if
[tex] \sqrt{5} x = \sqrt{3} x + \sqrt{7} [/tex]
find the value of x in the form
[tex] \sqrt{ \frac{a}{b} } [/tex]

Answers

Answer 1

Answer:

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Step-by-step explanation:

From the way it is written, the [tex]x[/tex] is outside the square root. I will rewrite it as:

[tex]x\sqrt{5} =x\sqrt{3} +\sqrt{7}[/tex]

[tex]x\sqrt{5}-x\sqrt{3}=\sqrt{7}[/tex]

[tex]x(\sqrt{5} - \sqrt{3} )=\sqrt{7}[/tex]

[tex]$x= \frac{\sqrt{7} }{\sqrt{5} - \sqrt{3}} \implies \frac{\sqrt{7}(\sqrt{5} + \sqrt{3}) }{2} $[/tex]

[tex]$x=\frac{1}{2} \sqrt{7} (\sqrt{5} + \sqrt{3} )$[/tex]

[tex]$x=\frac{\sqrt{35}}{2} +\frac{ \sqrt{21}}{2} $[/tex]

[tex]$x=\frac{\sqrt{35}+\sqrt{21}}{2} $[/tex]

Multiply denominator and numerator by 3

[tex]$x=\frac{3\sqrt{35}+3 \sqrt{21}}{6} $[/tex]

Factor [tex]\sqrt{3}[/tex]

[tex]\sqrt{3} (\sqrt{105}+3 \sqrt{7})[/tex]

[tex]$x=\frac{\sqrt{3} (\sqrt{105}+3 \sqrt{7})}{6} $[/tex]

Divide denominator and numerator by [tex]\sqrt{3}[/tex]

[tex]$x=\frac{\sqrt{105}+3 \sqrt{7}}{2\sqrt{3} } $[/tex]

Let's rewrite it again

[tex]$x=\frac{\sqrt{ (\sqrt{105}+3 \sqrt{7})^2}}{\sqrt{12} } $[/tex]

[tex]$x=\sqrt{ \frac{1}{12} \cdot (\sqrt{105}+3 \sqrt{7})^2}$[/tex]

It is already in the form [tex]$\sqrt{\frac{a}{b} } $[/tex]

Expanding the perfect square, we have

[tex]63+42\sqrt{15}+105[/tex]

[tex]$\frac{63}{12} +\frac{42\sqrt{15}}{12} +\frac{105}{12} $[/tex]

[tex]$\frac{21}{4} +\frac{7\sqrt{15}}{2} +\frac{35}{4} $[/tex]

Factor [tex]$\frac{7}{2} $[/tex]

[tex]$\frac{7}{2} (4+\sqrt{15} )$[/tex]

Therefore,

[tex]$x=\sqrt{\frac{7}{2} \left(4+\sqrt{15} \right)} $[/tex]

[tex]$x=\sqrt{\frac{7(4+\sqrt{15})}{2}} $[/tex]

Answer 2
x= 7/4 x 25/6 is the answer

Related Questions

Solve for v. 3v + 5v = 72 please simplify as much as possible! v = _ ?

Answers

Answer:

v is 9

Step-by-step explanation:

it is 9 because if you simplify it is 8v=72 or 9

Answer:

v = 9

Step-by-step explanation:

3v + 5v = 72

combine like terms

8v = 72

Divide by 8

8v/8 = 72/8

v =9

Find the hypotenuse and the shorter leg of a30°−60°−90° triangle, if the longer leg is 9 in.

Answers

Answer:

Since it's a 30-60-90 triangle, the hypotenuse should be  

6 √ 3

and the short leg is  

3 √ 3

Step-by-step explanation:

Ratio:

Short side:  1  

Hypotenuse:  2

Long Side:  √ 3

short side is one hope ihelped

Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. GA ∩ TN = I ∆GIT ≅ ∆_____ by _____

Answers

Answer:

The correct answer is;

ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Step-by-step explanation:

The given information are;

The point of intersection of GA ∩ TN = I

Segment TI is congruent to segment NI (Given)

Segment GI is congruent to segment IA (Given)

Angle ∠GIT is congruent to angle ∠AIN (Vertically opposite angles)

Therefore, we have;

Triangle, ΔGIT is congruent to triangle ΔNIA (Side Angle Side (SAS) rule of congruency)

Two triangles are said to be congruent by the Side Angle Side (SAS) rule of congruency,  when two of the sides and the included angle (the angle in between the two sides) of one of the triangle are equal to two sides and the included angle of the other triangle.

