Answer:
14√3
Step-by-step explanation:
4√12 + 2√27
First, simplify both terms:
4√3√4 + 2√9√3
4 * 2√3 + 2 * 3√3
8√3 + 6√3
Now, combine the terms:
14√3
To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we simplify each radical expression individually and then add the simplified expressions together, resulting in 5 times the square root of 3.
Explanation:To find the sum of 4 radical 12 and 2 radical 27 in simplest form, we first need to simplify each radical expression individually. The square root of 12 can be simplified as the square root of 4 times the square root of 3, which is 2 times the square root of 3. Similarly, the square root of 27 can be simplified as 3 times the square root of 3.
Now, we can add these simplified radical expressions. 4 radical 12 plus 2 radical 27 equals (2 times the square root of 3) plus (3 times the square root of 3). This can be simplified as 5 times the square root of 3.
Learn more about Simplifying radical expressions here:https://brainly.com/question/31873903
#SPJ2
Solve for x 2x+10) (4x-38
Answer:
8X2-38X-380
Step-by-step explanation:
(2x+10)(4x-38)
Expand the brackets.
2X(4X-38)+10(4X-38)
Multiple the inner ones by the outer ones
(2X)(4X)-(38)(2X)+(10)(4X)-(10)(38)
=> 8X2-78X+40X-380
8X2-38X-380
Solve for y in terms of x:
[tex]4 {x}^{2} + 8 {x}^{2}y = 8 {x}^{3} [/tex]
A.
[tex] \frac{2}{2x - 1} [/tex]
B.
[tex] \frac{2}{2x + 1} [/tex]
C.
[tex] \frac{2x - 1}{2} [/tex]
D.
[tex] \frac{2}{2x - 1} [/tex]
Answer:
8x^2y= 8x^3 - 4x^2
y = x - 1/2
y = (2x - 1)/2
the answer is c
3x3 +10x²-x-12=0
What are all the possible rational roots in the problem? (Please explain so I can understand)
Step-by-step explanation:
Given the equation
[tex]3x^3\:+10x^2-x-12=0[/tex]
Steps
[tex]3x^3+10x^2-x-12[/tex]
Rational Root Theorem definition
[tex]\mathrm{For\:a\:polynomial\:equation\:with\:integer\:coefficients:\quad }a_nx^n+a_{n-1}x^{n-1}+\ldots +a_0[/tex]
[tex]\mathrm{If\:}a_0\mathrm{\:and\:}a_n\mathrm{\:are\:integers,\:then\:if\:there\:is\:a\:rational\:solution}[/tex]
[tex]it\:could\:be\:found\:by\:checking\:all\:the\:numbers\:produced\:for\:\pm \frac{dividers\:of\:a_0}{dividers\:of\:a_n}[/tex]
[tex]a_0=12,\:\quad a_n=3[/tex]
[tex]\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:4,\:6,\:12,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:3[/tex]
[tex]\mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\quad \pm \frac{1,\:2,\:3,\:4,\:6,\:12}{1,\:3}[/tex]
Plugging x = -1 is False
[tex]3\left(-1\right)^3+10\left(-1\right)^2-\left(-1\right)-12=0[/tex]
[tex]-4=0[/tex] ∵L.H.S ≠ R.H.S
Plugging x = 1 is True
[tex]3\cdot \:1^3+10\cdot \:1^2-1-12=0[/tex]
[tex]0=0[/tex] ∵ L.H.S = R.H.S
Similarly,
x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
As
[tex]3\left(-3\right)^3+10\left(-3\right)^2-\left(-3\right)-12=0[/tex]
[tex]0=0[/tex] ∵ L.H.S = R.H.S
x = 3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -4/3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
As
[tex]3\left(-\frac{4}{3}\right)^3+10\left(-\frac{4}{3}\right)^2-\left(-\frac{4}{3}\right)-12=0[/tex] ∵ L.H.S = R.H.S
x = 4/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].
Hence, out of all the mentioned rational roots of the equation [tex]3x^3\:+10x^2-x-12=0[/tex], the rational roots which validate the equation are [tex]x=-\frac{4}{3},\:x=1,\:x=-3[/tex].
Keywords: rational roots, rational root theorem
Learn more about rational roots from brainly.com/question/7594092
#learnwithBrainly
.
(04.05)
Camryn ran for 13 minutes, walked for 17 minutes, ran for another 13 minutes, and then sat down and stretched in place for 17 minutes. Her total distance traveled is a function of time.
