Solve the following equation:
[tex]x + \sqrt{x+3} = 3 + 3\sqrt{1-x}[/tex]

Answers

Answer 1

Answer:

[tex]x+\sqrt{x+3}=3+3\sqrt{1-x}[/tex]

[tex]Remove~ Square ~root[/tex]

[tex]-36x^3+252x^2-540x+324=[/tex]

[tex]x^4-32x^3+286x^2-480x+225[/tex]

[tex]Now ~\mathrm{Switch\:sides}[/tex]

[tex]x^2-6x\sqrt{-x+1}-15x+18\sqrt{-x+1}+18=x+3[/tex]

[tex]\mathrm{Subtract\:}x^2-15x\mathrm{\:from\:both\:sides}[/tex]

[tex]x^2-6x\sqrt{-x+1}-15x+18\sqrt{-x+1}+18-\left(x^2-15x\right)=[/tex]

[tex]x+3-\left(x^2-15x\right)[/tex]

[tex]New ~Simplify[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}+18=-x^2+16x+3[/tex]

[tex]Subtract ~18~ from ~ both~ sides[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}+18-18=-x^2+16x+3-18[/tex]

[tex]Simplify[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}=-x^2+16x-15[/tex]

[tex]Now~ factor:[/tex]

[tex]-6x\sqrt{-x+1}+18\sqrt{-x+1}(-x+3)[/tex]

[tex]6\sqrt{-x+1}\left(-x+3\right)=-x^2+16x-15[/tex]

[tex]Solve~~-36x^{3}+252x^{2} -540x+324=x^{4} -32x^{3} +286x^{2} -480x+225=[/tex]

[tex]x=1,\:x=-3[/tex]

-----------------------hope it helps..have a nice day/night

Related Questions

-40 divided by what makes -4

Answers

Answer:

10

Step-by-step explanation:

<3

factorise:
k² - 2k - 8
with explaining the steps

Answers

Answer:

( k-4)(k+2)

Step-by-step explanation:

k² - 2k - 8

What 2 numbers multiply to -8 and add tp -2

-4*2 = -8

-4+2 = -2

( k-4)(k+2)

Refer to the attachment for steb-by-step explanation.

How many quarters are there in 5 and 3/4

Answers

Answer:

23

Each 1 has 4 quarters

5*4=20

20+3

23

Step-by-step explanation:

Two cables are attached to a 30-foot wall and a 22-foot wall. If the tie down for the cables is located in the center of a 40-foot wide alley between the two walls, what is the angle \thetaθ that is formed between the cables? Round your answer to the nearest whole number.

Answers

Answer:

76°

Step-by-step explanation:

Applying trigonometry :

Angle x ;

Tan x = opposite / adjacent

Tan x = (30/20)

x = tan^-1(30/20)

x = 56.31°

Angle y;

Tan y = opposite / adjacent

Tan y = (22/20)

x = tan^-1(22/20)

x = 47.73°

The angle θ ;

Sum of angles in a straight line = 180

56.31 + 47.73 + θ = 180°

θ = 75.96°

Please help
Honestly cant understand

Answers

Answer: x=20°

Explanation: Since UTX is a diameter, it is equal to 180°. You can now set up the equation (4x+2)+x+78=180. Then solve for x.

You should get, x=20.

pls help me i need help asap 30!! points pls help on all 4 questions

Answers

Answer:

b

d

a

d

Step-by-step explanation:

if im writing 200 post cards , and stamps are 0.36 cents a piece, how much money would 200 stamps be?

Answers

Answer:

72

Step-by-step explanation:

1 stamp costs 0.36 cents

Then, 200 post cards will cost 0.36 × 200 = 72

Answer:

$72 dollars

Step-by-step explanation:

200 x 0.36 = 72

What is the volume of the cylinder shown below?
15
10

Answers

Answer:

option B

Step-by-step explanation:

Given r = 10 , h = 15

[tex]Volume = \pi r^2 h = \pi \times 10^2 \times 15 = \pi \times 100 \times 15 = 1500 \pi \ cubic \ units[/tex]

Encuentra el volumen de un prisma rectangular que mide 14m de largo y 10 m de ancho 34m de altura.

