Find the x-intercept of the line whose equation is 8x+2y=4

Answer:

r ≤ 29, r-5, The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

Amount to spend = $24

Regular price = r

Sale = $5

Sale Price = r-5

The regular price will be at most $5 more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price :

r-5 ≤ 24

r ≤ 29

Therefore, the product Roopesh can afford is $29 or less than that.

What is the unknown? r ≤ 29

Which expression can represent the sale price? Sale price = r-5 (mentioned above)

Which comparison could be used? The sale price can be compared with the regular price

Which inequality represents the situation? r-5 ≤ 24

!!

Answer:

Vertical angles

Step-by-step explanation:

Vertical angles are the angles that happen opposite to each other in two intersecting lines. (These angles are congruent.)

Supplementary means that the two angles add up to be 180.

Complementary means the two angles add up to 90.

Linear pair are supplementary adjacent angles. (Adjacent means next to sharing the same vertex and a common ray.)

The given statement is the definition of vertical angles.

Vertical angles are either of two angles lying on opposite sides of two intersecting lines.

Supplementary angles are two angles whose sum is 180 degrees.

Complementary angles are two angles whose sum is 90 degrees.

Linear pair of angles are formed when two lines intersect each other at a single point.

According to the definition, these are vertical angles, which  two angles lying on opposite sides of two intersecting lines.

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Answer: The last one

Step-by-step explanation:

I think this because the graph starts from H the number of hours studied and when u add the numbers and divide them up which gives you the equation 65 + 50 . Any questions please text me. Have a nice day.

Answer:

17.8 cm²

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

ratio of areas = a² : b²

For the 2 similar cones

ratio of radii = 2 : 5, hence

ratio of areas = 2² : 5² = 4 : 25

Let x be the area of the smaller cone then by proportion

[tex]\frac{x}{4}[/tex] = [tex]\frac{111}{25}[/tex] ( cross- multiply )

25x = 444 ( divide both sides by 25 )

x = 17.76

Hence area of smaller cone = 17.8 cm² ( to the nearest tenth )

17.8 cm²

The total area of the surface of a 3-dimensional figure. The surface area of the solid object is the measure of the total area that the surface of the object occupies.

we must to course choose 3 dissimilar faces to capture length l, width w, or height h:

Given 2 similar figures with linear ratio = a: b, then

ratio of areas = a² : b²

For the 2 similar cones

ratio of radii = 2 : 5, hence

ratio of areas = 2² : 5² = 4 : 25

Let x be the area of the smaller cone then by proportion

[tex]\frac{x}{4} =\frac{111}{25}[/tex]

=  ( cross- multiply )

25x = 444 ( divide both sides by 25 )

x = 17.76

therefore an area of smaller cone = 17.8 cm² ( to nearest tenth )

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In the currency pair USD/CAN, USD is the base currency. The value of this base currency is always one unit. The relation between the pair demonstrates the concept that when one currency strengthens, the other weakens.

In the currency pair USD/CAN, USD is the base currency. It is then compared to the other currency, called the quote or counter currency, in this case, the Canadian dollar (CAN). The base currency is always worth one unit, and the exchange rate you see tells you how much of the counter currency it takes to buy one unit of the base currency. A fall in the Canada $/U.S. $ ratio means a rise in the U.S. $/Canada $ ratio, demonstrating the idea that the appreciation or strengthening of one currency often implies the depreciation or weakening of the other.

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In the currency pair USD/CAN, USD is the base currency.

Currency refers to a system of money used in a specific country or region, including coins and banknotes. It serves as a medium of exchange for goods and services. Currencies have different denominations and exchange rates, facilitating economic transactions within their respective jurisdictions.

In the currency pair USD/CAN, USD is the base currency. In a currency pair, the base currency represents the value of one unit of that currency in terms of the other currency. In this case, the USD/CAN currency pair means that 1 USD is equivalent to a certain amount of Canadian dollars. For example, if the exchange rate is 1 USD = 1.25 CAD, it means that 1 USD can be exchanged for 1.25 Canadian dollars.

