Answer:
9
Step-by-step explanation:
3 times the sum of 4 and 2 = 3*(4+2)
= 3 * 6
= 18
18 - 9 = 9
Find the inverse of the function f(x) = 2x² - 3x NO ABSURD ANSWERS IF YOU DON't WANT YOURSELVES TO GET REPORTED!
Answer:
[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-3x[/tex]
[tex]f(x)=y[/tex]
[tex]y=2x^2-3x[/tex]
Switch variables.
[tex]x=2y^2-3y[/tex]
Solve for y.
Multiply both sides by 8.
[tex]8x=16y^2-24y[/tex]
Add 9 on both sides.
[tex]8x+9=16y^2-24y+9[/tex]
Take the square root on both sides.
[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]
Add 3 on both sides.
[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]
Divide both sides by 4.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]
Simplify.
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]
[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]
Inverse y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]
Answer:
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Step-by-step explanation:
[tex] f^{-1}(x) = 2x^2 - 3x [/tex]
Change function notation to y.
[tex] y = 2x^2 - 3x [/tex]
Switch x and y.
[tex] x = 2y^2 - 3y [/tex]
Solve for y.
[tex] 2y^2 - 3y = x [/tex]
Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.
[tex] y^2 - \dfrac{3}{2}y = \dfrac{x}{2} [/tex]
1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.
Add 9/16 to both sides to complete the square.
[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]
Find common denominator on right side.
[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]
If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]
[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]
Simplify.
[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Back to function notation.
[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that a) the bit string has exactly two 1s; b) the bit string begins and ends with 0; c) the bit string has the sum of its digits equal to seven; d) the bit string has more 0s than 1s; e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
45/10241/415/128193/5129/512Step-by-step explanation:
There are 2^10 = 1024 bit strings of length 10.
a) There are 10C2 = 45 ways to have exactly two 1-bits in 10 bits
p(2 1-bits) = 45/1024
__
b) Of the four (4) possibilities for beginning and ending bits (00, 01, 11, 10), exactly one (1) of those is 00.
p(b0=0 & b9=0) = 1/4
__
c) There are 10C7 = 120 ways to have seven 1-bits in the bit string.
p(7 1-bits) = 120/1024 = 15/128
__
d) ∑10Ck {for k=0 to 4} = 386 is the total of the number of ways to have 0, 1, 2, 3, or 4 1-bits in the string. If there are more than that, there won't be more 0-bits than 1-bits
p(more 0 bits) = 386/1024 = 193/512
__
e) The string will have two 1-bits if it starts with 1 and there is a single 1-bit among the other 9 bits. There are 9 ways that can happen, among the 512 ways to have 9 remaining bits.
p(2 1-bits | first is a 1-bit) = 9/512
from the graph,determine the value of x when y= 0
Answer:
According to the graph, when y = 0, x = -0.4 and 2.3 .
Answer:
Step-by-step explanation:
when y=0,curve cuts x-axis and it cuts x-axis where x=-0.4
and x=2.3
In solving the formula A = (1/2)bh, in solving for h, you could first multiply both side by 1/2. True or False?
Answer:
False.
Step-by-step explanation:
If you multiply both sides by 1/2, you will get 1/4 at the right side.
So the correct way, to solve h, you have to divide both sides by 1/2.
Drag the tiles to the correct boxes to complete the pairs.
This table gives Information about vehicles sold at a dealership in a month.
Gasoline Diesel
18
5
Hatchback
Sedan
15
12
SUV
3
7
Analyze this data, and match each percentage to the description It represents. Round your answers to the nearest whole number.
30%
44%
21%
8%
42%
78%
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
tum. All rights reserved.
Answer:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21 %
Step-by-step explanation:
The given table represents the following:
Hatchbacks that run on Gasoline = 18
Hatchbacks that run on Diesel = 5
Total number of hatchbacks = 23
Sedan that run on Gasoline = 15
Sedans that run on Diesel = 12
Total number of sedans = 27
SUVs that run on Gasoline = 3
SUVs that run on Diesel = 7
Total number of SUVs = 23
Total number of gasoline vehicles = 36
Total number of Diesel vehicles = 24
To find:
the percentage of hatchbacks that run on gasoline
the percentage of diesel vehicles that are hatchbacks
Solution:
[tex]\text{Percentage of hatchbacks that run on gasoline = } \dfrac{\text{Number of hatchbacks on gasoline}}{\text{Total number of hatchbacks}}\times 100\\\Rightarrow \text{Percentage of hatchbacks that run on gasoline = } \dfrac{18}{23}\times 100 \approx 78\%[/tex]
[tex]\text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{\text{Number of hatchbacks that run on diesel}}{\text{Total number of diesel vehicles}}\times 100\\\Rightarrow \text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{5}{24}\times 100 \approx 21\%[/tex]
So, the answer is:
The percentage of hatchbacks that run on gasoline: 78%
The percentage of diesel vehicles that are hatchbacks: 21%
Answer:
I used a calculator and this is what can up with
Step-by-step explanation:
Real solutions pleases
Answer:
c
Step-by-step explanation:
Lea’s car travels an average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mike trip, what was the approximate cost of gas in dollars per gallon?