Which graph most accurately represents this scenario?
Answer:
The first one.
Step-by-step explanation:
The third and fourth ones can't be right because at when the line takes its first curve (just before .25 hours) it doesn't keep increasing in height, and she walked during that time.
The second one can't be right because when she started out she wasn't immediately between 1.25 and 1.5 miles.
That leaves only the first one.
The graph for the given situation is required.
The correct option is the first graph.
Let us convert the minutes to hour since the graph is shown in hours.
[tex]\dfrac{13}{60}=0.2167\ \text{hours}[/tex]
[tex]\dfrac{17}{60}=0.2833\ \text{hours}[/tex]
Whenever a line in a graph has an angle with the [tex]x[/tex] axis then there is a change of the [tex]y[/tex] axis with respect to change in [tex]x[/tex] axis.
That means slope
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
Here, the slope of an angled line will be
[tex]m=\dfrac{\text{Change in distance}}{\text{Change in time}}=\text{Speed}[/tex]
The slope here indicates constant speed.
From 0 to 0.2167 hours she ran at constant speed.
From 0.2167 to [tex]0.2167+0.2833=0.5[/tex] hours she walked
From 0.5 hours to [tex]0.5+0.2167=0.7167[/tex] hours she ran.
From 0.7167 hours to [tex]0.7167+0.2833=1[/tex] hour she sat and stretched.
The slope or angle will be more for the running sections compared to the walking sections as running is faster than walking.
And the graph will always be going up.
At the end when she is not moving the line will be a horizontal line because her position is not changing.
So, the correct option is the first graph.
Learn more:
https://brainly.com/question/18998090?referrer=searchResults
https://brainly.com/question/11606037?referrer=searchResults
How do you solve 0.0006 x 10^3
Answer:
0.6
Step-by-step explanation:
The the exponent is positive , move it 3 times to the right.
If it was a negative exponent , you would move it to the left.
What is -4 (1/8) -3(2/5)
Answer:
-17/10
Step-by-step explanation:
-4(1/8)-3(2/5)=-4/8-6/5=-20/40-48/40=-68/40=-17/10
Giovanna recibe actualmente un ingreso anual de $42 000. Normalmente, recibe
un aumento salarial de 2% al año debido al «costo de la vida».
1. Determine cuál sería la ecuación que representa su situación actual.
Answer:
[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]
Step-by-step explanation:
The salary per year is the combination of the $42000 per year (constant) plus the 2% rise per year. So the ecuation is:
Firt year [tex]S=(42000 + 0.02*42000)[/tex]
Second year [tex]S=(42000 + 0.02*42000)+0.02*(42000 + 0.2*42000)[/tex]
Generalizing:
[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]
Final answer:
The equation that represents Giovanna's current situation is Current Salary = $42,840.
Explanation:
The equation that represents Giovanna's current situation can be determined by using the formula for calculating annual salary with a percentage increase.
The formula is:
Current Salary = Initial Salary + (Percentage Increase * Initial Salary)
Using this formula, we can substitute the given values:
Initial Salary = $42,000
Percentage Increase = 2% (or 0.02)
Substituting these values into the formula:
Current Salary = $42,000 + (0.02 * $42,000)
Simplifying the equation:
Current Salary = $42,000 + $840
Current Salary = $42,840
Therefore, the equation that represents Giovanna's current situation is:
Current Salary = $42,840
what's a fraction that has a denominator of 6 and greater than 2/4
One vertex of a triangle is located at (0,5) on a coordinate grid. After a transformation the vertex is located at (5,0). Which transformations could have taken place? Select two options.
Answer:
Two options for this case will be,
Clockwise rotation : -90°
Anti-Clockwise rotation : +270°
Step-by-step explanation:
If we rotate the triangle clockwise -90° then the vertex will be at (5,0).
Similarly by rotatating it anti-clockwise for +270° it will be at same position
Answer:
C.) D.)
Step-by-step explanation:
89.1.19-G
Find the expected payback for a game in which you bet $8 on any number from 0 to 99. If your number comes up you get $400
The expected payback is
(Round to the nearest cent as needed.)
Enter your answer in the answer box and then click Check Answer.
$48.00
Answer:
-$4
Step-by-step explanation:
The expected payback formula is the sum of probability multiply the value
E(x) = p(x1)*x1 + p(x2)*x2 + .....
In this case, we have two possibility of payback
1) winning
The payback is $400 -$8 = $392
x1 = 392
The probability of winning is one out of 100 (since the choices are 0 to 99)
p(x1) = 1/100
2. Losing
The payback is -$8 since the person didn't win anything is loose
x2 = -8
Since there is only one winning number, the other 99 numbers are loosing numbers
p(x2) = 99/100
Therefore expected payback is
E(x) = p(x1)*x1 + p(x2)*x2
= (1/100)*392 + (99/100)*(-8)
= -400/100
= -$4
The expected payback for a game in which you bet $8 on any number from 0 to 99, and win $400 if your number comes up, is -$4.00, indicating an average loss of $4.00 per game.
Explanation:In this probability problem, you are betting $8 on a number from 0 to 99. This means there are 100 possible outcomes, each equally likely if the game is fair. Your profit if you win is $400. Since there's a 1 in 100 chance of winning, we can calculate the expected return as follows:
Expected Return = Probability of winning * Payoff when winning = (1/100) * $400 = $4.00
However, since you are always paying $8 to play the game, in expectation you are losing money in every game. The expected payback from this game is hence $4-$8=-$4.00 and not $48.00. In other words, we can anticipate losing $4.00 on average every time we play this game.
Learn more about Expected Return here:https://brainly.com/question/33695664
#SPJ11
rachel received a $70 gift card for a coffee store. she used it in buying some coffee that cost $7.44 per pound. after buying the coffee, she had $25.36 left on her card. how many pounds of coffee did she buy?
Answer:
6 pounds.
Step-by-step explanation:
70-25.36= 44.64 (the amount of money she spent)
44.64/7.44 (per pound cost)= 6
Answer:
Rachel bought 6 pounds of coffee.
Step-by-step explanation:
First, do $70-$25.36, because that will give you the total amount of money she spent on coffee.
$70-$25.36= $44.64.
Rachel spent $44.64 on coffee.
Next, you know that every pound of coffee costs $7.44.
So, $7.44x = $44.64
x= the number of pounds of coffee Rachel purchased.
So, we have to now isolate x.
$7.44x / $7.44 = $44.64 / $7.44
x= 6
Therefore, Rachel purchased 6 pounds of coffee.
If you need anymore help on any math problems, email me at: icecreamforest7@aol.com
I also tutor.
Hope this helps:)
h(x) = x2
j(x) = 2x2-5
find h(x) - j(x)
Answer:
Step-by-step explanation:
h(x) - j(x) => [tex]x^2-(2x^2-5)[/tex]
The negative sign out in front of the set of parenthesis changes the signs of everything inside the parenthesis, so now we have, without parenthesis:
[tex]x^2-2x^2+5[/tex] which simplifies down to
[tex]-x^2+5[/tex]
a car rental business rents a compact car at a daily rate of $29.20 plus 20 cents per mile. mike can afford to spend $54.00 on the car rental for one day. how many miles can he drive and stay within his budget?
Answer:
124 miles
Step-by-step explanation:
Since he has a budget of $54.00, we first deduct the fixed charge of $29.2
Money for the miles will be 54-29.2=$24.8
Cost per mile is $0.2
[tex]Miles=\frac {24.8}{0.2}=124 miles[/tex]
Therefore, Mike is limited to travel 124 miles with the car on hire
If you add 8 g of salicylic acid to 84 g of an ointment base what is the final concentration of the product
The final concentration of salicylic acid in the ointment is approximately 8.70%.
To calculate the final concentration of salicylic acid in the ointment base, we need to know the total mass of the product after mixing. The final concentration of salicylic acid is expressed as a percentage, which is the mass of salicylic acid divided by the total mass of the product, multiplied by 100.
Let's assume that when you add 8 g of salicylic acid to 84 g of the ointment base, there is no change in the total volume, and the two substances mix completely.
Total mass of the product = Mass of salicylic acid + Mass of ointment base
Total mass = 8 g + 84 g = 92 g
Now, we can calculate the final concentration of salicylic acid:
Final Concentration (%) = (Mass of salicylic acid / Total mass) * 100
Final Concentration (%) = (8 g / 92 g) * 100 ≈ 8.70%
So, the final concentration of salicylic acid in the ointment is approximately 8.70%.
To know more about acid:
https://brainly.com/question/7986456
#SPJ2
if 13 is added 101 times, the resulting number will be?
A)114
B)a factor of 13
C)A multiple of 13
D)A prime number
Answer:
c a multiple of 13
Step-by-step explanation:
The resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
It is given that:
if 13 is added 101 times:
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 13 + 13 + 13 + 13 ...... 101 times
Sequence can be defined as the systematic way of representing the data that follows a certain rule of arithmetic.
= 101×(13)
Thus, the resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.
Learn more about the number here:
brainly.com/question/17429689
#SPJ2
Plz help I’ve been struggling on this for a long time
Answer:
Step-by-step explanation:
the easiest way is to convert these fraction to decimals because as you can see on the number line the numbers are whole and decimals on the small tik mark
-3 3/4 would convert to as -3.75
1/2 would convert into 0.5
now plot those on a number line
*remember the small tiks are worth .25*
1. Which equation is the inverse of y = 2x2 + 25 ?
Is the square root of 34 a rational number
Answer:
No
Step-by-step explanation:
The square root of 34 does not multiply by itself
Yes, the square foot of 34 is a rational number
What are rational numbers?Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.
square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example √25 = 5 i.e 5 × 5 = 25
The square root of 34 is of a value
√34 = 5.381
This value can be converted into fraction
= 5381/1000
Therefore we can say that the square root of 34 is a rational number.
learn more about rational numbers from
https://brainly.com/question/12088221
#SPJ6
Below are the supply and demand equations for umbrellas in a certain market. In these equations, p represents price, D
represents demand, and S represents supply.
D-p+22
S = 3p – 36
What is p at the point of equilibrium, to the nearest tenth?
a. 19.3
b. 16.5
C. 13.4
d. 12.0
Please select the best answer from the choices provided
СА
The equilibrium price 'p' is found when setting the supply and demand equations equal to each other and solving for p. Doing so gives us p = 29, which is not available among the provided options, suggesting an error in the question or answer options.
Explanation:In the given situation, the point of equilibrium occurs when the quantity demanded (D) is equal to the quantity supplied (S). Therefore, we can set the demand equation equal to the supply equation and solve for p.
The equations at the moment are: D = p + 22 and S = 3p - 36.
Setting them equal to each other means setting D and S to the same value, resulting in: p + 22 = 3p – 36.
To solve for p, you first combine like terms, which will give you: 22 + 36 = 3p - p, simplifying that leads to: 58 = 2p.
Finally, to isolate p, divide both sides of the equation by 2: p = 58 / 2 = 29.
However, none of the options includes p = 29, which suggests there might be a typo or error in the provided choices or the equations.
Learn more about Equilibrium Price here:https://brainly.com/question/33384040
#SPJ3
Simplify.
Rewrite the expression in the form (7^3)^3
Answer:
7^9
Step-by-step explanation:
When dealing with exponents inside and outside parenthesis with only one term in the parenthesis, you multiply the exponents. By doing this, you get 7^3x3, which is 7^9
Answer:
40353607 or 7^9
Step-by-step explanation:
7 to the third power is 343
343 to the third power is 40353607 :)
But the exponents times each other equal nine. This will be your answer: 7^9
The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the greater number?
The greater number is 121
Step-by-step explanation:
The given is:
The sum of 2 positive numbers is 151The lesser number is 19 more than the square root of the greater numberWe need to find the greater number
Assume that the smaller number x and the greater number is y
∵ The smaller number is x and the greater number is y
∵ Their sum is 151
∴ x + y = 151 ⇒ (1)
∵ The lesser number is 19 more than the square root of the greater
number
∴ x = 19 + √y ⇒ (2)
- Substitute x in equation (1) by equation (2)
∵ (19 + √y) + y = 151
- Subtract 151 from both sides and re-arrange the terms from
the greatest power y
∴ y + √y - 132 = 0
Chang [tex]\sqrt{y}[/tex] to [tex]y^{\frac{1}{2}}[/tex] and substitute [tex]y^{\frac{1}{2}}[/tex] by h
∵ [tex]y^{\frac{1}{2}}[/tex] = h
∴ y = h²
- Substitute each y by h
∴ h² + h - 132 = 0
- Factorize it into two factors
∴ (h - 11) (h + 12) = 0
- Equate each factor by 0 to find h
∵ h - 11 = 0
- Add 11 to both sides
∴ h = 11
∵ h + 12 = 0
- subtract 12 from both sides
∴ h = -12
∵ h = [tex]y^{\frac{1}{2}}[/tex]
∴ [tex]y^{\frac{1}{2}}[/tex] = 11 and -12
∵ [tex]y^{\frac{1}{2}}[/tex] = √y
∴ √y = 11
∴ √y = -12 ⇒ rejected square root can't give -ve number
∴ √y = 11 only
- To find y square the both sides
∴ y = 121
The greater number is 121
Learn more:
You can learn more about the word problem in brainly.com/question/4034547
#LearnwithBrainly
The solution involves setting up two equations from the given information and then substituting one into the other to create a quadratic equation in terms of the greater number, x, and solving for x.
Explanation:The question involves finding two positive numbers given that their sum is 151 and that the lesser number is 19 more than the square root of the greater number. To find the greater number, let's denote the greater number as x and the lesser number as y. The two conditions given are:
x + y = 151 (The sum of the numbers is 151.)y = √x + 19 (The lesser number is 19 more than the square root of the greater number.)We can substitute the second condition into the first:
x + (√x + 19) = 151x + √x + 19 = 151√x + 19 = 151 - x(√x + 19)2 = (151 - x)2x + 2 * 19 * √x + 19^2 = [tex]151^2[/tex]- 2 * 151 * x + [tex]x^2[/tex]Subtract x from both sides and simplify:2 * 19 * √x +[tex]19^2[/tex] =[tex]151^2[/tex]- 2 * 151 * xThis equation can then be solved for x to find the greater number.After simplifying the quadratic equation and solving for x, we will find the value for the greater number.
3 and 6- solve by graphing
other two solve by substitution
Answer:
3. (x, y) = (3, 2)
6. (x, y) = (10, 4/3)
9. (x, y) = (-2, -1)
12. (x, y) = (8, 3)
Step-by-step explanation:
3, 6. See the attachment. 3 is graphed in red/orange. 6 is graphed in blue, purple.
__
9. Use the expression for y in the second equation to substitute for y in the first equation:
4(3x +5) -x = -2
12x +20 -x = -2 . . . eliminate parentheses
11x = -22 . . . . . . . . subtract 20, collect terms
x = -2 . . . . . . . . . . . divide by 11
y = 3(-2) +5 = -1 . . .substitute for x in the second equation
The solution is (x, y) = (-2, -1).
__
12. Subtract 3/4x from the second equation to get an expression for y:
y = 9 - 3/4x
Substitute that into the first equation:
3(9 -3/4x) -5/4x = -1
27 -9/4x -5/4x = -1 . . . . eliminate parentheses
-14/4x = -28 . . . . . . . . . . collect terms, subtract 27
x = 8 . . . . . . . . . . . . . . . . multiply by -4/14
y = 9 -3/4(8) = 3 . . . . . . substitute into the expression for y
The solution is (x, y) = (8, 3).
Divide, and then round the answer to two decimal places: 0.3572928 ÷ 0.419
Answer: 0.85
Step-by-step explanation:
step 1 0.3572928 / 0.419
count the number of figures yo have after the decimal point.
After counting , multiply both the numerator and the denominator
10000000 to make the whole expression a whole number for easy division.
we now 0.3572928 10000000
------------------ x ---------------
0.419 10000000
= 3572928
----------------
4190000
= 0.8527
Now to two decimal places
= 0.85
Write as a monomial in standard form: (−4x^2ya^3)^2
Answer:
[tex]\large\boxed{16a^6x^4y^2}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\=====================\\\\\left(-4x^2ya^3\right)^2=\\\\=(-4)^2(x^2)^2(y)^2(a^3)^2\\\\=(-4)(-4)x^{2\cdot2}y^2a^{3\cdot2}\\\\=16x^4y^2a^6[/tex]
The expression (−4x^2ya^3)^2 written as a monomial in standard form is 16x^4y^2a^6.
Explanation:To write the given expression, (−4x2ya3)2, as a monomial in standard form, we first need to calculate square ofeach part of the term inside the parentheses. The square of -4 is 16. The rule of exponents states that when raising a power to a power, you multiply the exponents. Therefore, the square of x2 is x4 (since 2*2=4), the square of y is y2, and the square of a3 is a6 (since 3*2=6). Combining these, we find that the expression in standard form is 16x4y2a6.
Learn more about Monomial Standard Form here:https://brainly.com/question/28867458
#SPJ11
which if the following describes the transformation of the graph y=x^2 in graphing y=-x^2-5
Answer:
Step-by-step explanation:
f: y=x^2
g: y= -x^2
h: y= -x^2-5
first we transform the graph of f to the graph of g using the reflexion across y-axis .
then we transform of g to the graph of h using the translation -5( vector j )
look at the photo below for the graphics.
