Suppose that n is a positive number and Log10 n = q. Which expression always equals the value of Log10 n^2?

[tex]\qquad[/tex]_________________________

[tex]\bf Multiplying\:by\:\: \purple{ \dfrac{5+\sqrt{3}}{5+\sqrt{3}}}\\[/tex]

[tex]\qquad[/tex][tex] \longrightarrow \bf \dfrac{1}{5 - 2\sqrt{3} } \times \dfrac{5 + 2\sqrt{3} }{5 + 2\sqrt{3} }\\ [/tex]

[tex]\qquad[/tex][tex]\longrightarrow \sf \dfrac{1(5 + 2\sqrt{3}) }{(5 - 2\sqrt{3})(5 + 2\sqrt{3}) } [/tex]

[tex]\qquad[/tex][tex]\longrightarrow \sf \dfrac{5 + 2\sqrt{3} }{ {(5)}^{2} - (2 \sqrt{3})^{2} } [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(5 \times 5) - (2 \times 2 \times \sqrt{3} \times \sqrt{3} )} [/tex]

[tex]\qquad[/tex][tex] \longrightarrow \sf \dfrac{5 + 2 \sqrt{3} }{(25) - (12)} [/tex]

[tex]\qquad[/tex][tex] \purple{ \longrightarrow \bf \dfrac{5 + 2 \sqrt{3} }{13} } [/tex]

[tex]\qquad[/tex]_________________________

Answer is 2/(5+√13)

Rationalize the denominator 1/ (5-2√3)

Answer:

How to solve your problem-  

9 + 3 2 = − 1 2

Step-by-step explanation:

− 9 +  3  2  =  − 1 2

9+3p2=-12

3 2  − 9 =  − 1 2

Answer:

equation of g(x) is 3-x

then,,

ie.. g(x)=3-x

Answer:

So Jennys Jean store charges the higher rate.

Step-by-step explanation:

Jeanys Jean store

Cost/pair = 20/1 = $20 per pair

Jeans warehouse

Cost/pairs = 36/2 = $18 per pair

So Jennys Jean store charges the higher rate.

Answer:

160

Step-by-step explanation:

4th square number: 16

12th square number: 144

16 + 144 = 160

Answer:

Cos C = adjecent/hypotenuse

Cos C = 14/50

divide the numerator and the denominator by 2

Cos C = 7/25

The answer is C

Answer:

each ornament was about 5 cents

Step-by-step explanation:

Hope this helps

May I get Braineist pls

Answer:

9

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-(-2))/(-6-(-7))

m=(7+2)/(-6+7)

m=9/1

m=9

[tex]2(4x+1)<3(2x-3)\\\\\implies 8x +2 < 6x -9\\\\\implies 8x <6x -9 -2\\\\\implies 8x -6x < -11\\\\\implies 2x<-11\\\\\implies x< -\dfrac{11}2\\\\\\\text{Interval,} ~ \left(-\infty, -\dfrac{11}2 \right)[/tex]

Answer:

x<3.5

Step-by-step explanation:

multiply 2 with 4x and 1 to get 8x + 2 < 3(2x-3). Then multiply 3 by 2x and -3 to get 8x + 2 < 6x- 9. Then subtract -6x on both sides to get 2x + 2< -9. Next subtract 2 from -9 so x is by itself and then you get 2x < 7. Finally divide 2 on each side so you leave x byitself completely. You get x > 3.5

I hope u get it right!

The price of the one notebook will be Rs. 10.6

If Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store, with a total of Rs. 95 paid in all, then;

1x + 4x + 4x = 95

9x = 95

x = 95/9

x = 10. 6

Hence the price of the one notebook will be Rs. 10.6

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Answer:

Step-by-step explanation:

Let the required distance be x.

We have a right triangle with vertical leg of 70 feet and the acute angle opposite to this leg is 22 degrees.

