(5x-2y)(a-b) -(2x-y)(a-b)​

a) The equation that represents the total amount that the twins earned is; j + r = 96000

b) An amount that represents what Ron earned in terms of what Jon earned is; r = 3j + 8000

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

We are told that;

j represents the amount that Jon earned

r represents the amount that Ron earned

Thus, if together they earned $96000, then we have;

j + r = 96000

Ron earned $8000 more than three times what Jon earned. Thus, we have;

r = 3j + 8000

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Answer:

Let's use a Venn diagram to solve this problem.

First, let's label the three regions of the Venn diagram: Computer only (C), Optional Maths only (M), and both Computer and Optional Maths (C ∩ M). We can also label the region outside the circles as neither Computer nor Optional Maths (N).

We know that 30% of the students like Computer only, which means that the percentage of students in region C is 30%. Similarly, 25% of the students like both Computer and Optional Maths, so the percentage of students in region C ∩ M is 25%.

We are also given that 5% of the students don't like either subject, so the percentage of students in region N is 5%.

Finally, we are told that 390 students like Optional Maths, which includes the students in regions M and C ∩ M. We don't know the percentage of students in region M, but we do know that the percentage of students in region C ∩ M is 25%.

Using this information, we can set up an equation to solve for the total number of students:

C + M + C ∩ M + N = 100%

Substituting the percentages we know, we get:

30% + M + 25% + 5% = 100%

Simplifying the equation, we get:

M = 40%

This means that 40% of the students like Optional Maths only, which is the percentage of students in region M.

Now we can use the fact that 390 students like Optional Maths to solve for the total number of students:

M + C ∩ M = 390

0.4T + 0.25T = 390

0.65T = 390

T = 600

Therefore, the total number of students is 600.

The statement that correctly explains the association in the scatter plot is; A. Since the y-values decrease as the x-values increase, the scatter plot shows a negative association.

When interpreting scatterplots, it is possible to claim that two variables have a negative connection when the values of one variable tend to fall as the values of the other variable rise.

Similarly to this, we can say that two variables have a positive connection when one variable's values tend to rise along with those of the other.

In the scatterplot shown, we can see that there is a negative correlation between the two variables because the y-value is falling while the x-axis is rising.

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Therefοre , the sοlutiοn οf the given prοblem οf lοgarithm cοmes οut tο be  ln(4) is the value οf x at which f(x) equals 0, and chοice is the right respοnse (2).

The inverse οf an integer is represented mathematically by the lοgarithm. Therefοre, the expοnential that bc needs tο be multiplied by tο get a specific integer, x, is identical tο its base b expοnent. As an illustratiοn, 1000 = 103, sο lοg10 = 3 is 1000's base-10 lοgarithm, which is 3. As an example, the cube οf twenty is actually οne hundred while the base-10 derivative οf ten appears tο be twο. lοg  100 = 2.

Here,

The fοrmula is prοvided as f(x) = 2e(2x) - 32. and we must determine the x-value at which f(x) equals a particular number. Let's wοrk thrοugh each sοlutiοn:

(1) ln(5/2):

[tex]\Rightarrow f(ln(5/2)) = 2e^{(2*ln(5/2))} - 32[/tex]

[tex]\Rightarrow2e^{(ln(25/4))} - 32[/tex]

[tex]\Rightarrow 2(25/4) - 32[/tex]

[tex]\Rightarrow -19/2[/tex]

As a result, f(ln(5/2)) does not equal 0.

(2)  ln(4):

[tex]\Rightarrow f(ln(4)) = 2e^{(2*ln(4))}- 32[/tex]

[tex]\Rightarrow 2e^{(ln(16))}- 32[/tex]

[tex]\Rightarrow 2(16) - 32[/tex]

[tex]\Rightarrow 0[/tex]

As a result, choice (2) is the appropriate response because f(ln(4)) equals 0.