Therefore, the correct answer is ΔGIT≅ ΔNIA by Side Angle Side (SAS) rule of congruency

Answer:

△GIT≅△AIN

By Rule: SAS

i need this quick!!! please hurry!! Solve the following proportion for X. X over 5 = 17 over 3 Round your answer to the nearest tenth.

Answers

Answer:

[tex]\huge\boxed{x = 28.3}[/tex]

Step-by-step explanation:

=> [tex]\frac{x}{5} = \frac{17}{3}[/tex]

Cross Multiplying

=> x * 3 = 5 * 17

=> 3x = 85

Dividing both sides by 3

=> x = 85/3

=> x = 28.3 (To nearest tenth)

Answer:

[tex]\Huge \boxed{x=28.3}[/tex]

Step-by-step explanation:

The proportion is given,

[tex]\displaystyle \frac{x}{5} =\frac{17}{3}[/tex]

We need the x variable isolated on one side, so we can find the value of x that makes the proportion true.

Multiply both sides of the equation by 5.

[tex]\displaystyle \frac{x}{5} \times (5)=\frac{17}{3} \times (5)[/tex]

Simplify the equation.

[tex]\displaystyle x=\frac{85}{3}[/tex]

[tex]x=28.33333333...[/tex]

The value of x that makes the proportion true is 28.3 (rounded to nearest tenth place).

Find the distance between (4.9) and (5, 12)

Answers

Answer:

[tex]\sqrt{10}[/tex]

Step-by-step explanation:

[tex]\sqrt{(x_{2} - x_{1}) ^ {2} + (y_{2} - y_{1}) ^ {2}}[/tex]

[tex]\sqrt{(5-4) ^ {2} + (12 - 9) ^ {2}} = \sqrt{1^{2}+3^{2}} = \sqrt{10}[/tex]

The answer is the last one.

Please Answer For Brainliest!!!


Answers

Answer:

C

Step-by-step explanation:

They want to find out altogether and the total number so add it up!

Answer: 72,132,204

Step-by-step explanation:

What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers?

Answers

A complex number. For the complex number a+bi, A is called the real part, and B is called the imaginary part
Me just needed points, srry

An atom consists of electrons, protons, and neutrons. Each electron has a charge of -1, each proton has a charge of +1, and each neutron has no charge. If 3 electrons are removed from each of 4 atoms, what is the combined net change to the charge of the 4 atoms?

Answers

Answer:

The net charge on the four atoms is 12

Step-by-step explanation:

The given parameters are;

The charge of each electron = -1

The charge of each proton = + 1

The charge of each neutron = neutral

Therefore, if 3 electrons are removed  from each of the three atoms, we have;

The quantity of net negative charge removed from the four atoms = 3 × -1 × 4 = -12

Given that the at the four atoms add equal  number of protons and electrons, we have;

Original charge on the four atoms = n×(-1) +  n×(+1) = 0

Therefore;

The net charge on the four atoms after removal of the 12 electrons  = Original charge - (-12)

The net charge on the four atoms = 0 - (-12) = +12

The net charge on the four atoms = +12.

The net change of the 4 atoms are 12

Which of the following inequalities is correct?

Answers

Answer:

b

Step-by-step explanation:

The first one is not. Think money. Would you rather be 1 dollar in the hole or 6 dollars in the hole? b = - 1. It is larger than - 6.

The third one is not correct either. -c = - 5

- b = 1

1 is larger than -5

The answer is the middle one

-b becomes 1 which is greater than 0.

B is the answer to that question

Please someone help me...​

Answers

use [tex] a^2-b^2=(a+b)(a-b)[/tex]

to get [tex] (\cos^3A-\sin^3A)(\cos^3A+\sin^3A)[/tex]

then use [tex] a^3+b^3=(a+b)(a^2+b^2-ab)[/tex]

and [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

also, [tex] \sin^2\theta+\cos^2\theta=1[/tex]

to get [tex](\cos A-\sin A)(1+\sin A\cos A)(\cos A+ \sin A)(1-\sin A\cos A)[/tex]

then again use the first identity In both pairs, i.e.