:)
Answer: a translation 5 units to the left
If f(x) = 6x – 4, then f^-1(x)=
Answer:
[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex]
Step-by-step explanation:
Given function.
[tex]f(x)=6x-4[/tex]
To find the inverse function [tex]f^{-1}(x)[/tex]
Step 1:
Replace [tex]f(x)[/tex] with[tex]y[/tex] in the function.
[tex]y=6x-4[/tex]
Step 2:
Interchange [tex]y[/tex] with [tex]x[/tex] in the equation.
[tex]x=6y-4[/tex]
Step 3:
Solve for [tex]y[/tex].
We have [tex]x=6y-4[/tex]
Adding 4 to both sides,
[tex]x+4=6y-4+4[/tex]
[tex]x+4=6y[/tex]
Dividing each term by 6 to isolate [tex]y[/tex]
[tex]\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}[/tex]
[tex]\frac{x}{6}+\frac{4}{6}=y[/tex]
Simplifying fractions by dividing the numerator and denominator by their GCF.
[tex]\frac{x}{6}+\frac{4\div 2}{6\div 2}=y[/tex]
[tex]\frac{x}{6}+\frac{2}{3}=y[/tex]
Thus the equation of [tex]y[/tex] is:
[tex]y=\frac{x}{6}+\frac{2}{3}[/tex]
Step 4:
Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex] (Answer)
Thus, we have the inverse function
how do I solve for y: 2 + y = -7 + 2y
Answer:
y=9
Step-by-step explanation:
2+y=-7+2y
2=-7+2y-y
2=-7+y
y=2-(-7)
y=2+7
y=9
Answer:
2 + y = -7 + 2y
collect like terms
y-2y=-7-2
-y=-9
y=9
Step-by-step explanation:
You have been asked to construct an aquarium that holds 1000 gallons. It will be a standard rectangular prism with restrictions that the length must be 1 foot longer than the width and the height must be 4.6 feet less than the length. Find the height of the aquarium to the nearest hundredth of an inch.
Answer:
The height of the aquarium is [tex]33.75\ in[/tex]
Step-by-step explanation:
Remember that
[tex]1\ gal=231\ in^3[/tex]
[tex]1\ ft=12\ in[/tex]
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
In this problem we have
[tex]V=1,000\ gal=1,000(231)=231,000\ in^3[/tex]
so
[tex]231,000=LWH[/tex] ----> equation A
[tex]L=W+1(12)[/tex] ---> [tex]W=L-12[/tex] --->equation B (convert ft to in)
[tex]H=L-4.6(12)[/tex]--->[tex]H=L-55.2[/tex] ---> equation C (convert ft to in)
substitute equation B and equation C in equation A
[tex]231,000=L(L-12)(L-55.2)[/tex]
solve for L
Apply distributive property
[tex]231,000=(L^2-12L)(L-55.2)[/tex]
[tex]231,000=L^3-55.2L^2-12L^2+662.4L[/tex]
[tex]L^3-67.2L^2+662.4L-231,000=0[/tex]
Solve the cubic equation by graphing
using a graphing tool
The solution is L=88.95 in
see the attached figure
Find the height of the aquarium H
[tex]H=L-55.2[/tex]
substitute the value of L
[tex]H=88.95-55.2=33.75\ in[/tex]
Find the value of W
[tex]W=88.95-12=76.95\ in[/tex]
help asap will give BRAINLIEST
What are the 3 undefined terms of geometry?
Point, polygon and parallel
Point, line and plane
Line, ray and segment
Measure, draw, and construct
Answer: point, line, and plane.
Step-by-step explanation:
Answer:
Hope it helps In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.
Step-by-step explanation:
Which equation has NO solution? A) 15x + 12 3 = 5x + 4 B) 8 − 4x 10 = 4 + 2x C) 4x − 20 2 = 2x − 10 D) 15x + 5 3 = 5x + 6
Assumption:
Something is missing in question. If we see deeply it is apparent that there is some issue with option b i.e. B) 8 − 4x 10 = 4 + 2x we assume that the questioner want to type B) 8-4x^10 = 4 + 2x.
Answer:
The correct answer is B) 8-4x^10 = 4 + 2x.
Step-by-step explanation:
All equations given is the question can be solve easily to determine the value of x. However if we solve equation mentioned in option b we cannot get single answer easily.
For example value of x in eq given in option A
15x + 123 = 5x+4
1oX = -119
X = -119/10
Answer:
The answer is d
Step-by-step explanation:
i just did it lol