(3) ln(8):

[tex]\Rightarrow f(ln(8)) = 2e^{(2*ln(8))} - 32[/tex]

[tex]\Rightarrow2e^{(ln(64))} - 32[/tex]

[tex]\Rightarrow 2(64) - 32[/tex]

[tex]\Rightarrow 96[/tex]

As a result, f(ln(8)) does not equal 0.

(4 y = ln(2/5):

This choice is illogical because we must determine the value of x, not y.

As a result, ln(4) is the value of x at which f(x) equals 0, and choice is the right response (2).

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The values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

The law of cosines states that we can find the side c opposite to an Angle C of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which the parameters are listed as follows:

The parameters for this problem are given as follows:

a = 3x, b = x + 5, c = y, C = θ.

Hence the expression is given as follows:

y² = (3x)² + (x + 5)² - 2(x + 5)(3x)(1/6)

y² = 9x² + x² + 10x + 25 - x² + 5x

y² = 9x² + 15x + 25.

Hence the values of a, b and c are given as follows:

a = 9, b = 15, c = 25.

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It will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.

First, we need to calculate the amount of money that we need to save in order to cover the cost of the trip. This can be done by subtracting the amount we have already saved from the total cost of the trip:

Total cost of trip = 2500

Amount already saved = 2200

Amount to save = 2500 - 2200 = 300

Next, we can use the compound interest formula to calculate how long it will take to earn 300 with an interest rate of 1.55% compounded annually. We can set up the formula as follows:

A = P(1 + i)n

where:

A = accumulated amount = 300 + 2200 = 2500 (the total cost of the trip)

P = principal = 2200

i = interest rate per year = 1.55%

n = number of years we need to save for

We can now solve for n:

2500 = 2200(1 + 0.0155)n

Divide both sides by 2200:

1.13636 = 1.0155n

Take the natural logarithm of both sides:

ln(1.13636) = n ln(1.0155)

Divide both sides by ln(1.0155):

n = ln(1.13636)/ln(1.0155) ≈ 4.4 years

Therefore, it will take approximately 4.4 years to earn enough money to go on the trip if we invest our 2200 in a savings account with a 1.55% interest rate compounded annually.that we rounded our final answer to the nearest tenth as instructed.

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Answer:

Since the number of bacteria doubles every 3 hours, after 3 hours there will be 400 x 2 = 800 bacteria. After 6 hours, there will be 800 x 2 = 1600 bacteria. After 9 hours, there will be 1600 x 2 = 3200 bacteria. After 12 hours, there will be 3200 x 2 = 6400 bacteria. Finally, after 15 hours, there will be 6400 x 2 = 12800 bacteria. Therefore, there will be 12800 bacteria at the end of 15 hours.

Step-by-step explanation:

The probability of having an older son is 1/2 in families with two children and The proportion of all sons who are eldest sons = 1/3, when each family has three children.

If each family has two children, then the two possible situations are that the family has two sons or a son and a daughter. So the chance of having an older son is 1/2 in families with two children. Thus, the proportion of all sons who are older sons is 1/2.

If each family has three children, then the possible situations are having three sons, two sons and one daughter, or two daughters and one son. If two sons and one daughter are there in the family, then the older one will be the eldest son. If two daughters and one son are there in the family, then the only son will be the eldest son.

Therefore, there is only one eldest son among three children in the second case. If the family has three sons, then the probability that the eldest son is responsible for taking care of their parents is 1. Hence, if each family has three children, the proportion of all sons who are eldest sons is 1/3.The following is the step-by-step answer to this question:

Probability of having an older son = 1/2 in families with two children. Probability of having an eldest son = 1/3 in families with three children. The proportion of all sons who are older sons = 1/2, when each family has two children. The proportion of all sons who are eldest sons = 1/3, when each family has three children.

