Please help me with this!!!!

Adam has 6,000 points.

Let's use algebra to solve this problem. Let's assume that Adam's points are represented by 'x'. According to the problem, Nick has 20% more points than Adam, so Nick's points can be represented as 'x + 20% of x' or '1.2x'. Given that Nick has 7,200 points, we can set up the equation 1.2x = 7,200 and solve for 'x'. Divide both sides of the equation by 1.2 to isolate 'x' and find that Adam has 6,000 points.

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Answer:

7x + 9

Yes they are equivalent

Step-by-step explanation:

The first expression given to us is

2x + 3 + 5x + 6

Let us call it equation (i)

Now we have to find equivalent expression to it

the given equation is 2x + 3 + 5x +6

similar terms are terms involving x and not involving x

so solving the equation gives

2x + 5x + 3 +6

= 7x + 9

Now we have two equations one is

2x + 3 +5x + 6              ...............(i)

Other is

7x + 9                            ..............(ii)

To check they are equivalent or not

Put x = 3 in equation (i)

2(3)+3+5(3)+6= 6 + 3 + 15 + 6

                      =30

Now put x=3 in second equation

7(3)+9=21 + 9

          =30

As the answer of both the equations are 30 so they are equivalent

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, the expression can be simplified to 7x + 9. Substituting x with 3 in both expressions shows that they have the same value, which is 30.

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, we add the coefficients of the like terms. In this case, the like terms are the terms with the same variable, which is x. So, 2x + 3 + 5x + 6 simplifies to 7x + 9. To show that this expression is equivalent to the original expression, we can substitute x with 3. So, when we replace x with 3, both expressions 2x + 3 + 5x + 6 and 7x + 9 result in the same value, which is 30.

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For [tex]f[/tex] to be differentiable, it must be continuous, so we need to have

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3^+}f(x)=f(3)[/tex]

By its definition, [tex]f(3)=3^2=9[/tex]. The one-sided limits are

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3}x^2=9[/tex]

[tex]\displaystyle\lim_{x\to3^+}f(x)=\lim_{x\to3}mx+b=3m+b[/tex]

so we require [tex]3m+b=9[/tex].

In order for [tex]f[/tex] to be differentiable at [tex]x=3[/tex], we also need to have [tex]f'(3)[/tex] exist, which requires that [tex]f'[/tex] also be continuous at [tex]x=3[/tex]. First, compute the derivatives of all pieces of [tex]f[/tex]:

[tex]f'(x)=\begin{cases}2x&\text{for }x<3\\?&\text{for }x=3\\m&\text{for }x>3\end{cases}[/tex]

[tex]f'[/tex] is continuous at [tex]x=3[/tex] if

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3^+}f'(x)=f'(3)[/tex]

The one-side limits are

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3}2x=6[/tex]

[tex]\displaystyle\lim_{x\to3^+}f'(x)=\lim_{x\to3}m=m[/tex]

so we need to have [tex]m=6[/tex], and moreover [tex]f[/tex] will be differentiable if we set [tex]f'(3)=6[/tex].

So with [tex]m=6[/tex], we must have [tex]3m+b=9\implies b=-9[/tex].

For the piecewise function f(x) = x^2 when x <= 3 and mx + b when x > 3, values m = 6 and b = -9 ensure differentiability at x = 3.

To make the piecewise function f(x) differentiable at x = 3, we need the two pieces, x^2 and mx + b, to smoothly connect at x = 3. This requires the values of m and b to ensure continuity of both function values and derivatives.

First, evaluate both pieces at x = 3:

x^2 when x <= 3 and mx + b when x > 3

For continuity, set these expressions equal to each other:

3^2 = m * 3 + b

This yields 9 = 3m + b. To ensure differentiability, the derivatives of both pieces must also match at x = 3:

f'(x) = 2x when x <= 3 and f'(x) = m when x > 3

For continuity of derivatives, set the derivatives equal to each other at x = 3:

2 * 3 = m

This gives m = 6. Substituting m = 6 into the continuity equation 9 = 3m + b gives b = -9.

