[tex]xy-3x^2+2x[/tex]
Factor by pulling out the x-term.
[tex]x(y-3x+2)[/tex]
Arrange as we get -
[tex]x(-3x+y+2)[/tex] ----------> Answer
Given the quadratic function f(x) = 4x^2 - 4x + 3, determine all possible solutions for f(x) = 0
Answer:
The solutions to the quadratic function are:
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)\:=\:4x^2\:-\:4x\:+\:3[/tex]
Let us determine all possible solutions for f(x) = 0
[tex]0=4x^2-4x+3[/tex]
switch both sides
[tex]4x^2-4x+3=0[/tex]
subtract 3 from both sides
[tex]4x^2-4x+3-3=0-3[/tex]
simplify
[tex]4x^2-4x=-3[/tex]
Divide both sides by 4
[tex]\frac{4x^2-4x}{4}=\frac{-3}{4}[/tex]
[tex]x^2-x=-\frac{3}{4}[/tex]
Add (-1/2)² to both sides
[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{3}{4}+\left(-\frac{1}{2}\right)^2[/tex]
[tex]x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]
[tex]\left(x-\frac{1}{2}\right)^2=-\frac{1}{2}[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solving
[tex]x-\frac{1}{2}=\sqrt{-\frac{1}{2}}[/tex]
[tex]x-\frac{1}{2}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex] ∵ [tex]\sqrt{-\frac{1}{2}}=\sqrt{-1}\sqrt{\frac{1}{2}}[/tex]
as
[tex]\sqrt{-1}=i[/tex]
so
[tex]x-\frac{1}{2}=i\sqrt{\frac{1}{2}}[/tex]
Add 1/2 to both sides
[tex]x-\frac{1}{2}+\frac{1}{2}=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
also solving
[tex]x-\frac{1}{2}=-\sqrt{-\frac{1}{2}}[/tex]
[tex]x-\frac{1}{2}=-i\sqrt{\frac{1}{2}}[/tex]
Add 1/2 to both sides
[tex]x-\frac{1}{2}+\frac{1}{2}=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
[tex]x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Therefore, the solutions to the quadratic function are:
[tex]x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}[/tex]
Determina la derivada de la siguiente función implícita y^3 + x^2 In y= 4x + 2
Answer:
[tex]\dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]
Step-by-step explanation:
[tex]y^3+x^2\ln y=4x+2[/tex]
Diferenciando con respecto a [tex]x[/tex]
[tex]3y^2\dfrac{dy}{dx}+2x\ln y+\dfrac{x^2}{y}\dfrac{dy}{dx}=4\\\Rightarrow (3y^2+\dfrac{x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow (\dfrac{3y^3+x^2}{y})\dfrac{dy}{dx}=4-2x\ln y\\\Rightarrow \dfrac{dy}{dx}=\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex]
La derivada de la función dada es [tex]\dfrac{4y-2xy\ln y}{3y^3+x^2}[/tex].
When signing the lease for her $825.00 per month rental property, Selah will have to pay the first month's rent, last month's rent, and a
security deposit equal to 25% of one month's rent. If Selah currently earns an average weekly net pay of $650.00, determine what percent
of her weekly pay she will need to save ishe wants to sign her lease in 8 weeks.
O a
2.8%
Ob 3.6%
OC 28%
Od 35.7%
Selah needs to save 35.7% of her weekly pay she will need to save if she wants to sign her lease in 8 weeks.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Starting from the bottom in 8 weeks Selah will earn $(8×650).
= $5200.
The cost of renting the property for 2 months is $(2×825).
= $1650.
And 25% of one month's rent as a security deposit is,
= (25/100)×825.
= $206.25.
So, The total amount she needs to sign is $(1650 + 206.25).
= $1856.25.
Therefore, The percentage of her weekly pay she will need to save is,
= (1856.25/5200)×100.
= 35.69% or 35.7%
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In the figure below, the distance from A to D is y, the distance from D to C is x and the distance from A to B is h.
Using trigonometric ratios we calculate the value of the variables as approximately x and y are 5.1 units and 3.1 units respectively .
Trigonometry is the branch of mathematics that is used for solving a right angled triangle if only one data is given.
Let us consider a triangle ABC right angled at B. BC is the base of the triangle and AC is the hypotenuse , therefore AB is the perpendicular.
The various trigonometric ratios used for solving a triangle are :
sin C = AB ÷ AC
cos C = BC ÷ AC
tan C = AB ÷ BC
Now in the given figure we can see that :
In ΔABC , using the trigonometric ratio of sin
sin ∠A = BC ÷ AB
or , sin 51° × AB = BC
or, BC = 10.102...
or, BC ≈ 10.1
Again in Δ BCD , using the trigonometric ratio of cos
cos ∠D = CD ÷ BD
or, CD ≈ 5.1
In ΔABC , using the trigonometric ratio of tan
tan ∠A = BC ÷ AC
or, tan 51° = 10.1 ÷ AC
or, AC = 8.178...
or, AC ≈ 8.2
Therefore the value of y is AC-DC = 8.2 - 5.1 = 3.1 units
The values of x and y are 5.1 units and 3.1 units respectively .
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Which of the following ratios is not equivalent to the other three 2/3 4to6 8to12 4/5
Answer:
The non-equivalent ratio is 4:5.
Step-by-step explanation:
2/3 4/6 and 8/12 are equivalent because they are all multiples of each other.
What are the roots of f(x)=x^3-x^2-5x-3?
Answer:
x=3 and x=-1
Step-by-step explanation:
Given Descartes' Rule of Signs, there is only one positive root and one negative root.
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient.
So P could be +1, -1, +3, or -3, while Q could be 1 or -1.
Therefore, P/Q could be +1, -1, +3, or -3.
Then we use synthetic division to find the correct factor(s):
1 | 1 -1 -5 -3
___ 1_0_ -5
1 0 -5 | -8
So (x-1) is not a factor
-1 | 1 -1 -5 -3
___-1_2_ 3
1 -2 -3 | 0
So (x+1) is a factor where the quotient is x^2-2x-3 or (x-3)(x+1)
3 | 1 -1 -5 -3
___ 3_6_ 3
1 2 1 | 0
So (x-3) is a factor where the quotient is x^2+2x+1 or (x+1)^2
Given (x-3) and (x+1) are factors, we now use the Zero Product Property:
(x-3)(x+1)=0
x-3=0
x=3
x+1=0
x=-1
So the roots are x=3 and x=-1
Dreyfus cashed a check for $145. The teller gave him five $20 bills, two $20 bills, and f $1 bills. How many $1 bills did he get?
Answer:
5 singles
Step-by-step explanation:
5 $20= 100
2 $20= 40
remainder is 5 singles
Answer:
5 $1 bills.
Step-by-step explanation:
The expression to reflect this problem is:
145 = 20(5) + 20(2) + 1x
145 = 100 + 40 + 1x
145 = 140 + 1x
145 - 140 = 140 + 1x - 140
5 = 1x
5 ÷ 1 = 1x ÷ 1
5 = x
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
Who likes my banana⤵️⤵️⤵️⤵️⤵️⤵️
Answer:
damm thats really good
Step-by-step explanation:
Answer:
ooooooo me :)
X
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify the following expression.
4(20+12)+(5-3)
Answer:
[tex] = 4(32) + (2) \\ = 128 + 2 \\ = 130[/tex]
HOPE THIS HELPS
Evaluate 4^2 - 6 ÷ 2 + 3=
Answer:The correct answer is 16
Step-by-step explanation:
4^2= 16
16-6/2+3
16-3+3
13+3=16
Paula knows the total cost for 100 students will be $750, and the cost total cost for 150 students is $1050. What is the caterer’s fixed cost and the rate per student served?
Step-by-step explanation:
the price charged for 100 students reflects the cost per student that applies to the order as a whole.
100 * 6 = $600, so the fixed cost is 750-600 = 150.
...
We can check this by substituting in the other equation.
Does 150*6 + 150 = 1050?
150*6=900
900+150 = 1050.
Yes, it does
...
We can express this relationship by the equation:
y = mx + b
where
y = total cost
m = $6 per student
x = number of students
b = fixed costs = 150
y = 6x + 150
The caterer’s fixed cost and the rate per student served is $6 and $150
How to choose what quantity to multiply the first equation?This method is actually called method of elimination to solve a system of linear equations.
We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).
If we have equations:
[tex]a_1x + b_1y = c_1\\a_2x + b_2y = c_2[/tex]
then, if we want to eliminate variable x, then we have to multiply equation 1 with
[tex]-\dfrac{a_2}{a_1}[/tex]
which will make coefficient of x in first equation as
[tex]a_1 \times - \dfrac{a_2}{a_1} = -a_1[/tex]
Then adding both equation will eliminate the variable x.
Given;
Cost of 100 students= $750
Cost of 150 students= %1050
Let the fixed cost of caterer be x
and the cost per student be y
x+100y=750...(1)
x+150y=1050...(2)
solving the above equations;
50y=300
y=6
x=750-600=150
The fixed cost is $150, while the per-student cost is $6.
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At 60 km per hour it takes archie 10 hours to travel from his house in Manila to his house in the province. If his rate will be 120 km per hour, how long will it take him to reach his house in the province from Manila
A. 5 hours
B. 8.5 hours
C. 6 hours
D. 7.5 hours
Pls i need it now
Answer:
a
Step-by-step explanation:
5 hours
Which pair of sneakers has the lowest sale price?
Answer:
15% off $30
Step-by-step explanation:
Marbles question:
John is told to find 3 specific marbles within a box of 60 marbles. The room is dark and he can’t see the marbles properly. He pours out 20 of these marbles, and blindly chooses 3 of them.
What are the chances he chooses the 3 specific marbles he was told to find?
The chances he chooses the 3 specific marbles he was told to find is 1/20.
How to calculate the probability?It should be noted that there are 60 marbles and he wants to find 3.
In this case, he poured out 20. Therefore, his chances of picking the three marbles will be 1 out of 20.
Therefore, the chances will be 1/20.
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Which of the following equations is equivalent to 4x-2=38
A. 5x=-50
B. X-20=30
C. 5x=50
D. 2x=10
If Max wants to build a rectangular walkway 4 ft wide by 1.5 ft deep by 20 ft long
from the house to the storage shed, what is the area of the walkway?
Square Feet
Answer:
80 ft^2
Step-by-step explanation:
The area of a rectangular walkway = L x W = 20 ft x 4ft = 80 ft
The function W(t) = 40e^–0.35t models the healing of a wound after t hours, where W(t) represents the wound area in square millimeters. What relationship do W(t) and t have?
when t = 0, W(t) > 40
when t = 0, W(t) 0, W(t) > 40
when t > 0, W(t) < 40
ASAP I'm taking test
Answer:
Pretty sure its D.
Step-by-step explanation:
Whenever I made t something higher than 0 I got something less than 40|
(Sorry if I didn't make it in time and if I did I'm taking the same test rn gl homie)
The value of function W(t) will be less then 40 if t > 0 thus option (D) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
W(t) = 40[tex]e^{-0.35t}[/tex]
By the law of indices,
W(t) = 40/[tex]e^{.035t}[/tex]
When t > 0 the value of [tex]e^{.035t}[/tex] > 1
Thus, t > 0 the value of W(t) < 40
Hence "The value of function W(t) will be less then 40 if t > 0".
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Nick bought 5 tickets to go to the amusement park for $65. If he wanted to buy 8 tickets, what would that cost him?
Answer:
$104
Step-by-step explanation:
First find how much 1 ticket costs
65/5= 13
Times that by 8
8x13=104
Calculate the constant of proportionality, k, for the given table.
Answer:
k = y/x
Step-by-step explanation:
1/5, 2/10, 3/15 . . . all equal to 1/5 which is what the value of k is; 'k' stands for constant of proportionality
Ceecee and Jose ate at a restaurant.
Ceecee gave a 20% tip on an $85 dinner bill.
Jose gave a 18% tip on a $80 dinner bill.
Who (Ceecee or Jose) gave the larger tip?
Use differentials to estimate the amount of metal in a closed cylindrical can that is 22 cm high and 10 cm in diameter if the metal in the top and the bottom is 0.4 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.) cm3
Answer:
97.43cm³
Step-by-step explanation:
h = 22cm
d = 10cm
r = d/2
= 10/2
= 5
dh = 2(0.4)
= 0.8
dr = 0.05
V = πr²h
dV = d(πr²h)
Such that
πd(r²h)
= π[(r²dh + hd(r²)]
dV = π[(r²dh + 2rhdr]------(1)
When we put the values above in this equation 1 above:
dV = π[(5)²*0.8 + 2*5*22*0.05]
= π(25*0.8+11)
= π31cm³
Multiply the value of pi with 31cm³
= 97.43cm³
sgshnsjmsngtjsdyjhsksykhm
i can't read it, its too blurry
anyways have a great day/night :)
Evaluate. 1 1/2÷4
A. 2 1/2
B. 12/2
C. 3/8
D. 6
the correct answer is C. 3/8
A penguin walks 10 feet in 6 seconds. How far does the penguin walk in 45 seconds
Answer:
70 ish
Step-by-step explanation:
Which shape is similar to shape x?
Answer:
the c oneStep-by-step explanation:
hope it will helpAnswer:
Step-by-step explanation:
Probably C but I sure wouldn't bet the farm on it. It looks like C is about 1.5 times the size of X
(PLEASE HELP THIS IS TIMED!!!)
Which graph represents the inequality x > 6?
Answer:
The last one
Step-by-step explanation
x is greater than six so you would go to the right and it has to be an open dot since it can't be the same as 6
Answer:
hello
Step-by-step explanation:
Which fraction shoes unit rate that is equal to the ratio 18:2
Answer: 9/1
Step-by-step explanation:
Please I need some answers
In each triangle ABC, angle C is a right angle. Find the value of the trig function indicated.
As given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is sin A = 3/5.
As given in the question,
In triangle ABC,
∠C = 90°
Side a is opposite to angle A
c is the hypotenuse opposite to angle C
a = 6
c = 10
sin A = ( opposite side) / Hypotenuse
⇒sin A = a/c
⇒sin A = 6/10
⇒sin A = 3/5
Therefore, as given triangle ABC, angle C is a right angle if a=6, c=10 then value of trigonometric function is sin A = 3/5.
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how can you tell when an equation in one variable has infinitely many soultions or no solution