solve for y
[tex]2y - 3 = \sqrt{ {3y}^{2} - 10y + 12} [/tex]
absurd answers will be reported!!​

Answers

Answer 1

Answer:

y = 3

Step-by-step explanation:

2y - 3 = [tex]\sqrt{3y^2-10y+12}[/tex]

square both sides to remove sqrt bracket

(2y - 3)^2 = ( [tex]\sqrt{3y^2-10y+12}[/tex] )^2

simplify both sides

(2y - 3)(2y - 3) = [tex]3y^2[/tex] - 10y + 12

[tex]4y^2[/tex] - 12y + 9 = [tex]3y^2[/tex] - 10y + 12

bring all value to left side

[tex]y^2[/tex] - 2y - 3 = 0

factor

(y - 3)(y + 1)

solve for y

y = 3, y = -1

When plugged back into the equation, only y = 3 is true

Answer 2

Answer:

y = 3

Step-by-step explanation :

[tex]2y - 3 = \sqrt{ 3y² - 10y + 12} [/tex]

Swap the sides both of the equation.

[tex]\sqrt{ 3y² - 10y + 12} = 2y - 3 [/tex]

To remove the brackets of equations square both side and simplify .

3y² - 10y + 12 = 4y² - 12y + 9

Move the expression to left-hand side and change its sign.

3y² - 10y + 12 - 4y² + 12y - 9 = 0

collect like terms

3y² - 4y² - 10y + 12y + 12 - 9 = 0

-y² + 2y + 3 = 0

Change the sign of expression. because it helps to solve.

y² - 2y - 3 = 0

Splits the term -2y

y² + y -3y - 3 = 0

Factor out y from the first pair and -3 from second pair of expression.

y ( y + 1 ) - 3 ( y + 1) = 0

Factor out y + 1 from the expression.

( y + 1 ) ( y - 3 ). = 0

When product and factors equals 0. at least one factor is 0.

y + 1 =0

y - 3 = 0

Solve for y

y = -1 and y = 3

If we plug the 3 as y in the expression we find that y = 3 is the true solution of this expression.

This equation has one solution which is y = 3.


Related Questions

PLEASE HELP! Which of the following ordered pairs is a solution to the given system of equations?

A. (12, 8)

B. (3, 5)

C. (-3, 3)

D. (0, 4)

Answers

Answer:

A number has to be the answer

Integrate with respect to x

-2/3√((2-5x)^3)

Answers

Hello,

[tex]\displaystyle \int {-\dfrac{2}{3} \sqrt{(2-5x)^3}} \, dx \\\\\displaystyle=-\dfrac{2}{3}*\dfrac{-1}{5} \int {-5*(2-5x)^{\frac{3}{2} }} \, dx \\\\\displaystyle=\dfrac{4}{3}*(2-5x)^{\frac{5}{2} }+C[/tex]

Can someone help me with this math homework please!

Answers

Answer:

2 and 3.

Step-by-step explanation:

2. and 3.

the total number of paintings depend upon the number of weeks that have passed as she adds 3 paintings every week to her collection.

1. can't be an option as output values depend upon the input values and hence not independent

4. can't be an option because each week that passes she adds 3 more paintings and since one input has 3 outputs, its not a function.

5. the number of weeks is the input value and number of paintings is the output value as you can later SEE how many paintings she has, not how many weeks it took her.

Answer:

(B, C, D)

Step-by-step explanation:

This scenario can be represented using this equation:

y = 3x + 7

y = total paintings after # of weeks (dependent variable)

x = # of weeks (independent variable)

3 = 3 paintings per week

7 = initial number of paintings

Let's evaluate each answer choice:

"The independent variable is represented by the ouput values"

No, this is wrong. The indepedent variable is the input values.

"The dependent variable is the total number of paintings"

This is correct. The total # of paintings is the output value, or the dependent variable.

"The total number of paintings depends on the number of weeks that have passed"

This is correct. The total # of paintings is the output value, or the dependent variable, because it depends on the # of weeks that pass by.

"This scenario is a function because for each week that passes, there will be exactly one total number of paintings"

This is correct. There is only one possible output for each input.

"The number of weeks is the output value"

No, this is wrong. The total # of paintings is the output value, not the # of weeks.