Answers

4,760m^3
14x10x34
140x34=4760

please help find x!! asap

Answers

Answer:

x = 60

Step-by-step explanation:

The angle 30 is on the same vertical line as the angle that is adjacent to the missing angle x. they form 90 degrees.

These two lines represent a system of equations.
What is the solution to that system?
Help ?

Answers

Answer: (-1,1)

Step-by-step explanation: Look at the intersection point of the lines

4x² + 3 = -7x
solve for x
x=_,_​

Answers

[tex]\displaystyle\bf 4x^2+3=-7x\\\\4x^2+7x+3=0 \\D=49-48=1 \\\\x_{1;2}=\frac{-7\pm1}{8} => x_1=-1\quad ; \quad x_2=-\frac{3}{4} \\\\\\Answer:\boxed{x_1=-1\quad ; \quad x_2=-\frac{3}{4} }[/tex]

Please help. Thank you. (30 points included) (Shown work)

Answers

Answer:

True

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.

HELP ASAP PLS I NEED HELP

Answers

Answer:

B

Step-by-step explanation:

r^2 is 0.9997, and after 10 years it'll be 95660

PLEASE PLEASE PLEASE HELP ME!!! IM SO CLOSE TO GETTING THE SCORE I NEED

explaining your answer = brainliest

The radius of a circle is 2 kilometers. What is the area of a sector bounded by a 36° arc?

answer has to be in SIMPLEST form

Answers

Answer:

[tex]\frac{2}{5} \pi[/tex] [tex]km^{2}[/tex]

Step-by-step explanation:

In this problem, we will use the following formula:

A = [tex](\frac{C}{360}) \pi r^{2}[/tex] , where r = radius & C = central angle

Step 1: Plug in for C and r.

A =  [tex](\frac{C}{360} )\pi r^{2}[/tex]A = [tex](\frac{36}{360})\pi 2^{2}[/tex]

Step 2: Solve.

A = [tex](\frac{1}{10})4\pi[/tex]A =  [tex]\frac{2}{5} \pi[/tex]

Final answer (simplified & exact):  [tex]\frac{2}{5} \pi[/tex] [tex]km^{2}[/tex]

Sorry it took so long to complete... kinda started with the wrong answer... But I hope this helps and that you have a great rest of your day!

Pls help I need this

Answers

Answer:

what you need help in we see nothing

can someone help please...

Answers

Answer:

the answer is median (b)

how do u find volume of a rectangle

Answers

Count up all the sides of the triangle and divide it by 3 if I’m
Not mistaken

Answer:

the length of the rectangle times the wedth of the rectangele by 2

Graph h(x)=-x^4 +3
Use the parabola tool then choose the vertex followed by one point on the parabola.

Answers

Hope this helps, the y intercept is 3 ans the x intercepts are +1.3 and -1.3

The y intercept is 3 and the x intercepts are +1.3 and -1.3

The graph is given below.

What is graph?

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

Here, we have,

h(x)=-x^4 +3

so, The y intercept is 3 and the x intercepts are +1.3 and -1.3

The graph is given below.

To learn more on graph click:

brainly.com/question/17267403

#SPJ2

the ratio of blue to yellow paint when mixed to make green paint is 3:2 what percentage of the green paint is made from yellow paint

Answers

Answer:

40%

Step-by-step explanation:

3 + 2 = 5

Since 2 is the ratio of yellow paint, 2/5 x 100 = 40%

Hope this helped!

I. NEED. HELP! PLEASE!

Answers

Answer:

x = 2.5

Step-by-step explanation:

We know the adjacent and the opposite sides to the angle in a right triangle

tan theta = opp / adj

tan 26 = 1.2 /x

x tan 26 = 1.2

x = 1.2 / tan 26

x =2.46036461

Rounding to the nearest tenth

x = 2.5

tan tita = opp/adj

tan 26°=1.2/x

x=1.2/tan 26

x=2.46

x=2.5

12
Activity 2
1. Express each as a unit rate.
a) A car travelled 150 km in 3 hour. Show your work.​

Answers

Given:

A car traveled 150 km in 3 hour.

To find:

The unit rate.

Solution:

We have,

Distance = 150 km

Time = 3 hours.

In this case speed is the unit rate.