[tex](\cos A-\sin A)(\cos A+ \sin A) \cdot (1+\sin A\cos A)(1-\sin A\cos A)[/tex]

to get [tex] \cos 2A (1-\sin^2A\cos^2A)[/tex]

multiply and divide by 4 to get the RHS.

because, [tex] \sin(2A)= 2\sin A \cos A[/tex]

squaring both sides, [tex] \sin^2 (2A)=4\sin^2A\cos^2A[/tex]

Answer:

they take the same form

Step-by-step explanation:

factor (1 - 1/4 sin ^2 (2A) )  (cos ^ 2 (A) -sin ^2(A))

= ( -sin 2A/ 2)  + 1 ) (sin (2A)/ 2) -1

= - (-1 + )  (sin 2A/2)  (1 +) (sin 2A/2) ( cos (A) + sin (A) (cos (A)- sin (A))

= (sin (2A) +sin 2) (sin (2A) -2)/4 = cos ^2(A) = (sin ^2(A)+cos (A) sin (A)) cos ^2(A) +s)

Yan has already finished Three-fifths of the 45 math problems he was assigned today. Each math problem took him 1 four-fifths of a minute to complete. If this pace continues, how much more time, to the nearest minute, will the rest of the problems take him to finish?

Answers

Answer:

[tex]\boxed{\sf 18\ problems = 22\ minutes}[/tex]

Step-by-step explanation:

Yan has finished = [tex]\frac{3}{5} of \ 45 \ maths \ problems[/tex]

Yan has finished = [tex]\frac{3}{5} * 45[/tex]

=> 3 * 9

=> 27 problems

Yan has problem left:

=> 45 - 27

=> 18 problems

1 problem = [tex]1 \frac{4}{5}[/tex] of a minute

1 problem = 1.2 minutes

18 problems = 1.2 * 18

18 problems = 21.6 minutes

18 problems ≈ 22 minutes

Answer:

[tex]\boxed{\sf 32 \ minutes}[/tex]

Step-by-step explanation:

Yan finished 3/5 of 45 math problems.

[tex]\frac{3}{5} \times 45=27[/tex]

Yan finished 27 math problems.

[tex]\sf 1\frac{4}{5} \ of \ a \ minute= 108 \ seconds=1.8 \ minutes[/tex]

Yan has [tex]45-27=18[/tex] problems left.

1 problem = 1.8 minutes

18 problems = [tex]1.8* 18=32.4[/tex] minutes

32.4 minutes to nearest minute will be 32 minutes.

Translate the following into an algebraic expression: a The number that is 40% more than five more than a number a.

Answers

Answer:

x = a + 8

Step-by-step explanation:

x = The number that is 40% more than five more than a number a.

x = 40% more than 5 (plus a)

5 * 0.6 = 3

5+3 = 8

x = a + 8

The answer is x=8+9.

Help, two of these questions plz

Answers

Answer:

First Answer: y= 64 and x=64

Second Answer: 1&4, 2&3, 6&7, 5&8

Step-by-step explanation:

First Answer: 63 and ∠y is the same measure since there are

Second answer: They are vertical angles, each of the pairs of opposite angles made by two intersecting lines.

Hope this helps:)

1) X = Y = 63 degrees
2) Angles 2= 3 = 6=7
Angles 1= 4=5 = 8

Find the slope of each line. Then tell what the slope represents.

Answers

Answer:

5.  Slope = 8.5

6.  Slope = -12

7.  Slope = 1

Step-by-step explanation:

Slope = y/x - y1/x1

5.  => 68/8 - 25.5/3

    => 68 - 25.5 / 8 - 3

    => 42.5 / 5

    => Slope = 8.5

6.  => 76/2 - 40/5

    => 76 - 40 / 2 - 5

    => 36 / -3

    => Slope = -12

7.  => 4/5.5 - (-1/.5)

    => 4 - (-1) / 5.5 - .5

    => 4 + 1 / 5.5 - .5

    => 5 / 5

    => Slope = 1

Answer:

5.  Slope = 8.5

6.  Slope = -12

7.  Slope = 1

Step-by-step explanation:

Slope = y/x - y1/x1

5.  => 68/8 - 25.5/3

    => 68 - 25.5 / 8 - 3

    => 42.5 / 5

    => Slope = 8.5

6.  => 76/2 - 40/5

    => 76 - 40 / 2 - 5

    => 36 / -3

   => Slope = -12

7.  => 4/5.5 - (-1/.5)

    => 4 - (-1) / 5.5 - .5

    => 4 + 1 / 5.5 - .5

    => 5 / 5

    => Slope = 1

I NEED THE ANSWER ASAP

The number of students who smoke cigarettes at Broxton College is decreasing at a rate of one smoker every 6.31 days. At what rate in smokers per year is the number of smokers declining? Assume 365 days in a year and round to the nearest tenth of a smoker per year

Answers

Answer:

57.8

Step-by-step explanation:

We can set up a proportion for this, assuming x is the smokers lost in 365 days.