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Answer:

60%

Step-by-step explanation:

To find percent change you take the new value, subtract it from the old value and then put that number over the original value. In this case it would be 960-600=360, 360/600=36/60=6/10 or 60 percent.

Answer:

D

Step-by-step explanation:

Find the total number of groups by subtracting the solo acts from the total acts:

24 - 8 = 16 group acts.

Now divide the number of group acts by the total number of acts:

16 /24 = =0.666

Multiply by 100:

0.666 x 100 = 66.6% = 66 2/3%

The answer is I.

Answer:

a) The length of the mid-segment  is 6.25 cm

b) The length of AT = 33 units

c) The value of x is 3

Step-by-step explanation:

a)

* Lets explain the mid-segment of a triangle

- A mid-segment of a triangle is a segment connecting the midpoints

 of two sides of a triangle

- This segment has two special properties

# It is parallel to the third side

# The length of the mid-segment is half the length of the third side

∵ The triangle is equilateral triangle

∴ All sides are equal in length

∵ the side lengths = 12.5 cm

∵ The length of the mid-segment = 1/2 the length of the third side

∴ The length of the mid-segment = 1/2 × 12.5 = 6.25 cm

* The length of the mid-segment  is 6.25 cm

b)

∵ UT is a perpendicular bisector of AB

∵ T lies on AB

∴ T is the mid-point of AB

∵ AT = BT

∵ AT = 3x + 6

∵ BT = 42 - x

- Equate AT and BT

∴ 3x + 6 = 42 - x

- Add x to both sides

∴ 4x + 6 = 42

- Subtract 6 from both sides

∴ 4x = 36

- Divide both sides by 4

∴ x = 9

∵ AT = 3x + 6

- Substitute x by 9

∴ AT = 3(9) + 6 = 27 + 6 = 33

* The length of AT = 33 units

c)

- In Δ ABC

∵ AB = BC

∴ Δ ABC is an isosceles triangle

∵ BD bisects angle ABC

- In the isosceles Δ the bisector of the vertex angle bisects the base

 of the triangle which is opposite to the vertex angle

∵ AC is the opposite side of the vertex B

∴ BD bisects the side AC at D

∴ AD = CD

∵ AD = 5x + 10

∵ CD = 28 - x

∴ 5x + 10 = 28 - x

- Add x to both sides

∴ 6x + 10 = 28

- Subtract 10 from both sides

∴ 6x = 18

- Divide both sides by 6

∴ x = 3

* The value of x is 3

The true statements are:

a) The length of the midsegment  is 6.25 cm

b) The length of AT = 33 units

c) The value of x is 3

The length of the midsegment

The length of the triangle is given as

L =12.5cm

So, the length of the midsegment is:

M = 0.5 * L

This gives

M = 0.5 * 12.5 cm

M = 6.25 cm

Hence, the length of the midsegment  is 6.25 cm

The length of AT

The given parameters are:

AT = 3x + 6 and TB = 42 - x.

Since point T is the perpendicular bisector, then we have:

3x + 6 = 42 - x

Collect like terms

3x +x = -6 + 42

Evaluate

4x = 36

Divide both sides by 4

x = 19

Recall that:

AT = 3x + 6

So, we have:

At = 3 * 9  + 6

At = 33

Hence. the length of AT = 33 units

The value of x

We have:

AD = 5x + 10

DC = 28 - x

So, we have:

5x + 10 =28 - x

Collect like terms

5x + x = 28 -10

6x =18

Divide

x =3

Hence, the value of x is 3

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Answer:

[tex]f(a)=5-8a+15a^2[/tex]

[tex]f(a+h)=5-8a-8h+15a^2+30ah+15h^2[/tex]

[tex]\frac{f(a+h)-f(a)}{h}=-8+30a+15h[/tex]

Step-by-step explanation:

We are given [tex]f(x)=5-8x+15x^2[/tex].

We want to find [tex]f(a)[/tex] so we just replace the x there with a giving us:

[tex]f(a)=5-8a+15a^2[/tex].

We want to find [tex]f(a+h)[/tex] so we just replace x with (a+h) now giving us:

[tex]f(a+h)=5-8(a+h)+15(a+h)^2[/tex].

