Answer:
[tex]f^{-1}(x) = 6(4-x) = 24-6x[/tex]
Step-by-step explanation:
Let [tex]y=f(x)[/tex] and swap x and y:
[tex]x = 4 - \frac{y}{6}[/tex]
Then, rearranging for y:
[tex]x+\frac{y}{6} = 4[/tex]
[tex]\frac{y}{6}= 4-x[/tex]
[tex]y= 6(4-x) = 24-6x[/tex]
Final answer:
Explaining the inverse function of a given function.
Explanation:
Inverse function of f(x) = 4 - x/6:
Replace f(x) with y: y = 4 - x/6.
Swap x and y: x = 4 - y/6.
Solve for y: y = 24 - 6x.
What is the distance ?
The solution is you need to subtract the y axis and x axis
Last year Jo paid £245 for her car insurance. This year she has to pay £883 for her car insurance. Work out the percentage increase in the cost of her car insurance.
Answer:
260%
Step-by-step explanation:
To solve how much the percentage increase cost of Jo's car insurance is, we first need to list down our variables.
1st year = £245
2nd year = £883
First off, we need to find the difference of the two.
Increase = £883 - £245
Increase = £638
Now to find the percentage increase, we take our increase and divide it by our 1st year's payment and multiply it by 100.
Percentage increase = [tex]\dfrac{638}{245}*100[/tex]
Percentage increase = [tex]2.60*100[/tex]
Percentage increase = 260%
So the percentage increase of last years payment to this years payment is 260%.
Jimmy pays $2.52 for each gallon of gas. Which table best represents the relationship between g, the number of gallons purchased, and m, the amount he pays for gas?
The table that best represents the relationship between the number of gallons purchased, g, and the amount paid for gas, m, will list m as multiples of $2.52 as per the linear relationship g: $2.52 * g.
Jimmy pays $2.52 for each gallon of gas. To find the best table representing the relationship between g, the number of gallons purchased, and m, the amount he pays for gas, we need to create a table where each entry form is the product of g and the price per gallon, which is $2.52.
For each gallon g, the total cost m would be:
For 1 gallon: m = 1 * $2.52 = $2.52
For 2 gallons: m = 2 * $2.52 = $5.04
For 3 gallons: m = 3 * $2.52 = $7.56
...and so on.
This pattern will continue since the relationship is linear, and the table representing it will list the total cost m corresponding to the number of gallons g based on this constant rate of $2.52 per gallon.
What is the wavelength of a sound wave that has a speed of 250 m/s and a frequency of 400 Hz?
I will give brainest if you help me asap! 15 POINTS!!
0.50 m *100 Hz
= 50m/s I really hope this helps!
Rugs sell for $8 per square foot Beth bought a 9-foot-long rectangular rug for $432 how wide was the rug
Can someone help me with these 3 questions? I am really stuck on them. Thank you so much. I'm offering 80 brainly points.
Answer:
not sure about the answers to all the other one but the answer to the 3rd question is y=1
3x or y=1/3x
Miss Penny inherits £390. She decides to save some of the money and spend the rest.
The ratio of savings to spending money is 5 : 8
How much does she save and how much does she spend?
Answer:
saving=150
spending=240
Step-by-step explanation:
390/13=30
savings=30*5
spending=30*8
Answer:
£150 saved; £240 spent.
Step-by-step explanation:
If the ratio of savings to spending is 5:8, we find the fractions representing the amount saved and the amount spent by adding up 5 and 8 and then forming fractions:
savings: 5/13
spending: 8/13
(5/13) of £390 is £150; this is the amount saved.
(8/13) of £390 is £240; this is the amount spent.
Find the area of the circle? Use 3.14 for pi.