Answer:
$3.60 per gallon.
Step-by-step explanation:
First, we look for the gallon of gas that will be used for a 172.5 mile trip:
30 miles = 1 gallon of gas
172.5 miles = ?
172.5 ÷ 30 = 5.75 gallons of gas
Let's find the approximate cost of gas in dollars per gallon:
5.75 gallons of gas = $20.70
1 gallon of gas = $?
20.70 ÷ 5.75 = $3.60
The answer is $3.60 per gallon.
What constant acceleration is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds? (Round your answer to two decimal places.) ft/s2
Answer: 12.22 ft/sec²
Step-by-step explanation:
An increase from 26 to 51 is an increase of 51 - 26 = 25 mi/hr
We need to do this in 3 seconds --> 25 mi/hr ÷ 3 sec
Note the following conversion: 1 mile = 5280 ft
[tex]\dfrac{25\ miles}{hr}\times \dfrac{1}{3\ sec}\times \dfrac{5280\ ft}{1\ mile}\times \dfrac{1\ hr}{60\ min}\times \dfrac{1\ min}{60\ sec} \\\\\\=\dfrac{5280(25)\ ft}{3(60)(60)\ sec^2}\\\\\\=\large\boxed{12.22\ ft\slash sec^2}[/tex]
The constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
What is acceleration?Acceleration can be defined as the rate of change of the velocity of an object with respect to time.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
As the velocity that is given to us is 51 miles/hour and 26 miles/hour, therefore, we first need to convert the units of the velocity in order to get the acceleration in ft/s².
[tex]\rm Final\ velocity= 51\ mi/hr = \dfrac{51\times 5280}{3600} = 74.8\ m\s^2[/tex]
[tex]\rm Initial\ velocity= 26\ mi/hr = \dfrac{26\times 5280}{3600} = 38.134\ m\s^2[/tex]
Now, acceleration is written as the ratio of the difference between the velocity and the time needed to increase or decrease the velocity of the object.
[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]
Substituting the values we will get,
[tex]\rm Acceleration = \dfrac{74.8-38.134}{3} = 12.22\ \ ft/s^2[/tex]
Hence, the constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².
Learn more about Acceleration:
https://brainly.com/question/12134554
2 concentric circles have radii 2cm and 3cm respectively, calculate the ratio of their areas
Answer:For the first circle the radius is 2cm and for the second circle the radius is 3cm,by taking the ratio of their areas:
πr^2:πR^2
π cancels out and we are left with only r^2:R^2
r=2cm and R=3cm
Therefore r^2:R^2=2^2:3^2
=4:9
The answer is 4:9
Step-by-step explanation:
Im needing an answer for this please!
Answer:
x=46 degrees
Step-by-step explanation:
first find the size of the other angles(let call z and y)
the sum of a straight angle is 180:
180=130+z
z=180-130=50
y=180-96=84
sum of angles of triangle =180
x+y+z=180
50+84+x=180
x=180-134=46 degrees
Answer:
46°
Step-by-step explanation:
Angle of a line = 180°
To find the other side of 130°
The other side = 180° - 130° = 50°
To find the other side of 96°
The other side = 180° - 96° = 84°
To find x°
Total angle of a triangle = 180°
180° = x° + 50° + 84°
x° = 180° - 134°
x° = 46°
To reach a window, you need a ladder to go up 16 feet on the side of your house. You
set the bottom of the ladder 4 feet from your house. Which choice is closest to the
shortest ladder you can use to reach the window?
possible solutions:
1. 20 feet 2. 4.5 feet
3. 272 feet 4. 16.5 feet
Answer:
4. 16.5
Step-by-step explanation:
You solve for the hypotenuse
a^2+b^2=c^2
16^2+4^2=c^2
256+16= the square root of 272
16.5
What is the product of 7/16 and -6/13 I will make you the brainlest
Answer:
[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]
Step-by-step explanation:
[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.