Use trigonometry:

[tex]y = -3x +12\\\\\text{Plug x = 0 to find y - intercept,}\\\\y = -3(0) +12 = 12\\\\\text{So, y-intercept is (0,12).}\\\\\text{Plug y=0 to find x - intercept,}\\\\0 = -3x +12\\\\\implies -3x = -12\\\\\implies 3x = 12\\\\\implies x = \dfrac{12}{3} = 4 \\\\\\\text{So, x - intercept is (4,0).}[/tex]

Answer:

44 dollars

Step-by-step explanation:

Since we need to find the total sales, we do 152 * .29, but we are estimating, therefore, instead we can do 150 * .29, which is 43.5. Rounding up we get 44, thus 44 is our answer

Answer:

y=-6x-4

Step-by-step explanation:

Any linear equation that has the slope of -6 is parallel to y=-6x+5

Answer:

x = 1.125 AKA x = 1 1/8 AKA x = 9/8

Step-by-step explanation:

CB to ED = 1 : 9

Scale Factor = 1/9

[tex]\frac{1}{9} = \frac{x}{x+9}[/tex] -> cross multiply

9x = x + 9

-x     -x

8x = 9

[tex]\frac{8x}{8} =\frac{9}{8}[/tex]

x = 9/8

The system of equations representing the number of Blue-ray discs and DVD's after t months are:

507 + 26t

925 - 12t

Each month, the number of DVD's sold decreases by 12, this can be modelled as:

number of DVD in opening month - (monthly decrease x number of months)

Number of DVD's in t months = 925 - 12t

Each month, the number of Blue-ray discs sold increases by 26, this can be modelled as:

number of blue-ray discs in opening month + (monthly increase x number of months)

Number of Blue-ray discs in t months = 507 + 26t

To learn more about growth rate, please check: https://brainly.com/question/18760477

Answer:

y intercept is 2

x intercept is -2.6

Step-by-step explanation:

4y=3x-8

4y-3x=8

y/2-x/2.6=1

y intercept is 2

x intercept is -2.6

intercept formula

y/B+x/A= 1

where B and A are intercepts

Answer:

Rate of sales tax = 6% of $60

Sales tax = [tex]\frac{6}{100}[/tex] × 60

               = $3.60

Answer:

$ 275

Step-by-step explanation:

20/100 = 55/x (20% is 55 of what number) (%/100 = is/of)

(100 * 55) / 20 = 275

Answer:

68.75

Step-by-step explanation:

Answer:

SAS is the answer

Step-by-step explanation:

Answer:

HL.

Step-by-step explanation:

Right triangles with the hypotenuse and one leg congruent

Answer: 0.6 is the answer

Answer:

65°

Step-by-step explanation:

x=180°-40°-75°

x=65°

Answer:

third option: log_2  1/3

Step-by-step explanation:

change of base formula:

log_b  a= (log_x a)/(log_x b)

(log 1/3)/(log 2)

apply reverse change of base formula

2 from log 2 becomes new base, and 1/3 becomes the other number

=log_2  1/3

The original logarithmic expression which when undergoes the change of base formula gives the expression ㏒ (1/3) / ㏒ (2) is third option ㏒₂ (1/3).

Given a logarithmic expression,

㏒ (1/3) / ㏒ (2)

This expression is the result of a logarithmic expression when undergoes change of base formula.

The change of base formula is as given below.

㏒ₐ (x) = ㏒ₙ (x) / ㏒ₙ (a)

Using the same formula here,

We have the expression ㏒ (1/3) / ㏒ (2).

Here x = 1/3 and a = 2

So, the required expression is,

㏒ₐ (x) = ㏒₂ (1/3)

Learn more about Logarithmic Expressions here :

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Answer:

x = 48

Step-by-step explanation:

Given a secant and a tangent from an external point to the circle, then

the product of the external part and the entire secant is equal to the square of the measure of the tangent , that is

2(2 + x) = 10² = 100 ( divide both sides by 2 )

2 + x = 50 ( subtract 2 from both sides )

x = 48

Answer:

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It is given that ️PQR & ️UVW are congruent to each other. According to CPCT, the corresponding angles in 2 triangles willl have the same measure. So, ∠R = ∠W, i.e, (10x - 18)° = 8x°

[tex]\mathfrak{10x - 18 = 8x} [/tex]

[tex]\mathfrak{10x - 8x = 18} [/tex]

[tex]\mathfrak{2x = 18} [/tex]

[tex]\mathfrak{x = \dfrac{18}{2}} [/tex]

[tex]\underline{\mathfrak{x = 9}} [/tex]

Measure of ∠R :

[tex]\mathfrak{8x} [/tex]

[tex]\mathfrak{8(9)} [/tex]

[tex]\boxed{\mathfrak{72^{\circ}}} [/tex]

 ღ ꪑ꠸᥅ꫀꪊ

Answer:

60 have 12 factors :1,2,3,4,5,6,10,12,15,20,30,60

Answer:

3 cups

Step-by-step explanation:

3/4 times 4 equals 12/4. divide and get 3.