We will need to distribute and multiply things out here for later use so let's go ahead and do that:

[tex]f(a+h)=5-8(a+h)+15(a+h)^2[/tex]

[tex]f(a+h)=5-8a-8h+15(a+h)(a+h)[/tex]

[tex]f(a+h)=5-8a-8h+15(a^2+2ah+h^2)[/tex]

[tex]f(a+h)=5-8a-8h+15a^2+30ah+15h^2[/tex]

We want to find [tex]\frac{f(a+h)-f(a)}{h}[/tex] where h is not 0.

This requires the parts we found above:

[tex]\frac{f(a+h)-f(a)}{h}[/tex]

[tex]\frac{(5-8a-8h+15a^2+30ah+15h^2)-(5-8a+15a^2)}{h}[/tex]

There are some thing that will zero out (cancel out) in the numerator.

You have 5-8a+15a^2 in both parenthesis and you are subtracting so that part zero's out so you have this now:

[tex]\frac{-8h+30ah+15h^2}{h}[/tex]

Now you can divide h from top and bottom giving you:

[tex]\frac{-8+30a+15h}{1}[/tex]

[tex]-8+30a+15h[/tex]

[tex]\log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log_315-\log_310=\log_3\dfrac{15}{10}=\boxed{\log_3\dfrac{3}{2}}[/tex]

Answer:

B.

Step-by-step explanation:

They have the same base so use the quotient rule (since they have a minus sign in between).

We are using this rule: [tex] log_a(b)-log_a(c)=log_a(\frac{b}{c})[/tex]

So we have  [tex] log_3(15)-log_3(10)=log_3(\frac{15}{10})[/tex]

We can reduce the inside fraction... 15/10=3/2

So the answer is B.

Answer:

50%

Step-by-step explanation:

There are 10 marbles total in the bag, and 5 of them are red. So, to find the probability of not drawing a red marble, you need to count how many marbles are not red.

There are 3 green marbles and 2 blue marbles so there are 5 marbles that are not red.

So you need to write this as a fraction so 5/10 of the marbles are not red.

None of the answer choices that are fractions match 5/10 or 1/2, so you need to convert 5/10 to a percent.

To convert it as a percent you divide 5 by 10, which is .50

Then you move the decimal point two places to the right so its 50%

So there is a 50% percent chance of not drawing a red marble.

Final answer:

The 100th term of the arithmetic sequence is found using the formula an = a1 + (n-1)d. In this sequence, the 100th term is -290.

Explanation:

The question asks for the 100th term of an arithmetic sequence with a common difference. The given sequence is 7, 4, 1, -2, ... which shows a constant decrease of 3 between consecutive terms, hence it's an arithmetic sequence with a common difference (-3). To find the 100th term (a100) of the sequence, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term, and d is the common difference.

Plugging in the values, we get:

We calculate the 100th term as follows:

a100 = 7 + (100 - 1)(-3)

a100 = 7 - 297

a100 = -290

Therefore, the 100th term of the sequence is -290.

Answer:

c. 6 units

Step-by-step explanation:

The diameter of a circle with a circumference of 18.84956 is 6 units.

Use the formula: C=2πr

d=C

π=18.85

π≈6

Answer:

c=3t is the equation

18 cubic yards of concrete is what we need for a 6 inch thick bridge.

Step-by-step explanation:

If something directly varies, that means there is a constant, k, such that when you multiply it to one variable you always get the other variable.

That is for this particular problem we have c=kt where c is cubic yards and t is thickness in inches.

So we are given from the first sentence: 12 cubic yards and 4 inches thick which means we have:

12=k(4)

Divide both sides by 4:

12/4=k

Simplify:

3=k

So the equation is c=3t for any point (c,t) in this relation.

So we want to know many cubic yards of concrete (we want to know (c) so that Dru can build a 6 inch (t) thick bridge.

c=3(6)

c=18

18 cubic yards

Answer:

Yea, it is A

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

The prime factorization of 24 is 2*2*2*3.

There prime factorization of 30 is 2*3*5.

They have 2*3 in common.