Answer:
A = 50.24 mm
Step-by-step explanation:
A = Pi*r^2
A = Pi*(4)^2
A = 16*Pi
A = 50.24 mm
Best regards
Answer:
50.24
Step-by-step explanation:
area of circle: (pi)r^2
r is the radius
given: r = 4
pi = 3.14
3.14(4)^2
3.14*16
50.24
the value of y varies directly with x, and when x = 1/4 , y = 25. What is the value of y when x is 2 1/3 need help ASAP
Answer:
[tex]y=233\frac{1}{3}[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem we have
For [tex]x=1/4, y=25[/tex]
Find the value of k (constant of proportionality)
[tex]y/x=k[/tex] -----> [tex]k=25/(1/4)=100[/tex]
The linear equation is
[tex]y=100x[/tex]
Find the value of y when the value of [tex]x=2\frac{1}{3}[/tex]
substitute the value of x in the equation but first convert to an improper fraction
[tex]x=2\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}[/tex]
[tex]y=100(\frac{7}{3})=\frac{700}{3}[/tex]
convert the result in mixed number
[tex]\frac{700}{3}=\frac{699}{3}+\frac{1}{3}=233\frac{1}{3}[/tex]
A photograph measures 10 in. wide by 18 in. long. The picture is reduced so that the length is 6 in.
What is the new width?
a: 13 in
b: 313 in
c: 1045 in
d: 30 in
explain your answer please
Answer:
Step-by-step explanation:
The length has been reduced to 6 inches from 18 inches.
That means the length has been reduced to 6/18 = 1/3 of its original size.
So the width must be reduced to 1/3 * 10 which is roughly 3.333 inches.
It doesn't look like any of them are right. i don't know how to make it right from the answers given.
The red line below is perpendicular to which of the following
Answer:
The y axis
Step-by-step explanation:
Perpendicular means for a line to create a 90 degree angle, like it does on the y axis.
Hope this helps!
How long does it take for a deposit of $1400 to double at 2% compounded continuously?
Answer:
34.66 yr
Step-by-step explanation:
The formula for interest compounded continuously is
[tex]A = Pe^{rt}[/tex]
Data:
P = $1400
r = 2 % = 0.02
Calculations:
(a) Calculate A
A = 2 × 1400 = $2800
(b) Calculate t
[tex]2800 = 1400e^{0.02t}[/tex]
[tex]2 = e^{0.02t}[/tex] Divided each side by 1400
ln2 = 0.02t Took the ln of each side
t = ln2/0.02 Divided each side by 0.02
t = 34.66 yr
It will take 34.66 yr for the investment to double at 2 % interest compounded continuously.
Check:
2800 = 1400e^{0.02×34.66}
2800 = 1400e^{0.6931}
2800 = 1400 × 2
2800 = 2800
What is the solution of 3 sqrt x+8=-4?
Answer:
[tex]x=-72[/tex]
Step-by-step explanation:
The given equation is [tex]\sqrt[3]{x+8}=-4[/tex].
We cube both sides of this equation to obtain;
[tex](\sqrt[3]{x+8})^3=(-4)^3[/tex].
This implies that;
[tex](x+8)=-64[/tex]
We group similar terms to obtain;
[tex]x=-64-8[/tex]
We simplify the right hand side of the equation to obtain;
[tex]x=-72[/tex]
Therefore x=-72 is the solution of the given equation.
The equation 3 √x + 8 = -4 has no solution. The square root term, when isolated, shows a contradiction since the square root of a non-negative number multiplied by a positive constant cannot be negative.
Explanation:The solution to the equation 3 √x + 8 = -4 involves finding the value of x for which the equation holds true. Given that √4 can be both 2 and -2, we explore the possibility of squaring both sides of an equation to solve for x. However, in this case, since the square root of a number cannot be negative and the original equation involves a square root on the left side, this hints at no solution being possible because the left side (involving the square root) will always be non-negative, and cannot equal a negative number.
Nevertheless, let's attempt to formally solve the equation. Isolating the square root term by subtracting 8 from both sides results in 3 √x = -12. At this point, we encounter a contradiction: the left side represents a non-negative value (since it's 3 times the square root of x), but the right side is negative. This confirms there are no real solutions to the equation because the square root of a non-negative number (x) cannot result in a negative value when multiplied by a positive constant (3).
Jonas has two jobs last year and he received two W-2 forms on the first W-2 form the figure in box 1 was $19,328.98 while on second W-2 form the figure in box 1 was $7174.86 what was Jonas gross income from the two jobs last year?
Answer:
Gross income of Jonas from the two jobs is $ 26,503.84
Step-by-step explanation:
W-2 form is used in USA by to employees to show the money earned by them.
The gross income of Jonas will be the sum of two values.
Gross income= $19,328.98 + $7174.86
= $ 26,503.84
Answer:
$26,503.84
Step-by-step explanation:
Jessica has 48 coins, some of them are nickels and some are dimes. How many of each does she have if she has $3.25 total?
Nickel = 0.05
Dime = 0.10
XNickels + YDimes = 3.25
0.05X + 0.1Y = 3.25
You could do this using trial and error.
You know the maximum amount of dimes you could have is 32. Because 32 * 0.1 = 3.20. If you had 33 dimes, you'd go over the limit.
You also know you need to have 48 coins. If you have 32 dimes and 1 nickel, you will not have 48 coins.
You can try any number below 32. I will try 16 because it's half of 32.
16 * 0.1 = 1.60
48 - 16 = 32 coins left
32 * 0.05 = 1.60
1.60 + 1.60 = 3.20
We're a nickel off, therefore we need to remove a nickel and add a dime.
17 * 0.1 = 1.70
48 - 17 = 31
31 * 0.05 = 1.55
1.70 + 1.55 = 3.25
Jessica will have 17 Dimes and 31 Nickels.Jessica has about 31 nickels, 17 dimes which is worth $3.25
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of nickels and y represent the number of dimes.
x + y = 48 (1)
Also:
0.05x + 0.1y = 3.25 (2)
x = 31, y = 17
Jessica has about 31 nickels, 17 dimes which is worth $3.25
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Lisa has 2 red dresses, 3 green dresses and x blue dresses hanging in her closet. If lisa chooses one dress at random, the probability that lisa will choose a red dress is 25%. How many blue dresses does lisa have?
Lisa has a total of 8 dresses in her closet. There are 2 red dresses, 3 green dresses, and the remaining 3 are blue dresses.
Explanation:The subject of the question is probability in Mathematics. In the problem, Lisa has a total of 2 red dresses and 3 green dresses. The quantity of blue dresses is represented by 'x'. It is stated that the probability of choosing a red dress is 25%. Each dress in her closet is an outcome for this probability calculation.
So, in total, she has 2(red dresses) + 3(green dresses) + x(blue dresses) = 100% of the dresses or total outcomes. Since the probability of picking a red dress is 25%, then 2 (red dresses) are 25% of the total outcomes.
To work out the total number of outcomes (total dresses), we calculate 100% ÷ 25% = 4, and then multiply this by the number of red dresses (which is 2), giving us 4*2 = 8 dresses in total.
As we know there are 2 red dresses and 3 green dresses, that leaves 8 (total dresses) - 2 (red) -3 (green) = 3 blue dresses. Thus, Lisa has three blue dresses in her closet.
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Lisa has 6 blue dresses.
Explanation:To find the number of blue dresses Lisa has, we need to set up an equation using the given information.
Lisa has 2 red dresses, 3 green dresses, and x blue dresses. The total number of dresses is 2 + 3 + x = 5 + x.
The probability of choosing a red dress is 25%, which can be written as 0.25.
This means that the number of red dresses divided by the total number of dresses equals 0.25. So, we have 2 / (5 + x) = 0.25.
Solving this equation for x, we find that Lisa has 6 blue dresses.
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Smart growth is an urban planning theory that promotes the development of suburbs surrounding major city centers.
True or False
the answer is false, i hope this helps
Answer:
The given statement is false.
Step-by-step explanation:
Smart growth is an urban planning theory that promotes the development of suburbs surrounding major city centers.
Rather smart growth is defined as a well planned economic development and community development with an aim to curb urban fall out and reduce the worsening environmental conditions.
Another term for measurement data is
A) quantitative data.
B) categorical data.
C) qualitative data.
Eliminate
D) bivariate data.
Measurement data refers to numerical information gathered by quantifying objects or events, known as quantitative data. It contrasts with qualitative, or categorical data, which describes non-numeric attributes. Quantitative data can be further classified into discrete or continuous based on the nature of the measurement.
Explanation:The term measurement data refers to data that quantifies objects or events. This type of data can be classified as either quantitative discrete or quantitative continuous, depending on whether the data can take on only integer values or any values within a continuous range. Therefore, another term for measurement data is A) quantitative data. Quantitative data is always expressed in numbers and includes measurements such as length, mass, and time.
For example, measuring the height of a plant in centimeters yields quantitative data because it provides a numerical measurement of the plant's height. Similarly, recording the number of books a person reads in a month gives quantitative data because it counts the books. This contrasts with qualitative or categorical data, which describes attributes or characteristics that cannot be measured numerically, such as the colors of houses or types of pets.
In summary, measurement data is best described as quantitative data because it involves numerical measurements or counts, making it essential for mathematical analysis and supporting scientific findings.
which of the following sets does the number 3.14 belong to ? -whole number , integers, rational numbers , irrational numbers, real numbers, non of the above . Select all that apply .
The number 3.14 is a rational number and since all rational numbers are real numbers, it is a real number too.
The set of numbers that 3.14 belongs to is a rational number and a real number.
A rational number simply means a number that has a whole number and a quotient. In this case, such a number has a whole number and decimal fractions.
Therefore, since the number given is 3.14, this implies that the number is a rational number. Also, it should be noted that a rational number is also a real number.
Therefore, 3.14 is a rational number and a real number
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Apply the definition of subtraction and properties of operations to find the result.
1/8-3/7-1/8
Final answer:
To find the result of 1/8 - 3/7 - 1/8, we need to find a common denominator for the fractions and then subtract them.
Explanation:
To find the result of 1/8 - 3/7 - 1/8, we need to apply the definition of subtraction and properties of operations. First, let's find a common denominator for the fractions. The common denominator for 8 and 7 is 56. Multiply the numerator and denominator of 1/8 by 7 to get 7/56. Multiply the numerator and denominator of 3/7 by 8 to get 24/56. Now subtract the fractions: (7/56) - (24/56) = -17/56. Finally, subtract 1/8 from -17/56. Multiply the numerator and denominator of 1/8 by 7 to get 7/56. Subtract the fractions: (-17/56) - (7/56) = -24/56.
What is the y intercept of the function f(x) = -2/3x + 1/3
Answer:
(0, 1/3)
Step-by-step explanation:
You find the y-intercept when the x value is 0, so plug in 0 for x and simplify
f(x) = -(2/9)(0) + 1/3
f(x) = 1/3
The y-intercept is at the point (0, 1/3)
Austin reads 8 books. He reads 4 more books than Emily. How many books does Emily read?
Answer: 4
Step-by-step explanation: Austin reads 8 he reads 4 more. 4+4=8
The elevations of three cities in the Netherlands are shown below. Which comparison is true?
Answer:
The answer is the first choice "A"
Step-by-step explanation:
I have done this test
The comparison which is true is Amsterdam is the same distance from sea level as Drachten.
How to find which comparison is true?Here negative sign indicates the direction.So, we can see the Amsterdam is at same distance from sea level as Drachten. The negative sign indicates that Amsterdam is 2 m below the sea level.
So, option A is correct.
Drachten is 2 m higher then the sea level and is clearly higher than Rotterdam which is 4 m below the sea level.So, option B is incorrect.
The distance of Rotterdam from sea level is 4 m whereas that of Drachten is 2 m. So the distance of Rotterdam from sea level is greater than that of Drachten.So option C is incorrect.
Rotterdam which is 4 m below the sea level and is clearly lower than Amsterdam which is 2 m below the sea level.So option D is incorrect.
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Plz help me!!!!!!!!!!!
Answer: c) imaginary
Step-by-step explanation:
(√5) is irrational but (√-1 )is not a valid number, therefore, (√-5) is imaginary.
area of 2 triangles area of 3 rectangles surface area= total area of triangles and rectangles. the surface area
What do you mean? I dont understand.
Answer:
52.8cm
Step-by-step explanation:
Add the area of all the faces together and you get 52.8
The prices for a video game at 5 different stores are 39.99, 44.99, 29.99, 35.99, and 31.99. What is the mode(s) of the data
The mode is the value that appears most frequently in a set of data. In the provided data ($39.99, $44.99, $29.99, $35.99, and $31.99), each value appears only once, so this set has no mode.
The mode of a set of data is the value that appears most frequently. Taking into account the prices for a video game at five different stores, which are
$39.99, $44.99, $29.99, $35.99, and $31.99, we need to determine if any of these values appear more than once.
Since each price appears only once, there is no repeating value, therefore this set of data has no mode.
To understand the concept better, if we had a set of prices in which at least one price appears more than once, that repeating price would be considered the mode. For example, if we had the prices $29.99, $29.99, $35.99, $39.99, and $44.99, then the mode would be $29.99 because it appears twice.
Given: circle k(O), m AM=125°, m EF=31°, m∠MAF=75°. Find: m∠AME
Answer:
58°
Step-by-step explanation:
If m AM=125°, then m∠AOM=125°.
If m∠MAF=75°, then m∠MOF=150° (because central angle MOF subtends on the same arc as inscribed angle MAF).
Thus,
m∠FOA=360°-150°-125°=85°.
If mEF=31°, then m∠EOF=31° (as central angle subtended on the arc EF).
Hence,
m∠EOA=m∠EOF+m∠FOA=31°+85°=116°.
Angle EOA is central angle subtended on arc EA, angle AME is inscribed angle subtended on arc AE, thus
m∠AME=1/2m∠EOA=58°.
1.) In a class of 45 students , 80% received A’s on a Math test . How many students received an A?
2.) Mary spent 15 dollars. If this was 20% of her earnings, how much money did she earn ?
Step-by-step explanation:
1) 45 times 0.8 (which is equivalent to 80 percent) is 36 students.
2) 15 divided by 0.2 is 75, so she earned 75 dollars
What features do all right triangles have in common
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is that there is a right angle(90 degrees) and also there are three sides.
Explanation: Since all right triangles have a right angle, and also is a triangle, they have three sides and one is 90 degrees.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
The common features of all the right angled triangles are the highest angle is the right angle (90°), Pythagorean theorem is applicable.
What is a triangle?Any figure bounded by 3 sides and the sum of all the internal angles is 180° is called a angled triangle.
What is a right angled triangle?Any triangle whose one angle is 90° is called a right angled triangle.
How to find what features do all right triangles have in common?The common features of all the right angled triangles are discussed below:
All the right angled triangles have one angle 90°.The side opposite to the right angle( 90° ) is the longest and is called the hypotenuse.Pythagorean Theorem is applicable which says that squares of the length of the hypotenuse is equal to the sum of the squares of the lengths of the base and perpendicular.These are the common features.
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The density of a fish tank is 0.5 fish per feet3. There are 30 fish in the tank. What is the volume of the tank
Answer:
60 cubic feet.
Step-by-step explanation:
The fish are 0.5 per cubic foot. This means 1 fish occupies 2 cubic feet. So if there are 30 fishes then there must be 60 cubic feet.
Answer:Instead of dividing the diameter by two to get the radius, the coworker multiplied the diameter by two, getting a value of 340 feet for the radius. Here’s the incorrect calculation:
volume of a cylinder ≈ 3.14 × (radius)2 × height
= 3.14 × (340 ft)2 × (60 ft)
= 3.14 × (115,600 ft2) × (60 ft)
= 21,779,040 ft3
Step-by-step explanation: