how to solve for X

4/X=12/7.5

Final answer:

To combine the expression 4 log x - 6 log (x+2) into a single logarithm, we use the exponentiation and division rules for logarithms to obtain log((x^4)/(x+2)^6).

Explanation:

To write the expression 4 log x - 6 log (x+2) as a single logarithm, we can apply log rules.

The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log x.

The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y.

The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log x - log y.

Using these rules, we can

rewrite the given expression:

4 log x - 6 log (x+2) can be rewritten as log(x^4) - log((x+2)^6), which simplifies to log((x^4)/(x+2)^6) according to the division rule for logarithms.

The expression [tex]4 log x - 6 log (x+2)[/tex] can be simplified as a single logarithm by using the logarithm properties of exponents and division, resulting in [tex]log(x^4 / (x+2)^6).[/tex]

The student is asking to write the expression [tex]4 log x - 6 log (x+2)[/tex] as a single logarithm. To do this, we recall two important properties of logarithms:

Using these properties, we can rewrite the expression:

Therefore, the expression [tex]4 log x - 6 log (x+2)[/tex] written as a single logarithm is[tex]log(x^4 / (x+2)^6).[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

Andy tested gemstones already = 30

Jacob tested gemstones already = 40

Total gemstones tested by Andy and Jacob already = 30+40 = 70

Andy continue to test gemstones per hour = 30

Jacob continue to test gemstones per hour = 25

Total gemstones tested by Andy and Jacob per hour = 30 +25 = 55

The total number of gemstones tested by Andy and Jacob after x hours will be: 55x

So, the equation will be: f(x) = 55x + 70

After 5 hours i.e. x =5

f(5) = 55(5) + 70

f(5) = 275 + 70

f(5) = 345

Andy and Jacob will have tested 345 gemstones in 5 hours.

So, Option C is correct.

Answer:

brainliest ps :)

Step-by-step explanation:

her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s

The inequality for the given information can be written as 6.5 > s.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25.

The inequality can be written as:-

$4.00 + ( s x 0.5 )

7.25-4 > ( s x 0.5 )

3.25 > ( s x 0.5 )

6.5 > s

To know more about inequality follow

https://brainly.com/question/28626109

#SPJ2

Answer:

- i + 4

Step-by-step explanation:

Given a complex number a + bi then the complex conjugate is a - bi

Note the real part remains unchanged while the sign of the imaginary part is negated.

Hence conjugate of i + 4 = - i + 4

Answer:

-100

Step-by-step explanation:

Answer:

-100

Step-by-step explanation:

You need to multiply

-20 x 5= -100

Hope this helped please mark me the brainliest answer? Have a good day :)

Answer:

the answer is 61units

n=61

Step-by-step explanation:

Answer: $8.2

Step-by-step explanation:

Answer:

8.2 dollars an hour is the answer

Step-by-step explanation:

50.43 divided by 6.15 is 8.2

Answer:

Maggie bought 77 pencil sharpeners

$46.20 divided by .60 = 77

Step-by-step explanation:

46.20÷0.60= 77

Maggie can buy 77 pencil sharpeners is she would like

Please, please, pppllleeeeaassssee

Mark Brainlyest

Answer:

The answer is A; 19

Step-by-step explanation:

4 × (3/4 - 2/4) + 3 × 6

= 4 × 1/4 + 3 × 6

= 1 + 3 × 6

= 1 + 18

= 19

Answer is 1)

3V= pi•h•r^2 divide both sides by (pi•h) ; 3V/pi•h = r^2; sqrt (3V/pi•h) =r

The number √{13} is an irrational number because it cannot be expressed as a ratio of two integers and is not a whole number or integer either.

The number √{13} is not a whole number, an integer, or a rational number because it cannot be expressed as a ratio of two integers. The square root of a positive number that is not a perfect square is always irrational. Therefore, the only correct choice for the type of number that represents √{13} is (Choice D) Irrational.

This ODE is separable:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx[/tex]

Integrating both sides gives

[tex]\ln|y|=-\dfrac4x+C[/tex]

Given the initial condition [tex]y(-4)=1[/tex] we find

[tex]\ln|1|=-\dfrac4{-4}+C\implies C=-1[/tex]

so that the particular solution is

[tex]\ln|y|=-\dfrac4x-1[/tex]

[tex]\implies y=e^{-(1+4/x)})[/tex]

so the answer is D.

Answer:

The answer would be B. The highest price and the lowest price of the game differ by less than $14. Hope this helps!

B. The highest price and the lowest price of the game differ by less than $14.

Given is that the the price of Song Hero showed greater variability. This means their prices are more varied in range.