2*3=6.

So we can divide numerator (top) and denominator (bottom) by 6 and this will reduce the fraction into simplest form.

[tex]\frac{24}{30}=\frac{24 \div 6}{30 \div 6}=\frac{4}{5}[/tex]

The simplified version of the fraction 24/30 is 4/5

Fraction is a mathematical number by which we can describe a part of a whole item.

A fraction has two parts, the top part is called numerator & the bottom part is called denominator.

Example : [tex]\frac{5}{7}[/tex] , where 5 is the numerator & 7 is the denominator.

The given fraction is 24/30

The prime factorisation of 24 gives 2×2×2×3 , i.e. 2×2×(2×3)

The prime factorisation of 30 gives 2×3×5 , i.e. 5×(2×3)

Common in both 24 & 30 is 2×3, i.e. 6

So, we have to divide numerator & denominator of the given fraction by 6 to get the simplified form.

Hence, 24/30 = (24/6)/(30/6) = 4/5

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Answer:

BT is Congruent to CT

Step-by-step explanation:

Since these two triangles are said to be congruent, that means that their side lengths and angle measures are congruent as well. So, since BT corresponds to CT in the diagram, they must be congruent.

Answer:

BT≅CT

Step-by-step explanation:

If two triangles are congruent it means that they have the same size and shape, or that they mirror each other. Since the side, AT, is common to both triangles, the congruent triangles are mirrored in this case, which means that side CT in ∠CAT corresponds to side BT in ∠BAT.

Answer:

90 yards

Step-by-step explanation:

If the length of a rectangle is four times it’s width and the area of the rectangle is 324 ft.², its perimeter is 90 yards.

Formula: Length = Area / Width

P = 2(4x) + 2(x)

P = 72 + 18

Its perimeter if 90 ft.

If length of the rectangle be l & width of the rectangle be w.

Then Area of the rectangle (A) = Length × Width

                                                   = (l × w) sq. unit

If length of the rectangle be l & width of the rectangle be w.

Then, Perimeter of the rectangle = 2×(l+w) unit

Given, Area of the rectangle = 324 sq. ft

Let, Width (w) = x unit

So, Length (l) = 4 times it's width = 4x unit

∴ Area = l × w = (4x)(x)

⇒ 324 = 4x²

⇒ x² = 324/4

⇒ x² = 81

⇒ x = [tex]\sqrt{}[/tex]81

⇒ x = 9  (neglecting negative value)

So, it's width = 9 ft.

Then, its length = (4×9) ft. = 36 ft.

∴ Perimeter =  2×(l+w) =  2×(36+9) ft. =  (2×45) ft. = 90ft.

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Answer:

Step-by-step explanation:

We have

the rectangle 12ft × 6ft

two triangles with the base b = 12ft and the height h = 8ft

two triangles with the base b = 6ft and the height h = 9.5ft.

The formula of an area of a rectangle l × w:

[tex]A=lw[/tex]

Substitute:

[tex]A_1=(12)(6)=72\ dt^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_2=\dfrac{(12)(8)}{2}=48\ ft^2[/tex]

[tex]A_3=\dfrac{(6)(9.5)}{2}=28.5\ ft^2[/tex]

The Surface Area:

[tex]S.A.=A_1+2A_2+2A_3[/tex]

Substitute:

[tex]S.A.=72+2(48)+2(28.5)=225\ ft^2[/tex]

Answer:

Total surface area of the pyramid = 225 ft²

Step-by-step explanation:

Total surface area of the given pyramid is defined by  

(Area of rectangular base) + 2(area of two triangular sides with height 8 ft and base 12 ft) + 2(area of two triangles with height 9.5 ft and base 6 ft)

Total surface area = (12×6) + 2[[tex]\frac{1}{2}\times(h)(b)[/tex]]+2[[tex]\frac{1}{2}\times(h')(b')[/tex]]

= 72 + 2[[tex]\frac{1}{2}\times(8)(12)[/tex]]+2[[tex]\frac{1}{2}\times(9.5)(6)[/tex]]

= 72 + 96 + 57

= 225 ft²

Therefore, total surface area of the pyramid is 225 ft²

Answer:

B. 271 square units

Step-by-step explanation:

The area is the sum of 3 rectangles areas

step 1         12 * 19 = 228

step 2       3 * 3   = 9

step 3      2 * 17 = 34

Now, we add all the answers we got to get the area.