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Answer:

(1, 2 )

Step-by-step explanation:

y = - 2x + 4 → (1)

y = 3x - 1 → (2)

substitute y = 3x - 1 into (1)

3x - 1 = - 2x + 4 ( add 2x to both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

y = 3(1) - 1 = 3 - 1 = 2

solution is (1, 2 )

To measure length ABAC=3.5 cm, open the compass,=3.5cm is a positive value because. Hence, BD will be higher than BC. Cut an arc on ray BX using point B as the center. Let D be where the arc crosses BX.

A point where two lines meet produces an angle.

The breadth of the "opening" between these two rays is referred to as a "angle". It is depicted by the figure.

Radians, a unit of circularity or rotation, and degrees are two common units used to describe angles.

By connecting two rays at their ends, one can make an angle in geometry. The sides or limbs of the angle are what are meant by these rays.

The limbs and the vertex are the two main parts of an angle.

The common terminal of the two beams is the shared vertex.

According to our question-

draw perpendicular bisector of CD

A where perpendicular bisector intersects BD

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The journal entry to close the Income Summary will include a C) credit to Emile, Capital for $26,667.

To close the Income Summary account, the net income of $40,000 needs to be allocated to the partners' capital accounts based on their profit and loss sharing ratio.

Dana is allocated 2/3 of the net income, which is $26,667 (2/3 x $40,000). Emile is allocated 1/3 of the net income, which is $13,333 (1/3 x $40,000).

Therefore, the journal entry to close the Income Summary account would be:

Credit Income Summary for $26,667 (to close the account)

Debit Dana, Capital for $26,667 (to allocate Dana's share of net income)

Debit Emile, Capital for $13,333 (to allocate Emile's share of net income)

This is calculated by multiplying the net income of $40,000 by the ratio of Emile's share (1/3), which equals $26,667.

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Answer:

Step-by-step explanation:

If h is the height of the ball off the ground, if we want to find the time, t, when the ball hits the ground again, we set h equal to 0, because the height of something when it is on the ground is 0.

[tex]0=-t^2+4t[/tex] and solve for the values of t. Begin by factoring out a -t:

[tex]0=-t(t-4)[/tex]

By the Zero Product Property, either -t = 0 or t - 4 = 0. We already know that at time 0 the ball hit the ground for the first time because that was given in the problem. That means that the ball hit the ground for the second time 4 seconds later.

Answer:

x=3
y=4

Step-by-step explanation:

y=3x-9
5x+4y=32

You substitute what y is into the equation:
5x + 4(3x - 9) = 32
5x + 12x - 36 = 32
17x - 36 = 32
17x = 68
x = 4
Now you substitute x into y:
y = 3x - 9
12 - 9 = 3
y = 3

Answer: 7

Step-by-step explanation:

To find the median, we need to first put the data points in order from least to greatest:

2, 3, 5, 9, 12, 21

There are six data points, so the median is the middle value. In this case, the middle two values are 5 and 9. To find the median, we take the average of these two numbers:

(5 + 9) / 2 = 7

Therefore, the median number of songs written by the members of Python Sunboat is 7.

Answer:

We can use the expression 2x = y , where 'x' is the amount she saves yesterday and y being the amount she saves this day.

Table = if x = 0 , y = 0
            if x = 1 , y = 2
            if x = 2 , y =4
            if x = 4 , y= 8

Twο pοints (8,8) and (-2,6) are the set οf the equatiοn  [tex]y < \frac{3}{4} x+6\\[/tex] οf the graph [tex]y = \frac{3}{4} x+6[/tex].

Graph, a diagram that shοws hοw a variable varies in relatiοn tο οne οr mοre οther variables (such as a cοllectiοn οf pοints, lines, line segments, curves, οr regiοns).

