and remainder.
Translating the statement, two added to the quotient of a number x and y, into mathematical expression gives us,
[tex]\frac{x}{y} +2[/tex]
To know more about Quotient, visit:
https://brainly.com/question/16134410
#SPJ13
The scatter plot shows the number of years of experience
(a)
Let's use the given equation to calculate the value of y when x = 7:
[tex]\begin{gathered} y=0.92x+7.88\\ \\ y=0.92\cdot7+7.88\\ \\ y=6.44+7.88\\ \\ y=14.32 \end{gathered}[/tex]Therefore the hourly pay rate is $14.32.
(b)
Now, let's use x = 0 and calculate the value of y:
[tex]\begin{gathered} y=0.92\cdot0+7.88\\ \\ y=7.88 \end{gathered}[/tex]Therefore the hourly pay rate is $7.88.
(c)
The relation of increase in hourly pay rate by increase of years of experience is given by the slope of the line.
The slope is the constant value multiplying the variable x in the equation.
That means if the value of x increases by 1, the value of y increases by the slope value, that is, 0.92.
Therefore the predicted increase is $0.92.
in the equation c²-4=0 c is equal to
Given the following equation:
[tex]c^2-4=0[/tex]notice that we can factor the expression using the conjugate binomials:
[tex]\begin{gathered} c^2-4=0 \\ \Rightarrow(c-2)(c+2)=0 \end{gathered}[/tex]thus, the only values for c that make the equation true are c = 2 and c = -2
Graph the inequality: 24x+20y<24
The given inequality is:
24x + 20y < 24
Let x = 0
24(0) + 20y < 24
20y < 24
y < 24/20
y < 1.2
Let y = 0
24x + 20(0) < 24
24x < 24
x < 24/24
x < 1
Considering the points:
For y = 0, x < 1
For x = 0, y < 1.2
The graph of the inequality is plotted below
Write an equation for each line.9р87n3215689-9-8-2-6 -5 -3-2 -1 0-1-2-3-4-5m-6-7-8-9No
Answers:
line l: y = 4
line m: y = -2x + 4
line n: y = x - 1
line p: x = -4
Explanation:
To find the equation of a line we can use the following:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where (x1, y1) and (x2, y2) are two points in the line.
So, to find the equation for line l, we need to identify 2 points in the line. So, these points can be (1, 4) and (2, 4). So, replacing (x1, y1) by (1, 4) and (x2, y2) by (2, 4), we get that the equation of the line l is:
[tex]\begin{gathered} y-4=\frac{4-4}{2-1}(x-1) \\ y-4=\frac{0}{2}(x-1) \\ y-4=0(x-1) \\ y-4=0 \\ y=4 \end{gathered}[/tex]Therefore, the equation of line l is y = 4
In the same way, the equation of the black line m can be calculated replacing (x1, y1) by (2, 0) and (x2, y2) by (0, 4). So, the equation of the line m is:
[tex]\begin{gathered} y-0=\frac{4-0}{0-2}(x-2) \\ y=\frac{4}{-2}(x-2) \\ y=-2(x-2) \\ y=-2x+4 \end{gathered}[/tex]Therefore, the equation of line m is y = -2x + 4
So, the equation of the green line n can be calculated using the points (1, 0) and (3,2). Then, replacing (x1, y1) by (1, 0) and (x2, y2) by (3, 2), we get:
[tex]\begin{gathered} y-0=\frac{2-0}{3-1}(x-1) \\ y=\frac{2}{2}(x-1) \\ y=1(x-1) \\ y=x-1 \end{gathered}[/tex]Therefore, the equation of line n is y = x - 1
Finally, to calculate the equation of line p, we can't use the equation above, so we need to know that the vertical lines have equations with the form:
x = contact.
Since the vertical line is located at x = -4, the equation of the line p is x = -4
Mario's has $893.11 In his savings account. The bank stated that he will be charged a $17 fee if his balance is less than $400 at any point. Yesterday.
he cashed a check of $500 from his account. What was his balance after the withdrawal?