Therefore, the values m = 6 and b = -9 make the piecewise function f(x) differentiable at x = 3.

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Answer: A. 4

The largest exponent in the polynomial tells us the max number of roots, x intercepts, or zeroes of the function. In this case, that happens to be 4. This is the degree of the polynomial. It is considered a quartic polynomial. It is also a trinomial since it has 3 terms (3x^4, x^2 and 1)

Answer:

ITs A

Step-by-step explanation:

The highest degree is 4 ( 3x^4)  so the maximum number of zeroes is 4.

Answer:

Option d is correct.

Domain = all real number

range = positive real numbers

Step-by-step explanation:

Given the function: [tex]y=f(x) = a^x[/tex]

Domain of the function is all real numbers except where the expression is undefined.

In this case, there is no real number that makes the expression undefined.

Domain of f(x) = [tex](-\infty , \infty)[/tex] = {a | a∈R}

Range is the set of all valid  f(x) values.

[tex](0,1) \cup (1, \infty)[/tex]

[tex]\{y | y\neq 1 , y>0\}[/tex]

Therefore, Domain is all real number and the range of function is positive real number

Answer:

12 years will it take for light from the star to reach Earth.

Step-by-step explanation:

As per the given statement: A certain star is 1.135 × 10^14 km away from Earth. If light travels at 9.4607 × 10^12 km per year.

⇒Speed of light travel = [tex]9.4607 \times 10^{12}[/tex] km per year

and Distance of a certain star from the Earth = [tex]1.135 \times 10^{14}[/tex] km

To find how long will it take for light from the star to reach Earth.

Using Formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

or

[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]

Substitute the given values we have;;

[tex]\text{Time} = \frac{1.135 \times 10^{14}}{9.4607 \times 10^{12}}[/tex]

Simplify:

Time = 11.9969981 year ≈ 12 years

therefore, 12 years will it take for light from the star to reach Earth.

Answer: [tex]\frac{2}{27}[/tex]

Step-by-step explanation:

blue = 8  , red = 6  , green = 4  , total = 18

red     and     green

 [tex]\frac{6}{18}[/tex]        x         [tex]\frac{4}{18}[/tex]

= [tex]\frac{1}{3}[/tex]         x         [tex]\frac{2}{9}[/tex]

= [tex]\frac{2}{27}[/tex]

Answer:

A 0.2 L water was filled into the bottle from faucet each seconds.

Step-by-step explanation:

Unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or  6 miles per hour, they are called unit rates.

Given the statement: A 2 liter bottle is filled completely with water from a faucet in 10 seconds.

⇒ In 10 sec  a  2L bottle  is completely filled with water  from a faucet.

Unit rate per second =  [tex]\frac{2}{10} = \frac{1}{5} = 0.2 L[/tex]

Therefore, 0.2 L water was filled into the bottle each seconds.

Answer:

0.2

Step-by-step explanation:

Answer:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.

The input value is [tex]\boxed{x =  3}.[/tex] Option (d) is correct.

Further explanation:

The output values of the function are known as range and the input values on which function is defined is known as the domain of the function.

Given:

The options are as follows,

(a). [tex]x =  - 3[/tex]

(b). [tex]x = -1[/tex]

(c). [tex]x = 1[/tex]

(d). [tex]x = 3[/tex]

Explanation:

The functions are [tex]f\left( x \right){\text{ and }}g\left( x \right).[/tex]

It has been observed from the graph that the line of the functions [tex]f\left( x \right){\text{ and }}g\left( x \right)[/tex] intersects each other at [tex]x = 3.[/tex]

The input value is [tex]\boxed{x =  3}[/tex]. Option (d) is correct.

Option (a) is not correct.

Option (b) is not correct.

Option (d) is not correct.

Option (d) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Relation and Function

Keywords: relations, functions, all relation are functions, all functions are relations, no relations are functions, no functions are relation, one-to-one, onto, graph representation, paired, y-value, x-values, origin.