Nοw we have tο find the value οf the equatiοn i.e. [tex]y < \frac{3}{4} x+6\\[/tex],

(x, y) = (8,8) , we get 8 < 12 , First pοint

(x, y) = (-4,3) , we get 3 = 3 , Nο match

(x, y) = (6,-2) , we get -2 < 10.5 , Secοnd Pοint

(x, y) = (0, 8) , we get 8 > 6 , Nο Match

(x, y) = (-9,2) , we get 2>-0.75 , Nο Match

Sο, we get οur pοints, which are pοints (8,8) and (-2,6) fοr the equatiοn [tex]y < \frac{3}{4} x+6\\[/tex].

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Decimals are used to write a number that is not an integer. Decimals are numbers between integers.

The supermarket chain of Product are :

Bakery, Beverages, Non-food and pharmaceutical products (such as cigarettes, lottery tickets and over-the-counter medicines), rental of DVDs, books and magazines, including supermarket tabloids, greeting cards, toys, a small number of household items such as light bulbs, Personal care such as cosmetics, soaps, shampoos, Produce (fresh fruits and vegetables), etc.

Decimals are used together to represent whole numbers and fractions. Here we will separate whole numbers and fractions by inserting a “.”, called a decimal point. In decimal form, we write this as 1.5 pizzas.

Decimals are used to write a number that is not an integer. Decimals are numbers between integers. An example is 12.5, which is a decimal number between 12 and 13. Greater than 12, but less than 13.

Continuing with the previous example, 12.5 is the same number as the fractional 12½. This is true regardless of the complexity of the decimal point. For example, the number 0. 75 equals ¾. If you want, you can go further and say that 0.75 equals 75%.

Complete Question:

Investigate supermarket chain products, observe which products have decimals in their values, list 10 products and use them to perform different decimal operations, build a word problem and demonstrate your understanding of decimals.

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Answer:

y = 2x - 6

Step-by-step explanation:

Using the 'y=mx+c' form,

Since m = 2,

y = 2x + c

Substituting (1, -4) into the above equation:

-4 = 2 + c

c = -6

Hence,

y = 2x - 6

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Using the law of sines, the length of the other side of the sail, which is the third side of the isosceles formed, is calculated as about 32.5 feet.

An isosceles triangle is a triangle with at least two sides of equal length.

Let's call the length of the other side of the sail "x". Since the sail is an isosceles triangle, the other two angles opposite the two equal sides are also equal, each measuring (180 - 54)/2 = 63 degrees.

We can use the law of cosines to find x:

x² = 23² + 23² - 2(23)(23)cos(63)

x² = 1054.75

x ≈ 32.5

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Answer: $4496

Step-by-step explanation:

Since we know that one pack of croissanwich costs $562, multiply $562 by 8 to get $4496.

The given sequence is a recursive sequence. Hence -2, 9, -24, 75 is the first four terms of the sequence.

The given sequence is a recursive sequence, where each term is defined in terms of the previous term. Here, each term is obtained by multiplying the previous term by -3 and adding 3. The first term, a1, is given. Using this, we can find the second term, a2, and then using a2, we can find a3, and so on.

Given: an = -3an-1 + 3 and a1 = -2

To find: the first four terms of the sequence

a1 = -2

a2 = -3a1 + 3 = -3(-2) + 3 = 9

a3 = -3a2 + 3 = -3(9) + 3 = -24

a4 = -3a3 + 3 = -3(-24) + 3 = 75

Therefore, the first four terms of the sequence are: -2, 9, -24, 75.

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After 45 blue counters are removed, the remaining number of blue counters is 63 more than yellow counters. Setting up an equation, we find that there were 162 blue counters to start with.

Let's start by assigning variables to the unknowns:

Let x be the number of yellow counters.

Then, the number of blue counters is 3x.

After 45 blue counters are removed, the number of blue counters is 3x - 45.

Finally, there are 63 more blue counters than yellow, so we can set up the equation:

3x - 45 = x + 63

Solving for x, we get:

2x = 108

x = 54

Therefore, there were 3x = 3(54) = 162 blue counters to start with.