= 228 + 34 + 9 =   271 square units

The area of the polygon is:

A = 2 × 12 + 14(12+2) + 3(12 + 2 + 3)

A = 2 × 12 + 14 × 14 + 3 × 17

A = 24 + 196 + 51

A = 220 + 51

A = 271 cm²

Answer:

A.

Step-by-step explanation:

[tex]y=2x+4[/tex]

[tex]y=x^2+x-2[/tex]

Both equations are solved for y so I'm just going to substitute

the 1st  y  (the 2x+4) into the second equation's y.

[tex]2x+4=x^2+x-2[/tex]

I'm going to get everything on one side so I have 0=ax^2+bx+c.

Subtract 2x and subtract 4 on both sides:

[tex]0=x^2-x-6[/tex]

Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.

These numbers are -3 and 2.

So the factored form of our equation is:

[tex]0=(x-3)(x+2)[/tex]

This means we have x-3=0 or x+2=0.

x-3=0

Add 3 on both sides:

x=3

x+2=0

Subtract 2 on both sides:

x=-2

So now we need to find y. I'm going to choose to use the easier equation:

y=2x+4.

If x=3, then y=2(3)+4=6+4=10.  The ordered pair (3,10) is a solution.

If x=-2, then y=2(-2)+4=-4+4=0.  The orded pair (-2,0) is a solution.

Answer:

7 lbs

Step-by-step explanation:

Given:

apples per pound= 88 cents

total money= $6.00

                   =600 cents

Now

1 lb= 88 cents

let x be the pounds of apple in 600 cents then

x lb=600 cents

By cross-multiplication we get:

600=88x

x=600/88

x= 6.81

x=7 pounds

7 pounds of apple can be bought by $6.00 !

Answer: 7 lb

Step-by-step explanation:

You know that in that fruit stand each pound of apple costs 88 cents.

Therefore, if you have $6.00, you need to divide this amount by 88 cents ($0.88 ) in order to calculate the pounds of apples you can buy.

Therefore, the pounds of apples you can buy to the nearest whole number is the following:

[tex]amount\ of\ apples=\frac{6.00}{0.88}=7\ lb[/tex]

Answer:

78

Step-by-step explanation:

Multiply f(x) and g(x) then evaluate for x = - 5

f(x) × g(x)

= (- 2x - 7)(- 4x + 6) ← substitute x = - 5 into the expression

= (10 - 7)(20 + 6)

= 3 × 26

= 78

For this case we have the following functions:

[tex]f (x) = - 2x-7\\g (x) = - 4x + 6[/tex]

We must find [tex](f * g) (x).[/tex] By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex](f * g) (x) = (- 2x-7) (- 4x + 6)[/tex]

We apply distributive property keeping in mind that:

[tex]- * - = +\\- * + = -\\(f * g) (x) = 8x ^ 2-12x + 28x-42\\(f * g) (x) = 8x ^ 2 + 16x-42[/tex]

We evaluate in [tex]x = -5[/tex]:

[tex](f * g) (- 5) = 8 (-5) ^ 2 + 16 (-5) -42\\(f * g) (- 5) = 8 * 25-80-42\\(f * g) (- 5) = 200-80-42\\(f * g) (- 5) = 78[/tex]

Answer:

[tex](f * g) (- 5) = 78[/tex]

Answer:

x = -7/2 and 3

Step-by-step explanation:

Use foil. Solve for x.

Answer:

The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3

Step-by-step explanation:

* Lets explain how to factor a trinomial in the form ax² ± bx ± c:

- Look at the c term first.  

# If the c term is a positive number, then its factors r , s  will both

  be positive or both be negative.

# a has two factors h and k

# The sum of c and a is b.

# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs

# If the c term is a negative number, then either r or s will be negative,

   but not both.