[tex]Speed=\dfrac{Distance}{Time}[/tex]

Substituting the given values, we get

[tex]Speed=\dfrac{150\text{ km}}{3\text{ hr}}[/tex]

[tex]Speed=50\text{ km/h}[/tex]

Therefore, the unit rate is 50 km/h.

PLEASE HELP ME WITH THIS

Answers

-3 is the 3rd box and you go down 3 spaces then over 2

Which number could represent point Z

Answers

10 1/2 would be the place u dotted Z down

the sum of the squares of two consecutive integers is 481. Find the integers​

Answers

Answer:

{15, 16} or {-15, -16}

Step-by-step explanation:

Quick solution:

take half of the sum (approx. 240), sqrt(240)=15.5

So the numbers are 15 and 16.  and also the negative equivalents since squares are always positive.

Exact method:

Let

x=smaller integer,

x+1 = next integer.

sum:

x²⁺(x+1)^2 = 481

2x^2 + 2x + 1 = 481

2x^2 + 2x - 480 = 0

x^2 + x -240 = 0

x = 15 or x = -16

so the integers are

either

{15, 16} or {-15, -16}

The sum of the squares of two consecutive integers is 481 will be -15 & -16 and 15 and 16.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Successive numbers are those that follow one another continually, from lowest to biggest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.

Assume 'x' is the number and the successive number is (x + 1).

The sum of the square of the consecutive number is 481. Then the equation of the number is given as,

x² + (x + 1)² = 481

Simplify the equation, then we have

x² + (x + 1)² = 481

x² + x² + 2x + 1 = 481

2x² + 2x - 480 = 0

x² + x - 240 = 0

x² + 16x - 15x - 240 = 0

x(x + 16) - 15(x + 16) = 0

(x + 16)(x - 15) = 0

x = 15, -16

Then the successive numbers are given as,

x + 1 = 15 + 1

x + 1 = 16

x + 1 = - 16 + 1

x + 1 = - 15

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

Solve for x.
2/5 ≤ x-4

Answers

2/5 ≤ x-4

0.4 ≤ x-4

let's just add 4 on both sides

0.4 +4 ≤ x-4 +4

4.4 ≤ x

simple as that. just handle inequalities like you would handle equations

Which graph shows the solution to the system of linear inequalities?
x+5y>5
Y<2x+4
PLEASE HELP!!!

Answers

Answer:

x+5y >5 => red

y< 2x+4 => blue

Step-by-step explanation:

you can substitute x and y in each inequality to determine

Kadeesha has a point card for a movie theater.
She receives 50 rewards points just for signing up she earns 12.5 points for each visit to the movie theater she needs at least 210 points for a free movie ticket right and solve for an inequality the number of visits kadeesha can make to earn her first free movie ticket

Answers

Answer:

50 + 12.5 v ≥ 210

She needs at least 13 visits

Step-by-step explanation:

points for signing up + points per visit* number of visits ≥  210

50 + 12.5 v ≥ 210

Subtract 50 from each side

50 + 12.5 v -50 ≥ 210-50

12.5 v ≥ 160

Divide by 12.5

12.5 v/12.5 ≥ 160/12.5

v ≥ 12.8

She needs at least 13 visits

Answer:

Step-by-step explanation:

Find the value of x in the isosceles triangle shown below​

Answers

Answer:

x²+4² =8²

x²+16 =64

x² =64-16.

x² =48

x. =√48

answer is option D

Answer:

D

Step-by-step explanation:

The segment x is a perpendicular bisector and divides the triangle into 2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles, then

x² + 4² = 8²

x² + 16 = 64 ( subtract 16 from both sides )

x² = 48 ( take the square root of both sides )

x = [tex]\sqrt{48}[/tex] → D

Hey!! Can you guys help me !!

No links!!
No spams!!

Ahmed paid $34 000 for a car. His car decreased in value by 40% at the end of the first year. The value at the end of the second year was 10% less than the value at the end of the first year. . Calculate the value of Ahmed's car after 2 years .​

Answers

First step:

40% of 34 000

40/100 * 34 000 = 13 600

subtract : 34000 - 13 600 = 20 400

Second step:

10% of 20 400

10/100 * 20 400 = 2040

subtract : 20 400 - 2040 = $ 18 360

Final Answer = $ 18 360
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