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By secant line formula, the slopes corresponding to the lines are listed below:

In this problem we have nine representations of lines, whose slopes must be determined. A line is represented by equations of the form:

y = m · x + b

Where:

According to analytic geometry, slope can be found by knowning the location of two points (initial, final) set on Cartesian plane and secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Case 1: (x₁, y₁) = (0, - 3), (x₂, y₂) = (2, 1)

m = (2 - 0) / [1 - (- 3)]

m = 2 / 4

m = 1 / 2

Case 2: (x₁, y₁) = (- 3, 2), (x₂, y₂) = (1, - 3)

m = (- 3 - 2) / [1 - (- 3)]

m = - 5 / 4

Case 3: (x₁, y₁) = (- 3, - 4), (x₂, y₂) = (2, 3)

m = [3 - (- 4)] / [2 - (- 3)]

m = 7 / 5

Case 4: (x₁, y₁) = (0, 3), (x₂, y₂) = (3, - 3)

m = (- 3 - 3) / (3 - 0)

m = - 6 / 3

m = - 2

Case 5: (x₁, y₁) = (- 2, 1), (x₂, y₂) = (3, 2)

m = (2 - 1) / [3 - (- 2)]

m = 1 / 5

Case 6: (x₁, y₁) = (- 4, 3), (x₂, y₂) = (4, 1)

m = (1 - 3) / [4 - (- 4)]

m = - 2 / 8

m = - 1 / 4

Case 7: (x₁, y₁) = (2, - 4), (x₂, y₂) = (4, 2)

m = [2 - (- 4)] / (4 - 2)

m = 6 / 2

m = 3

Case 8: (x₁, y₁) = (- 4, - 1), (x₂, y₂) = (0, - 3)

m = [- 3 - (- 1)] / [0 - (- 4)]

m = - 2 / 4

m = - 1 / 2

Case 9: (x₁, y₁) = (- 2, 0), (x₂, y₂) = (4, 1)

m = (1 - 0) / [4 - (- 2)]

m = 1 / 6

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Answer: [tex]x=24[/tex]

Step-by-step explanation: Since the ratio of 6:3 is a 2:1 ratio simplified, you know that x will need to double the value on the other side. Therefore, you can just multiply 12 by 2 to get the x-value which is 24. Another method is to see that the 3 on the other side of the ratio is 1/4 the value of 12. This means that the 6 is 1/4 the value of x. if you multiply 4 on both sides x=24. Those are the two methods I recommend you use to solve these ratio problems.

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{Equation:}\\\\\large\boxed{\mathsf{6:3}}\\\\\large\textsf{Simplifying for:}\\\\\large\boxed{\rightarrow \mathsf{x:12}}\\\\\large\textsf{Simplifying:}\\\\\large\boxed{\mathsf{\rightarrow 6\times 4: 3\times4}}\\\\\large\boxed{\mathsf{\rightarrow{24:12}}}\\\\\\\huge\text{Therefore your answer should be: }\\\huge\boxed{\mathsf{\bold{24}:12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

problem 1. 53/20 problem 2. 24/27. Problem 3. 22/48

Step-by-step explanation:

to solve the first two, the process is similar. For the first one, they can be simplifed back into fraction form and not mixed form, so 1 2/5 can be simplified by multiplying 5 by one then adding it to 2, which gives you 7/5, and the same process for 2 1/2, multiply 2 by two, get 4 add it to one to get 5/2. Now we have 7/5 + 5/2, when we have fractions that we need to add or subtract, but down have the same bottom number, the easiest way to get a answer is to multiply both bottom numbers together then multiply the top number by the opposite bottom number, so 5x4 = 20, 4x7=28, 5x5=25, and we get 28/20 + 25/20 = 53/20. The process for problem two is the same, but just with subtraction and different numbers.

for problem three, the process is almost the same, but the steps differ. The bag is made up of R G and P counters, 3/8 of them are red, 1/6 are green, and the rest are purple because nothing else is in the bag. So another way of saying this is 3/8 + 1/6 + purple = Full Amount in bag. But now we need purple, so we know 1/2 one half and so does 2/4, and since we have fractions we can find the amount in the bag by adding them, 3/8 + 1/6 = 26/48, and we know the full bag is 1/1 or 48/48, and fhe only one left is purple, so to get purple, we subtract 48/48 from 26/48 and get 22/48 which is the amount of purple.