His balance was
Answer: $376.11 I believe is the answer
Step-by-step explanation:
Since the $500 made the balance go below $400 he got charged a $17 fee which made his balance go to $376.11
Find all zeroes of h(x)=2x⁴-x³-18x²+9x
When you have a polynomial with no independent term you can start by factorizing the polynomial, as follows:
[tex]h(x)=2x^4-x^3-18x^2+9x[/tex]The common factor is x, then:
[tex]h(x)=x(2x^3-x^2-18x+9)[/tex]Now you have a third-degree polynomial inside the ( ), let's called it j(x):
[tex]j(x)=2x^3-x^2-18x+9[/tex]You need to factorize this polynomial, then find all the numbers that divide the independent term 9.
These numbers are:
[tex]1,-1,3,-3[/tex]Let's probe if any of these numbers makes j(x)=0:
[tex]\begin{gathered} j(1)=2(1)^3-(1)^2-18(1)+9 \\ j(1)=2-1-18+9_{} \\ j(1)=-8 \end{gathered}[/tex]Then 1 is not a root, let's try -1:
[tex]\begin{gathered} j(-1)=2(-1)^3-(-1)^2-18(-1)+9 \\ j(-1)=-2-1+18+9 \\ j(-1)=24 \end{gathered}[/tex]Then -1 is not a root, let's try 3:
[tex]\begin{gathered} j(3)=2(3)^3-(3)^2-18(3)+9 \\ j(3)=2\cdot27-9-18\cdot3+9 \\ j(3)=54-9-54+9 \\ j(3)=0 \end{gathered}[/tex]Then 3 is a root and you can apply synthetic division to find the others:
The new polynomial is:
[tex]2x^2+5x-3[/tex]Now you can factorize it as follows:
[tex]2x^2+5x-3=(2x-1)(x+3)[/tex]And finally, your 4th-grade polynomial can be written as:
[tex]h(x)=x(x-3)(2x-1)(x+3)[/tex]Thus, the zeros are at:
[tex]\begin{gathered} x=0 \\ (x-3)=0\text{ then x=3} \\ (2x-1)=0\text{ then x=1/2} \\ (x+3)=0\text{ then x=-3} \end{gathered}[/tex]The answer is 0, 3, 1/2 and -3
A tennis ball has a diameter of 2.5”. Find the total surface area of the smallest cylindrical can that can hold three tennis balls vertically (including the top and the bottom) around answer to the nearest hundredth. No pi in your answer.
For the cylinder to be able to contain the balls it has to have a radius equals to the radius of the ball, then the radius of the cylinder must be at least 1.25 inches. The height of the cylinder is 3 times the 'height' of each sphere, which is equal to the diameter of the sphere, the diamenter of a sphere is 2 times its radius then the height of the cylinder is h=6r = 7.5 inches.
Finally we apply the formula for the surface area of a cylinder:
[tex]\begin{gathered} A=\text{ 2}\pi rh\text{ + 2}\pi r^2=\text{ 2}\pi\text{ (1.25 in }\cdot7.5in+(1.25in)^2)=68.72in^2 \\ \end{gathered}[/tex]Got stuck, just need help solving the the measure of arc LP.
mLP = 17°
Explanation:The perpendicular bisectors from the center to the vertical lines are equal.
Therefore:
mLM = mNP
8x - 56 = 5x + 22
8x - 5x = 22 + 56
3x = 78
x = 78/3
x = 26
Note that:
mLM + mMN + mNP + mLP = 360° (sum of angles at a point)
(8x - 56) + 39 + (5x + 22) + mLP = 360
8x + 5x - 56 + 39 + 22 = 360
13x + 5 + mLP = 360
mLP = 360 - 5 - 13x
mLP = 355 - 13x
mLP = 355 - 13(26)
mLP = 355 - 338
mLP = 17°