[tex]\frac{1}{6.31} = \frac{x}{365}[/tex]

Using the cross products property, we know that x will be equal to:

[tex](365\cdot1) \div 6.31\\365\div6.31\\\\\approx 57.8[/tex]

Hope this helped!

57.8 is the answer to this problem

what number would you subtract from each side of inquality to solve y+3/8>16​

Answers

Answer: I would subtract 3/8 from both sides

Explanation:

y + 3/8 > 16
y > 16 - 3/8 (subtract 3/8 from both side)
y > 128/8 - 3/8
y > 125/8

Answer:

[tex]y > 125[/tex]

Step-by-step explanation:

[tex]y + \frac{3}{8} > 16 \\ y > 16 - \frac{3}{8} [/tex]

[tex]y > (16 \times 8) - ( \frac{3}{8} \times 8) [/tex]

[tex]y > 128 - 3[/tex]

[tex]y > 125[/tex]

What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.

Answers

Answer:

[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^4-5x^2-14=0[/tex]

Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:

[tex]u=x^2[/tex]

Then by substitution:

[tex]u^2-5x-14=0[/tex]

Now we can solve normally. Factor:

[tex](u-7)(u+2)=0[/tex]

Zero Product Property:

[tex]u=7\text{ or } u=-2[/tex]

Back-substitute:

[tex]x^2=7\text{ and } x^2=-2[/tex]

Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:

[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]

Therefore, our solutions are:

[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]

Two joggers start from different locations and simultaneously begin heading toward each other. One of the joggers jogs 19mph, while the other jogs 17mph. If the two joggers are 324 miles apart how many hours will it take before they meet?

Answers

Answer:

errror

Step-by-step explanation:

Error good luck buddy

How is 200,000 + 7,000 +500 + 3 written in standard form?

Answers

Answer:

207,503

Step-by-step explanation:

you just have to add the 4 numbers so you get 207,503

━━━━━━━☆☆━━━━━━━

▹ Answer

207,503

▹ Step-by-Step Explanation

200,000 + 7,000 + 500 + 3

= 207,503

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

What property is used in the second step of solving the inequality below?

5 x minus 9 less-than 91
______Given_______
5 x less-than 100
__________________
x less-than 20
Multiplication Property
Identity Property
Addition Property
Multiplication Property
Transitive Property

Answers

Answer:

Addition property

Step-by-step explanation:

Given the inequality:

5x - 9 < 91

The step to take here to move 9 to the other side, is to perform the addition property by adding 9 to both sides.

Thus,

5x - 9 + 9 < 91 + 9

5x < 100

The final step is to perform the division property by dividing both sides by 5, in order to solve for x.

5x/5 < 100/5

x < 20.

Addition property
Hope
This helps

a 20-foot flagpole casts a 6-foot Shadow how tall is a nearby building that casts a 30-foot shadow

Answers

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

Answer :

The building would be 100ft tall. You have to take 20/6 = ?/30 The difference between 6 and 30 is x5. Then all you have to do is 20x5 and you get 100ft.

can somewon plz help me

Answers

Answer:

1253 in^3

Step-by-step explanation:

The volume of the smaller container is (7 in)(5 in)(5 in) = 175 in^3.

The volume of the larger one is (11 in)(14 in)(7 in) = 1078 in^3

The total volume is the sum of these two volumes:  1253 in^3

Answer:

1253 in^3

Step-by-step explanation:

Volume of small one is 7*5*5 = 175

Volume of the large one is 11*14*7 = 1078

To find the total volume we add them up. We get 1253 and since we are talking about volume it is 1253 inches cubed

The formula for the area of a circle is A= ar?m where A is the area and r is the radius. The subject of
the formula is A. Rearrange the formula to make r the subject.