Then do 16*13=208.
Simplify by dividing both by 2.
You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].
Your final simplified answer is [tex]\frac{-21}{104}[/tex]
I hope this helps!
A staining solution bottle in a medical laboratory contains 30 ounces (oz). A blood staining test requires 3/4 oz of solution. A tissue staining test requires 1/2 oz of solution. If four blood tests and five tissue tests are performed, how many oz of solution are left in the bottle
Answer:
24.5 oz
Step-by-step explanation:
First lets calculate the blood tests, 3/4 oz of solution.
3/4 multiplied by four tests= 3. (.75*4=3)
So 3 oz of Blood Tests were performed, now lets calculate the amount of tissue staining tests for performed.
1/2 multiplied by five tests= 5/2 or 2.5 oz of tests. (.5*5=2.5)
3oz+2.5=5.5oz
Now let's subtract that amount by 30.
30-5.5=24.5
MATH HELP ME ASAP PLS!!!
Answer: D) Front - $35.00 Back - $22.50
Step-by-step explanation:
b+12.5=f
600f+450b=31,125
Substitute
600(b+12.5)+450b=31,125
Distribute
600b+7500+450b=31,125
Combine like terms
1050b+7500=31125
Subtract 7500
1050b=23625
Divide by 1050
b=22.5
Thus, the back tickets cost $22.50.
Hope it helps <3
Find the area of a circle with a radius of 8. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answer:
64π units²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
= π × 8²
= 64π units²
A sphere and a cylinder have the same radius and height. The volume of the cylinder is 50 feet cubed. A cylinder with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere?
Answer:
Volume of the sphere is 66.67r/h
Step-by-step explanation:
Hello,
Volume of a sphere = ⁴/₃πr³
Volume of a cylinder = πr²h
The volume of the cylinder = 50ft³
But the cylinder and sphere both have the same radius and height
Volume of a cylinder = πr²h
50 = πr²h
Make r² the subject of formula
r² = 50/πh
Volume of a sphere = ⁴/₃πr³
Put r² into the volume of a sphere
Volume of a sphere = ⁴/₃π(50/πh)r
Volume of a sphere = ⁴/₃ × 50r/h
Volume of a sphere = ²⁰⁰/₃ r/h
Volume of a sphere = 66.67r/h
The volume of the sphere is 66.67r/h
8/15 simplify the quotient to get ?
Answer:
0.5333333333 or 0.53 when simplified.
Step-by-step explanation:
8/15 is simply 8÷15
15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3
I hope this helps.
Jose rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 91 cents for each mile driven. Jose had to pay $218.28 when he returned the truck. For how many miles did he drive the truck?
Answer:
219
Step-by-step explanation:
do total minus base fee which is
218.28-18.99=199.29
and than
199.29(which is money paid on miles) divided by 91. which is 219
2 and 2/5 ÷ (− 1/4 ) = ?
Answer:
-9.6
Step-by-step explanation:
[tex]2\frac{2}{5} =2.40\\-\frac{1}{4} =-0.25[/tex]
If change them into decimals it looks like that.
Then all you have to do is use standard calculator to find the answer.
[tex]\frac{2.40 }{-0.25} =-9.6[/tex]
Answer:9 and 3/8
Step-by-step explanation:
you have to make 2 and 2/5 into an improper fraction then make the -1/4 into a -4/1 then multiply across to make 48/5 then you have to reduce down to 8 and 8/5. but that cant happen so you reduce again and get 9 and 3/8.
first correct answer gets best marks and make it short not super-long please and hurry
Answer:
b > 3 2/15
Step-by-step explanation:
To make it easier to solve convert the mixed fraction to a fraction.
2 3/5 = 13/5
Now, multiply the fraction by 3/3 so that you will have a common denominator.
13/5 × 3/3 = 39/15
Now you solve for b.
39/15 < b - 8/15
39/15 + 8/15 < (b - 8/15) + 8/15
47/15 < b
b > 47/15
Convert the fraction to a mixed fraction to find the answer
47/15 = 3 2/15
b > 3 2/15
Which system has no solution?
Check all that appy.
Please help WILL GET REPORTED IF ANSWERS NONSENSE FOR POINTS I am really struggling and need help It is a lot of points so try answering as much
Answer:
301.59
Step-by-step explanation:
your answer was almost right you just forgot to multiply by 9
Maxim has been offered positions by two car dealers. The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold. The second pays a salary of $20,000 plus a commission of $500 for each car sold. How many cars would need to be sold to make the total pay the same?