Answer:

15 students joined the radio-controlled model club

Step-by-step explanation:

The students joining the  radio-controlled model club were divided into three equal groups i.e

a) Radio-controlled boat group

b) Radio-controlled car group

c) Radio-controlled airplane group

10 new students joined the Radio-controlled airplane group  and the new sum of students in this group is 15.

This implies that there were 5 students in Radio-controlled airplane group  before the joining of 10 new students.

In the starting, the three groups have equal number of students which means that Radio-controlled boat group, Radio-controlled car group, Radio-controlled airplane group  have 5 students in each group. Thus, In the beginning there were total 15 students who joined the radio-controlled model club

Answer: b

Step-by-step explanation:

NOTE:

hypothesis : If two lines intersect at right angles

conclusion: then the two lines are perpendicular

Answer:

P =44 + 4xy

Step-by-step explanation:

To find the perimeter of a triangle, add up the three sides

P = 29+15+4xy

P =44 + 4xy

Answer: 2x + y

Step-by-step explanation:

logₐ(3) = x

logₐ(5) = y

logₐ(45) = logₐ(3²· 5)

             = logₐ(3)² + logₐ(5)

             = 2 logₐ(3) + logₐ(5)

             = 2     x      +   y        substituted given values (stated above)

Step-by-step explanation:

Here we make use of the laws of logarithms:

log_a(PQ) = log_a(P)+log_a(Q)

which implies the following corollary

log_a(P^2) = log_a(P)+log_a(P) = 2log_a(P)

Notice how the log of a product is reduced to the sum of the log of the factors.  (Advantage is taken of this fact in the use of logarithm tables before the wide-spread use of electronic calculators (pre-70's) )

So substituting

x=log_a(3)

y=log_a(5)

we have

log_a(45) = log_a(3^2 * 5) = log_a(3^2) + log_a(5)=2log_a(3)+log_a(5)

=2x+y

Answer:

If the shape is a square,then it is a rectangle.

Step-by-step explanation:

The hypothesis of the statement is the one which follows after if,

If the shape is a square.

The conclusion of the statement is the sentence that follows after then,

Then it is a rectangle.

The statement 'All squares are rectangles' translates into an if-then form as 'If a shape is a square, then it is a rectangle'. The hypothesis is 'a shape is a square' and the conclusion is 'it is a rectangle'.

The geometrical statement 'All squares are rectangles' can be translated into an if-then form as follows: 'If a shape is a square, then it is a rectangle'. In this statement, the hypothesis is 'a shape is a square' and the conclusion is 'it is a rectangle'. This means that if we start with a shape and it happens to be a square (which is our condition or hypothesis), then it must also necessarily be a rectangle (which is our end result or conclusion). This is because all the properties of a rectangle - having all angles being 90 degrees and opposite sides being equal - are also properties of a square.

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Answer:

44

Step-by-step explanation:

8 * 5 1/2 =

8/1 * 11/2  =

88/2 =

44

Answer:

44

Step-by-step explanation:

HOPE THIS HELPS!

Answer:

The senior's ticket cost is A, $5.

Step-by-step explanation:

say a children's ticket was $7; 7 + 7 + 14

so if an adult ticket is twice as much, let's say it was $10 per adult ticket.

one adult ticket plus two children's tickets would be $24 with these numbers.

two seniors ($5) + one children's ticket ($7) would be $17

therefore, we can conclude that a senior's ticket would cost $5

Answer:

Triangle ABE is congruent to triangle CBD.

Step-by-step explanation:

Given two congruent triangles BAE and BCD where B is an apex of both triangles.

Given AB=BC, CD=AE, BE=BD

& also ∠AEB=∠BDC, ∠DCB=∠BAE, ∠ABE=∠CBD

By CPCT i.e. Corresponding parts of corresponding triangles

Correspondimg sides and angles area in the same position or spot in two different triangles.

Hence, Triangle ABE is congruent to triangle CBD.

Answer:

$1808263    

Step-by-step explanation:

We're given with the below information:-

Initial price of the building = Principal amount (P) = $590000

Rate of interest (r) = 14% = 0.14

Time in years (t) = 2020 - 2012 = 8

The formula to calculate the final amount where interest is continuously  compounded each year is :-

[tex]A = Pe^{rt}[/tex]                              [e is the mathematical const = 2.71828]

Plugging in the values of P, e, r, and t in the above formula, we get

[tex]A = 590000*2.71828^{0.14*8}[/tex]

=> A= 1808262.6

=> A = $1808263     (rounded off to the nearest whole dollar)

So, she expect to sell the building in 2020 for an amount of $1808263

Answer:\

180000

Step-by-step explanatii took

In this problem, it is determined that Shelby can buy up to 11 small balloons and at least 3 large balloons with her $15 budget. Seven distinct combinations of small (x) and large (y) balloons are possible given the constraints x ≤ 11, y ≥ 3, and the total cost not exceeding $15.

Based on the information provided, we're dealing with inequalities and trying to determine how many small and large balloons Shelby can purchase with a budget of $15. Since Shelby needs at least 3 large balloons, we know y ≥ 3. Considering the remaining money for the small balloons, and given that small balloons cost $0.95, the maximum number (x) can be obtained by subtracting the cost for 3 large balloons from the total budget and dividing the remainder by the cost of a small balloon. Let's calculate it: $15 - $4.35 ($1.45 x 3 for large balloons) = $10.65. Then, $10.65 / $0.95 ≈ 11. Thus, x ≤ 11.

The outcome of the calculations thus suggests the possible pairs (x,y) for purchasing balloons are in such a way that Shelby can purchase up to 11 small balloons and needs at least 3 large balloons. Hence, 0.95x + 1.45y ≤ 15, with the constraints x ≤ 11 and y ≥ 3. Seven distinct combinations of small (x) and large (y) balloons are possible given these restrictions.

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Answer:

The function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

Step-by-step explanation:

As given

If 30 gumballs can be purchased for 3 dollars .

i.e

30 gumballs = $3

Now find out the cost of one  gumballs .

[tex]1\ gumballs = \$ \frac{3}{30}[/tex]

[tex]1\ gumballs = \$ \frac{1}{10}[/tex]

[tex]1\ gumballs = \$\ 0.1[/tex]

As 1 dollar = 100 cents

[tex]1\ gumballs = 0.1\times 100\ cents[/tex]

[tex]1\ gumballs = \frac{1\times 100}{10} \ cents[/tex]

1 gumballs = 10 cents

Thus the cost of one gumball is 10 cents .

As d = dozen gumballs.

Let us assume that the cost for ‘d' dozen gumballs = y

Than the function becomes

y = 10d

Therefore the  function that represents the cost in cents of ‘d' dozen gumballs is y = 10d .

Answer: choices B, C, D and E

B) triangle RSP is similar to triangle ZXY

C) triangle SRP is similar to triangle XZY

D) triangle PSR is similar to triangle YXZ

E) triangle RPS is similar to triangle ZYX

In short, the answers is nearly everything but the first and last answer choice

================================================

For the first triangle, angle S is 54 degrees. In the other triangle, angle X is also 54 degrees. This means that the two angles correspond as they are equal to one another. The answer will have the letters S and X show up in the same position, whether that position is the first, second or third place of the three letter sequence.

Choice A is not one of the answers. RPS ~ XYZ is false because of what I mentioned above. We see that S is shown last in RPS while X is shown first in XYZ. The letters S and X do not correspond together, so we can cross choice A off the list.

Choice B is one of the answers because we have R corresponding to Z (first letters of each sequence RSP and ZXY; both are 41 degrees) and we have S correspond to X, and we have P correspond to Y (both the same measure as well)

Choice C is another answer for similar reasons as choice B. The only difference is that R and S have swapped, so have X and Z. The order is important or else things wouldn't line up properly.

Choice D is another answer. Again we have the same correspondence of P to Y (both in the first slot), S to X (second slot), and R to Z (third slot). For each slot, the pair of angles are both the same measure.

Choice E is another answer. Similar reasons as before, just a different order.

Choice F is not one of the answers. We see that P and Z occupy the second slots, but they aren't congruent angles.

Answer:

2,3,4,5 u-u welcome child

Step-by-step explanation:

Answer:

1) 3

2) {x = 9 or x = -1}

3) (b) The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Step-by-step explanation:

Problem 1

3 - 2 [tex]\frac{\sqrt{11} }{2} + \sqrt{11}[/tex]

i) Cancelling out the 2's from the top and bottom of the middle term, we get

3 - [tex]\sqrt{11} + \sqrt{11}[/tex]

ii) Cancelling out -[tex]\sqrt{11}[/tex] and +[tex]\sqrt{11}[/tex], we get

3 as the simplified form

Problem 2

x-1 = [tex]\sqrt{6x+10}[/tex]

Our first goal is to get rid off the radical on the right side

i) Squaring both sides, we get

[tex](x-1)^{2}[/tex]=[tex](\sqrt{6x+10})^{2}[/tex]

ii) (x-1)*(x-1) = 6x+10

iii) Applying the distributive property (a+b)(c+d) = ac+ad+bc+bd to the left side of the equation, we get

(x)(x)+(x)(-1)+(-1)(x)+(-1)(-1) = 6x+10

=> [tex]x^{2}[/tex]-x-x+1 = 6x+10

=> [tex]x^{2}[/tex]-2x+1 = 6x+10

iv) Subtract 6x from both sides, we get

[tex]x^{2}[/tex]-2x+1-6x = 6x+10-6x

v) Cancelling out 6x and -6x from the right side, we get

[tex]x^{2}[/tex]-2x-6x+1 = 10

=> [tex]x^{2}[/tex]-8x+1 = 10

vi) Subtracting 10 from both the sides, we get

[tex]x^{2}[/tex]-8x+1-10 = 10-10

vii) Cancelling out 10 and 10 from the right side, we have

[tex]x^{2}[/tex]-8x-10+1 = 0

=> 1[tex]x^{2}[/tex]-8x-9 = 0

viii) Coefficient of the first term = 1

Multiplying the coefficient of the first term and the last term, we get

1*(-9) = -9

We need to find out two such factors of -9 which when added should give the middle term -8

So, -9 and +1 are the two factors of -9 which when added gives us the middle term -8

ix) Rewriting the middle term, we get

[tex]x^{2}[/tex]-9x+x-9 = 0

x) Factoring out x from the first two terms and factoring out 1 from the last two terms, we get

x(x-9)+1(x-9)=0

xi) Factoring out x-9 from both the terms, we get

(x-9)(x+1)=0

xii) Either x-9=0 or x+1=0

xiii) Solving x-9=0, we get x=9

xiv) Solving x+1=0, we get x= -1

So, solution set {x = 9 or x = -1}

Problem 3

5 − 3i

a) In order to graph the complex number 5-3i, we need to move right by 5 units on the real axis and then move down by 3 units on the imaginary axis.

See figure attached

b) A complex number is in the form of z= a+ bi

i) Comparing 5-3i with a+bi, we get a=5 and b = -3

The modulus is given by

|z| = [tex]\sqrt{a^{2}+b^{2} }[/tex]

ii) Plugging in a=5 and b=-3, we get

|z| = [tex]\sqrt{5^{2}+(-3)^{2} }[/tex]  

iii) |z| = [tex]\sqrt{25+9} [/tex]

iv) |z| = [tex]\sqrt{34}[/tex]

The modulus of the complex number 5-3i is [tex]\sqrt{34}[/tex]

Answer:

A. 8 rows.

B. 3 toy soldiers.

Step-by-step explanation:

We are told that Meliza has 43 toys soldiers, she line them up 5 to fight imaginary zombies .

A. Let us find the greatest multiple of 5 from 43.

Multiples of 5 are: 5,10, 15, 20, 25, 30, 35, 40, 45,..

We can see the greatest multiple of 5 from 43 is 40.

Let us divide 40 by 5 to find the number of rows that Meliza can make.

[tex]\text{Number of rows with 5 soldiers in each row}=\frac{40}{5}=8[/tex]

Therefore, Meliza can make 8 rows of 5 from 43 toy soldiers.

B. To find the number of soldier in last row we will subtract 40 from 43.

[tex]\text{Number of toy soldier in last row}=43-40=3[/tex]

Therefore, the number of toy soldiers in last row will be 3 soldiers.

Answer:g hvt

Step-by-step explanation:

Answer:

2. 9

3.12 p^4 - 1/2 p^3 -8p^2 + 2p

Step-by-step explanation:

The degree of the polynomial is found by taking the number of the highest exponent.  We add the exponent when there is more than one variable in a term

5m^6n^3 =  degree (6+3)  = 9

3m^4n^2 = degree (4+2) = 6

So the polynomial is degree 9

Standard from is written from largest exponent to smallest exponent

12 p^4 - 1/2 p^3 -8p^2 + 2p

Answer:

I would say your answer is $873.60

Step-by-step explanation:

$840.00

Tax (4%)

$33.60

Gross Amount (including tax)

$873.60

sorry if im wrong

Answer:

A

Step-by-step explanation:

Your first step is to figure out what f(x) is. You should start with x = 0. f(x) has a value of - 4.  That only tells you that whatever x is or what it is coupled with, the constant term is - 4.

What you know so far is that y = x something - 4

Now go to work on some of the other numbers. It really doesn't look linear so don't try it.

What happens when x = 16? Somehow f(x) winds up being 0. What can cause that?

First of all it can't be y = ax - 4. We've already establish the constant must be  - 4

What about y = ax^2 - 4

That cannot be either. y = 16^2*a - 4  ?? y = 256ax  - 4. No other value will fit the bill.

By looking at g(x) you get the idea that y = a*sqrt(x) - 4 might have something to do with f(x). The most obvious value for a = 1, so try it first.

Now try some of the other values.

And that's what the table says.

The red graph is y = sqrt(x) - 4

The blue graph is y = 4*sqrt(x) - 8

Answer

It looks like A is the answer.

g(x) has a y intercept of - 8

f(x) has a y intercept of - 4

==============

The two intercepts are not equal. If they were they would start from the same point.   B is incorrect

==============

C is wrong. the x intercepts are distinct points. One is 4 and the other is 16 I think.

0 = sqrt(x) - 4

4 =  sqrt(x)                Square both sides.

16 = x                         This is the x intercept of the red line

The other intercept = 4 (Blue line). I'll leave you to work it out. Leave a not if you can't.

========================

A and D can't  both be true. Since A is true, D can't be.

The answer is: 6,641.40$

Explanation:

Six thousand= 6,000

Six hundred= 600

Forty one= 41

Forty cents: .40

Now add all of these together:

6,000

+  600

+      41

+          0.40

Which will give you 6,641.40$

I hope this helps! :)

-LizzyIsTheQueen

Answer:

A

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition y = 2 when x = 10

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{1}{5}[/tex] x ← equation of variation

when x = 40, then

y = [tex]\frac{1}{5}[/tex] × 40 = 8 → A

The value of y when x = 40 with the same proportion will be 8 thus option (A) is correct.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

If y varies directly with x.

y ∝ x

y = kx

k = y/x

Thus, k will be the same for both conditions.

2/10 = y/40

1/5 = y/40

40/5 = y

8 = y

Hence "The value of y when x = 40 with the same proportion will be 8 ".

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Answer:

x=6

Step-by-step explanation:

If ABCD is a parallelogram, then AB = CD

AB=CD

10x-15 = 6x+9

Subtract 6x from each side

10x-6x -15 = 6x-6x+9

4x-15 = 9

Add 15 to each side

4x-15+15 = 9+15

4x = 24

Divide by 4 on each side

4x/4 =24/4

x=6

Look at the picture.

The equation:

10x - 15 = 6x + 9       add 15 to both sides

10x = 6x + 24      subtract 6x from both sides

4x = 24    divide both sides by 4