# a has two factors h and k

# The difference of c and a is b.

# The brackets are (hx + r)(kx - s) where a = hk , c = rs and b = rk - hs

* Lets solve the problem

∵ The equation is 2x² + x - 21 = 0

∵ The general form of the equation is ax² + bx + c = 0

∴ a = 2 , b = 1 , c = -21

∵ c is negative

∴ its factors r and s have different sign

∵ a = 2

∵ The factors of a are h , k

∵ 2 = 2 × 1

∴ h = 2 and k = 1

∵ -21 = 7 × -3

∴ r = 7 and s = -3

∵ The brackets are (hx + r)(kx - s)

∴ 2x² + x - 21 = (2x + 7)(x - 3)

∵ 2x² + x - 21 = 0

∴ (2x + 7)(x - 3) = 0

- Equate each bracket by 0

∴ 2x + 7 = 0 ⇒ subtract 7 from both sides

∴ 2x = -7 ⇒ divide both sides by 2

∴ x = -7/2 = -3.5

- OR

∴ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∴ The solutions are -3.5 and 3

* The factors are (2x + 7)(x - 3) and the solutions are -3.5 and 3

Answer:

77.3 to the nearest tenth.

Step-by-step explanation:

The total of the scores on the set of 27 tests

= 78*27 = 2106.

After  2 more had joined the total score is 2106 + 69 + 66

= 2241.

So the new mean score = 2241 / 29

= 77.3.

Answer:

77.3

Step-by-step explanation:

Recall that the arithmetic mean is found as follows:

             sum of all data

a. m. = ---------------------------

             number of data

                                                                              sum

The mean score of 27 test results is thus 78 = --------

                                                                                27

Note that we can find the sum of all 27 of the original scores by multiplying 78 by 27:  2106.

Now we include two more scores.  Instead of the original sum, 2106, we have

                   2106 + 69 + 66

a. mean = ---------------------------

                              29

which comes out to 2241/29 = 77.3

Answer:

c.

Step-by-step explanation:

That is the only answer choice that makes the most sense.

±10 = √100; in this case, they want the non-negative value, so it is 10.

Answer: c. 100

Step-by-step explanation: √-81 and √-3 are not possibly unless complex numbers applied

√100 = 10 > 9 valid answer

√27 = 5.196 < 9 invalid answer

√3 = 1.732 < 9 invalid answer

√81 = 9 ≡ 9 invalid answer

Only c is the answer.

Hope it helped!

Answer:

- 3

Step-by-step explanation -

- 5x from both sides -> 3 = -1x .

then divide each side by - 1 -> -3 = x

Answer:

-3

Step-by-step explanation:

5x+3=4x

Subtract 5x on both sides.

5x+3-5x=4x-5x

Simplify.

3=-1x

3=-x

Take opposite of both sides.

-3=x

x=-3

Answer:

The GCF of 42 and 60 is 6

Step-by-step explanation:

42: 1,2,3,6,7,14,21,42

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

Answer:

6

Step-by-step explanation:

Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42

Factors of 60 = 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 and 60

The highest factor which comes in both 42 and 60 is 6

Answer:

other answer is wrong this is the correct answer 100%

Step-by-step explanation:

x= 1

and

x= "n.a."

Answer:

Option C. [tex]ln(\frac{2x^{3}}{3y})[/tex]

Step-by-step explanation:

The given logarithmic expression is:

[tex]ln(2x)+2ln(x)-ln(3y)[/tex]

Using the power rule of logarithms: [tex]blog(a)=log(b)^{a}[/tex], the above expression can be written as:

[tex]ln(2x)+ln(x)^{2}-ln(3y)[/tex]

Using the product rule of logarithms: [tex]log(a)+log(b) =log(ab)[/tex], the above expression can be simplified further to:

[tex]ln(2x \times x^{2}) - ln(3y)\\\\=ln(2x^{3})- ln(3y)[/tex]

Using the quotient rule of logarithms: [tex]log(a)-log(b)=log(\frac{a}{b})[/tex], the above expression can be written as:

[tex]ln(\frac{2x^{3}}{3y})[/tex]

Hence option C gives the correct simplified answer.