Answer:
20 cars
Step-by-step explanation:
Solve for x!
10000+1000x(the first company)=20000+500x (the second company)
-10000 -10000
1000x=10000+500x
-500x -500x
500x=10000
divide by 500 on both sides,
x=20
Check!
First company: 10000+1000(20)=10000+20000=30000
Second company: 20000+500(20)=20000+10000=30000!
30000=30000
Hope this helped!
Number of cars would need to be sold to make the total pay same is 20
What is Equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
What is Expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context
Given,
The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold
therefore the expression is
10000+1000x
where x is the number of car sold
The second pays a salary of $20,000 plus a commission of $500 for each car sold
Then the expression will be
20000+500x
How many cars would need to be sold to make the total pay the same is
10000+1000x=20000+500x
1000x-500x=20000-10000
500x=10000
x=20
Hence, the number of cars would need to be sold to make the total pay the same is 20
Learn more about Equation and Expression here
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Complete the sentence by selecting the correct word from each drop-down menu. The middle value of a data set that is ordered from least to greatest is called the ____ . This value is a measure of ____. The options for the first ____ are mean/median/range The options for the second ____ are center/range/variation
Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.
Step-by-step explanation:
There are three measures of the center: 1) Mean 2) Median 3) Mode
Mean : Average value of the data
Mode = The most repeated value.
Median is the middlemost value in a well-ordered data.
It measures the center of the data.
Hence, the completed statement would be:
The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.
Answer:
First ____ is median
Second ____ is center
Step-by-step explanation:
The median is the middle value of a set of numbers, and is found in the center.
A printer ink cartridge that can print 550 pages has already printed 127 pages. Which solution represents the correct equation and answer to the question, "How many more pages, P, can still be printed?"
P + 127 = 550 P = 423
Answer:
P = 423
P + 127 = 550
Step-by-step explanation:
Determine the nature of the roots: 2x^(2) +8x +3=0 a. two distinct real solutions c. cannot be determined b. no real solutions d. a unique real solution
Answer:
a
Step-by-step explanation:
Given a quadratic equation in standard form ax² + bx + c = 0 (a ≠ 0 )
Then the discriminant b² - 4ac determines the nature of the roots.
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then no real roots
Given
2x² + 8x + 3 = 0 ← in standard form
with a = 2, b = 8, c = 3 , then
b² - 4ac = 8² - (4 × 2 × 3) = 64 - 24 = 40
Since b² - 4ac > 0 then 2 real and distinct roots → a
Answer:
a
Step-by-step explanation:
Find the volume of a rectangular prism with a height of 18 if the base has a length of 9 and a width of 17.
Select one:
O a. 2678 units cubed
O b. 2049 units cubed
O c. 2754 units cubed
O d. 2957 units cubed
Hey there! I'm happy to help!
To find the volume of a rectangular prism, you simply multiply each of the three different sides!
18×9×17=2754
Therefore, the volume of this rectangular prism is c. 2754 units cubed.
Now you can find the volume of a rectangular prism! Have a wonderful day!
Please answer this correct answer now fast
Answer:
WX = 8 mm
Step-by-step explanation:
To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].
We use the law of sines in the blue triangle to do such:
[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]
Now we can use this value in the larger right angle triangle where WX is the opposite side to angle [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:
[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]
which rounded to the nearest integer gives
WX = 8 mm
PLZ HELP (BRAINLIEST)
Answer:
C. y = 0.5x + 5
Hope that helps.
Kini and Duke are each working during the summer to earn money in addition to their weekly allowance, and they are saving all of their money. Kini earns $9 an hour at her job, and her allowance is $8 per week. Duke earns $7.50 an hour, and his allowance is $17 per week. How many hours do Kini and Duke need to work in order to save the same amount of money in one week?
Answer:
6 hours
Step-by-step explanation:
Denote the working time T
=> The amount of money that Kini can save after 1 working week:
A1 = 8 + 9T
=> The amount of money that Duke can save after 1 working week:
A2 = 17 + 7.5T
If Kini and Duke save the same amount of money after 1 working week, then:
A1 = A2
=> 8 + 9T = 17 + 7.5T
=> 9T - 7.5T = 17 - 8
=> 1.5T = 9
=> T = 6
=> By working 6 hours in the 1st week, Kini and Duke will save the same amount of money.