Hope it helps (●'◡'●)

15. ABCD is a cyclic quadrilateral in which
AB = BC and ABC = 70°.
AD produced meets BC produced at the
point P, where APB = 30°.
Calculate
a) ADB
b) ABD

Answers

Answer:

a) ∠ADB is 55°

b) ∠ABD is 45°

Step-by-step explanation:

a) In the cyclic quadrilateral ABCD, we have;

Segment AB = Segment BC

∠ABC = 70°

Therefore, ∠ADC = 180° - 70° = 110° (Opposite angles are supplementary)

∠ADC + ∠CDP = 180° (Sum of angles on a straight line)

∴ ∠CDP = 180° - ∠ADC

∠CDP = 180° - 110° = 70°

∠DCP = 180° - 70° - 30° = 80°, (Angle sum property)

Similar to ∠DCP = ∠DAB = 80° (Exterior angle of a cyclic quadrilateral)

∠CAB = ∠ACB = (180° - 70°)/2 = 55° (Base angles of isosceles triangle ΔABC)

∠ADB = ∠ACB = 55° (Inscribed angle of a circle subtended by the same chord)

∠ADB = 55°

b) ∠ABD = 180° - ∠DAB - ∠ADB

∴ ∠ABD = 180° - 55° - 80° = 45°

∠ABD = 45°

Please help ASAP and please explain how you got the answer.

Answers

Answer:

The third one

Step-by-step explanation:

All show complementary angles ( angles that add up to 90 degrees ) except for the third one

First one: shows a square within the two angles which indicates that the angles form a right angle ( 90 degree angle ) meaning that they are complementary angles

Second: the angles add up to equal 90 ( 50 + 40 = 90 ) hence they are complementary angles

Third one: the angles form a straight line. Angles that form a straight line add up to equal 180 and are known as supplementary angles

Fourth: the angles shown add up to 90 ( 65 + 25 = 90) hence they are complementary angles

All are complementary but the third one

Write the following compound statement in symbolic form.

If I do not study hard, then I will not pass geometry and graduate high school.

Answers

Answer:

A conjunction is a compound statement formed by combining two statements using the word and . In symbolic logic, the conjunction of p and q is written p∧q . A conjunction is true only if both the statements in it are true.

Step-by-step explanation:

worth 10 points please help me ASAP!

Answers

Answer:

(-1,-1)

Step-by-step explanation:

If you multiply the x and y points of A, (-3,-3), by 1/3 then you find: (-1,-1).

Lola needs to sign 96 invitations. Using a stopwatch that measures time to tenths of a second, it takes Lola 5.3 seconds to sign her full name. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of seconds Lola needs to sign all 96 invitations?

508 seconds
510 seconds
509 seconds
508.8 seconds

Answers

Answer:

508.8 seconds

Step-by-step explanation:

The most accurate determination mathematically is to assume that Lola will maintain an average of 5.3 seconds per signature as she signs all 96 invitations.

Therefore, multiply the time it takes her to sign each invitation (5.3 seconds) by the total number of invitations there are (96 invitations) to get the projected total amount of time that it will take Lola to sign all 96 invitations:[tex]96\cdot 5.3=\boxed{508.8\text{ seconds}}[/tex]

Answer:

508.8 seconds (8.48 minutes)

Step-by-step explanation:

96 × 5.3 = 508.8

hey guys, can you help me out?

Answers

Answer:

Step-by-step explanation:

it is incorrect at step 3

it should be 12*10^(9-5)

=12*10^4

It takes 20 minutes to fill a wading pool. The pool has developed a leak through which it will empty in 30 minutes.
If the hole is not fixed, how long will it take to fill the wading pool?

Answers

In t minutes, t/20 of the pool is filled and t/30 of it is emptied.

t/20 - t/30 = 1
multiply both sides by LCM 60.

3t - 2t = 60
t = 60

The pool is filled in 60 minutes.

Which of the following
is most likely the next step in the series?

Answers

Answer:

B.

Step-by-step explanation:

The numbers are always in the blue side, and the blue side starts at facing right, left, right, and then left.

b. is the answer for the questions

Question 4 of 10 What is the equation of the following line? Be sure to scroll down first to see all answer options. (6,2) O A y= 22 B. y=-3x O c. y=6x O D. y = 1 x O E y=3x O F. y = 1 x​

Answers

E y=3x

By using a (the slope) equals delta y divided by delta x

The equation of the line will be y = 1/3x. The correct option is F.