If Song Hero was priced between $35 and $49 during the 10-month period, This means the variability of Star chasers is less than [tex]49-35=$14[/tex]

Since, $14 is Song Hero’s range, the range for Star chasers should be less.

Therefore, option B is correct.

Answer:

1725ft^2

Step-by-step explanation:

Hi!

First you have to find your two bases B1 and B2, which are 50 and 65.

Then you find the height, which is 30ft.

Finally, you plug those into the equation 1/2*h*(B1+B2) and solve.

1/2*30*(50+65)

1/2*30*(115)

15*115

1725ft^2 is your answer.

I hope this helps!

Answer:

Standard Deviation is:  2.09762 or rounded to nearest tenth is 2.1

Step-by-step explanation:

Answer: Option A

50 minutes

Step-by-step explanation:

Observe in the diagram that the vertical axis represents the score obtained and the horizontal axis represents the study time.

To find out how many hours the person with a score of 81 studied, locate the point that is at a vertical distance of 81.

Now draw a vertical line from this point to the horizontal axis. Note that the vertical line traced intercepts the vertical axis at x= 50

Then the person who got a score of 81 studied 50 minutes

The answer is the option A

Answer:

The value of x is 10, and the value of y is 6

Step-by-step explanation:

ABC and GEF are congruent

so

x - 8 = 2

x = 10

x - y = 4

10 - y = 4

y = 10 - 4

y = 6

Answer

x = 10, y = 6

Answer:

x = 10 and y = 6

Step-by-step explanation:

In the given figure ΔABC and ΔGEF are congruent which means all the corresponding sides of the given triangles should be congruent.

So measure of AC = mfg

x - 8 = 2

x = 2 + 8

x = 10

Similarly mBC = mEF

x - y = 4

10 - y = 4

y = 10 - 4 = 6

Therefore, answer are x = 10 and y = 6

The maximum happens at x = -b/2a

x = -48/2(-16) = 3/2

Now replace x in the equation and solve for y:

y = 48(3/2) - 16(3/2)^2

y =  -72 - 36

y = 36

The maximum height is 36 feet.

Answer:

1. D ∠4 and ∠5

2. C 37°

3. A 50°

Step-by-step explanation:

1. Complementary angles are those that add up to 90°.

From the diagram you can see that angles 4 and 5 together form right angle, so angles 4 and 5 are complementary.

2. Angles 1 and 4 are vertical angles. Vertical angles have the same measure, so

∠4=∠1=37°

3. From 1,

∠4+∠5=90°

From 2

∠1=∠4

Since ∠1=40°, then ∠4=40°

So,

∠5=90°-40°=50°

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

  variables that can be expressed by an equation in which one

  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

 constant of variation

* Now lets solve the problem

# V is varies directly with the square  of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

 by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

Answer:

y = 9.75

Step-by-step explanation:

(4y - 3)2 = 72

Opening the brackets;

8y - 6 = 72

8y = 72 + 6 = 78

y = 78 ÷ 8 = 9.75

Answer:

[tex]y = \frac{3+6\sqrt{2}}{4}\text{ and } y = \frac{3-6\sqrt{2}}{4}[/tex]

Step-by-step explanation:

Given quadratic equation,

[tex](4y-3)^2=72[/tex]

[tex]\implies 4y - 3 = \pm \sqrt{72}[/tex]   ( Taking root on both sides )

[tex]4y=3 \pm 6\sqrt{2}[/tex]     ( Additive property of equality ),

[tex]y = \frac{3 \pm 6\sqrt{2}}{4}[/tex]   ( Division property of equality )

[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ or }y =\frac{3-6\sqrt{2}}{4}[/tex]

Hence, the solution of the given equation is,

[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ and }y =\frac{3-6\sqrt{2}}{4}[/tex]

Answer:

1.4 inches

Step-by-step explanation:

The picture is a rectangle 8 cm by 6 cm. The area of a rectangle is length * width. The area of the picture is 8 cm * 6 cm = 48 cm^2

After the mat is applied, the area doubles, so the new area will be 2 * 48 cm^2 = 96 cm^2.

Let the width of the mat be x. The mat has the same width all around the rectangular picture, so it adds x on each side of the length and x on each side of the width.

old length: 8

new length: 2x + 8

old width: 6

new width: 2x + 6

Area of the new rectangle with mat = new length * new width

area = (2x + 8)(2x + 6)

The new area is 96, so that give us an equation.