Answer:

(5, -1) or x = 5, y = -1

Step-by-step explanation:

[tex]\mathrm{Substitute\:}y=2x-11[/tex]

[tex]\begin{bmatrix}2x+3\left(2x-11\right)=7\end{bmatrix}[/tex]

[tex]8x-33=7[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:8x-33=7[/tex]

[tex]8x=40[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}8[/tex]

[tex]\frac{8x}{8}=\frac{40}{8}[/tex]

[tex]x=5[/tex]

[tex]y= 2x-11 \\ \mathrm{Substitute\:}x=5[/tex]

[tex]y=2\cdot \:5-11[/tex]

[tex]y=-1[/tex]

Answer:

(5, - 1 )

Step-by-step explanation:

2x + 3y = 7 → (1)

y = 2x - 11 → (2)

substitute y = 2x - 11 into (1)

2x + 3(2x - 11) = 7

2x + 6x - 33 = 7

8x - 33 = 7 ( add 33 to both sides )

8x = 40 ( divide both sides by 8 )

x = 5

substitute x = 5 into (2)

y = 2(5) - 11 = 10 - 11 = - 1

solution is (5, - 1 )

Answer:

[tex]9.9[/tex]

Step-by-step explanation:

Interpreted:

[tex]3^2-(4\div5\div8)+1[/tex]

1) Simplify 4 ÷ 5 to 0.8.

[tex]3^2-0.8\div8+1[/tex]

2) Simplify 3² to 9.

[tex]9-0.8\div8+1[/tex]

3) Simplify 0.8 ÷ 8 to 0.1.

[tex]9-0.1+1[/tex]

4) Simplify 9 - 0.1 to 8.9.

[tex]8.9+1[/tex]

5) Simplify.

[tex]9.9[/tex]

Answer:

? = 7.2

Step-by-step explanation:

The given equation is comprised of two ratios.

Using the given ratio 5.4 : 3, we can reduce it and see the ratio is 1.8 : 1

Now, using the same idea for the unknown value, we must multiply 1.8 by 4, giving 7.2.

Answer:

Geometric sequences and exponential functions are alike in that they both involve repeated multiplication by a constant factor. In a geometric sequence, each term is found by multiplying the previous term by the same constant factor. In an exponential function, the value of the function is found by raising a constant base to an exponent that increases by a constant amount.

However, they differ in the way they are expressed. In a geometric sequence, each term is written as a discrete value in the sequence, while in an exponential function, the value of the function is written as a continuous function of the input variable. Additionally, geometric sequences are often used to model discrete phenomena, while exponential functions are often used to model continuous phenomena.

Step-by-step explanation:

6 pounds of chocolate worth $1.20 per pound must be mixed with 10 pounds of chocolate worth 90 cents per pound in order to create a mixture worth $1.00 per pound.

To produce a mixture worth $1.00 a pound, 6 pounds of chocolate worth $1.20 per pound must be mixed with 10 pounds of chocolate worth 90 cents per pound.

Let us proceed as follows:

x is the amount of chocolate worth $1.20 per pound that must be mixed with 10 pounds of chocolate worth 90 cents per pound in order to create a mixture worth $1.00 per pound.

Using the formula:

Price of chocolate (x) + Price of chocolate ($0.90) = Price of mixture ($1.00)

The following equation can be created:

1.20x + 0.9(10) = 1(10 + x)

Simplify: 1.20x + 9 = 10 + x1.20x - x = 10 - 91.20x - x = 1

Divide both sides by 0.2 to simplify the equation:

6x = 5x = 6

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