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

The slope of the line is calculated as,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

The two points are (6,2) and (0,0). Calculate the slope of the line,

[tex]m = \dfrac{0 - 2}{0-6}[/tex]

m = 1 / 3

The equation of the line can be written as,

y = mx +c

y = 1/3x + 0

y = 1/3x

To know more about an equation of the line follow

https://brainly.com/question/18831322

#SPJ7

prove that:sin3A/sinA - cos3A/cosA=2​

Answers

The result essentially follows directly from the triple-angle identities,

sin(3A) = 3 sin(A) cos²(A) - sin³(A)

cos(3A) = cos³(A) - 3 sin²(A) cos(A)

Then

sin(3A)/sin(A) = 3 cos²(A) - sin²(A)

cos(3A)/cos(A) = cos²(A) - 3 sin²(A)

and

sin(3A)/sin(A) - cos(3A)/cos(A)

= 3(cos²(A) + sin²(A)) - (sin²(A) + cos²(A))

= 3 - 1

= 2

Ronald brought a jacket on Friday that had original price if $45. It was on sale at 10% off its original price. Which formula shows what Ronald paid after 7% sales tax was added?

A. 1.07(45-10)
B. 1.03(45)
C. 1.07(45-45(.1))
D. 1.1(45-45(.7))

Answers

the answer is D 1.1(45-45(.7))

Find the volume.
Use = 3.14
cone
h = 14 in.
r = 9.9 in.
in 3
h
Type the correct answer rounded to two
decimal places, pls help it would be so appreciated

Answers

Answer:

Volume of the cone given rounded to two decimal places is 1415.65in

Explanation:

Volume of a cone

[tex] = \pi {r}^{2} \frac{h}{3} [/tex]

[tex] = (3.14)( {9.9}^{2} )( \frac{14}{3} )[/tex]

[tex] = 3.14 \: \times \: 98.01 \: \times \: 4.6[/tex]

[tex] = 1415.65644[/tex]

You bought 4 boxes of facial tissue for $3.79. which is the better buy than the one you made?

Answers

I don’t get it please specify with more details

help me pls I dont get this

Answers

Answer:

D

Step-by-step explanation:

The answer is D because if you flip those circles down and wrap the rectangle around it will create a cylinder

Convert 6 centimeters per second to miles per hour.
0.13 mph
7.87 mph
0.07 mph
5.87 mph

Answers

Answer:

A, 0.13 mph.

Step-by-step explanation:

To get that, divide the cm/sec by 44.704.

6/44.704 ≈ 0.13

help and explain ///////////////////////////

Answers

Hello,

First, you must understand that

(f-g)(x) means f(x)-g(x) it is the difference of two functions :

f(x)=2x+4 and g(x)=3x-7

f(5)=2*5+4=10+4=14

g(5)=3*5-7=15-7=8

So, (f-g)(5)= f(5)-g(5)=14-8=6

Answer A: none of the choices are correct.

An other way to do it:

(f-g)(x)=f(x)-g(x)=2x+4-(3x-7)= 2x-3x+4+7=-x+11

if x= 5 then (f-g)(5)=-5+11=6

square root of 10 using graph.
please help​

Answers

Step-by-step explanation:

final answer is 4 91 1 6 this is square root of 10

Which correctly completed the statement given below?

Answers

I haven’t did one of theses in forever but I thinks its C

Answer:

C = <CDB, SAS

You can prove side BD because of the reflexive property (using two of the same sides to prove something) and you are given the other side and the angle. So, since you have a side, angle, and side in that order, you can prove it with SAS.

Two square based pyramids are joined, total volume is 2700mm, perpendicular height 16mm on top pyramid and 20mm on the other, joint base has length and width of x, find x. Please help me..

Answers

Answer:

15 mm

Step-by-step explanation:

Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.

Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.

For the first pyramid, the volume is:

V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.

Since the pyramid has a height of 16 mm, hence:

V₁ = 16x²/3

the second pyramid, the volume is:

V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.

Since the pyramid has a height of 20 mm, hence:

V₂ = 20x²/3

Since the total volume (V) of the pyramid is 2700 mm³, hence:

V = V₁ + V₂

V = 16x²/3 + 20x²/3

2700 = 16x²/3 + 20x²/3

2700 = 36x²/3

36x² = 8100

x² = 225

x = 15 mm

For how many integer values of M is M/30 strictly between 1/3 and 3/5?

Answers

Answer:

6 possible intergers brainliest me

Answer:

its 7

Step-by-step explanation:

Which equation represents the line that passes through (-8,11) and
and (4, 7/2)?

A) y = -5/8x + 6
B) y = -5/8x + 16
C) y = 15/2x - 49
D) y = -15/2x + 71

Answers

Answer:

A) y = -5/8x + 6

Step-by-step explanation:

y2 - y`1 / x2 - x1

7/2 - 11 / 4 - (-8)

-15/2  / 12

= -5/8

y = -5/8x + b

11 = -5/8(-8) + b

11 = 5 + b

6 = b

Answer:

Option (A)

y = - 5 / 8 x + 6

Step-by-step explanation:

Two points are

(x', y') = ( - 8, 11 )

(x'', y'') = (4, 7/2)

The equation o line passing through two points is given by

[tex](y - y') = \frac{y'' - y'}{x''-x'}(x-x')\\\\(y - 11)= \frac{\frac{7}{2}-11}{4+8} (x + 8)\\\\y - 11 = \frac{-5}{8}(x + 8)\\\\y -11 = \frac{-5x}{8} - 5\\\\y = \frac{-5x}{8} + 6[/tex]

So, option (A) is correct.  

help me out ! <33
i give high points
thiss is a histogram there are some other information shown...

Answers

Answer:

0.287671233 or 42/146

Step-by-step explanation:

It's not a clear photo, but I tried my best. Probablilty is just what they're looking for over the total amount.

So the amount of people traveling over 4km is 42 based on the graph.

And the total number of people is 146.

(I don't know if the last bar in the graph represents 10 or 20 people)

So 42/146 = 0.287671233

Forgive me if I'm wrong, but I couldn't see the image clearly.

Good luck!

The difference between the set of non-negative real numbers and the set of positive real numbers is:
A.an infinite set B.a null set C.a singleton set D.Null set

Answers

Answer:

C; A singleton set

Step-by-step explanation:

Mathematically, when a number is non-negative; it is either positive or zero

Now, this is because 0 identifies as neither a positive or a negative number

hence, when we find the difference between the two sets, the only number that stands out unmatched is the value 0

What this mean is that we are having a set with a single number result

So we have our answer as {0}

Which is a singleton set

A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries negative 10, 0, 0, negative 4, negative 6, 0.
Which is a y-intercept of the continuous function in the table?

Answers

Hello,

[tex]\begin{array}{c|c|c|}&x&f(x)\\1&-4&-10\\2&-3&0\\3&-2&0\\4&-1&-4\\5&0&-6******\\6&1&0\\\end{array}\\[/tex]

y-intercept is -6

If x=0 then y=-6

find the missing side. round to the nearest tenth.
24) HELP ITS DUE IN THE MORNING

A) 14.2
C) 13.8
B) 9.2
D) 15.7

25.
A)37.6
B)30.8
C)45.1
D)5.5

Answers

Answer:

24) x = 9.2

25) x = 30.8

Step-by-step explanation:

Given

See attachment for triangles

Solving (24)

To solve for x, we make use of cosine formula

i.e.

cos(40) = adjacent ÷ hypotenuse

So, we have:

cos(40) = x ÷ 12

Multiply both sides by 12

12 cos(40) = x

12 * 0.7660 = x

x = 9.2

Solving (25)

To solve for x, we make use of sine formula

i.e.

sin(25) = opposite ÷ hypotenuse

So, we have:

sin(25) = 13 ÷ x

Multiply both sides by

x sin(25) = 13

Divide by sin(25)

x = 13 ÷ sin(25)

Using a calculator

x = 30.8

i13(12)-2give answer​

Answers

154 I might be wrong tho

Rachel, Trey, and Juan sent a total of 85 text messages over their cell phones during the weekend. Rachel sent 10 more messages than Trey. Juan sent 3 times as many messages as Rachel. How many messages did they each send?

Answers

Answer:

Trey = 9 text messages

Rachel = 19 text messages

Juan = 57 text messages

Step-by-step explanation:

Let

Number of messages Trey sent = x

Number of messages Rachel sent = x + 10

Number of messages Juan sent = 3(x + 10)

Total messages = 85

Total = Trey + Rachel + Juan

85 = x + (x + 10) + 3(x + 10)

85 = x + x + 10 + 3x + 30

85 = 5x + 40

85 - 40 = 5x

45 = 5x

x = 45/5

x = 9

Number of messages Trey sent = x = 9 text messages

Number of messages Rachel sent = x + 10

= 9 + 10

= 19 text messages

Number of messages Juan sent = 3(x + 10)

= 3(9 + 10)

= 3(19)

= 57 text messages

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