Answers

Hi there! :)

Answer:

[tex]\sqrt{\frac{A}{\pi } } = r[/tex]

Step-by-step explanation:

Formula for the area of a circle:

[tex]A = \pi r^{2}[/tex]

Rearrange the equation in terms of "r":

Divide 'π' from both sides:

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

Take the square root of both sides:

[tex]\sqrt{\frac{A}{\pi } } = r[/tex]

Answer:

[tex]r = \sqrt{ \frac{A}{ \pi}}[/tex]

Step-by-step explanation:

[tex]A =\pi r^2 \\Divide\: both \:sides\:of\:the\:equation \\\frac{A}{ \pi} =\frac{ \pi r^2}{ \pi} \\r^2 = \frac{A}{ \pi} \\\sqrt{r^2} =\sqrt{ \frac{A}{ \pi}} \\\\r = \sqrt{ \frac{A}{ \pi}}[/tex]

Graph the rational function
f (x)=- 3x + 1
-x+2

Answers

Answer:

Step-by-step explanation:

You must show that this is a rational function.  As written, it is not such.

         -3x + 1

f(x) = ------------

           -x + 2

is a rational function; the horizontal line --------- indicates division.

If we let x grow large, the graph approaches the horizontal line y = 3, which we call "the horizontal asymptote."  There is a vertical asymptote at x = 2, which we know because the denominator will be zero at that x value.  The vertical intercept is

f(0) = 1/2, or (0, 1/2).

As x decreases towards negative infinity, the graph approaches the horizontal line (horizontal asymptote) y = 3.

y=3 seems the best out of this

9.
The Sir Walter Scott Mental Health Center has a budget of $20.000 for recruiting costs
the position of Facility Director. The Center has spent $5,300 on advertising expenses and
$3,500 on interviewing expenses. They are willing to pay 5.5% commission on selling the
selected individual's home. What is the maximum selling price that the Sir Walter Scott
Mental Health Center would pay 5.5% commission on in order to stay at or below the
$20,000 in total recruiting costs?

Answers

Answer:

Hey there!

5300+3500=8800

20000-8800=11200

1.055x=11200

x can be at most 10616 dollars.

Hope this helps :)

At most, it can be 10068

PLEASE HELP! Will mark brainliest! Find the slope of the line:

Answers

Answer:

Step-by-step explanation:

I think 3-y slope

PLEASE HELP ME!! I WILL GIVE BRAINLIEST!!

Find the output, y, when the input, x, is -5.

Answers

Answer:

[tex]\boxed{y = -2}[/tex]

Step-by-step explanation:

Hey there!

To find y when x is -5 we go to -5 on the x-axis.

When at -5 find where the blue line is vertical to -5,

which is -2.

Hope this helps :)

The Answer is:

y = - 2

i need the answer plz

Answers

Answer:

Step-by-step explanation:

The second answer choice correctly shows the result of multiplying functions m and n together.

It’s the second choice

PLEASE HELP ASAP I WILL REWARD BRAINLIEST one unit up, one unit down, one unit left, one unit right,

Answers

Answer:

y=x+2

Step-by-step explanation:

Since 1 up, 1 down, 1 left, and 1 right would all cancel out so you would still get y=x+2

Answer:

see below

Step-by-step explanation:

will make it simple.

1 unit up : y = |x+2| + 1

1 unit down : y = |x+2| - 1

1 unit to the left : y = |x + 3|

1 unit to the right : y = |x+1|

hope it helps.  if its wrong, then please report it wo we can delete of correct it.

Please show ALL work!!!!

Answers

Answer:

[tex]$\boxed{\log _2\left(\frac{zx^2}{y^2} \right) +\log _9(y^4 x^{12})} $[/tex]

Step-by-step explanation:

[tex]\log _2z+2\log _2x+4\log _9y+12\log _9x-2\log _2y[/tex]

We have logarithms in base 2 and 9. Let's rewrite it:

[tex]\log _2z+2\log _2x-2\log _2y+4\log _9y+12\log _9x[/tex]

Remember that:

[tex]\boxed{p\log _bc=\log _b c^p}[/tex]

[tex]\log _2z+\log _2 x^2 -\log _2y^2 +\log _9y^4+\log _9x^{12}[/tex]

Remember the Product Rule:

[tex]\boxed{\log_b(xy)=\log_bx + \log_by}[/tex]

[tex]\log _2(zx^2) -\log _2y^2 +\log _9(y^4 x^{12})[/tex]

Finally, remember the Quotient Rule:

[tex]$\boxed{\log_b\left(\frac{x}{y} \right)=\log_bx - \log_by}$[/tex]

[tex]$\log _2\left(\frac{zx^2}{y^2} \right) +\log _9(y^4 x^{12})$[/tex]

Answer


I only know how to get the answer but not explain
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