(2x + 8)(2x + 6) = 96

Use FOIL on the left side:

4x^2 + 12x + 16x + 48 = 96

Combine like terms, and subtract 96 from both sides:

4x^2 + 28x - 48 = 0

Divide both sides by 4:

x^2 + 7x - 12 = 0

To factor the trinomial, we need two numbers that add to 7 and multiply to -12. There are no such numbers, so we need to use the quadratic formula.

x = [-b +/- sqrt(b^2 - 4ac)]/(2a)

x = [-7 +/- sqrt(7^2 - 4(1)(-12)]/[2(1)]

x = [-7 +/- sqrt(49 + 48)]/2

x = [-7 +/- sqrt(97)]/2

x = 1.4 or x = -8.4

Since the mat cannot have a negative width, the negative solution is discarded.

Answer: The width of the mat is 1.4 inches.

Answer:

A. [tex]g(x)=(x-4)^2[/tex]

Step-by-step explanation:

The graph of [tex]f(x)=x^2[/tex] is transformed to obtain the graph of g(x).

We can see from the diagram that, f(x) is shifted 4 units to the right to obtain the graph of g(x).

Therefore [tex]g(x)=f(x-4)[/tex].

Hence the equation of g(x) is

[tex]g(x)=(x-4)^2[/tex]

The correct answer is A.

The equation of the graph of g(x) is g(x) = (x - 4)²

From the graph shown, we can see that the f(x) = x² as shown is shifted   4 units to the right to obtain the graph of g(x).

Then, we have that this shift can be achieved by replacing x in the equation of f(x) with x - 4 to represent the horizontal shift.

We have the equation of the graph of g(x), to be;

g(x) = (x - 4)²

This equation represents a horizontal shift of the graph of f(x) by by 4 units to the right, as g(x) remains the same shape f(x) but is  shifted horizontally to the right by 4 units.

Learn about graphs at: https://brainly.com/question/19040584

#SPJ3

Answer:

C. 66

Step-by-step explanation:

32 + x =98

The sum of interior angles of a triangle add up to the exterior opposite angle;

solving for x yields;

x = 98 - 32

x = 66 degrees

Answer:

x = 66°

Step-by-step explanation:

Since DAC is a straight line, the angles must add up to 180° and 98° is given so the missing angles is 180° - 98° = 82°

Angles in a triangle add up 180° and 32° and 82° are given →

x + 32° + 82° = 180°

x + 114° = 180°

x = 66°

Answer:

a. 2,2,3,3

b. 1.7 2.2 pi= 3.14 3.4= 2,2,3,3

Step-by-step explanation:

Answer:

The area of one of the bases is 0.96 ft²

The area of each lateral rectangular face is 4.8 ft²

The surface area of the paperweight is 6.72 ft²

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to

SA=2B+LA

where

B is the area of one of the bases

LA is the lateral area of the prism

Find the area of one of the bases B

B=(0.8)(1.2)=0.96 ft²

Find the lateral area LA

The lateral area is the area of each lateral rectangular face

LA=2[(0.8)(1.2)]+2[(1.2)(1.2)]=4.8 ft²

Find the surface area

SA=2(0.96)+4.8=6.72 ft²

Answer: 1.44, 0.96, and then 6.72.

Step-by-step explanation:

the person who answered first is wrong.

Answer:

1)163.28 (3.14*52)

2)13ft 6in (163.28/12)

3)129 times

4) 31 times

Step-by-step explanation:

1) multiply 52 times pie(3.14)

2)divide 163.28(your total) by 12

3) 1760 divided by 52

4) 1760 divided by 56.52

this is for the other 2 ones

Answer:

The vertical asymptote is [tex]x=3[/tex]

Step-by-step explanation:

we know that

The vertical asymptote is the value of x that makes the denominator equal to zero:

In this problem we have

[tex]f(x)=\frac{6}{x-3}[/tex]

[tex]x-3=0[/tex]

Solve for x:

[tex]x-3+3=0+3[/tex]

[tex]x=3[/tex]

The vertical asymptote is [tex]x=3[/tex]

see the attached figure to better understand the problem

Answer:

The area of the kite is 60 square feet

Step-by-step explanation:

The area of a kite is given as half multiplied by the product of the diagonals.

The longer diagonal measures 30 feet.

The shorter diagonal measures 4 feet.

The area of the kite is; [tex]\frac{1}{2}*30*4=60[/tex]

ANSWER

The area of the kite is 60 square feet

EXPLANATION

The area of a kite is half times the product of the diagonals.

The longer diagonal is 10+20=30 feet.

The shorter diagonal is 2+2 =4 feet.

The area of this kite

[tex] = \frac{1}{2} \times 30 \times 4[/tex]

This simplifies to,

[tex] = 60 {ft}^{2} [/tex]

Therefore the area of the kite is 60 square feet

Answer:

34.48

Step-by-step explanation:

Use PEMDAS

12.98-(7.6÷19)+22

12.98-0.4+22

12.48+22

34.48

Answer:

34.480000000000000000000000

Step-by-step explanation: